1,1,164,0,0.509754," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(12 i \, A + 18 \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(18 i \, A + 18 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(6 i \, A + 8 \, B\right)} a + {\left({\left(3 i \, A + 3 \, B\right)} a e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(9 i \, A + 9 \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(9 i \, A + 9 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(3 i \, A + 3 \, B\right)} a\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*((12*I*A + 18*B)*a*e^(4*I*d*x + 4*I*c) + (18*I*A + 18*B)*a*e^(2*I*d*x + 2*I*c) + (6*I*A + 8*B)*a + ((3*I*A + 3*B)*a*e^(6*I*d*x + 6*I*c) + (9*I*A + 9*B)*a*e^(4*I*d*x + 4*I*c) + (9*I*A + 9*B)*a*e^(2*I*d*x + 2*I*c) + (3*I*A + 3*B)*a)*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
2,1,109,0,0.492263," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(A - 2 i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, {\left(A - i \, B\right)} a + {\left({\left(A - i \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\right)} a\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,"-(2*(A - 2*I*B)*a*e^(2*I*d*x + 2*I*c) + 2*(A - I*B)*a + ((A - I*B)*a*e^(4*I*d*x + 4*I*c) + 2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (A - I*B)*a)*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
3,1,64,0,0.664721," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, B a - {\left({\left(-i \, A - B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-i \, A - B\right)} a\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*B*a - ((-I*A - B)*a*e^(2*I*d*x + 2*I*c) + (-I*A - B)*a)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
4,1,36,0,0.562970," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-i \, B a \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + A a \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{d}"," ",0,"(-I*B*a*log(e^(2*I*d*x + 2*I*c) + 1) + A*a*log(e^(2*I*d*x + 2*I*c) - 1))/d","A",0
5,1,62,0,0.570061," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-2 i \, A a + {\left({\left(i \, A + B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-i \, A - B\right)} a\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*a + ((I*A + B)*a*e^(2*I*d*x + 2*I*c) + (-I*A - B)*a)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(2*I*d*x + 2*I*c) - d)","A",0
6,1,111,0,0.468216," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, {\left(A - i \, B\right)} a - {\left({\left(A - i \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\right)} a\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,"(2*(2*A - I*B)*a*e^(2*I*d*x + 2*I*c) - 2*(A - I*B)*a - ((A - I*B)*a*e^(4*I*d*x + 4*I*c) - 2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (A - I*B)*a)*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
7,1,166,0,0.413808," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(18 i \, A + 12 \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-18 i \, A - 18 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(8 i \, A + 6 \, B\right)} a + {\left({\left(-3 i \, A - 3 \, B\right)} a e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(9 i \, A + 9 \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-9 i \, A - 9 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(3 i \, A + 3 \, B\right)} a\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*((18*I*A + 12*B)*a*e^(4*I*d*x + 4*I*c) + (-18*I*A - 18*B)*a*e^(2*I*d*x + 2*I*c) + (8*I*A + 6*B)*a + ((-3*I*A - 3*B)*a*e^(6*I*d*x + 6*I*c) + (9*I*A + 9*B)*a*e^(4*I*d*x + 4*I*c) + (-9*I*A - 9*B)*a*e^(2*I*d*x + 2*I*c) + (3*I*A + 3*B)*a)*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
8,1,206,0,0.416295," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, {\left(4 \, A - 3 i \, B\right)} a e^{\left(6 i \, d x + 6 i \, c\right)} - 36 \, {\left(A - i \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(16 \, A - 13 i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - 8 \, {\left(A - i \, B\right)} a - 3 \, {\left({\left(A - i \, B\right)} a e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, {\left(A - i \, B\right)} a e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, {\left(A - i \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\right)} a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\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,"-1/3*(6*(4*A - 3*I*B)*a*e^(6*I*d*x + 6*I*c) - 36*(A - I*B)*a*e^(4*I*d*x + 4*I*c) + 2*(16*A - 13*I*B)*a*e^(2*I*d*x + 2*I*c) - 8*(A - I*B)*a - 3*((A - I*B)*a*e^(8*I*d*x + 8*I*c) - 4*(A - I*B)*a*e^(6*I*d*x + 6*I*c) + 6*(A - I*B)*a*e^(4*I*d*x + 4*I*c) - 4*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (A - I*B)*a)*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
9,1,230,0,0.446288," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(30 i \, A + 42 \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(66 i \, A + 72 \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(50 i \, A + 58 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(14 i \, A + 16 \, B\right)} a^{2} + {\left({\left(6 i \, A + 6 \, B\right)} a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(24 i \, A + 24 \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(36 i \, A + 36 \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(24 i \, A + 24 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(6 i \, A + 6 \, B\right)} a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\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,"1/3*((30*I*A + 42*B)*a^2*e^(6*I*d*x + 6*I*c) + (66*I*A + 72*B)*a^2*e^(4*I*d*x + 4*I*c) + (50*I*A + 58*B)*a^2*e^(2*I*d*x + 2*I*c) + (14*I*A + 16*B)*a^2 + ((6*I*A + 6*B)*a^2*e^(8*I*d*x + 8*I*c) + (24*I*A + 24*B)*a^2*e^(6*I*d*x + 6*I*c) + (36*I*A + 36*B)*a^2*e^(4*I*d*x + 4*I*c) + (24*I*A + 24*B)*a^2*e^(2*I*d*x + 2*I*c) + (6*I*A + 6*B)*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)","A",0
10,1,175,0,0.413344," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, {\left(3 \, A - 5 i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(5 \, A - 6 i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(6 \, A - 7 i \, B\right)} a^{2} + 3 \, {\left({\left(A - i \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, {\left(A - i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\right)} a^{2}\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*(3*(3*A - 5*I*B)*a^2*e^(4*I*d*x + 4*I*c) + 3*(5*A - 6*I*B)*a^2*e^(2*I*d*x + 2*I*c) + (6*A - 7*I*B)*a^2 + 3*((A - I*B)*a^2*e^(6*I*d*x + 6*I*c) + 3*(A - I*B)*a^2*e^(4*I*d*x + 4*I*c) + 3*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + (A - I*B)*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)","A",0
11,1,125,0,0.558717," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-2 i \, A - 6 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-2 i \, A - 4 \, B\right)} a^{2} + {\left({\left(-2 i \, A - 2 \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-4 i \, A - 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-2 i \, A - 2 \, B\right)} a^{2}\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,"((-2*I*A - 6*B)*a^2*e^(2*I*d*x + 2*I*c) + (-2*I*A - 4*B)*a^2 + ((-2*I*A - 2*B)*a^2*e^(4*I*d*x + 4*I*c) + (-4*I*A - 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (-2*I*A - 2*B)*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
12,1,97,0,0.720138," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-2 i \, B a^{2} + {\left({\left(A - 2 i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - 2 i \, B\right)} a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + {\left(A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A 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*B*a^2 + ((A - 2*I*B)*a^2*e^(2*I*d*x + 2*I*c) + (A - 2*I*B)*a^2)*log(e^(2*I*d*x + 2*I*c) + 1) + (A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
13,1,102,0,0.620774," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-2 i \, A a^{2} + {\left(B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - B a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + {\left({\left(2 i \, A + B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-2 i \, A - B\right)} 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*a^2 + (B*a^2*e^(2*I*d*x + 2*I*c) - B*a^2)*log(e^(2*I*d*x + 2*I*c) + 1) + ((2*I*A + B)*a^2*e^(2*I*d*x + 2*I*c) + (-2*I*A - B)*a^2)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(2*I*d*x + 2*I*c) - d)","A",0
14,1,123,0,0.508990," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(3 \, A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(2 \, A - i \, B\right)} a^{2} - {\left({\left(A - i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\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 - I*B)*a^2*e^(2*I*d*x + 2*I*c) - (2*A - I*B)*a^2 - ((A - I*B)*a^2*e^(4*I*d*x + 4*I*c) - 2*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + (A - I*B)*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
15,1,180,0,0.553791," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(30 i \, A + 18 \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-36 i \, A - 30 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(14 i \, A + 12 \, B\right)} a^{2} + {\left({\left(-6 i \, A - 6 \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(18 i \, A + 18 \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-18 i \, A - 18 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(6 i \, A + 6 \, B\right)} 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 + 18*B)*a^2*e^(4*I*d*x + 4*I*c) + (-36*I*A - 30*B)*a^2*e^(2*I*d*x + 2*I*c) + (14*I*A + 12*B)*a^2 + ((-6*I*A - 6*B)*a^2*e^(6*I*d*x + 6*I*c) + (18*I*A + 18*B)*a^2*e^(4*I*d*x + 4*I*c) + (-18*I*A - 18*B)*a^2*e^(2*I*d*x + 2*I*c) + (6*I*A + 6*B)*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)","A",0
16,1,227,0,0.456391," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, {\left(7 \, A - 5 i \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, {\left(12 \, A - 11 i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(29 \, A - 25 i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(8 \, A - 7 i \, B\right)} a^{2} - 3 \, {\left({\left(A - i \, B\right)} a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, {\left(A - i \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, {\left(A - i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\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*(3*(7*A - 5*I*B)*a^2*e^(6*I*d*x + 6*I*c) - 3*(12*A - 11*I*B)*a^2*e^(4*I*d*x + 4*I*c) + (29*A - 25*I*B)*a^2*e^(2*I*d*x + 2*I*c) - (8*A - 7*I*B)*a^2 - 3*((A - I*B)*a^2*e^(8*I*d*x + 8*I*c) - 4*(A - I*B)*a^2*e^(6*I*d*x + 6*I*c) + 6*(A - I*B)*a^2*e^(4*I*d*x + 4*I*c) - 4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + (A - I*B)*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)","A",0
17,1,282,0,0.656066," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(360 i \, A + 480 \, B\right)} a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(1050 i \, A + 1170 \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(1230 i \, A + 1390 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(690 i \, A + 770 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(150 i \, A + 166 \, B\right)} a^{3} + {\left({\left(60 i \, A + 60 \, B\right)} a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(300 i \, A + 300 \, B\right)} a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(600 i \, A + 600 \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(600 i \, A + 600 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(300 i \, A + 300 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(60 i \, A + 60 \, B\right)} 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*((360*I*A + 480*B)*a^3*e^(8*I*d*x + 8*I*c) + (1050*I*A + 1170*B)*a^3*e^(6*I*d*x + 6*I*c) + (1230*I*A + 1390*B)*a^3*e^(4*I*d*x + 4*I*c) + (690*I*A + 770*B)*a^3*e^(2*I*d*x + 2*I*c) + (150*I*A + 166*B)*a^3 + ((60*I*A + 60*B)*a^3*e^(10*I*d*x + 10*I*c) + (300*I*A + 300*B)*a^3*e^(8*I*d*x + 8*I*c) + (600*I*A + 600*B)*a^3*e^(6*I*d*x + 6*I*c) + (600*I*A + 600*B)*a^3*e^(4*I*d*x + 4*I*c) + (300*I*A + 300*B)*a^3*e^(2*I*d*x + 2*I*c) + (60*I*A + 60*B)*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
18,1,227,0,0.677379," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(12 \, {\left(2 \, A - 3 i \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, {\left(19 \, A - 23 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(23 \, A - 27 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(13 \, A - 15 i \, B\right)} a^{3} + 6 \, {\left({\left(A - i \, B\right)} a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, {\left(A - i \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, {\left(A - i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\right)} a^{3}\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*(12*(2*A - 3*I*B)*a^3*e^(6*I*d*x + 6*I*c) + 3*(19*A - 23*I*B)*a^3*e^(4*I*d*x + 4*I*c) + 2*(23*A - 27*I*B)*a^3*e^(2*I*d*x + 2*I*c) + (13*A - 15*I*B)*a^3 + 6*((A - I*B)*a^3*e^(8*I*d*x + 8*I*c) + 4*(A - I*B)*a^3*e^(6*I*d*x + 6*I*c) + 6*(A - I*B)*a^3*e^(4*I*d*x + 4*I*c) + 4*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + (A - I*B)*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
19,1,178,0,0.637305," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-24 i \, A - 48 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-42 i \, A - 66 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-18 i \, A - 26 \, B\right)} a^{3} + {\left({\left(-12 i \, A - 12 \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-36 i \, A - 36 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-36 i \, A - 36 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-12 i \, A - 12 \, B\right)} 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*((-24*I*A - 48*B)*a^3*e^(4*I*d*x + 4*I*c) + (-42*I*A - 66*B)*a^3*e^(2*I*d*x + 2*I*c) + (-18*I*A - 26*B)*a^3 + ((-12*I*A - 12*B)*a^3*e^(6*I*d*x + 6*I*c) + (-36*I*A - 36*B)*a^3*e^(4*I*d*x + 4*I*c) + (-36*I*A - 36*B)*a^3*e^(2*I*d*x + 2*I*c) + (-12*I*A - 12*B)*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
20,1,172,0,0.759473," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(A - 4 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, {\left(A - 3 i \, B\right)} a^{3} + {\left({\left(3 \, A - 4 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(3 \, A - 4 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(3 \, A - 4 i \, B\right)} a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + {\left(A a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, A a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + A 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,"(2*(A - 4*I*B)*a^3*e^(2*I*d*x + 2*I*c) + 2*(A - 3*I*B)*a^3 + ((3*A - 4*I*B)*a^3*e^(4*I*d*x + 4*I*c) + 2*(3*A - 4*I*B)*a^3*e^(2*I*d*x + 2*I*c) + (3*A - 4*I*B)*a^3)*log(e^(2*I*d*x + 2*I*c) + 1) + (A*a^3*e^(4*I*d*x + 4*I*c) + 2*A*a^3*e^(2*I*d*x + 2*I*c) + A*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
21,1,138,0,0.640026," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-2 i \, A + 2 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-2 i \, A - 2 \, B\right)} a^{3} + {\left({\left(i \, A + 3 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-i \, A - 3 \, B\right)} a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + {\left({\left(3 i \, A + B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-3 i \, A - B\right)} 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)} - d}"," ",0,"((-2*I*A + 2*B)*a^3*e^(2*I*d*x + 2*I*c) + (-2*I*A - 2*B)*a^3 + ((I*A + 3*B)*a^3*e^(4*I*d*x + 4*I*c) + (-I*A - 3*B)*a^3)*log(e^(2*I*d*x + 2*I*c) + 1) + ((3*I*A + B)*a^3*e^(4*I*d*x + 4*I*c) + (-3*I*A - B)*a^3)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(4*I*d*x + 4*I*c) - d)","A",0
22,1,179,0,0.455003," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, {\left(3 \, A - i \, B\right)} a^{3} + {\left(i \, B a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 i \, B a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, B a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - {\left({\left(4 \, A - 3 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(4 \, A - 3 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 \, A - 3 i \, B\right)} 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,"(2*(4*A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - 2*(3*A - I*B)*a^3 + (I*B*a^3*e^(4*I*d*x + 4*I*c) - 2*I*B*a^3*e^(2*I*d*x + 2*I*c) + I*B*a^3)*log(e^(2*I*d*x + 2*I*c) + 1) - ((4*A - 3*I*B)*a^3*e^(4*I*d*x + 4*I*c) - 2*(4*A - 3*I*B)*a^3*e^(2*I*d*x + 2*I*c) + (4*A - 3*I*B)*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
23,1,180,0,0.569905," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(48 i \, A + 24 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-66 i \, A - 42 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(26 i \, A + 18 \, B\right)} a^{3} + {\left({\left(-12 i \, A - 12 \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(36 i \, A + 36 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-36 i \, A - 36 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(12 i \, A + 12 \, B\right)} 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 + 24*B)*a^3*e^(4*I*d*x + 4*I*c) + (-66*I*A - 42*B)*a^3*e^(2*I*d*x + 2*I*c) + (26*I*A + 18*B)*a^3 + ((-12*I*A - 12*B)*a^3*e^(6*I*d*x + 6*I*c) + (36*I*A + 36*B)*a^3*e^(4*I*d*x + 4*I*c) + (-36*I*A - 36*B)*a^3*e^(2*I*d*x + 2*I*c) + (12*I*A + 12*B)*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
24,1,228,0,0.885457," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(12 \, {\left(3 \, A - 2 i \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, {\left(23 \, A - 19 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(27 \, A - 23 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(15 \, A - 13 i \, B\right)} a^{3} - 6 \, {\left({\left(A - i \, B\right)} a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, {\left(A - i \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, {\left(A - i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\right)} a^{3}\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*(12*(3*A - 2*I*B)*a^3*e^(6*I*d*x + 6*I*c) - 3*(23*A - 19*I*B)*a^3*e^(4*I*d*x + 4*I*c) + 2*(27*A - 23*I*B)*a^3*e^(2*I*d*x + 2*I*c) - (15*A - 13*I*B)*a^3 - 6*((A - I*B)*a^3*e^(8*I*d*x + 8*I*c) - 4*(A - I*B)*a^3*e^(6*I*d*x + 6*I*c) + 6*(A - I*B)*a^3*e^(4*I*d*x + 4*I*c) - 4*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + (A - I*B)*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
25,1,284,0,0.666268," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-480 i \, A - 360 \, B\right)} a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(1170 i \, A + 1050 \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-1390 i \, A - 1230 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(770 i \, A + 690 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-166 i \, A - 150 \, B\right)} a^{3} + {\left({\left(60 i \, A + 60 \, B\right)} a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(-300 i \, A - 300 \, B\right)} a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(600 i \, A + 600 \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-600 i \, A - 600 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(300 i \, A + 300 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-60 i \, A - 60 \, B\right)} 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 - 360*B)*a^3*e^(8*I*d*x + 8*I*c) + (1170*I*A + 1050*B)*a^3*e^(6*I*d*x + 6*I*c) + (-1390*I*A - 1230*B)*a^3*e^(4*I*d*x + 4*I*c) + (770*I*A + 690*B)*a^3*e^(2*I*d*x + 2*I*c) + (-166*I*A - 150*B)*a^3 + ((60*I*A + 60*B)*a^3*e^(10*I*d*x + 10*I*c) + (-300*I*A - 300*B)*a^3*e^(8*I*d*x + 8*I*c) + (600*I*A + 600*B)*a^3*e^(6*I*d*x + 6*I*c) + (-600*I*A - 600*B)*a^3*e^(4*I*d*x + 4*I*c) + (300*I*A + 300*B)*a^3*e^(2*I*d*x + 2*I*c) + (-60*I*A - 60*B)*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
26,1,334,0,0.480431," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(840 i \, A + 1080 \, B\right)} a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(3060 i \, A + 3420 \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(4840 i \, A + 5400 \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(4080 i \, A + 4500 \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(1776 i \, A + 1944 \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(316 i \, A + 344 \, B\right)} a^{4} + {\left({\left(120 i \, A + 120 \, B\right)} a^{4} e^{\left(12 i \, d x + 12 i \, c\right)} + {\left(720 i \, A + 720 \, B\right)} a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(1800 i \, A + 1800 \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(2400 i \, A + 2400 \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(1800 i \, A + 1800 \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(720 i \, A + 720 \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(120 i \, A + 120 \, B\right)} a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\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,"1/15*((840*I*A + 1080*B)*a^4*e^(10*I*d*x + 10*I*c) + (3060*I*A + 3420*B)*a^4*e^(8*I*d*x + 8*I*c) + (4840*I*A + 5400*B)*a^4*e^(6*I*d*x + 6*I*c) + (4080*I*A + 4500*B)*a^4*e^(4*I*d*x + 4*I*c) + (1776*I*A + 1944*B)*a^4*e^(2*I*d*x + 2*I*c) + (316*I*A + 344*B)*a^4 + ((120*I*A + 120*B)*a^4*e^(12*I*d*x + 12*I*c) + (720*I*A + 720*B)*a^4*e^(10*I*d*x + 10*I*c) + (1800*I*A + 1800*B)*a^4*e^(8*I*d*x + 8*I*c) + (2400*I*A + 2400*B)*a^4*e^(6*I*d*x + 6*I*c) + (1800*I*A + 1800*B)*a^4*e^(4*I*d*x + 4*I*c) + (720*I*A + 720*B)*a^4*e^(2*I*d*x + 2*I*c) + (120*I*A + 120*B)*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
27,1,279,0,0.442078," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(30 \, {\left(5 \, A - 7 i \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 15 \, {\left(31 \, A - 37 i \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 5 \, {\left(113 \, A - 131 i \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, {\left(64 \, A - 73 i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(70 \, A - 79 i \, B\right)} a^{4} + 30 \, {\left({\left(A - i \, B\right)} a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, {\left(A - i \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, {\left(A - i \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, {\left(A - i \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, {\left(A - i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\right)} a^{4}\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,"-4/15*(30*(5*A - 7*I*B)*a^4*e^(8*I*d*x + 8*I*c) + 15*(31*A - 37*I*B)*a^4*e^(6*I*d*x + 6*I*c) + 5*(113*A - 131*I*B)*a^4*e^(4*I*d*x + 4*I*c) + 5*(64*A - 73*I*B)*a^4*e^(2*I*d*x + 2*I*c) + (70*A - 79*I*B)*a^4 + 30*((A - I*B)*a^4*e^(10*I*d*x + 10*I*c) + 5*(A - I*B)*a^4*e^(8*I*d*x + 8*I*c) + 10*(A - I*B)*a^4*e^(6*I*d*x + 6*I*c) + 10*(A - I*B)*a^4*e^(4*I*d*x + 4*I*c) + 5*(A - I*B)*a^4*e^(2*I*d*x + 2*I*c) + (A - I*B)*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
28,1,230,0,0.484254," ","integrate((a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-72 i \, A - 120 \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-180 i \, A - 252 \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-152 i \, A - 200 \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-44 i \, A - 56 \, B\right)} a^{4} + {\left({\left(-24 i \, A - 24 \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-96 i \, A - 96 \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-144 i \, A - 144 \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-96 i \, A - 96 \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-24 i \, A - 24 \, B\right)} a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\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,"1/3*((-72*I*A - 120*B)*a^4*e^(6*I*d*x + 6*I*c) + (-180*I*A - 252*B)*a^4*e^(4*I*d*x + 4*I*c) + (-152*I*A - 200*B)*a^4*e^(2*I*d*x + 2*I*c) + (-44*I*A - 56*B)*a^4 + ((-24*I*A - 24*B)*a^4*e^(8*I*d*x + 8*I*c) + (-96*I*A - 96*B)*a^4*e^(6*I*d*x + 6*I*c) + (-144*I*A - 144*B)*a^4*e^(4*I*d*x + 4*I*c) + (-96*I*A - 96*B)*a^4*e^(2*I*d*x + 2*I*c) + (-24*I*A - 24*B)*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
29,1,246,0,1.044759," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(5 \, A - 12 i \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 54 \, {\left(A - 2 i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(6 \, A - 11 i \, B\right)} a^{4} + 3 \, {\left({\left(7 \, A - 8 i \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, {\left(7 \, A - 8 i \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(7 \, A - 8 i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(7 \, A - 8 i \, B\right)} a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 3 \, {\left(A a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, A a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, A a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + A 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*(6*(5*A - 12*I*B)*a^4*e^(4*I*d*x + 4*I*c) + 54*(A - 2*I*B)*a^4*e^(2*I*d*x + 2*I*c) + 4*(6*A - 11*I*B)*a^4 + 3*((7*A - 8*I*B)*a^4*e^(6*I*d*x + 6*I*c) + 3*(7*A - 8*I*B)*a^4*e^(4*I*d*x + 4*I*c) + 3*(7*A - 8*I*B)*a^4*e^(2*I*d*x + 2*I*c) + (7*A - 8*I*B)*a^4)*log(e^(2*I*d*x + 2*I*c) + 1) + 3*(A*a^4*e^(6*I*d*x + 6*I*c) + 3*A*a^4*e^(4*I*d*x + 4*I*c) + 3*A*a^4*e^(2*I*d*x + 2*I*c) + A*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)","B",0
30,1,254,0,0.761137," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{10 \, B a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-4 i \, A - 2 \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-4 i \, A - 8 \, B\right)} a^{4} + {\left({\left(4 i \, A + 7 \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(4 i \, A + 7 \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-4 i \, A - 7 \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-4 i \, A - 7 \, B\right)} a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + {\left({\left(4 i \, A + B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(4 i \, A + B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-4 i \, A - B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-4 i \, A - B\right)} a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{d e^{\left(6 i \, d x + 6 i \, c\right)} + d e^{\left(4 i \, d x + 4 i \, c\right)} - d e^{\left(2 i \, d x + 2 i \, c\right)} - d}"," ",0,"(10*B*a^4*e^(4*I*d*x + 4*I*c) + (-4*I*A - 2*B)*a^4*e^(2*I*d*x + 2*I*c) + (-4*I*A - 8*B)*a^4 + ((4*I*A + 7*B)*a^4*e^(6*I*d*x + 6*I*c) + (4*I*A + 7*B)*a^4*e^(4*I*d*x + 4*I*c) + (-4*I*A - 7*B)*a^4*e^(2*I*d*x + 2*I*c) + (-4*I*A - 7*B)*a^4)*log(e^(2*I*d*x + 2*I*c) + 1) + ((4*I*A + B)*a^4*e^(6*I*d*x + 6*I*c) + (4*I*A + B)*a^4*e^(4*I*d*x + 4*I*c) + (-4*I*A - B)*a^4*e^(2*I*d*x + 2*I*c) + (-4*I*A - B)*a^4)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(6*I*d*x + 6*I*c) + d*e^(4*I*d*x + 4*I*c) - d*e^(2*I*d*x + 2*I*c) - d)","B",0
31,1,255,0,0.617601," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{10 \, A a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(A - 2 i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 \, {\left(2 \, A - i \, B\right)} a^{4} - {\left({\left(A - 4 i \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(A - 4 i \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(A - 4 i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - 4 i \, B\right)} a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - {\left({\left(7 \, A - 4 i \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(7 \, A - 4 i \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(7 \, A - 4 i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(7 \, A - 4 i \, B\right)} a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{d e^{\left(6 i \, d x + 6 i \, c\right)} - d e^{\left(4 i \, d x + 4 i \, c\right)} - d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(10*A*a^4*e^(4*I*d*x + 4*I*c) + 2*(A - 2*I*B)*a^4*e^(2*I*d*x + 2*I*c) - 4*(2*A - I*B)*a^4 - ((A - 4*I*B)*a^4*e^(6*I*d*x + 6*I*c) - (A - 4*I*B)*a^4*e^(4*I*d*x + 4*I*c) - (A - 4*I*B)*a^4*e^(2*I*d*x + 2*I*c) + (A - 4*I*B)*a^4)*log(e^(2*I*d*x + 2*I*c) + 1) - ((7*A - 4*I*B)*a^4*e^(6*I*d*x + 6*I*c) - (7*A - 4*I*B)*a^4*e^(4*I*d*x + 4*I*c) - (7*A - 4*I*B)*a^4*e^(2*I*d*x + 2*I*c) + (7*A - 4*I*B)*a^4)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(6*I*d*x + 6*I*c) - d*e^(4*I*d*x + 4*I*c) - d*e^(2*I*d*x + 2*I*c) + d)","A",0
32,1,245,0,1.145458," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(72 i \, A + 30 \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-108 i \, A - 54 \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(44 i \, A + 24 \, B\right)} a^{4} - 3 \, {\left(B a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, B a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, B a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - B a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + {\left({\left(-24 i \, A - 21 \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(72 i \, A + 63 \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-72 i \, A - 63 \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(24 i \, A + 21 \, B\right)} 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 + 30*B)*a^4*e^(4*I*d*x + 4*I*c) + (-108*I*A - 54*B)*a^4*e^(2*I*d*x + 2*I*c) + (44*I*A + 24*B)*a^4 - 3*(B*a^4*e^(6*I*d*x + 6*I*c) - 3*B*a^4*e^(4*I*d*x + 4*I*c) + 3*B*a^4*e^(2*I*d*x + 2*I*c) - B*a^4)*log(e^(2*I*d*x + 2*I*c) + 1) + ((-24*I*A - 21*B)*a^4*e^(6*I*d*x + 6*I*c) + (72*I*A + 63*B)*a^4*e^(4*I*d*x + 4*I*c) + (-72*I*A - 63*B)*a^4*e^(2*I*d*x + 2*I*c) + (24*I*A + 21*B)*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
33,1,228,0,0.568655," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(6 \, {\left(5 \, A - 3 i \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 9 \, {\left(7 \, A - 5 i \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(25 \, A - 19 i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(14 \, A - 11 i \, B\right)} a^{4} - 6 \, {\left({\left(A - i \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, {\left(A - i \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, {\left(A - i \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, {\left(A - i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\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*(6*(5*A - 3*I*B)*a^4*e^(6*I*d*x + 6*I*c) - 9*(7*A - 5*I*B)*a^4*e^(4*I*d*x + 4*I*c) + 2*(25*A - 19*I*B)*a^4*e^(2*I*d*x + 2*I*c) - (14*A - 11*I*B)*a^4 - 6*((A - I*B)*a^4*e^(8*I*d*x + 8*I*c) - 4*(A - I*B)*a^4*e^(6*I*d*x + 6*I*c) + 6*(A - I*B)*a^4*e^(4*I*d*x + 4*I*c) - 4*(A - I*B)*a^4*e^(2*I*d*x + 2*I*c) + (A - I*B)*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
34,1,284,0,1.157131," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-840 i \, A - 600 \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(2220 i \, A + 1860 \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-2620 i \, A - 2260 \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(1460 i \, A + 1280 \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-316 i \, A - 280 \, B\right)} a^{4} + {\left({\left(120 i \, A + 120 \, B\right)} a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(-600 i \, A - 600 \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(1200 i \, A + 1200 \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-1200 i \, A - 1200 \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(600 i \, A + 600 \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-120 i \, A - 120 \, B\right)} 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 - 600*B)*a^4*e^(8*I*d*x + 8*I*c) + (2220*I*A + 1860*B)*a^4*e^(6*I*d*x + 6*I*c) + (-2620*I*A - 2260*B)*a^4*e^(4*I*d*x + 4*I*c) + (1460*I*A + 1280*B)*a^4*e^(2*I*d*x + 2*I*c) + (-316*I*A - 280*B)*a^4 + ((120*I*A + 120*B)*a^4*e^(10*I*d*x + 10*I*c) + (-600*I*A - 600*B)*a^4*e^(8*I*d*x + 8*I*c) + (1200*I*A + 1200*B)*a^4*e^(6*I*d*x + 6*I*c) + (-1200*I*A - 1200*B)*a^4*e^(4*I*d*x + 4*I*c) + (600*I*A + 600*B)*a^4*e^(2*I*d*x + 2*I*c) + (-120*I*A - 120*B)*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
35,1,332,0,0.714437," ","integrate(cot(d*x+c)^7*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(30 \, {\left(9 \, A - 7 i \, B\right)} a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} - 45 \, {\left(19 \, A - 17 i \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, {\left(135 \, A - 121 i \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 15 \, {\left(75 \, A - 68 i \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, {\left(81 \, A - 74 i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(86 \, A - 79 i \, B\right)} a^{4} - 30 \, {\left({\left(A - i \, B\right)} a^{4} e^{\left(12 i \, d x + 12 i \, c\right)} - 6 \, {\left(A - i \, B\right)} a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, {\left(A - i \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} - 20 \, {\left(A - i \, B\right)} a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, {\left(A - i \, B\right)} a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 6 \, {\left(A - i \, B\right)} a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A - i \, B\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*(30*(9*A - 7*I*B)*a^4*e^(10*I*d*x + 10*I*c) - 45*(19*A - 17*I*B)*a^4*e^(8*I*d*x + 8*I*c) + 10*(135*A - 121*I*B)*a^4*e^(6*I*d*x + 6*I*c) - 15*(75*A - 68*I*B)*a^4*e^(4*I*d*x + 4*I*c) + 6*(81*A - 74*I*B)*a^4*e^(2*I*d*x + 2*I*c) - (86*A - 79*I*B)*a^4 - 30*((A - I*B)*a^4*e^(12*I*d*x + 12*I*c) - 6*(A - I*B)*a^4*e^(10*I*d*x + 10*I*c) + 15*(A - I*B)*a^4*e^(8*I*d*x + 8*I*c) - 20*(A - I*B)*a^4*e^(6*I*d*x + 6*I*c) + 15*(A - I*B)*a^4*e^(4*I*d*x + 4*I*c) - 6*(A - I*B)*a^4*e^(2*I*d*x + 2*I*c) + (A - I*B)*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
36,1,181,0,0.822307," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(10 i \, A - 14 \, B\right)} d x e^{\left(6 i \, d x + 6 i \, c\right)} + {\left({\left(20 i \, A - 28 \, B\right)} d x + 9 \, A + i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left({\left(10 i \, A - 14 \, B\right)} d x + 10 \, A + 10 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 \, {\left({\left(A + 2 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, {\left(A + 2 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(A + 2 i \, B\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) + A + i \, B}{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*((10*I*A - 14*B)*d*x*e^(6*I*d*x + 6*I*c) + ((20*I*A - 28*B)*d*x + 9*A + I*B)*e^(4*I*d*x + 4*I*c) + ((10*I*A - 14*B)*d*x + 10*A + 10*I*B)*e^(2*I*d*x + 2*I*c) - 4*((A + 2*I*B)*e^(6*I*d*x + 6*I*c) + 2*(A + 2*I*B)*e^(4*I*d*x + 4*I*c) + (A + 2*I*B)*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) + A + I*B)/(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
37,1,130,0,0.743047," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A + 5 i \, B\right)} d x e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(2 \, {\left(3 \, A + 5 i \, B\right)} d x - i \, A + 9 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left({\left(4 i \, A - 4 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(4 i \, A - 4 \, B\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) - i \, A + B}{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*(3*A + 5*I*B)*d*x*e^(4*I*d*x + 4*I*c) + (2*(3*A + 5*I*B)*d*x - I*A + 9*B)*e^(2*I*d*x + 2*I*c) + ((4*I*A - 4*B)*e^(4*I*d*x + 4*I*c) + (4*I*A - 4*B)*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - I*A + B)/(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","A",0
38,1,67,0,0.780055," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(-2 i \, A + 6 \, B\right)} d x e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, B e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - A - i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*((-2*I*A + 6*B)*d*x*e^(2*I*d*x + 2*I*c) + 4*I*B*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - A - I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)","A",0
39,1,42,0,0.561482," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(A - i \, B\right)} d x e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(2*(A - I*B)*d*x*e^(2*I*d*x + 2*I*c) + I*A - B)*e^(-2*I*d*x - 2*I*c)/(a*d)","A",0
40,1,65,0,0.674581," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(-6 i \, A + 2 \, B\right)} d x e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, A e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) + A + i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*((-6*I*A + 2*B)*d*x*e^(2*I*d*x + 2*I*c) + 4*A*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) - 1) + A + I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)","A",0
41,1,131,0,0.584555," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, A + 3 i \, B\right)} d x e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(2 \, {\left(5 \, A + 3 i \, B\right)} d x - 9 i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left({\left(-4 i \, A + 4 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(4 i \, A - 4 \, B\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) - i \, A + B}{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*(5*A + 3*I*B)*d*x*e^(4*I*d*x + 4*I*c) - (2*(5*A + 3*I*B)*d*x - 9*I*A + B)*e^(2*I*d*x + 2*I*c) - ((-4*I*A + 4*B)*e^(4*I*d*x + 4*I*c) + (4*I*A - 4*B)*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - I*A + B)/(a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))","A",0
42,1,189,0,0.616853," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(14 i \, A - 10 \, B\right)} d x e^{\left(6 i \, d x + 6 i \, c\right)} + {\left({\left(-28 i \, A + 20 \, B\right)} d x - A - 9 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left({\left(14 i \, A - 10 \, B\right)} d x + 10 \, A + 10 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 \, {\left({\left(2 \, A + i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, {\left(2 \, A + i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(2 \, A + i \, B\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) - A - i \, B}{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*A - 10*B)*d*x*e^(6*I*d*x + 6*I*c) + ((-28*I*A + 20*B)*d*x - A - 9*I*B)*e^(4*I*d*x + 4*I*c) + ((14*I*A - 10*B)*d*x + 10*A + 10*I*B)*e^(2*I*d*x + 2*I*c) - 4*((2*A + I*B)*e^(6*I*d*x + 6*I*c) - 2*(2*A + I*B)*e^(4*I*d*x + 4*I*c) + (2*A + I*B)*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - A - I*B)/(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
43,1,251,0,0.633551," ","integrate(cot(d*x+c)^4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(9 \, A + 7 i \, B\right)} d x e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(18 \, {\left(9 \, A + 7 i \, B\right)} d x - 51 i \, A + 3 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(18 \, {\left(9 \, A + 7 i \, B\right)} d x - 81 i \, A + 33 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(6 \, {\left(9 \, A + 7 i \, B\right)} d x - 65 i \, A + 33 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left({\left(24 i \, A - 24 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-72 i \, A + 72 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(72 i \, A - 72 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-24 i \, A + 24 \, B\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 i \, A + 3 \, B}{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*(6*(9*A + 7*I*B)*d*x*e^(8*I*d*x + 8*I*c) - (18*(9*A + 7*I*B)*d*x - 51*I*A + 3*B)*e^(6*I*d*x + 6*I*c) + (18*(9*A + 7*I*B)*d*x - 81*I*A + 33*B)*e^(4*I*d*x + 4*I*c) - (6*(9*A + 7*I*B)*d*x - 65*I*A + 33*B)*e^(2*I*d*x + 2*I*c) + ((24*I*A - 24*B)*e^(8*I*d*x + 8*I*c) + (-72*I*A + 72*B)*e^(6*I*d*x + 6*I*c) + (72*I*A - 72*B)*e^(4*I*d*x + 4*I*c) + (-24*I*A + 24*B)*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 3*I*A + 3*B)/(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
44,1,147,0,0.519827," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-28 i \, A + 68 \, B\right)} d x e^{\left(6 i \, d x + 6 i \, c\right)} + {\left({\left(-28 i \, A + 68 \, B\right)} d x - 8 \, A - 44 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(7 \, A + 11 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 16 \, {\left({\left(A + 2 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(A + 2 i \, B\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) + A + i \, B}{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*((-28*I*A + 68*B)*d*x*e^(6*I*d*x + 6*I*c) + ((-28*I*A + 68*B)*d*x - 8*A - 44*I*B)*e^(4*I*d*x + 4*I*c) - (7*A + 11*I*B)*e^(2*I*d*x + 2*I*c) + 16*((A + 2*I*B)*e^(6*I*d*x + 6*I*c) + (A + 2*I*B)*e^(4*I*d*x + 4*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) + A + I*B)/(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))","A",0
45,1,84,0,0.692251," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(4 \, {\left(A + 7 i \, B\right)} d x e^{\left(4 i \, d x + 4 i \, c\right)} - 16 \, B e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - {\left(4 i \, A - 8 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"-1/16*(4*(A + 7*I*B)*d*x*e^(4*I*d*x + 4*I*c) - 16*B*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - (4*I*A - 8*B)*e^(2*I*d*x + 2*I*c) + I*A - B)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
46,1,55,0,0.654777," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left({\left(-4 i \, A - 4 \, B\right)} d x e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, B e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*((-4*I*A - 4*B)*d*x*e^(4*I*d*x + 4*I*c) + 4*I*B*e^(2*I*d*x + 2*I*c) - A - I*B)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
47,1,54,0,0.644725," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(A - i \, B\right)} d x e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, A e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*(4*(A - I*B)*d*x*e^(4*I*d*x + 4*I*c) + 4*I*A*e^(2*I*d*x + 2*I*c) + I*A - B)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
48,1,83,0,1.232710," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left({\left(-28 i \, A + 4 \, B\right)} d x e^{\left(4 i \, d x + 4 i \, c\right)} + 16 \, A e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) + 4 \, {\left(2 \, A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*((-28*I*A + 4*B)*d*x*e^(4*I*d*x + 4*I*c) + 16*A*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) - 1) + 4*(2*A + I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
49,1,155,0,0.815394," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(17 \, A + 7 i \, B\right)} d x e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(4 \, {\left(17 \, A + 7 i \, B\right)} d x - 44 i \, A + 8 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(11 i \, A - 7 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left({\left(-32 i \, A + 16 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(32 i \, A - 16 \, B\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) - i \, A + B}{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*(17*A + 7*I*B)*d*x*e^(6*I*d*x + 6*I*c) - (4*(17*A + 7*I*B)*d*x - 44*I*A + 8*B)*e^(4*I*d*x + 4*I*c) - (11*I*A - 7*B)*e^(2*I*d*x + 2*I*c) - ((-32*I*A + 16*B)*e^(6*I*d*x + 6*I*c) + (32*I*A - 16*B)*e^(4*I*d*x + 4*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - I*A + B)/(a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))","A",0
50,1,213,0,0.628171," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(124 i \, A - 68 \, B\right)} d x e^{\left(8 i \, d x + 8 i \, c\right)} + {\left({\left(-248 i \, A + 136 \, B\right)} d x - 48 \, A - 44 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left({\left(124 i \, A - 68 \, B\right)} d x + 95 \, A + 55 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(7 \, A + 5 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 32 \, {\left({\left(2 \, A + i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - 2 \, {\left(2 \, A + i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(2 \, A + i \, B\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) - A - i \, B}{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*A - 68*B)*d*x*e^(8*I*d*x + 8*I*c) + ((-248*I*A + 136*B)*d*x - 48*A - 44*I*B)*e^(6*I*d*x + 6*I*c) + ((124*I*A - 68*B)*d*x + 95*A + 55*I*B)*e^(4*I*d*x + 4*I*c) - 2*(7*A + 5*I*B)*e^(2*I*d*x + 2*I*c) - 32*((2*A + I*B)*e^(8*I*d*x + 8*I*c) - 2*(2*A + I*B)*e^(6*I*d*x + 6*I*c) + (2*A + I*B)*e^(4*I*d*x + 4*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - A - I*B)/(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
51,1,173,0,0.819167," ","integrate(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(15 \, A + 49 i \, B\right)} d x e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(12 \, {\left(15 \, A + 49 i \, B\right)} d x - 66 i \, A + 330 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(51 i \, A - 117 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(-13 i \, A + 19 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left({\left(-96 i \, A + 288 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-96 i \, A + 288 \, B\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) - 2 i \, A + 2 \, B}{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*(12*(15*A + 49*I*B)*d*x*e^(8*I*d*x + 8*I*c) + (12*(15*A + 49*I*B)*d*x - 66*I*A + 330*B)*e^(6*I*d*x + 6*I*c) - (51*I*A - 117*B)*e^(4*I*d*x + 4*I*c) - (-13*I*A + 19*B)*e^(2*I*d*x + 2*I*c) - ((-96*I*A + 288*B)*e^(8*I*d*x + 8*I*c) + (-96*I*A + 288*B)*e^(6*I*d*x + 6*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 2*I*A + 2*B)/(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))","A",0
52,1,103,0,1.100659," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(12 i \, A - 180 \, B\right)} d x e^{\left(6 i \, d x + 6 i \, c\right)} - 96 i \, B e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 6 \, {\left(3 \, A + 11 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 3 \, {\left(3 \, A + 5 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, A + 2 i \, B\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*((12*I*A - 180*B)*d*x*e^(6*I*d*x + 6*I*c) - 96*I*B*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 6*(3*A + 11*I*B)*e^(4*I*d*x + 4*I*c) - 3*(3*A + 5*I*B)*e^(2*I*d*x + 2*I*c) + 2*A + 2*I*B)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
53,1,78,0,0.772592," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(12 \, {\left(A - i \, B\right)} d x e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(6 i \, A + 18 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(3 i \, A - 9 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, A - 2 \, B\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"-1/96*(12*(A - I*B)*d*x*e^(6*I*d*x + 6*I*c) - (6*I*A + 18*B)*e^(4*I*d*x + 4*I*c) - (3*I*A - 9*B)*e^(2*I*d*x + 2*I*c) + 2*I*A - 2*B)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
54,1,75,0,0.669862," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(-12 i \, A - 12 \, B\right)} d x e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, {\left(A + i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 3 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, A - 2 i \, B\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*((-12*I*A - 12*B)*d*x*e^(6*I*d*x + 6*I*c) + 6*(A + I*B)*e^(4*I*d*x + 4*I*c) - 3*(A - I*B)*e^(2*I*d*x + 2*I*c) - 2*A - 2*I*B)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
55,1,76,0,0.504238," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, {\left(A - i \, B\right)} d x e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(18 i \, A + 6 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(9 i \, A - 3 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, A - 2 \, B\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(12*(A - I*B)*d*x*e^(6*I*d*x + 6*I*c) + (18*I*A + 6*B)*e^(4*I*d*x + 4*I*c) + (9*I*A - 3*B)*e^(2*I*d*x + 2*I*c) + 2*I*A - 2*B)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
56,1,103,0,0.592788," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(-180 i \, A + 12 \, B\right)} d x e^{\left(6 i \, d x + 6 i \, c\right)} + 96 \, A e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) + 6 \, {\left(11 \, A + 3 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(5 \, A + 3 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, A + 2 i \, B\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*((-180*I*A + 12*B)*d*x*e^(6*I*d*x + 6*I*c) + 96*A*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) - 1) + 6*(11*A + 3*I*B)*e^(4*I*d*x + 4*I*c) + 3*(5*A + 3*I*B)*e^(2*I*d*x + 2*I*c) + 2*A + 2*I*B)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
57,1,175,0,0.513413," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(49 \, A + 15 i \, B\right)} d x e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(12 \, {\left(49 \, A + 15 i \, B\right)} d x - 330 i \, A + 66 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(117 i \, A - 51 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(19 i \, A - 13 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left({\left(-288 i \, A + 96 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(288 i \, A - 96 \, B\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) - 2 i \, A + 2 \, B}{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*(12*(49*A + 15*I*B)*d*x*e^(8*I*d*x + 8*I*c) - (12*(49*A + 15*I*B)*d*x - 330*I*A + 66*B)*e^(6*I*d*x + 6*I*c) - (117*I*A - 51*B)*e^(4*I*d*x + 4*I*c) - (19*I*A - 13*B)*e^(2*I*d*x + 2*I*c) - ((-288*I*A + 96*B)*e^(8*I*d*x + 8*I*c) + (288*I*A - 96*B)*e^(6*I*d*x + 6*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 2*I*A + 2*B)/(a^3*d*e^(8*I*d*x + 8*I*c) - a^3*d*e^(6*I*d*x + 6*I*c))","A",0
58,1,231,0,0.539181," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(1332 i \, A - 588 \, B\right)} d x e^{\left(10 i \, d x + 10 i \, c\right)} + {\left({\left(-2664 i \, A + 1176 \, B\right)} d x - 618 \, A - 330 i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left({\left(1332 i \, A - 588 \, B\right)} d x + 1017 \, A + 447 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - 14 \, {\left(13 \, A + 7 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(23 \, A + 17 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 96 \, {\left({\left(7 \, A + 3 i \, B\right)} e^{\left(10 i \, d x + 10 i \, c\right)} - 2 \, {\left(7 \, A + 3 i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(7 \, A + 3 i \, B\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) - 2 \, A - 2 i \, B}{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*I*A - 588*B)*d*x*e^(10*I*d*x + 10*I*c) + ((-2664*I*A + 1176*B)*d*x - 618*A - 330*I*B)*e^(8*I*d*x + 8*I*c) + ((1332*I*A - 588*B)*d*x + 1017*A + 447*I*B)*e^(6*I*d*x + 6*I*c) - 14*(13*A + 7*I*B)*e^(4*I*d*x + 4*I*c) - (23*A + 17*I*B)*e^(2*I*d*x + 2*I*c) - 96*((7*A + 3*I*B)*e^(10*I*d*x + 10*I*c) - 2*(7*A + 3*I*B)*e^(8*I*d*x + 8*I*c) + (7*A + 3*I*B)*e^(6*I*d*x + 6*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 2*A - 2*I*B)/(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
59,1,117,0,0.604399," ","integrate(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(24 \, {\left(A + 31 i \, B\right)} d x e^{\left(8 i \, d x + 8 i \, c\right)} - 384 \, B e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + {\left(-48 i \, A + 312 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(36 i \, A - 96 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-16 i \, A + 24 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*(24*(A + 31*I*B)*d*x*e^(8*I*d*x + 8*I*c) - 384*B*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + (-48*I*A + 312*B)*e^(6*I*d*x + 6*I*c) + (36*I*A - 96*B)*e^(4*I*d*x + 4*I*c) + (-16*I*A + 24*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
60,1,87,0,0.604342," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(24 i \, A + 24 \, B\right)} d x e^{\left(8 i \, d x + 8 i \, c\right)} + 24 \, {\left(A - 2 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 36 i \, B e^{\left(4 i \, d x + 4 i \, c\right)} - 8 \, {\left(A + 2 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, A + 3 i \, B\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*((24*I*A + 24*B)*d*x*e^(8*I*d*x + 8*I*c) + 24*(A - 2*I*B)*e^(6*I*d*x + 6*I*c) + 36*I*B*e^(4*I*d*x + 4*I*c) - 8*(A + 2*I*B)*e^(2*I*d*x + 2*I*c) + 3*A + 3*I*B)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
61,1,78,0,0.498629," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{{\left(24 \, {\left(A - i \, B\right)} d x e^{\left(8 i \, d x + 8 i \, c\right)} - 24 \, B e^{\left(6 i \, d x + 6 i \, c\right)} - 12 i \, A e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, B e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"-1/384*(24*(A - I*B)*d*x*e^(8*I*d*x + 8*I*c) - 24*B*e^(6*I*d*x + 6*I*c) - 12*I*A*e^(4*I*d*x + 4*I*c) + 8*B*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
62,1,79,0,0.757190," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(-24 i \, A - 24 \, B\right)} d x e^{\left(8 i \, d x + 8 i \, c\right)} + 24 \, A e^{\left(6 i \, d x + 6 i \, c\right)} + 12 i \, B e^{\left(4 i \, d x + 4 i \, c\right)} - 8 \, A e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, A - 3 i \, B\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*((-24*I*A - 24*B)*d*x*e^(8*I*d*x + 8*I*c) + 24*A*e^(6*I*d*x + 6*I*c) + 12*I*B*e^(4*I*d*x + 4*I*c) - 8*A*e^(2*I*d*x + 2*I*c) - 3*A - 3*I*B)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
63,1,88,0,0.757514," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(24 \, {\left(A - i \, B\right)} d x e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(48 i \, A + 24 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 36 i \, A e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(16 i \, A - 8 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*(24*(A - I*B)*d*x*e^(8*I*d*x + 8*I*c) + (48*I*A + 24*B)*e^(6*I*d*x + 6*I*c) + 36*I*A*e^(4*I*d*x + 4*I*c) + (16*I*A - 8*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
64,1,121,0,0.638936," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(-744 i \, A + 24 \, B\right)} d x e^{\left(8 i \, d x + 8 i \, c\right)} + 384 \, A e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) + 24 \, {\left(13 \, A + 2 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 12 \, {\left(8 \, A + 3 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, {\left(3 \, A + 2 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, A + 3 i \, B\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*((-744*I*A + 24*B)*d*x*e^(8*I*d*x + 8*I*c) + 384*A*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) - 1) + 24*(13*A + 2*I*B)*e^(6*I*d*x + 6*I*c) + 12*(8*A + 3*I*B)*e^(4*I*d*x + 4*I*c) + 8*(3*A + 2*I*B)*e^(2*I*d*x + 2*I*c) + 3*A + 3*I*B)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
65,1,193,0,1.198860," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{24 \, {\left(129 \, A + 31 i \, B\right)} d x e^{\left(10 i \, d x + 10 i \, c\right)} - {\left(24 \, {\left(129 \, A + 31 i \, B\right)} d x - 1632 i \, A + 312 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(684 i \, A - 216 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(148 i \, A - 72 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(29 i \, A - 21 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left({\left(-1536 i \, A + 384 \, B\right)} e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(1536 i \, A - 384 \, B\right)} 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) - 3 i \, A + 3 \, B}{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*(24*(129*A + 31*I*B)*d*x*e^(10*I*d*x + 10*I*c) - (24*(129*A + 31*I*B)*d*x - 1632*I*A + 312*B)*e^(8*I*d*x + 8*I*c) - (684*I*A - 216*B)*e^(6*I*d*x + 6*I*c) - (148*I*A - 72*B)*e^(4*I*d*x + 4*I*c) - (29*I*A - 21*B)*e^(2*I*d*x + 2*I*c) - ((-1536*I*A + 384*B)*e^(10*I*d*x + 10*I*c) + (1536*I*A - 384*B)*e^(8*I*d*x + 8*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 3*I*A + 3*B)/(a^4*d*e^(10*I*d*x + 10*I*c) - a^4*d*e^(8*I*d*x + 8*I*c))","A",0
66,1,249,0,0.751542," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(8424 i \, A - 3096 \, B\right)} d x e^{\left(12 i \, d x + 12 i \, c\right)} + {\left({\left(-16848 i \, A + 6192 \, B\right)} d x - 4104 \, A - 1632 i \, B\right)} e^{\left(10 i \, d x + 10 i \, c\right)} + {\left({\left(8424 i \, A - 3096 \, B\right)} d x + 6384 \, A + 2316 i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - 8 \, {\left(158 \, A + 67 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(211 \, A + 119 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(17 \, A + 13 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 384 \, {\left({\left(11 \, A + 4 i \, B\right)} e^{\left(12 i \, d x + 12 i \, c\right)} - 2 \, {\left(11 \, A + 4 i \, B\right)} e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(11 \, A + 4 i \, B\right)} 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) - 3 \, A - 3 i \, B}{384 \, {\left(a^{4} d e^{\left(12 i \, d x + 12 i \, c\right)} - 2 \, 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*((8424*I*A - 3096*B)*d*x*e^(12*I*d*x + 12*I*c) + ((-16848*I*A + 6192*B)*d*x - 4104*A - 1632*I*B)*e^(10*I*d*x + 10*I*c) + ((8424*I*A - 3096*B)*d*x + 6384*A + 2316*I*B)*e^(8*I*d*x + 8*I*c) - 8*(158*A + 67*I*B)*e^(6*I*d*x + 6*I*c) - (211*A + 119*I*B)*e^(4*I*d*x + 4*I*c) - 2*(17*A + 13*I*B)*e^(2*I*d*x + 2*I*c) - 384*((11*A + 4*I*B)*e^(12*I*d*x + 12*I*c) - 2*(11*A + 4*I*B)*e^(10*I*d*x + 10*I*c) + (11*A + 4*I*B)*e^(8*I*d*x + 8*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 3*A - 3*I*B)/(a^4*d*e^(12*I*d*x + 12*I*c) - 2*a^4*d*e^(10*I*d*x + 10*I*c) + a^4*d*e^(8*I*d*x + 8*I*c))","A",0
67,1,444,0,0.534329," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{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)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) - 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)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) - 8 \, \sqrt{2} {\left({\left(119 \, A - 92 i \, B\right)} e^{\left(7 i \, d x + 7 i \, c\right)} + 7 \, {\left(37 \, A - 16 i \, B\right)} e^{\left(5 i \, d x + 5 i \, c\right)} + 35 \, {\left(7 \, A - 4 i \, B\right)} 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}}}{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*(105*(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*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - 105*(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*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - 8*sqrt(2)*((119*A - 92*I*B)*e^(7*I*d*x + 7*I*c) + 7*(37*A - 16*I*B)*e^(5*I*d*x + 5*I*c) + 35*(7*A - 4*I*B)*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
68,1,387,0,0.497452," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{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{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\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{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) + \sqrt{2} {\left({\left(-80 i \, A - 136 \, B\right)} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(-80 i \, A - 160 \, B\right)} e^{\left(3 i \, d x + 3 i \, c\right)} - 120 \, B 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*(15*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - 15*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) - sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) + sqrt(2)*((-80*I*A - 136*B)*e^(5*I*d*x + 5*I*c) + (-80*I*A - 160*B)*e^(3*I*d*x + 3*I*c) - 120*B*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
69,1,336,0,0.728331," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)*(A+B*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{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) - 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) - 8 \, \sqrt{2} {\left({\left(3 \, A - 2 i \, B\right)} 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}}}{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((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - 3*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - 8*sqrt(2)*((3*A - 2*I*B)*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
70,1,278,0,1.065105," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} B \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)} - d \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) + d \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right)}{4 \, d}"," ",0,"1/4*(8*sqrt(2)*B*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c) - d*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) + d*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) - sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)))/d","B",0
71,1,451,0,0.685979," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) - \frac{1}{4} \, \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) - \frac{1}{2} \, \sqrt{\frac{A^{2} a}{d^{2}}} \log\left(\frac{16 \, {\left(3 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{2} + 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^{2} a}{d^{2}}} \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) + \frac{1}{2} \, \sqrt{\frac{A^{2} a}{d^{2}}} \log\left(\frac{16 \, {\left(3 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{2} - 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^{2} a}{d^{2}}} \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)"," ",0,"1/4*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - 1/4*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - 1/2*sqrt(A^2*a/d^2)*log(16*(3*A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2 + 2*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(A^2*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/A) + 1/2*sqrt(A^2*a/d^2)*log(16*(3*A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2 - 2*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(A^2*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/A)","B",0
72,1,649,0,0.672231," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{{\left(A^{2} - 4 i \, A B - 4 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(48 i \, A + 96 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(16 i \, A + 32 \, B\right)} a^{2} + 32 \, \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{{\left(A^{2} - 4 i \, A B - 4 \, B^{2}\right)} a}{d^{2}}} \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)}}{i \, A + 2 \, B}\right) + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{{\left(A^{2} - 4 i \, A B - 4 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(48 i \, A + 96 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(16 i \, A + 32 \, B\right)} a^{2} - 32 \, \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{{\left(A^{2} - 4 i \, A B - 4 \, B^{2}\right)} a}{d^{2}}} \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)}}{i \, A + 2 \, B}\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*((d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - (d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) - sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - (d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-(A^2 - 4*I*A*B - 4*B^2)*a/d^2)*log(((48*I*A + 96*B)*a^2*e^(2*I*d*x + 2*I*c) + (16*I*A + 32*B)*a^2 + 32*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-(A^2 - 4*I*A*B - 4*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/(I*A + 2*B)) + (d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-(A^2 - 4*I*A*B - 4*B^2)*a/d^2)*log(((48*I*A + 96*B)*a^2*e^(2*I*d*x + 2*I*c) + (16*I*A + 32*B)*a^2 - 32*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-(A^2 - 4*I*A*B - 4*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/(I*A + 2*B)) + 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
73,1,734,0,0.589121," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{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)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\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)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) - {\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{{\left(49 \, A^{2} - 56 i \, A B - 16 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(4 \, {\left(336 i \, A + 192 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(112 i \, A + 64 \, B\right)} a^{2} + \sqrt{2} {\left(128 i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + 128 i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{{\left(49 \, A^{2} - 56 i \, A B - 16 \, B^{2}\right)} a}{d^{2}}} \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)}}{4 \, {\left(7 i \, A + 4 \, B\right)}}\right) + {\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{{\left(49 \, A^{2} - 56 i \, A B - 16 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(4 \, {\left(336 i \, A + 192 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(112 i \, A + 64 \, B\right)} a^{2} + \sqrt{2} {\left(-128 i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - 128 i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{{\left(49 \, A^{2} - 56 i \, A B - 16 \, B^{2}\right)} a}{d^{2}}} \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)}}{4 \, {\left(7 i \, A + 4 \, B\right)}}\right) - 4 \, \sqrt{2} {\left({\left(3 \, A - 4 i \, B\right)} e^{\left(5 i \, d x + 5 i \, c\right)} + 4 \, A e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(A + 4 i \, B\right)} 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*(4*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - 4*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - (d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt((49*A^2 - 56*I*A*B - 16*B^2)*a/d^2)*log(1/4*(4*(336*I*A + 192*B)*a^2*e^(2*I*d*x + 2*I*c) + 4*(112*I*A + 64*B)*a^2 + sqrt(2)*(128*I*a*d*e^(3*I*d*x + 3*I*c) + 128*I*a*d*e^(I*d*x + I*c))*sqrt((49*A^2 - 56*I*A*B - 16*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/(7*I*A + 4*B)) + (d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt((49*A^2 - 56*I*A*B - 16*B^2)*a/d^2)*log(1/4*(4*(336*I*A + 192*B)*a^2*e^(2*I*d*x + 2*I*c) + 4*(112*I*A + 64*B)*a^2 + sqrt(2)*(-128*I*a*d*e^(3*I*d*x + 3*I*c) - 128*I*a*d*e^(I*d*x + I*c))*sqrt((49*A^2 - 56*I*A*B - 16*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/(7*I*A + 4*B)) - 4*sqrt(2)*((3*A - 4*I*B)*e^(5*I*d*x + 5*I*c) + 4*A*e^(3*I*d*x + 3*I*c) + (A + 4*I*B)*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
74,1,824,0,0.873264," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{24 \, {\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{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\right) - 24 \, {\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{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{{\left(8 \, A^{2} - 16 i \, A B - 8 \, B^{2}\right)} a}{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)}}{i \, A + B}\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)} \sqrt{-\frac{{\left(81 \, A^{2} - 252 i \, A B - 196 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(432 i \, A + 672 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(144 i \, A + 224 \, B\right)} a^{2} + 32 \, \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{{\left(81 \, A^{2} - 252 i \, A B - 196 \, B^{2}\right)} a}{d^{2}}} \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)}}{9 i \, A + 14 \, B}\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)} \sqrt{-\frac{{\left(81 \, A^{2} - 252 i \, A B - 196 \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(432 i \, A + 672 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(144 i \, A + 224 \, B\right)} a^{2} - 32 \, \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{{\left(81 \, A^{2} - 252 i \, A B - 196 \, B^{2}\right)} a}{d^{2}}} \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)}}{9 i \, A + 14 \, B}\right) - 4 \, \sqrt{2} {\left({\left(31 i \, A + 18 \, B\right)} e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(5 i \, A + 6 \, B\right)} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(i \, A - 18 \, B\right)} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(27 i \, A - 6 \, B\right)} 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*(24*(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*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - 24*(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*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) - sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-(8*A^2 - 16*I*A*B - 8*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(I*A + B)) - 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)*sqrt(-(81*A^2 - 252*I*A*B - 196*B^2)*a/d^2)*log(((432*I*A + 672*B)*a^2*e^(2*I*d*x + 2*I*c) + (144*I*A + 224*B)*a^2 + 32*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-(81*A^2 - 252*I*A*B - 196*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/(9*I*A + 14*B)) + 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)*sqrt(-(81*A^2 - 252*I*A*B - 196*B^2)*a/d^2)*log(((432*I*A + 672*B)*a^2*e^(2*I*d*x + 2*I*c) + (144*I*A + 224*B)*a^2 - 32*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-(81*A^2 - 252*I*A*B - 196*B^2)*a/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/(9*I*A + 14*B)) - 4*sqrt(2)*((31*I*A + 18*B)*e^(7*I*d*x + 7*I*c) + (5*I*A + 6*B)*e^(5*I*d*x + 5*I*c) + (I*A - 18*B)*e^(3*I*d*x + 3*I*c) + (27*I*A - 6*B)*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
75,1,471,0,0.558017," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - 105 \, \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + \sqrt{2} {\left({\left(-1512 i \, A - 1688 \, B\right)} a e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(-3192 i \, A - 2968 \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(-2520 i \, A - 3080 \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-840 i \, A - 840 \, B\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}}}{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*(105*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) - 105*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) + sqrt(2)*((-1512*I*A - 1688*B)*a*e^(7*I*d*x + 7*I*c) + (-3192*I*A - 2968*B)*a*e^(5*I*d*x + 5*I*c) + (-2520*I*A - 3080*B)*a*e^(3*I*d*x + 3*I*c) + (-840*I*A - 840*B)*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
76,1,419,0,0.733768," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - 15 \, \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - 8 \, \sqrt{2} {\left({\left(25 \, A - 27 i \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + 10 \, {\left(4 \, A - 3 i \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + 15 \, {\left(A - i \, B\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}}}{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((32*A^2 - 64*I*A*B - 32*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt((32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) - 15*sqrt((32*A^2 - 64*I*A*B - 32*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt((32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) - 8*sqrt(2)*((25*A - 27*I*B)*a*e^(5*I*d*x + 5*I*c) + 10*(4*A - 3*I*B)*a*e^(3*I*d*x + 3*I*c) + 15*(A - I*B)*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
77,1,364,0,0.641758," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - 3 \, \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - \sqrt{2} {\left({\left(24 i \, A + 40 \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(24 i \, A + 24 \, B\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}}}{12 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/12*(3*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) - 3*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) - sqrt(2)*((24*I*A + 40*B)*a*e^(3*I*d*x + 3*I*c) + (24*I*A + 24*B)*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
78,1,518,0,0.659287," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{8 i \, \sqrt{2} B a \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)} - 2 \, \sqrt{\frac{A^{2} a^{3}}{d^{2}}} d \log\left(\frac{16 \, {\left(3 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{2} + 2 \, \sqrt{2} \sqrt{\frac{A^{2} a^{3}}{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 \, \sqrt{\frac{A^{2} a^{3}}{d^{2}}} d \log\left(\frac{16 \, {\left(3 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{2} - 2 \, \sqrt{2} \sqrt{\frac{A^{2} a^{3}}{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{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{d^{2}}} d \log\left(\frac{{\left({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{d^{2}}} d \log\left(\frac{{\left({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right)}{4 \, d}"," ",0,"1/4*(8*I*sqrt(2)*B*a*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c) - 2*sqrt(A^2*a^3/d^2)*d*log(16*(3*A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2 + 2*sqrt(2)*sqrt(A^2*a^3/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) + 2*sqrt(A^2*a^3/d^2)*d*log(16*(3*A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2 - 2*sqrt(2)*sqrt(A^2*a^3/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((32*A^2 - 64*I*A*B - 32*B^2)*a^3/d^2)*d*log(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt((32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) - sqrt((32*A^2 - 64*I*A*B - 32*B^2)*a^3/d^2)*d*log(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt((32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)))/d","B",0
79,1,686,0,0.587841," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{\sqrt{-\frac{{\left(9 \, A^{2} - 12 i \, A B - 4 \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left({\left(144 i \, A + 96 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(48 i \, A + 32 \, B\right)} a^{2} + 32 \, \sqrt{2} \sqrt{-\frac{{\left(9 \, A^{2} - 12 i \, A B - 4 \, B^{2}\right)} a^{3}}{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)}}{3 i \, A + 2 \, B}\right) - \sqrt{-\frac{{\left(9 \, A^{2} - 12 i \, A B - 4 \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left({\left(144 i \, A + 96 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(48 i \, A + 32 \, B\right)} a^{2} - 32 \, \sqrt{2} \sqrt{-\frac{{\left(9 \, A^{2} - 12 i \, A B - 4 \, B^{2}\right)} a^{3}}{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)}}{3 i \, A + 2 \, B}\right) - \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - \sqrt{2} {\left(-4 i \, A a e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, A 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*(sqrt(-(9*A^2 - 12*I*A*B - 4*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(((144*I*A + 96*B)*a^2*e^(2*I*d*x + 2*I*c) + (48*I*A + 32*B)*a^2 + 32*sqrt(2)*sqrt(-(9*A^2 - 12*I*A*B - 4*B^2)*a^3/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)/(3*I*A + 2*B)) - sqrt(-(9*A^2 - 12*I*A*B - 4*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(((144*I*A + 96*B)*a^2*e^(2*I*d*x + 2*I*c) + (48*I*A + 32*B)*a^2 - 32*sqrt(2)*sqrt(-(9*A^2 - 12*I*A*B - 4*B^2)*a^3/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)/(3*I*A + 2*B)) - sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) + sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) - sqrt(2)*(-4*I*A*a*e^(3*I*d*x + 3*I*c) - 4*I*A*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
80,1,766,0,0.570156," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{\frac{{\left(121 \, A^{2} - 264 i \, A B - 144 \, B^{2}\right)} a^{3}}{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 \, {\left(528 i \, A + 576 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(176 i \, A + 192 \, B\right)} a^{2} + \sqrt{2} \sqrt{\frac{{\left(121 \, A^{2} - 264 i \, A B - 144 \, B^{2}\right)} a^{3}}{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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(11 i \, A + 12 \, B\right)}}\right) - \sqrt{\frac{{\left(121 \, A^{2} - 264 i \, A B - 144 \, B^{2}\right)} a^{3}}{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 \, {\left(528 i \, A + 576 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(176 i \, A + 192 \, B\right)} a^{2} + \sqrt{2} \sqrt{\frac{{\left(121 \, A^{2} - 264 i \, A B - 144 \, B^{2}\right)} a^{3}}{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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(11 i \, A + 12 \, B\right)}}\right) - 4 \, \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 4 \, \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 4 \, \sqrt{2} {\left({\left(7 \, A - 4 i \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + 4 \, A a e^{\left(3 i \, d x + 3 i \, c\right)} - {\left(3 \, A - 4 i \, B\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}}}{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*(sqrt((121*A^2 - 264*I*A*B - 144*B^2)*a^3/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*(528*I*A + 576*B)*a^2*e^(2*I*d*x + 2*I*c) + 4*(176*I*A + 192*B)*a^2 + sqrt(2)*sqrt((121*A^2 - 264*I*A*B - 144*B^2)*a^3/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)))*e^(-2*I*d*x - 2*I*c)/(11*I*A + 12*B)) - sqrt((121*A^2 - 264*I*A*B - 144*B^2)*a^3/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*(528*I*A + 576*B)*a^2*e^(2*I*d*x + 2*I*c) + 4*(176*I*A + 192*B)*a^2 + sqrt(2)*sqrt((121*A^2 - 264*I*A*B - 144*B^2)*a^3/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)))*e^(-2*I*d*x - 2*I*c)/(11*I*A + 12*B)) - 4*sqrt((32*A^2 - 64*I*A*B - 32*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt((32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) + 4*sqrt((32*A^2 - 64*I*A*B - 32*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt((32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) + 4*sqrt(2)*((7*A - 4*I*B)*a*e^(5*I*d*x + 5*I*c) + 4*A*a*e^(3*I*d*x + 3*I*c) - (3*A - 4*I*B)*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
81,1,854,0,0.684385," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{-\frac{{\left(529 \, A^{2} - 1012 i \, A B - 484 \, B^{2}\right)} a^{3}}{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({\left(1104 i \, A + 1056 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(368 i \, A + 352 \, B\right)} a^{2} + 32 \, \sqrt{2} \sqrt{-\frac{{\left(529 \, A^{2} - 1012 i \, A B - 484 \, B^{2}\right)} a^{3}}{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)}}{23 i \, A + 22 \, B}\right) - 3 \, \sqrt{-\frac{{\left(529 \, A^{2} - 1012 i \, A B - 484 \, B^{2}\right)} a^{3}}{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({\left(1104 i \, A + 1056 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(368 i \, A + 352 \, B\right)} a^{2} - 32 \, \sqrt{2} \sqrt{-\frac{{\left(529 \, A^{2} - 1012 i \, A B - 484 \, B^{2}\right)} a^{3}}{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)}}{23 i \, A + 22 \, B}\right) - 24 \, \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 24 \, \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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({\left(8 i \, A + 8 \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{-\frac{{\left(32 \, A^{2} - 64 i \, A B - 32 \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 4 \, \sqrt{2} {\left({\left(49 i \, A + 42 \, B\right)} a e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(11 i \, A - 18 \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(-17 i \, A - 42 \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(21 i \, A + 18 \, B\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}}}{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*(3*sqrt(-(529*A^2 - 1012*I*A*B - 484*B^2)*a^3/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(((1104*I*A + 1056*B)*a^2*e^(2*I*d*x + 2*I*c) + (368*I*A + 352*B)*a^2 + 32*sqrt(2)*sqrt(-(529*A^2 - 1012*I*A*B - 484*B^2)*a^3/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)/(23*I*A + 22*B)) - 3*sqrt(-(529*A^2 - 1012*I*A*B - 484*B^2)*a^3/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(((1104*I*A + 1056*B)*a^2*e^(2*I*d*x + 2*I*c) + (368*I*A + 352*B)*a^2 - 32*sqrt(2)*sqrt(-(529*A^2 - 1012*I*A*B - 484*B^2)*a^3/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)/(23*I*A + 22*B)) - 24*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) + 24*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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(((8*I*A + 8*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt(-(32*A^2 - 64*I*A*B - 32*B^2)*a^3/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)/((2*I*A + 2*B)*a)) + 4*sqrt(2)*((49*I*A + 42*B)*a*e^(7*I*d*x + 7*I*c) + (11*I*A - 18*B)*a*e^(5*I*d*x + 5*I*c) + (-17*I*A - 42*B)*a*e^(3*I*d*x + 3*I*c) + (21*I*A + 18*B)*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
82,1,535,0,0.752898," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{315 \, \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - 315 \, \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + \sqrt{2} {\left({\left(-9600 i \, A - 10336 \, B\right)} a^{2} e^{\left(9 i \, d x + 9 i \, c\right)} + {\left(-28080 i \, A - 26352 \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(-35280 i \, A - 37296 \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(-21840 i \, A - 21840 \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-5040 i \, A - 5040 \, B\right)} 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}}}{1260 \, {\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,"1/1260*(315*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) - 315*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) + sqrt(2)*((-9600*I*A - 10336*B)*a^2*e^(9*I*d*x + 9*I*c) + (-28080*I*A - 26352*B)*a^2*e^(7*I*d*x + 7*I*c) + (-35280*I*A - 37296*B)*a^2*e^(5*I*d*x + 5*I*c) + (-21840*I*A - 21840*B)*a^2*e^(3*I*d*x + 3*I*c) + (-5040*I*A - 5040*B)*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
83,1,481,0,0.560179," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - 105 \, \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - 16 \, \sqrt{2} {\left(2 \, {\left(91 \, A - 100 i \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + 7 \, {\left(61 \, A - 55 i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 350 \, {\left(A - i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 105 \, {\left(A - i \, B\right)} 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}}}{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*(105*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) - 105*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) - 16*sqrt(2)*(2*(91*A - 100*I*B)*a^2*e^(7*I*d*x + 7*I*c) + 7*(61*A - 55*I*B)*a^2*e^(5*I*d*x + 5*I*c) + 350*(A - I*B)*a^2*e^(3*I*d*x + 3*I*c) + 105*(A - I*B)*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
84,1,424,0,0.856703," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - 15 \, \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - \sqrt{2} {\left({\left(320 i \, A + 416 \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(560 i \, A + 560 \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(240 i \, A + 240 \, B\right)} 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}}}{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(-(128*A^2 - 256*I*A*B - 128*B^2)*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*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) - 15*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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*I*A + 16*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) - sqrt(2)*((320*I*A + 416*B)*a^2*e^(5*I*d*x + 5*I*c) + (560*I*A + 560*B)*a^2*e^(3*I*d*x + 3*I*c) + (240*I*A + 240*B)*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
85,1,614,0,0.495608," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, \sqrt{\frac{A^{2} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{16 \, {\left(3 \, A a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{3} + 2 \, \sqrt{2} \sqrt{\frac{A^{2} 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 a}\right) - 6 \, \sqrt{\frac{A^{2} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{16 \, {\left(3 \, A a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{3} - 2 \, \sqrt{2} \sqrt{\frac{A^{2} 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 a}\right) - 3 \, \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 3 \, \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 8 \, \sqrt{2} {\left({\left(3 \, A - 8 i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 3 \, {\left(A - 2 i \, B\right)} 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*(6*sqrt(A^2*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(16*(3*A*a^3*e^(2*I*d*x + 2*I*c) + A*a^3 + 2*sqrt(2)*sqrt(A^2*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*a)) - 6*sqrt(A^2*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(16*(3*A*a^3*e^(2*I*d*x + 2*I*c) + A*a^3 - 2*sqrt(2)*sqrt(A^2*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*a)) - 3*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) + 3*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) + 8*sqrt(2)*((3*A - 8*I*B)*a^2*e^(3*I*d*x + 3*I*c) + 3*(A - 2*I*B)*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
86,1,706,0,0.577987," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{\sqrt{-\frac{{\left(25 \, A^{2} - 20 i \, A B - 4 \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left({\left(240 i \, A + 96 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(80 i \, A + 32 \, B\right)} a^{3} + 32 \, \sqrt{2} \sqrt{-\frac{{\left(25 \, A^{2} - 20 i \, A B - 4 \, B^{2}\right)} 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)}}{{\left(5 i \, A + 2 \, B\right)} a}\right) - \sqrt{-\frac{{\left(25 \, A^{2} - 20 i \, A B - 4 \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left({\left(240 i \, A + 96 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(80 i \, A + 32 \, B\right)} a^{3} - 32 \, \sqrt{2} \sqrt{-\frac{{\left(25 \, A^{2} - 20 i \, A B - 4 \, B^{2}\right)} 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)}}{{\left(5 i \, A + 2 \, B\right)} a}\right) - \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - \sqrt{2} {\left({\left(-4 i \, A - 8 \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-4 i \, A + 8 \, B\right)} 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*(sqrt(-(25*A^2 - 20*I*A*B - 4*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(((240*I*A + 96*B)*a^3*e^(2*I*d*x + 2*I*c) + (80*I*A + 32*B)*a^3 + 32*sqrt(2)*sqrt(-(25*A^2 - 20*I*A*B - 4*B^2)*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)/((5*I*A + 2*B)*a)) - sqrt(-(25*A^2 - 20*I*A*B - 4*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(((240*I*A + 96*B)*a^3*e^(2*I*d*x + 2*I*c) + (80*I*A + 32*B)*a^3 - 32*sqrt(2)*sqrt(-(25*A^2 - 20*I*A*B - 4*B^2)*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)/((5*I*A + 2*B)*a)) - sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) + sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) - sqrt(2)*((-4*I*A - 8*B)*a^2*e^(3*I*d*x + 3*I*c) + (-4*I*A + 8*B)*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
87,1,778,0,0.726666," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{\frac{{\left(529 \, A^{2} - 920 i \, A B - 400 \, B^{2}\right)} 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 \, {\left(1104 i \, A + 960 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(368 i \, A + 320 \, B\right)} a^{3} + \sqrt{2} \sqrt{\frac{{\left(529 \, A^{2} - 920 i \, A B - 400 \, B^{2}\right)} a^{5}}{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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(23 i \, A + 20 \, B\right)} a}\right) - \sqrt{\frac{{\left(529 \, A^{2} - 920 i \, A B - 400 \, B^{2}\right)} 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 \, {\left(1104 i \, A + 960 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(368 i \, A + 320 \, B\right)} a^{3} + \sqrt{2} \sqrt{\frac{{\left(529 \, A^{2} - 920 i \, A B - 400 \, B^{2}\right)} a^{5}}{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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(23 i \, A + 20 \, B\right)} a}\right) - 4 \, \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 4 \, \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 4 \, \sqrt{2} {\left({\left(11 \, A - 4 i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 4 \, A a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - {\left(7 \, A - 4 i \, B\right)} 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*(sqrt((529*A^2 - 920*I*A*B - 400*B^2)*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*(1104*I*A + 960*B)*a^3*e^(2*I*d*x + 2*I*c) + 4*(368*I*A + 320*B)*a^3 + sqrt(2)*sqrt((529*A^2 - 920*I*A*B - 400*B^2)*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)))*e^(-2*I*d*x - 2*I*c)/((23*I*A + 20*B)*a)) - sqrt((529*A^2 - 920*I*A*B - 400*B^2)*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*(1104*I*A + 960*B)*a^3*e^(2*I*d*x + 2*I*c) + 4*(368*I*A + 320*B)*a^3 + sqrt(2)*sqrt((529*A^2 - 920*I*A*B - 400*B^2)*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)))*e^(-2*I*d*x - 2*I*c)/((23*I*A + 20*B)*a)) - 4*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) + 4*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) + 4*sqrt(2)*((11*A - 4*I*B)*a^2*e^(5*I*d*x + 5*I*c) + 4*A*a^2*e^(3*I*d*x + 3*I*c) - (7*A - 4*I*B)*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
88,1,868,0,0.734618," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{-\frac{{\left(2025 \, A^{2} - 4140 i \, A B - 2116 \, B^{2}\right)} 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({\left(2160 i \, A + 2208 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(720 i \, A + 736 \, B\right)} a^{3} + 32 \, \sqrt{2} \sqrt{-\frac{{\left(2025 \, A^{2} - 4140 i \, A B - 2116 \, B^{2}\right)} 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)}}{{\left(45 i \, A + 46 \, B\right)} a}\right) - 3 \, \sqrt{-\frac{{\left(2025 \, A^{2} - 4140 i \, A B - 2116 \, B^{2}\right)} 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({\left(2160 i \, A + 2208 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(720 i \, A + 736 \, B\right)} a^{3} - 32 \, \sqrt{2} \sqrt{-\frac{{\left(2025 \, A^{2} - 4140 i \, A B - 2116 \, B^{2}\right)} 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)}}{{\left(45 i \, A + 46 \, B\right)} a}\right) - 24 \, \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 24 \, \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{-\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 4 \, \sqrt{2} {\left({\left(91 i \, A + 66 \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(-7 i \, A - 42 \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(-59 i \, A - 66 \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(39 i \, A + 42 \, B\right)} 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*(3*sqrt(-(2025*A^2 - 4140*I*A*B - 2116*B^2)*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(((2160*I*A + 2208*B)*a^3*e^(2*I*d*x + 2*I*c) + (720*I*A + 736*B)*a^3 + 32*sqrt(2)*sqrt(-(2025*A^2 - 4140*I*A*B - 2116*B^2)*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)/((45*I*A + 46*B)*a)) - 3*sqrt(-(2025*A^2 - 4140*I*A*B - 2116*B^2)*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(((2160*I*A + 2208*B)*a^3*e^(2*I*d*x + 2*I*c) + (720*I*A + 736*B)*a^3 - 32*sqrt(2)*sqrt(-(2025*A^2 - 4140*I*A*B - 2116*B^2)*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)/((45*I*A + 46*B)*a)) - 24*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) + 24*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt(-(128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) + 4*sqrt(2)*((91*I*A + 66*B)*a^2*e^(7*I*d*x + 7*I*c) + (-7*I*A - 42*B)*a^2*e^(5*I*d*x + 5*I*c) + (-59*I*A - 66*B)*a^2*e^(3*I*d*x + 3*I*c) + (39*I*A + 42*B)*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
89,1,948,0,0.659597," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{{\left(131769 \, A^{2} - 261360 i \, A B - 129600 \, B^{2}\right)} 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(64 \, {\left(17424 i \, A + 17280 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 64 \, {\left(5808 i \, A + 5760 \, B\right)} a^{3} + \sqrt{2} \sqrt{\frac{{\left(131769 \, A^{2} - 261360 i \, A B - 129600 \, B^{2}\right)} a^{5}}{d^{2}}} {\left(2048 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} + 2048 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)}}{64 \, {\left(363 i \, A + 360 \, B\right)} a}\right) - 3 \, \sqrt{\frac{{\left(131769 \, A^{2} - 261360 i \, A B - 129600 \, B^{2}\right)} 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(64 \, {\left(17424 i \, A + 17280 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 64 \, {\left(5808 i \, A + 5760 \, B\right)} a^{3} + \sqrt{2} \sqrt{\frac{{\left(131769 \, A^{2} - 261360 i \, A B - 129600 \, B^{2}\right)} a^{5}}{d^{2}}} {\left(-2048 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} - 2048 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)}}{64 \, {\left(363 i \, A + 360 \, B\right)} a}\right) - 192 \, \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 192 \, \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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({\left(16 i \, A + 16 \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(128 \, A^{2} - 256 i \, A B - 128 \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 4 \, \sqrt{2} {\left(13 \, {\left(65 \, A - 56 i \, B\right)} a^{2} e^{\left(9 i \, d x + 9 i \, c\right)} - 2 \, {\left(215 \, A - 392 i \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 4 \, {\left(35 \, A - 104 i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, {\left(407 \, A - 392 i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 3 \, {\left(107 \, A - 104 i \, B\right)} 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}}}{768 \, {\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,"-1/768*(3*sqrt((131769*A^2 - 261360*I*A*B - 129600*B^2)*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(1/64*(64*(17424*I*A + 17280*B)*a^3*e^(2*I*d*x + 2*I*c) + 64*(5808*I*A + 5760*B)*a^3 + sqrt(2)*sqrt((131769*A^2 - 261360*I*A*B - 129600*B^2)*a^5/d^2)*(2048*I*d*e^(3*I*d*x + 3*I*c) + 2048*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)/((363*I*A + 360*B)*a)) - 3*sqrt((131769*A^2 - 261360*I*A*B - 129600*B^2)*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(1/64*(64*(17424*I*A + 17280*B)*a^3*e^(2*I*d*x + 2*I*c) + 64*(5808*I*A + 5760*B)*a^3 + sqrt(2)*sqrt((131769*A^2 - 261360*I*A*B - 129600*B^2)*a^5/d^2)*(-2048*I*d*e^(3*I*d*x + 3*I*c) - 2048*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)/((363*I*A + 360*B)*a)) - 192*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) + 192*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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(((16*I*A + 16*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((128*A^2 - 256*I*A*B - 128*B^2)*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)/((4*I*A + 4*B)*a^2)) + 4*sqrt(2)*(13*(65*A - 56*I*B)*a^2*e^(9*I*d*x + 9*I*c) - 2*(215*A - 392*I*B)*a^2*e^(7*I*d*x + 7*I*c) - 4*(35*A - 104*I*B)*a^2*e^(5*I*d*x + 5*I*c) + 2*(407*A - 392*I*B)*a^2*e^(3*I*d*x + 3*I*c) - 3*(107*A - 104*I*B)*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
90,1,453,0,0.591824," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{15 \, {\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 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 15 \, {\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 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + \sqrt{2} {\left(2 \, {\left(35 \, A + 103 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, {\left(25 \, A + 41 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 30 \, {\left(7 \, A + 11 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 30 \, A + 30 i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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*(15*(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*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) - 15*(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*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) + sqrt(2)*(2*(35*A + 103*I*B)*e^(6*I*d*x + 6*I*c) + 10*(25*A + 41*I*B)*e^(4*I*d*x + 4*I*c) + 30*(7*A + 11*I*B)*e^(2*I*d*x + 2*I*c) + 30*A + 30*I*B)*sqrt(a/(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
91,1,396,0,0.628766," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{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 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + 2 \, \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} - 2 \, \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + \sqrt{2} {\left({\left(-30 i \, A + 14 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-36 i \, A + 36 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i \, A + 6 \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) - 3*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) - 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(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) + sqrt(2)*((-30*I*A + 14*B)*e^(4*I*d*x + 4*I*c) + (-36*I*A + 36*B)*e^(2*I*d*x + 2*I*c) - 6*I*A + 6*B)*sqrt(a/(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
92,1,333,0,0.574341," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{\frac{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - a d \sqrt{\frac{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + 2 \, \sqrt{2} {\left({\left(A + 5 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"-1/4*(a*d*sqrt((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*e^(I*d*x + I*c)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) - a*d*sqrt((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*e^(I*d*x + I*c)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) + 2*sqrt(2)*((A + 5*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(a*d)","B",0
93,1,339,0,0.544649," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{-\frac{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + 2 \, \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - a d \sqrt{-\frac{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} - 2 \, \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \sqrt{2} {\left({\left(2 i \, A - 2 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, A - 2 \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"-1/4*(a*d*sqrt(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*e^(I*d*x + I*c)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) - a*d*sqrt(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*e^(I*d*x + I*c)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) - 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(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*((2*I*A - 2*B)*e^(2*I*d*x + 2*I*c) + 2*I*A - 2*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(a*d)","B",0
94,1,581,0,0.636985," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{\frac{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - a d \sqrt{\frac{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 2 \, a d \sqrt{\frac{A^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{16 \, {\left(3 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{2} + 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{A^{2}}{a d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{A}\right) + 2 \, a d \sqrt{\frac{A^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{16 \, {\left(3 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{2} - 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{A^{2}}{a d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{A}\right) + 2 \, \sqrt{2} {\left({\left(A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"1/4*(a*d*sqrt((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*e^(I*d*x + I*c)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) - a*d*sqrt((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*e^(I*d*x + I*c)*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) - 2*a*d*sqrt(A^2/(a*d^2))*e^(I*d*x + I*c)*log(16*(3*A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2 + 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(A^2/(a*d^2)))*e^(-2*I*d*x - 2*I*c)/A) + 2*a*d*sqrt(A^2/(a*d^2))*e^(I*d*x + I*c)*log(16*(3*A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2 - 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(A^2/(a*d^2)))*e^(-2*I*d*x - 2*I*c)/A) + 2*sqrt(2)*((A + I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/(a*d)","B",0
95,1,746,0,0.530576," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\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 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + 2 \, \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} - 2 \, \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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{A^{2} + 4 i \, A B - 4 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left({\left(-48 i \, A + 96 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-16 i \, A + 32 \, B\right)} a^{2} + 32 \, \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{A^{2} + 4 i \, A B - 4 \, B^{2}}{a d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{-i \, A + 2 \, B}\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{A^{2} + 4 i \, A B - 4 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left({\left(-48 i \, A + 96 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-16 i \, A + 32 \, B\right)} a^{2} - 32 \, \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{A^{2} + 4 i \, A B - 4 \, B^{2}}{a d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{-i \, A + 2 \, B}\right) + \sqrt{2} {\left({\left(-6 i \, A + 2 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, A e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, A - 2 \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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*((a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) - (a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) - 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(-(2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) - (a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(-(A^2 + 4*I*A*B - 4*B^2)/(a*d^2))*log(((-48*I*A + 96*B)*a^2*e^(2*I*d*x + 2*I*c) + (-16*I*A + 32*B)*a^2 + 32*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(-(A^2 + 4*I*A*B - 4*B^2)/(a*d^2)))*e^(-2*I*d*x - 2*I*c)/(-I*A + 2*B)) + (a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(-(A^2 + 4*I*A*B - 4*B^2)/(a*d^2))*log(((-48*I*A + 96*B)*a^2*e^(2*I*d*x + 2*I*c) + (-16*I*A + 32*B)*a^2 - 32*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(-(A^2 + 4*I*A*B - 4*B^2)/(a*d^2)))*e^(-2*I*d*x - 2*I*c)/(-I*A + 2*B)) + sqrt(2)*((-6*I*A + 2*B)*e^(4*I*d*x + 4*I*c) - 4*I*A*e^(2*I*d*x + 2*I*c) + 2*I*A - 2*B)*sqrt(a/(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
96,1,841,0,0.727508," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, {\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 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 4 \, {\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 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left({\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)} + \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{2 \, A^{2} - 4 i \, A B - 2 \, B^{2}}{a d^{2}}}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + {\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{121 \, A^{2} + 88 i \, A B - 16 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left(4 \, {\left(-528 i \, A + 192 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(-176 i \, A + 64 \, B\right)} a^{2} + \sqrt{2} {\left(128 i \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + 128 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{121 \, A^{2} + 88 i \, A B - 16 \, B^{2}}{a d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(-11 i \, A + 4 \, B\right)}}\right) - {\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{121 \, A^{2} + 88 i \, A B - 16 \, B^{2}}{a d^{2}}} \log\left(\frac{{\left(4 \, {\left(-528 i \, A + 192 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(-176 i \, A + 64 \, B\right)} a^{2} + \sqrt{2} {\left(-128 i \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} - 128 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{121 \, A^{2} + 88 i \, A B - 16 \, B^{2}}{a d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(-11 i \, A + 4 \, B\right)}}\right) + 4 \, \sqrt{2} {\left(3 \, {\left(A + 2 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, {\left(3 \, A + i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(7 \, A + 6 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, A + 2 i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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*(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*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) - 4*(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*A^2 - 4*I*A*B - 2*B^2)/(a*d^2))*log(((4*I*A + 4*B)*a*e^(I*d*x + I*c) + 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((2*A^2 - 4*I*A*B - 2*B^2)/(a*d^2)))*e^(-I*d*x - I*c)/(I*A + B)) + (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((121*A^2 + 88*I*A*B - 16*B^2)/(a*d^2))*log(1/4*(4*(-528*I*A + 192*B)*a^2*e^(2*I*d*x + 2*I*c) + 4*(-176*I*A + 64*B)*a^2 + sqrt(2)*(128*I*a^2*d*e^(3*I*d*x + 3*I*c) + 128*I*a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((121*A^2 + 88*I*A*B - 16*B^2)/(a*d^2)))*e^(-2*I*d*x - 2*I*c)/(-11*I*A + 4*B)) - (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((121*A^2 + 88*I*A*B - 16*B^2)/(a*d^2))*log(1/4*(4*(-528*I*A + 192*B)*a^2*e^(2*I*d*x + 2*I*c) + 4*(-176*I*A + 64*B)*a^2 + sqrt(2)*(-128*I*a^2*d*e^(3*I*d*x + 3*I*c) - 128*I*a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((121*A^2 + 88*I*A*B - 16*B^2)/(a*d^2)))*e^(-2*I*d*x - 2*I*c)/(-11*I*A + 4*B)) + 4*sqrt(2)*(3*(A + 2*I*B)*e^(6*I*d*x + 6*I*c) - 2*(3*A + I*B)*e^(4*I*d*x + 4*I*c) - (7*A + 6*I*B)*e^(2*I*d*x + 2*I*c) + 2*A + 2*I*B)*sqrt(a/(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
97,1,439,0,0.611364," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} {\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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 3 \, \sqrt{\frac{1}{2}} {\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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \sqrt{2} {\left(2 \, {\left(19 \, A + 26 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, {\left(17 \, A + 29 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, {\left(2 \, A + 3 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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*(3*sqrt(1/2)*(a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt((A^2 - 2*I*A*B - B^2)/(a^3*d^2))*log((sqrt(2)*sqrt(1/2)*(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((A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 3*sqrt(1/2)*(a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt((A^2 - 2*I*A*B - B^2)/(a^3*d^2))*log((sqrt(2)*sqrt(1/2)*(-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((A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*(2*(19*A + 26*I*B)*e^(6*I*d*x + 6*I*c) + 3*(17*A + 29*I*B)*e^(4*I*d*x + 4*I*c) + 6*(2*A + 3*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*sqrt(a/(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
98,1,372,0,0.636908," ","integrate(tan(d*x+c)^2*(A+B*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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{-\frac{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} - {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + \sqrt{2} {\left({\left(8 i \, A - 38 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(7 i \, A - 13 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\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(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 3*sqrt(1/2)*a^2*d*sqrt(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^3*d^2)) - (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + sqrt(2)*((8*I*A - 38*B)*e^(4*I*d*x + 4*I*c) + (7*I*A - 13*B)*e^(2*I*d*x + 2*I*c) - I*A + B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
99,1,368,0,0.551139," ","integrate(tan(d*x+c)*(A+B*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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \sqrt{2} {\left(2 \, {\left(A + 4 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(A + 7 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\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((A^2 - 2*I*A*B - B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*sqrt(1/2)*(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((A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 3*sqrt(1/2)*a^2*d*sqrt((A^2 - 2*I*A*B - B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*sqrt(1/2)*(-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((A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*(2*(A + 4*I*B)*e^(4*I*d*x + 4*I*c) + (A + 7*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
100,1,373,0,0.490309," ","integrate((A+B*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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{-\frac{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} - {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \sqrt{2} {\left({\left(4 i \, A + 2 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(5 i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\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(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 3*sqrt(1/2)*a^2*d*sqrt(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^3*d^2)) - (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*((4*I*A + 2*B)*e^(4*I*d*x + 4*I*c) + (5*I*A + B)*e^(2*I*d*x + 2*I*c) + I*A - B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
101,1,621,0,0.542588," ","integrate(cot(d*x+c)*(A+B*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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 6 \, a^{2} d \sqrt{\frac{A^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{16 \, {\left(3 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{2} + 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{A^{2}}{a^{3} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{A}\right) + 6 \, a^{2} d \sqrt{\frac{A^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{16 \, {\left(3 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{2} - 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{A^{2}}{a^{3} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{A}\right) + \sqrt{2} {\left(2 \, {\left(5 \, A + 2 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(11 \, A + 5 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\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((A^2 - 2*I*A*B - B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*sqrt(1/2)*(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((A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 3*sqrt(1/2)*a^2*d*sqrt((A^2 - 2*I*A*B - B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*sqrt(1/2)*(-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((A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 6*a^2*d*sqrt(A^2/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(16*(3*A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2 + 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(A^2/(a^3*d^2)))*e^(-2*I*d*x - 2*I*c)/A) + 6*a^2*d*sqrt(A^2/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(16*(3*A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2 - 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(A^2/(a^3*d^2)))*e^(-2*I*d*x - 2*I*c)/A) + sqrt(2)*(2*(5*A + 2*I*B)*e^(4*I*d*x + 4*I*c) + (11*A + 5*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
102,1,810,0,0.987280," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} {\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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} \log\left(\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 3 \, \sqrt{\frac{1}{2}} {\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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} \log\left(-\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} - {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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 \, A^{2} + 12 i \, A B - 4 \, B^{2}}{a^{3} d^{2}}} \log\left(\frac{{\left({\left(-144 i \, A + 96 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-48 i \, A + 32 \, B\right)} a^{2} + 32 \, \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{9 \, A^{2} + 12 i \, A B - 4 \, B^{2}}{a^{3} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{-3 i \, A + 2 \, B}\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 \, A^{2} + 12 i \, A B - 4 \, B^{2}}{a^{3} d^{2}}} \log\left(\frac{{\left({\left(-144 i \, A + 96 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-48 i \, A + 32 \, B\right)} a^{2} - 32 \, \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{9 \, A^{2} + 12 i \, A B - 4 \, B^{2}}{a^{3} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{-3 i \, A + 2 \, B}\right) + \sqrt{2} {\left({\left(-28 i \, A + 10 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-13 i \, A + B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(16 i \, A - 10 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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*(3*sqrt(1/2)*(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 3*sqrt(1/2)*(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^3*d^2)) - (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 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*A^2 + 12*I*A*B - 4*B^2)/(a^3*d^2))*log(((-144*I*A + 96*B)*a^2*e^(2*I*d*x + 2*I*c) + (-48*I*A + 32*B)*a^2 + 32*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(-(9*A^2 + 12*I*A*B - 4*B^2)/(a^3*d^2)))*e^(-2*I*d*x - 2*I*c)/(-3*I*A + 2*B)) + 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*A^2 + 12*I*A*B - 4*B^2)/(a^3*d^2))*log(((-144*I*A + 96*B)*a^2*e^(2*I*d*x + 2*I*c) + (-48*I*A + 32*B)*a^2 - 32*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(-(9*A^2 + 12*I*A*B - 4*B^2)/(a^3*d^2)))*e^(-2*I*d*x - 2*I*c)/(-3*I*A + 2*B)) + sqrt(2)*((-28*I*A + 10*B)*e^(6*I*d*x + 6*I*c) + (-13*I*A + B)*e^(4*I*d*x + 4*I*c) + (16*I*A - 10*B)*e^(2*I*d*x + 2*I*c) + I*A - B)*sqrt(a/(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
103,1,901,0,0.568259," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{3} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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{529 \, A^{2} + 552 i \, A B - 144 \, B^{2}}{a^{3} d^{2}}} \log\left(\frac{{\left(4 \, {\left(-1104 i \, A + 576 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(-368 i \, A + 192 \, B\right)} a^{2} + \sqrt{2} {\left(128 i \, a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + 128 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{529 \, A^{2} + 552 i \, A B - 144 \, B^{2}}{a^{3} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(-23 i \, A + 12 \, B\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{529 \, A^{2} + 552 i \, A B - 144 \, B^{2}}{a^{3} d^{2}}} \log\left(\frac{{\left(4 \, {\left(-1104 i \, A + 576 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(-368 i \, A + 192 \, B\right)} a^{2} + \sqrt{2} {\left(-128 i \, a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} - 128 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{529 \, A^{2} + 552 i \, A B - 144 \, B^{2}}{a^{3} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(-23 i \, A + 12 \, B\right)}}\right) + 4 \, \sqrt{2} {\left({\left(37 \, A + 28 i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - 3 \, {\left(11 \, A + 5 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(50 \, A + 29 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(7 \, A + 5 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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((A^2 - 2*I*A*B - B^2)/(a^3*d^2))*log((sqrt(2)*sqrt(1/2)*(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((A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 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((A^2 - 2*I*A*B - B^2)/(a^3*d^2))*log((sqrt(2)*sqrt(1/2)*(-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((A^2 - 2*I*A*B - B^2)/(a^3*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 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((529*A^2 + 552*I*A*B - 144*B^2)/(a^3*d^2))*log(1/4*(4*(-1104*I*A + 576*B)*a^2*e^(2*I*d*x + 2*I*c) + 4*(-368*I*A + 192*B)*a^2 + sqrt(2)*(128*I*a^3*d*e^(3*I*d*x + 3*I*c) + 128*I*a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((529*A^2 + 552*I*A*B - 144*B^2)/(a^3*d^2)))*e^(-2*I*d*x - 2*I*c)/(-23*I*A + 12*B)) - 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((529*A^2 + 552*I*A*B - 144*B^2)/(a^3*d^2))*log(1/4*(4*(-1104*I*A + 576*B)*a^2*e^(2*I*d*x + 2*I*c) + 4*(-368*I*A + 192*B)*a^2 + sqrt(2)*(-128*I*a^3*d*e^(3*I*d*x + 3*I*c) - 128*I*a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((529*A^2 + 552*I*A*B - 144*B^2)/(a^3*d^2)))*e^(-2*I*d*x - 2*I*c)/(-23*I*A + 12*B)) + 4*sqrt(2)*((37*A + 28*I*B)*e^(8*I*d*x + 8*I*c) - 3*(11*A + 5*I*B)*e^(6*I*d*x + 6*I*c) - (50*A + 29*I*B)*e^(4*I*d*x + 4*I*c) + 3*(7*A + 5*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*sqrt(a/(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
104,1,457,0,0.600302," ","integrate(tan(d*x+c)^4*(A+B*tan(d*x+c))/(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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} \log\left(\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} \log\left(-\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} - {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \sqrt{2} {\left({\left(463 i \, A - 983 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(657 i \, A - 1527 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(168 i \, A - 348 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-23 i \, A + 33 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 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(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^5*d^2)) - (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*((463*I*A - 983*B)*e^(8*I*d*x + 8*I*c) + (657*I*A - 1527*B)*e^(6*I*d*x + 6*I*c) + (168*I*A - 348*B)*e^(4*I*d*x + 4*I*c) + (-23*I*A + 33*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*sqrt(a/(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
105,1,393,0,0.473532," ","integrate(tan(d*x+c)^3*(A+B*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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + 2 \, {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + 2 \, {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) + \sqrt{2} {\left({\left(83 \, A + 463 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, {\left(32 \, A + 97 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(8 \, A + 13 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, A + 3 i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\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((A^2 - 2*I*A*B - B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(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((A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + 2*(4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 15*sqrt(1/2)*a^3*d*sqrt((A^2 - 2*I*A*B - B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(-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((A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + 2*(4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + sqrt(2)*((83*A + 463*I*B)*e^(6*I*d*x + 6*I*c) + 2*(32*A + 97*I*B)*e^(4*I*d*x + 4*I*c) - 2*(8*A + 13*I*B)*e^(2*I*d*x + 2*I*c) + 3*A + 3*I*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
106,1,391,0,0.869014," ","integrate(tan(d*x+c)^2*(A+B*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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{-\frac{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} - {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + \sqrt{2} {\left({\left(-3 i \, A + 83 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(6 i \, A + 64 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(6 i \, A - 16 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, A + 3 \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\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(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 15*sqrt(1/2)*a^3*d*sqrt(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^5*d^2)) - (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + sqrt(2)*((-3*I*A + 83*B)*e^(6*I*d*x + 6*I*c) + (6*I*A + 64*B)*e^(4*I*d*x + 4*I*c) + (6*I*A - 16*B)*e^(2*I*d*x + 2*I*c) - 3*I*A + 3*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
107,1,394,0,0.529849," ","integrate(tan(d*x+c)*(A+B*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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + 2 \, {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + 2 \, {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - \sqrt{2} {\left({\left(17 \, A - 3 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, {\left(8 \, A + 3 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(2 \, A - 3 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, A - 3 i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\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((A^2 - 2*I*A*B - B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(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((A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + 2*(4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 15*sqrt(1/2)*a^3*d*sqrt((A^2 - 2*I*A*B - B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(-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((A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + 2*(4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*((17*A - 3*I*B)*e^(6*I*d*x + 6*I*c) + 2*(8*A + 3*I*B)*e^(4*I*d*x + 4*I*c) - 2*(2*A - 3*I*B)*e^(2*I*d*x + 2*I*c) - 3*A - 3*I*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
108,1,392,0,0.626169," ","integrate((A+B*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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{-\frac{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} - {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \sqrt{2} {\left({\left(23 i \, A + 17 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(34 i \, A + 16 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(14 i \, A - 4 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\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(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 15*sqrt(1/2)*a^3*d*sqrt(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^5*d^2)) - (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*((23*I*A + 17*B)*e^(6*I*d*x + 6*I*c) + (34*I*A + 16*B)*e^(4*I*d*x + 4*I*c) + (14*I*A - 4*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
109,1,645,0,0.616470," ","integrate(cot(d*x+c)*(A+B*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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + 2 \, {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + 2 \, {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 60 \, a^{3} d \sqrt{\frac{A^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{16 \, {\left(3 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{2} + 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{A^{2}}{a^{5} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{A}\right) + 60 \, a^{3} d \sqrt{\frac{A^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{16 \, {\left(3 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + A a^{2} - 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{A^{2}}{a^{5} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{A}\right) + \sqrt{2} {\left({\left(123 \, A + 23 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, {\left(72 \, A + 17 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(12 \, A + 7 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, A + 3 i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\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((A^2 - 2*I*A*B - B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(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((A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + 2*(4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 15*sqrt(1/2)*a^3*d*sqrt((A^2 - 2*I*A*B - B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(-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((A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + 2*(4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 60*a^3*d*sqrt(A^2/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(16*(3*A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2 + 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(A^2/(a^5*d^2)))*e^(-2*I*d*x - 2*I*c)/A) + 60*a^3*d*sqrt(A^2/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(16*(3*A*a^2*e^(2*I*d*x + 2*I*c) + A*a^2 - 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(A^2/(a^5*d^2)))*e^(-2*I*d*x - 2*I*c)/A) + sqrt(2)*((123*A + 23*I*B)*e^(6*I*d*x + 6*I*c) + 2*(72*A + 17*I*B)*e^(4*I*d*x + 4*I*c) + 2*(12*A + 7*I*B)*e^(2*I*d*x + 2*I*c) + 3*A + 3*I*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
110,1,829,0,0.790259," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} \log\left(\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} \log\left(-\frac{{\left(4 \, \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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} - {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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{25 \, A^{2} + 20 i \, A B - 4 \, B^{2}}{a^{5} d^{2}}} \log\left(\frac{{\left({\left(-240 i \, A + 96 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-80 i \, A + 32 \, B\right)} a^{2} + 32 \, \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{25 \, A^{2} + 20 i \, A B - 4 \, B^{2}}{a^{5} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{-5 i \, A + 2 \, B}\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{25 \, A^{2} + 20 i \, A B - 4 \, B^{2}}{a^{5} d^{2}}} \log\left(\frac{{\left({\left(-240 i \, A + 96 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-80 i \, A + 32 \, B\right)} a^{2} - 32 \, \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{25 \, A^{2} + 20 i \, A B - 4 \, B^{2}}{a^{5} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{-5 i \, A + 2 \, B}\right) + \sqrt{2} {\left({\left(-403 i \, A + 123 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-151 i \, A + 21 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(280 i \, A - 120 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(31 i \, A - 21 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 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(-(A^2 - 2*I*A*B - B^2)/(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(-(A^2 - 2*I*A*B - B^2)/(a^5*d^2)) - (4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 30*(a^3*d*e^(7*I*d*x + 7*I*c) - a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(-(25*A^2 + 20*I*A*B - 4*B^2)/(a^5*d^2))*log(((-240*I*A + 96*B)*a^2*e^(2*I*d*x + 2*I*c) + (-80*I*A + 32*B)*a^2 + 32*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(-(25*A^2 + 20*I*A*B - 4*B^2)/(a^5*d^2)))*e^(-2*I*d*x - 2*I*c)/(-5*I*A + 2*B)) + 30*(a^3*d*e^(7*I*d*x + 7*I*c) - a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(-(25*A^2 + 20*I*A*B - 4*B^2)/(a^5*d^2))*log(((-240*I*A + 96*B)*a^2*e^(2*I*d*x + 2*I*c) + (-80*I*A + 32*B)*a^2 - 32*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(-(25*A^2 + 20*I*A*B - 4*B^2)/(a^5*d^2)))*e^(-2*I*d*x - 2*I*c)/(-5*I*A + 2*B)) + sqrt(2)*((-403*I*A + 123*B)*e^(8*I*d*x + 8*I*c) + (-151*I*A + 21*B)*e^(6*I*d*x + 6*I*c) + (280*I*A - 120*B)*e^(4*I*d*x + 4*I*c) + (31*I*A - 21*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*sqrt(a/(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
111,1,925,0,0.681305," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{30 \, \sqrt{\frac{1}{2}} {\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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + 2 \, {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 30 \, \sqrt{\frac{1}{2}} {\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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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{A^{2} - 2 i \, A B - B^{2}}{a^{5} d^{2}}} + 2 \, {\left(4 i \, A + 4 \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) + 15 \, {\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{1849 \, A^{2} + 1720 i \, A B - 400 \, B^{2}}{a^{5} d^{2}}} \log\left(\frac{{\left(4 \, {\left(-2064 i \, A + 960 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(-688 i \, A + 320 \, B\right)} a^{2} + \sqrt{2} {\left(128 i \, a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} + 128 i \, 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{1849 \, A^{2} + 1720 i \, A B - 400 \, B^{2}}{a^{5} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(-43 i \, A + 20 \, B\right)}}\right) - 15 \, {\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{1849 \, A^{2} + 1720 i \, A B - 400 \, B^{2}}{a^{5} d^{2}}} \log\left(\frac{{\left(4 \, {\left(-2064 i \, A + 960 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(-688 i \, A + 320 \, B\right)} a^{2} + \sqrt{2} {\left(-128 i \, a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} - 128 i \, 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{1849 \, A^{2} + 1720 i \, A B - 400 \, B^{2}}{a^{5} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(-43 i \, A + 20 \, B\right)}}\right) + 2 \, \sqrt{2} {\left({\left(773 \, A + 403 i \, B\right)} e^{\left(10 i \, d x + 10 i \, c\right)} - 6 \, {\left(97 \, A + 42 i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(931 \, A + 431 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, {\left(153 \, A + 83 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(19 \, A + 14 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, A + 3 i \, B\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{240 \, {\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,"-1/240*(30*sqrt(1/2)*(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((A^2 - 2*I*A*B - B^2)/(a^5*d^2))*log(1/2*(sqrt(2)*sqrt(1/2)*(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((A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + 2*(4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 30*sqrt(1/2)*(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((A^2 - 2*I*A*B - B^2)/(a^5*d^2))*log(1/2*(sqrt(2)*sqrt(1/2)*(-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((A^2 - 2*I*A*B - B^2)/(a^5*d^2)) + 2*(4*I*A + 4*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 15*(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((1849*A^2 + 1720*I*A*B - 400*B^2)/(a^5*d^2))*log(1/4*(4*(-2064*I*A + 960*B)*a^2*e^(2*I*d*x + 2*I*c) + 4*(-688*I*A + 320*B)*a^2 + sqrt(2)*(128*I*a^4*d*e^(3*I*d*x + 3*I*c) + 128*I*a^4*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((1849*A^2 + 1720*I*A*B - 400*B^2)/(a^5*d^2)))*e^(-2*I*d*x - 2*I*c)/(-43*I*A + 20*B)) - 15*(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((1849*A^2 + 1720*I*A*B - 400*B^2)/(a^5*d^2))*log(1/4*(4*(-2064*I*A + 960*B)*a^2*e^(2*I*d*x + 2*I*c) + 4*(-688*I*A + 320*B)*a^2 + sqrt(2)*(-128*I*a^4*d*e^(3*I*d*x + 3*I*c) - 128*I*a^4*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((1849*A^2 + 1720*I*A*B - 400*B^2)/(a^5*d^2)))*e^(-2*I*d*x - 2*I*c)/(-43*I*A + 20*B)) + 2*sqrt(2)*((773*A + 403*I*B)*e^(10*I*d*x + 10*I*c) - 6*(97*A + 42*I*B)*e^(8*I*d*x + 8*I*c) - (931*A + 431*I*B)*e^(6*I*d*x + 6*I*c) + 3*(153*A + 83*I*B)*e^(4*I*d*x + 4*I*c) + 2*(19*A + 14*I*B)*e^(2*I*d*x + 2*I*c) + 3*A + 3*I*B)*sqrt(a/(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
112,1,475,0,0.800726," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{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)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - 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)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) + {\left({\left(-1288 i \, A - 1408 \, B\right)} a e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-2632 i \, A - 2272 \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-2072 i \, A - 2432 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-728 i \, A - 608 \, B\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}}}{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*(105*(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((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - 105*(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((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) + ((-1288*I*A - 1408*B)*a*e^(6*I*d*x + 6*I*c) + (-2632*I*A - 2272*B)*a*e^(4*I*d*x + 4*I*c) + (-2072*I*A - 2432*B)*a*e^(2*I*d*x + 2*I*c) + (-728*I*A - 608*B)*a)*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
113,1,428,0,0.626747," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{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{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\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{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - 8 \, {\left({\left(20 \, A - 23 i \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, {\left(5 \, A - 4 i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(10 \, A - 13 i \, B\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}}}{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*(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 - 8*A*B + 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - 15*(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 - 8*A*B + 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - 8*((20*A - 23*I*B)*a*e^(4*I*d*x + 4*I*c) + 6*(5*A - 4*I*B)*a*e^(2*I*d*x + 2*I*c) + (10*A - 13*I*B)*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
114,1,368,0,0.598488," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))*(A+B*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{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - {\left({\left(24 i \, A + 32 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(24 i \, A + 16 \, B\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}}}{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 + 8*A*B - 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - 3*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - ((24*I*A + 32*B)*a*e^(2*I*d*x + 2*I*c) + (24*I*A + 16*B)*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
115,1,310,0,1.162818," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{8 i \, B 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}} + \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} d \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} d \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right)}{4 \, d}"," ",0,"1/4*(8*I*B*a*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 - 8*A*B + 4*I*B^2)*a^2/d^2)*d*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*d*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)))/d","B",0
116,1,362,0,0.713733," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) + {\left(-8 i \, A a e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, A 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 + 8*A*B - 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - (d*e^(2*I*d*x + 2*I*c) - d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) + (-8*I*A*a*e^(2*I*d*x + 2*I*c) - 8*I*A*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
117,1,423,0,0.737024," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),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{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\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{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - 8 \, {\left({\left(4 \, A - 3 i \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, A a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(2 \, A - 3 i \, B\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}}}{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 - 8*A*B + 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*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 - 8*A*B + 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - 8*((4*A - 3*I*B)*a*e^(4*I*d*x + 4*I*c) + 2*A*a*e^(2*I*d*x + 2*I*c) - (2*A - 3*I*B)*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
118,1,482,0,0.787342," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{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{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\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{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - {\left({\left(184 i \, A + 160 \, B\right)} a e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-8 i \, A - 80 \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-88 i \, A - 160 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(104 i \, A + 80 \, B\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}}}{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*(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((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - 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((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*log((2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - ((184*I*A + 160*B)*a*e^(6*I*d*x + 6*I*c) + (-8*I*A - 80*B)*a*e^(4*I*d*x + 4*I*c) + (-88*I*A - 160*B)*a*e^(2*I*d*x + 2*I*c) + (104*I*A + 80*B)*a)*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
119,1,547,0,0.774932," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{315 \, \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} a^{4}}{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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 315 \, \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} a^{4}}{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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) + {\left({\left(-8088 i \, A - 8728 \, B\right)} a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-22800 i \, A - 20960 \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-28224 i \, A - 29904 \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-17520 i \, A - 17120 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-4008 i \, A - 3928 \, B\right)} 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}}}{1260 \, {\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,"1/1260*(315*sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*a^4/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 - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 315*sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*a^4/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 - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) + ((-8088*I*A - 8728*B)*a^2*e^(8*I*d*x + 8*I*c) + (-22800*I*A - 20960*B)*a^2*e^(6*I*d*x + 6*I*c) + (-28224*I*A - 29904*B)*a^2*e^(4*I*d*x + 4*I*c) + (-17520*I*A - 17120*B)*a^2*e^(2*I*d*x + 2*I*c) + (-4008*I*A - 3928*B)*a^2)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
120,1,497,0,1.438239," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 105 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 8 \, {\left({\left(301 \, A - 337 i \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(679 \, A - 613 i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(539 \, A - 563 i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(161 \, A - 167 i \, B\right)} 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}}}{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*(105*sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 105*sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 8*((301*A - 337*I*B)*a^2*e^(6*I*d*x + 6*I*c) + (679*A - 613*I*B)*a^2*e^(4*I*d*x + 4*I*c) + (539*A - 563*I*B)*a^2*e^(2*I*d*x + 2*I*c) + (161*A - 167*I*B)*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
121,1,436,0,0.706180," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 15 \, \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - {\left({\left(280 i \, A + 344 \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(480 i \, A + 432 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(200 i \, A + 184 \, B\right)} 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^2 + 32*A*B - 16*I*B^2)*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((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 15*sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - ((280*I*A + 344*B)*a^2*e^(4*I*d*x + 4*I*c) + (480*I*A + 432*B)*a^2*e^(2*I*d*x + 2*I*c) + (200*I*A + 184*B)*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
122,1,385,0,0.644104," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 3 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 8 \, {\left({\left(3 \, A - 7 i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(3 \, A - 5 i \, B\right)} 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^2 - 32*A*B + 16*I*B^2)*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 3*sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 8*((3*A - 7*I*B)*a^2*e^(2*I*d*x + 2*I*c) + (3*A - 5*I*B)*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
123,1,384,0,0.599601," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(4 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(4 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) + {\left({\left(-8 i \, A - 8 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-8 i \, A + 8 \, B\right)} 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^2 + 32*A*B - 16*I*B^2)*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) + ((-8*I*A - 8*B)*a^2*e^(2*I*d*x + 2*I*c) + (-8*I*A + 8*B)*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
124,1,437,0,1.037123," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 3 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 8 \, {\left({\left(7 \, A - 3 i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, A a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(5 \, A - 3 i \, B\right)} 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^2 - 32*A*B + 16*I*B^2)*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((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 3*sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 8*((7*A - 3*I*B)*a^2*e^(4*I*d*x + 4*I*c) + 2*A*a^2*e^(2*I*d*x + 2*I*c) - (5*A - 3*I*B)*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
125,1,498,0,0.558131," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 15 \, \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - {\left({\left(344 i \, A + 280 \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-88 i \, A - 200 \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-248 i \, A - 280 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(184 i \, A + 200 \, B\right)} 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^2 + 32*A*B - 16*I*B^2)*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((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 15*sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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((4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - ((344*I*A + 280*B)*a^2*e^(6*I*d*x + 6*I*c) + (-88*I*A - 200*B)*a^2*e^(4*I*d*x + 4*I*c) + (-248*I*A - 280*B)*a^2*e^(2*I*d*x + 2*I*c) + (184*I*A + 200*B)*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
126,1,557,0,0.935020," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} a^{4}}{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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 105 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} a^{4}}{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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 8 \, {\left({\left(337 \, A - 301 i \, B\right)} a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 6 \, {\left(46 \, A - 63 i \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 10 \, {\left(5 \, A - 14 i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 18 \, {\left(22 \, A - 21 i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(167 \, A - 161 i \, B\right)} 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}}}{420 \, {\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,"1/420*(105*sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*a^4/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 - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 105*sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*a^4/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 - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 8*((337*A - 301*I*B)*a^2*e^(8*I*d*x + 8*I*c) - 6*(46*A - 63*I*B)*a^2*e^(6*I*d*x + 6*I*c) - 10*(5*A - 14*I*B)*a^2*e^(4*I*d*x + 4*I*c) + 18*(22*A - 21*I*B)*a^2*e^(2*I*d*x + 2*I*c) - (167*A - 161*I*B)*a^2)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
127,1,557,0,0.863415," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{315 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} a^{6}}{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(8 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 315 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} a^{6}}{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(8 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 16 \, {\left({\left(957 \, A - 1051 i \, B\right)} a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 5 \, {\left(579 \, A - 547 i \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, {\left(171 \, A - 173 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, {\left(429 \, A - 433 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(123 \, A - 124 i \, B\right)} 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}}}{1260 \, {\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,"-1/1260*(315*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*a^6/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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 315*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*a^6/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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 16*((957*A - 1051*I*B)*a^3*e^(8*I*d*x + 8*I*c) + 5*(579*A - 547*I*B)*a^3*e^(6*I*d*x + 6*I*c) + 21*(171*A - 173*I*B)*a^3*e^(4*I*d*x + 4*I*c) + 5*(429*A - 433*I*B)*a^3*e^(2*I*d*x + 2*I*c) + 4*(123*A - 124*I*B)*a^3)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
128,1,492,0,0.578637," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 105 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - {\left({\left(4368 i \, A + 5104 \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(10752 i \, A + 10336 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(9072 i \, A + 8816 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2688 i \, A + 2624 \, B\right)} 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}}}{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*(105*sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 105*sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - ((4368*I*A + 5104*B)*a^3*e^(6*I*d*x + 6*I*c) + (10752*I*A + 10336*B)*a^3*e^(4*I*d*x + 4*I*c) + (9072*I*A + 8816*B)*a^3*e^(2*I*d*x + 2*I*c) + (2688*I*A + 2624*B)*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
129,1,443,0,0.574563," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 15 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 16 \, {\left({\left(25 \, A - 39 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(15 \, A - 19 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(5 \, A - 6 i \, B\right)} 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}}}{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((-64*I*A^2 - 128*A*B + 64*I*B^2)*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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 15*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 16*((25*A - 39*I*B)*a^3*e^(4*I*d*x + 4*I*c) + 3*(15*A - 19*I*B)*a^3*e^(2*I*d*x + 2*I*c) + 4*(5*A - 6*I*B)*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
130,1,400,0,0.516163," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} a^{6}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - d\right)} \log\left(\frac{{\left(8 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 3 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} a^{6}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - d\right)} \log\left(\frac{{\left(8 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) + {\left({\left(-48 i \, A - 80 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-48 i \, A + 16 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 64 \, B 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)} - d\right)}}"," ",0,"1/12*(3*sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*a^6/d^2)*(d*e^(4*I*d*x + 4*I*c) - d)*log((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 3*sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*a^6/d^2)*(d*e^(4*I*d*x + 4*I*c) - d)*log((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) + ((-48*I*A - 80*B)*a^3*e^(4*I*d*x + 4*I*c) + (-48*I*A + 16*B)*a^3*e^(2*I*d*x + 2*I*c) + 64*B*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) - d)","B",0
131,1,434,0,0.641119," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 3 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 16 \, {\left({\left(5 \, A - 3 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(A + 3 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 \, A 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^2 - 128*A*B + 64*I*B^2)*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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 3*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 16*((5*A - 3*I*B)*a^3*e^(4*I*d*x + 4*I*c) + (A + 3*I*B)*a^3*e^(2*I*d*x + 2*I*c) - 4*A*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
132,1,498,0,0.851690," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 15 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - {\left({\left(624 i \, A + 400 \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-288 i \, A - 320 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-528 i \, A - 400 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(384 i \, A + 320 \, B\right)} 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}}}{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((64*I*A^2 + 128*A*B - 64*I*B^2)*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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 15*sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - ((624*I*A + 400*B)*a^3*e^(6*I*d*x + 6*I*c) + (-288*I*A - 320*B)*a^3*e^(4*I*d*x + 4*I*c) + (-528*I*A - 400*B)*a^3*e^(2*I*d*x + 2*I*c) + (384*I*A + 320*B)*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
133,1,557,0,1.216636," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} a^{6}}{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(8 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 105 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} a^{6}}{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(8 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 16 \, {\left({\left(319 \, A - 273 i \, B\right)} a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 3 \, {\left(109 \, A - 133 i \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 5 \, {\left(19 \, A - 21 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(129 \, A - 133 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 \, {\left(41 \, A - 42 i \, B\right)} 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}}}{420 \, {\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,"1/420*(105*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*a^6/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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 105*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*a^6/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((8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 16*((319*A - 273*I*B)*a^3*e^(8*I*d*x + 8*I*c) - 3*(109*A - 133*I*B)*a^3*e^(6*I*d*x + 6*I*c) - 5*(19*A - 21*I*B)*a^3*e^(4*I*d*x + 4*I*c) + 3*(129*A - 133*I*B)*a^3*e^(2*I*d*x + 2*I*c) - 4*(41*A - 42*I*B)*a^3)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
134,1,706,0,1.389221," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{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{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} \log\left(\frac{2 \, {\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} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 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{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} \log\left(-\frac{2 \, {\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} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 6 \, {\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} + 12 \, A B + 9 i \, B^{2}}{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} + 12 \, A B + 9 i \, B^{2}}{a^{2} d^{2}}} + 2 \, A + 3 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 6 \, {\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} + 12 \, A B + 9 i \, B^{2}}{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} + 12 \, A B + 9 i \, B^{2}}{a^{2} d^{2}}} - 2 \, A - 3 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 2 \, {\left({\left(-27 i \, A + 19 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-30 i \, A + 38 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, A + 3 \, B\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}}}{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*(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*log(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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*log(-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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 6*(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 + 12*A*B + 9*I*B^2)/(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 + 12*A*B + 9*I*B^2)/(a^2*d^2)) + 2*A + 3*I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 6*(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 + 12*A*B + 9*I*B^2)/(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 + 12*A*B + 9*I*B^2)/(a^2*d^2)) - 2*A - 3*I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 2*((-27*I*A + 19*B)*e^(4*I*d*x + 4*I*c) + (-30*I*A + 38*B)*e^(2*I*d*x + 2*I*c) - 3*I*A + 3*B)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
135,1,621,0,0.893287," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} + 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - a d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} + 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 2 \, a d \sqrt{\frac{i \, A^{2} - 4 \, A B - 4 i \, B^{2}}{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} - 4 \, A B - 4 i \, B^{2}}{a^{2} d^{2}}} + i \, A - 2 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 2 \, a d \sqrt{\frac{i \, A^{2} - 4 \, A B - 4 i \, B^{2}}{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} - 4 \, A B - 4 i \, B^{2}}{a^{2} d^{2}}} - i \, A + 2 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 2 \, {\left({\left(A + 9 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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)}}{8 \, a d}"," ",0,"-1/8*(a*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(1/2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) + 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - a*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(1/2*((-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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) + 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a*d*sqrt((I*A^2 - 4*A*B - 4*I*B^2)/(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 - 4*A*B - 4*I*B^2)/(a^2*d^2)) + I*A - 2*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 2*a*d*sqrt((I*A^2 - 4*A*B - 4*I*B^2)/(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 - 4*A*B - 4*I*B^2)/(a^2*d^2)) - I*A + 2*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 2*((A + 9*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*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*d)","B",0
136,1,570,0,0.718776," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{2 \, {\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} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - a d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{2 \, {\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} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 2 \, a d \sqrt{\frac{i \, B^{2}}{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 \, B^{2}}{a^{2} d^{2}}} + i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 2 \, a d \sqrt{\frac{i \, B^{2}}{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 \, B^{2}}{a^{2} d^{2}}} - i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, {\left({\left(i \, A - B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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)}}{8 \, a d}"," ",0,"-1/8*(a*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - a*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(-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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a*d*sqrt(I*B^2/(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*B^2/(a^2*d^2)) + I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 2*a*d*sqrt(I*B^2/(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*B^2/(a^2*d^2)) - I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*((I*A - B)*e^(2*I*d*x + 2*I*c) + I*A - B)*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*d)","B",0
137,1,571,0,0.707487," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} + 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - a d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} + 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) + 2 \, a d \sqrt{\frac{i \, A^{2}}{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}}{a^{2} d^{2}}} + i \, A\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, a d \sqrt{\frac{i \, A^{2}}{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}}{a^{2} d^{2}}} - i \, A\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 2 \, {\left({\left(A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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)}}{8 \, a d}"," ",0,"1/8*(a*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(1/2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) + 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - a*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(1/2*((-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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) + 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 2*a*d*sqrt(I*A^2/(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/(a^2*d^2)) + I*A)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*a*d*sqrt(I*A^2/(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/(a^2*d^2)) - I*A)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 2*((A + I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*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*d)","B",0
138,1,703,0,0.746454," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} \log\left(\frac{2 \, {\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} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} \log\left(-\frac{2 \, {\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} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) + 2 \, {\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} + 4 \, A B + i \, B^{2}}{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} + 4 \, A B + i \, B^{2}}{a^{2} d^{2}}} + 2 \, A + i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, {\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} + 4 \, A B + i \, B^{2}}{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} + 4 \, A B + i \, B^{2}}{a^{2} d^{2}}} - 2 \, A - i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 2 \, {\left({\left(-9 i \, A + B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 8 i \, A e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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}}}{8 \, {\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,"1/8*((a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*log(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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - (a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*log(-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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 2*(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 + 4*A*B + I*B^2)/(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 + 4*A*B + I*B^2)/(a^2*d^2)) + 2*A + I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*(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 + 4*A*B + I*B^2)/(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 + 4*A*B + I*B^2)/(a^2*d^2)) - 2*A - I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 2*((-9*I*A + B)*e^(4*I*d*x + 4*I*c) - 8*I*A*e^(2*I*d*x + 2*I*c) + I*A - B)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
139,1,795,0,0.667721," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\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)} \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} + 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 3 \, {\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)} \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} + 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) + 6 \, {\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)} \sqrt{\frac{9 i \, A^{2} - 12 \, A B - 4 i \, B^{2}}{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{9 i \, A^{2} - 12 \, A B - 4 i \, B^{2}}{a^{2} d^{2}}} + 3 i \, A - 2 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 6 \, {\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)} \sqrt{\frac{9 i \, A^{2} - 12 \, A B - 4 i \, B^{2}}{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{9 i \, A^{2} - 12 \, A B - 4 i \, B^{2}}{a^{2} d^{2}}} - 3 i \, A + 2 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 2 \, {\left({\left(19 \, A + 27 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(19 \, A + 3 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(35 \, A + 27 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, A + 3 i \, B\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}}}{24 \, {\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,"-1/24*(3*(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))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*log(1/2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) + 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*(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))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*log(1/2*((-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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) + 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 6*(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))*sqrt((9*I*A^2 - 12*A*B - 4*I*B^2)/(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((9*I*A^2 - 12*A*B - 4*I*B^2)/(a^2*d^2)) + 3*I*A - 2*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 6*(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))*sqrt((9*I*A^2 - 12*A*B - 4*I*B^2)/(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((9*I*A^2 - 12*A*B - 4*I*B^2)/(a^2*d^2)) - 3*I*A + 2*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 2*((19*A + 27*I*B)*e^(6*I*d*x + 6*I*c) - (19*A + 3*I*B)*e^(4*I*d*x + 4*I*c) - (35*A + 27*I*B)*e^(2*I*d*x + 2*I*c) + 3*A + 3*I*B)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
140,1,660,0,0.764795," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 2 \, a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) + a^{2} d \sqrt{\frac{-49 i \, A^{2} + 322 \, A B + 529 i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left({\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 \, A^{2} + 322 \, A B + 529 i \, B^{2}}{a^{4} d^{2}}} + 7 \, A + 23 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - a^{2} d \sqrt{\frac{-49 i \, A^{2} + 322 \, A B + 529 i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left({\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 \, A^{2} + 322 \, A B + 529 i \, B^{2}}{a^{4} d^{2}}} - 7 \, A - 23 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + 2 \, {\left({\left(6 i \, A - 42 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(5 i \, A - 9 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\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(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"1/32*(2*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(2*((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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-2*((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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + a^2*d*sqrt((-49*I*A^2 + 322*A*B + 529*I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*((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*I*A^2 + 322*A*B + 529*I*B^2)/(a^4*d^2)) + 7*A + 23*I*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - a^2*d*sqrt((-49*I*A^2 + 322*A*B + 529*I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*((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*I*A^2 + 322*A*B + 529*I*B^2)/(a^4*d^2)) - 7*A - 23*I*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + 2*((6*I*A - 42*B)*e^(4*I*d*x + 4*I*c) + (5*I*A - 9*B)*e^(2*I*d*x + 2*I*c) - I*A + B)*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)/(a^2*d)","B",0
141,1,664,0,0.550343," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} + 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) - 2 \, a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} + 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) - a^{2} d \sqrt{\frac{i \, A^{2} + 14 \, A B - 49 i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left({\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 \, A^{2} + 14 \, A B - 49 i \, B^{2}}{a^{4} d^{2}}} + i \, A + 7 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + a^{2} d \sqrt{\frac{i \, A^{2} + 14 \, A B - 49 i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left({\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 \, A^{2} + 14 \, A B - 49 i \, B^{2}}{a^{4} d^{2}}} - i \, A - 7 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - 2 \, {\left(2 \, {\left(A + 3 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(A + 5 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"-1/32*(2*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/4*((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((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2)) + 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/4*((-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((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2)) + 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - a^2*d*sqrt((I*A^2 + 14*A*B - 49*I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*((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((I*A^2 + 14*A*B - 49*I*B^2)/(a^4*d^2)) + I*A + 7*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + a^2*d*sqrt((I*A^2 + 14*A*B - 49*I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*((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((I*A^2 + 14*A*B - 49*I*B^2)/(a^4*d^2)) - I*A - 7*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - 2*(2*(A + 3*I*B)*e^(4*I*d*x + 4*I*c) + (A + 5*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*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)/(a^2*d)","B",0
142,1,658,0,0.536748," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 2 \, a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - a^{2} d \sqrt{\frac{-i \, A^{2} + 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left({\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 \, A^{2} + 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} + A + i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + a^{2} d \sqrt{\frac{-i \, A^{2} + 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left({\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 \, A^{2} + 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} - A - i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - 2 \, {\left({\left(2 i \, A + 2 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(3 i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"-1/32*(2*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(2*((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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-2*((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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - a^2*d*sqrt((-I*A^2 + 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*((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((-I*A^2 + 2*A*B + I*B^2)/(a^4*d^2)) + A + I*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + a^2*d*sqrt((-I*A^2 + 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*((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((-I*A^2 + 2*A*B + I*B^2)/(a^4*d^2)) - A - I*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - 2*((2*I*A + 2*B)*e^(4*I*d*x + 4*I*c) + (3*I*A + B)*e^(2*I*d*x + 2*I*c) + I*A - B)*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)/(a^2*d)","B",0
143,1,664,0,0.978948," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} + 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) - 2 \, a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} + 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) + a^{2} d \sqrt{\frac{49 i \, A^{2} + 14 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left({\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 \, A^{2} + 14 \, A B - i \, B^{2}}{a^{4} d^{2}}} + 7 i \, A + B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - a^{2} d \sqrt{\frac{49 i \, A^{2} + 14 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left({\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 \, A^{2} + 14 \, A B - i \, B^{2}}{a^{4} d^{2}}} - 7 i \, A - B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + 2 \, {\left(2 \, {\left(3 \, A + i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(7 \, A + 3 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"1/32*(2*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/4*((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((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2)) + 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/4*((-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((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2)) + 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + a^2*d*sqrt((49*I*A^2 + 14*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*((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*I*A^2 + 14*A*B - I*B^2)/(a^4*d^2)) + 7*I*A + B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - a^2*d*sqrt((49*I*A^2 + 14*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*((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*I*A^2 + 14*A*B - I*B^2)/(a^4*d^2)) - 7*I*A - B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + 2*(2*(3*A + I*B)*e^(4*I*d*x + 4*I*c) + (7*A + 3*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*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)/(a^2*d)","B",0
144,1,762,0,0.723891," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} \log\left(\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 2 \, {\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} \log\left(-\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) + {\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 \, A^{2} + 322 \, A B + 49 i \, B^{2}}{a^{4} d^{2}}} \log\left(\frac{{\left({\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 \, A^{2} + 322 \, A B + 49 i \, B^{2}}{a^{4} d^{2}}} + 23 \, A + 7 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - {\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 \, A^{2} + 322 \, A B + 49 i \, B^{2}}{a^{4} d^{2}}} \log\left(-\frac{{\left({\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 \, A^{2} + 322 \, A B + 49 i \, B^{2}}{a^{4} d^{2}}} - 23 \, A - 7 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + 2 \, {\left({\left(-42 i \, A + 6 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-33 i \, A + B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(10 i \, A - 6 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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}}}{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*(a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*log(2*((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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*(a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*log(-2*((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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + (a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))*sqrt((-529*I*A^2 + 322*A*B + 49*I*B^2)/(a^4*d^2))*log(1/8*((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*I*A^2 + 322*A*B + 49*I*B^2)/(a^4*d^2)) + 23*A + 7*I*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - (a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))*sqrt((-529*I*A^2 + 322*A*B + 49*I*B^2)/(a^4*d^2))*log(-1/8*((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*I*A^2 + 322*A*B + 49*I*B^2)/(a^4*d^2)) - 23*A - 7*I*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + 2*((-42*I*A + 6*B)*e^(6*I*d*x + 6*I*c) + (-33*I*A + B)*e^(4*I*d*x + 4*I*c) + (10*I*A - 6*B)*e^(2*I*d*x + 2*I*c) + I*A - B)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)))/(a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))","B",0
145,1,861,0,1.178352," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, {\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)} \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} + 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) - 6 \, {\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)} \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} + 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) + 3 \, {\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)} \sqrt{\frac{2209 i \, A^{2} - 2162 \, A B - 529 i \, B^{2}}{a^{4} d^{2}}} \log\left(-\frac{{\left({\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{2209 i \, A^{2} - 2162 \, A B - 529 i \, B^{2}}{a^{4} d^{2}}} + 47 i \, A - 23 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - 3 \, {\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)} \sqrt{\frac{2209 i \, A^{2} - 2162 \, A B - 529 i \, B^{2}}{a^{4} d^{2}}} \log\left(\frac{{\left({\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{2209 i \, A^{2} - 2162 \, A B - 529 i \, B^{2}}{a^{4} d^{2}}} - 47 i \, A + 23 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + 2 \, {\left(2 \, {\left(101 \, A + 63 i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(103 \, A + 27 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(269 \, A + 129 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(13 \, A + 9 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, A + 3 i \, B\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}}}{96 \, {\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,"-1/96*(6*(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))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2))*log(1/4*((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((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2)) + 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 6*(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))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2))*log(1/4*((-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((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2)) + 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 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))*sqrt((2209*I*A^2 - 2162*A*B - 529*I*B^2)/(a^4*d^2))*log(-1/8*((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((2209*I*A^2 - 2162*A*B - 529*I*B^2)/(a^4*d^2)) + 47*I*A - 23*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - 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))*sqrt((2209*I*A^2 - 2162*A*B - 529*I*B^2)/(a^4*d^2))*log(1/8*((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((2209*I*A^2 - 2162*A*B - 529*I*B^2)/(a^4*d^2)) - 47*I*A + 23*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + 2*(2*(101*A + 63*I*B)*e^(8*I*d*x + 8*I*c) - (103*A + 27*I*B)*e^(6*I*d*x + 6*I*c) - (269*A + 129*I*B)*e^(4*I*d*x + 4*I*c) + 3*(13*A + 9*I*B)*e^(2*I*d*x + 2*I*c) + 3*A + 3*I*B)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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))","B",0
146,1,777,0,0.677824," ","integrate(tan(d*x+c)^(9/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, {\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)} \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} \log\left(\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 3 \, {\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)} \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} \log\left(-\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 3 \, {\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)} \sqrt{\frac{-841 i \, A^{2} + 4408 \, A B + 5776 i \, B^{2}}{a^{6} d^{2}}} \log\left(\frac{{\left({\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{-841 i \, A^{2} + 4408 \, A B + 5776 i \, B^{2}}{a^{6} d^{2}}} + 29 \, A + 76 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 3 \, {\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)} \sqrt{\frac{-841 i \, A^{2} + 4408 \, A B + 5776 i \, B^{2}}{a^{6} d^{2}}} \log\left(-\frac{{\left({\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{-841 i \, A^{2} + 4408 \, A B + 5776 i \, B^{2}}{a^{6} d^{2}}} - 29 \, A - 76 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 2 \, {\left({\left(146 i \, A - 348 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(187 i \, A - 492 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(33 i \, A - 69 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-7 i \, A + 10 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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}}}{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*(3*(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*log(2*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*log(-2*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((-841*I*A^2 + 4408*A*B + 5776*I*B^2)/(a^6*d^2))*log(1/8*((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((-841*I*A^2 + 4408*A*B + 5776*I*B^2)/(a^6*d^2)) + 29*A + 76*I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 3*(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((-841*I*A^2 + 4408*A*B + 5776*I*B^2)/(a^6*d^2))*log(-1/8*((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((-841*I*A^2 + 4408*A*B + 5776*I*B^2)/(a^6*d^2)) - 29*A - 76*I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 2*((146*I*A - 348*B)*e^(8*I*d*x + 8*I*c) + (187*I*A - 492*B)*e^(6*I*d*x + 6*I*c) + (33*I*A - 69*B)*e^(4*I*d*x + 4*I*c) + (-7*I*A + 10*B)*e^(2*I*d*x + 2*I*c) + I*A - B)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)))/(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))","B",0
147,1,685,0,0.805674," ","integrate(tan(d*x+c)^(7/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) - 3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) - 3 \, a^{3} d \sqrt{\frac{36 i \, A^{2} - 348 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{{\left({\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{36 i \, A^{2} - 348 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} + 6 i \, A - 29 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 3 \, a^{3} d \sqrt{\frac{36 i \, A^{2} - 348 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left({\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{36 i \, A^{2} - 348 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} - 6 i \, A + 29 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 2 \, {\left(2 \, {\left(10 \, A + 73 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(14 \, A + 41 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(5 \, A + 8 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(3*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((-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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((36*I*A^2 - 348*A*B - 841*I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-1/8*((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((36*I*A^2 - 348*A*B - 841*I*B^2)/(a^6*d^2)) + 6*I*A - 29*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 3*a^3*d*sqrt((36*I*A^2 - 348*A*B - 841*I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((36*I*A^2 - 348*A*B - 841*I*B^2)/(a^6*d^2)) - 6*I*A + 29*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 2*(2*(10*A + 73*I*B)*e^(6*I*d*x + 6*I*c) + (14*A + 41*I*B)*e^(4*I*d*x + 4*I*c) - (5*A + 8*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*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)/(a^3*d)","B",0
148,1,676,0,0.688692," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 3 \, a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) + 3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 12 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left({\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 \, A^{2} - 12 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} + A - 6 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 12 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{{\left({\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 \, A^{2} - 12 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} - A + 6 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 2 \, {\left({\left(-2 i \, A + 20 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(i \, A + 14 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(2 i \, A - 5 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\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(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(3*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(2*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-2*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 3*a^3*d*sqrt((-I*A^2 - 12*A*B + 36*I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((-I*A^2 - 12*A*B + 36*I*B^2)/(a^6*d^2)) + A - 6*I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 3*a^3*d*sqrt((-I*A^2 - 12*A*B + 36*I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-1/8*((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((-I*A^2 - 12*A*B + 36*I*B^2)/(a^6*d^2)) - A + 6*I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 2*((-2*I*A + 20*B)*e^(6*I*d*x + 6*I*c) + (I*A + 14*B)*e^(4*I*d*x + 4*I*c) + (2*I*A - 5*B)*e^(2*I*d*x + 2*I*c) - I*A + B)*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)/(a^3*d)","B",0
149,1,635,0,0.631086," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) - 3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) - 24 \, a^{3} d \sqrt{-\frac{i \, B^{2}}{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 \, B^{2}}{64 \, a^{6} d^{2}}} + B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 24 \, a^{3} d \sqrt{-\frac{i \, B^{2}}{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 \, B^{2}}{64 \, a^{6} d^{2}}} - B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 2 \, {\left(2 \, {\left(2 \, A - i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(4 \, A + i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(A - 2 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"-1/96*(3*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((-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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 24*a^3*d*sqrt(-1/64*I*B^2/(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*B^2/(a^6*d^2)) + B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 24*a^3*d*sqrt(-1/64*I*B^2/(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*B^2/(a^6*d^2)) - B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 2*(2*(2*A - I*B)*e^(6*I*d*x + 6*I*c) + (4*A + I*B)*e^(4*I*d*x + 4*I*c) - (A - 2*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*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)/(a^3*d)","B",0
150,1,630,0,0.925777," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 3 \, a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 24 \, a^{3} d \sqrt{-\frac{i \, A^{2}}{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 \, A^{2}}{64 \, a^{6} d^{2}}} + A\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 24 \, a^{3} d \sqrt{-\frac{i \, A^{2}}{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 \, A^{2}}{64 \, a^{6} d^{2}}} - A\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 2 \, {\left({\left(2 i \, A + 4 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(5 i \, A + 4 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(4 i \, A - B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"-1/96*(3*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(2*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-2*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 24*a^3*d*sqrt(-1/64*I*A^2/(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^2/(a^6*d^2)) + A)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 24*a^3*d*sqrt(-1/64*I*A^2/(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^2/(a^6*d^2)) - A)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 2*((2*I*A + 4*B)*e^(6*I*d*x + 6*I*c) + (5*I*A + 4*B)*e^(4*I*d*x + 4*I*c) + (4*I*A - B)*e^(2*I*d*x + 2*I*c) + I*A - B)*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)/(a^3*d)","B",0
151,1,682,0,0.604337," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) - 3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) + 3 \, a^{3} d \sqrt{\frac{36 i \, A^{2} + 12 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left({\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{36 i \, A^{2} + 12 \, A B - i \, B^{2}}{a^{6} d^{2}}} + 6 i \, A + B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 3 \, a^{3} d \sqrt{\frac{36 i \, A^{2} + 12 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{{\left({\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{36 i \, A^{2} + 12 \, A B - i \, B^{2}}{a^{6} d^{2}}} - 6 i \, A - B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 2 \, {\left(2 \, {\left(10 \, A + i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(26 \, A + 5 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(7 \, A + 4 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(3*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((-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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 3*a^3*d*sqrt((36*I*A^2 + 12*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((36*I*A^2 + 12*A*B - I*B^2)/(a^6*d^2)) + 6*I*A + B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 3*a^3*d*sqrt((36*I*A^2 + 12*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-1/8*((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((36*I*A^2 + 12*A*B - I*B^2)/(a^6*d^2)) - 6*I*A - B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 2*(2*(10*A + I*B)*e^(6*I*d*x + 6*I*c) + (26*A + 5*I*B)*e^(4*I*d*x + 4*I*c) + (7*A + 4*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*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)/(a^3*d)","B",0
152,1,782,0,0.481215," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\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)} \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} \log\left(\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 3 \, {\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)} \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} \log\left(-\frac{2 \, {\left({\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) + 3 \, {\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)} \sqrt{\frac{-841 i \, A^{2} + 348 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} \log\left(\frac{{\left({\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{-841 i \, A^{2} + 348 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} + 29 \, A + 6 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 3 \, {\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)} \sqrt{\frac{-841 i \, A^{2} + 348 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} \log\left(-\frac{{\left({\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{-841 i \, A^{2} + 348 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} - 29 \, A - 6 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 2 \, {\left({\left(-146 i \, A + 20 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-105 i \, A + 6 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(49 i \, A - 19 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(9 i \, A - 6 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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}}}{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*(3*(a^3*d*e^(8*I*d*x + 8*I*c) - a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*log(2*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*(a^3*d*e^(8*I*d*x + 8*I*c) - a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*log(-2*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 3*(a^3*d*e^(8*I*d*x + 8*I*c) - a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((-841*I*A^2 + 348*A*B + 36*I*B^2)/(a^6*d^2))*log(1/8*((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((-841*I*A^2 + 348*A*B + 36*I*B^2)/(a^6*d^2)) + 29*A + 6*I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 3*(a^3*d*e^(8*I*d*x + 8*I*c) - a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((-841*I*A^2 + 348*A*B + 36*I*B^2)/(a^6*d^2))*log(-1/8*((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((-841*I*A^2 + 348*A*B + 36*I*B^2)/(a^6*d^2)) - 29*A - 6*I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 2*((-146*I*A + 20*B)*e^(8*I*d*x + 8*I*c) + (-105*I*A + 6*B)*e^(6*I*d*x + 6*I*c) + (49*I*A - 19*B)*e^(4*I*d*x + 4*I*c) + (9*I*A - 6*B)*e^(2*I*d*x + 2*I*c) + I*A - B)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)))/(a^3*d*e^(8*I*d*x + 8*I*c) - a^3*d*e^(6*I*d*x + 6*I*c))","B",0
153,1,875,0,0.681965," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, {\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)} \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) - 3 \, {\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)} \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} \log\left(\frac{{\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) + 3 \, {\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)} \sqrt{\frac{5776 i \, A^{2} - 4408 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} \log\left(-\frac{{\left({\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{5776 i \, A^{2} - 4408 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} + 76 i \, A - 29 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 3 \, {\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)} \sqrt{\frac{5776 i \, A^{2} - 4408 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} \log\left(\frac{{\left({\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{5776 i \, A^{2} - 4408 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} - 76 i \, A + 29 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 2 \, {\left(2 \, {\left(174 \, A + 73 i \, B\right)} e^{\left(10 i \, d x + 10 i \, c\right)} - {\left(144 \, A + 41 i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(423 \, A + 154 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(79 \, A + 40 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(11 \, A + 8 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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}}}{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*(3*(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))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*log(1/8*((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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*(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))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*log(1/8*((-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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 3*(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))*sqrt((5776*I*A^2 - 4408*A*B - 841*I*B^2)/(a^6*d^2))*log(-1/8*((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((5776*I*A^2 - 4408*A*B - 841*I*B^2)/(a^6*d^2)) + 76*I*A - 29*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 3*(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))*sqrt((5776*I*A^2 - 4408*A*B - 841*I*B^2)/(a^6*d^2))*log(1/8*((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((5776*I*A^2 - 4408*A*B - 841*I*B^2)/(a^6*d^2)) - 76*I*A + 29*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 2*(2*(174*A + 73*I*B)*e^(10*I*d*x + 10*I*c) - (144*A + 41*I*B)*e^(8*I*d*x + 8*I*c) - (423*A + 154*I*B)*e^(6*I*d*x + 6*I*c) + (79*A + 40*I*B)*e^(4*I*d*x + 4*I*c) + (11*A + 8*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)))/(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))","B",0
154,1,755,0,0.583598," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left({\left(4 \, A - 3 i \, B\right)} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(4 \, A + i \, B\right)} 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{{\left(-16 i \, A^{2} - 56 \, A B + 49 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(4 i \, A + 7 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, A + 7 \, B\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 \, d \sqrt{\frac{{\left(-16 i \, A^{2} - 56 \, A B + 49 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 i \, A + 7 \, B}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(-16 i \, A^{2} - 56 \, A B + 49 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(4 i \, A + 7 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, A + 7 \, B\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 \, d \sqrt{\frac{{\left(-16 i \, A^{2} - 56 \, A B + 49 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 i \, A + 7 \, B}\right) - 4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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 \, d \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + 4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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 \, d \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right)}{8 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/8*(2*sqrt(2)*((4*A - 3*I*B)*e^(3*I*d*x + 3*I*c) + (4*A + I*B)*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((-16*I*A^2 - 56*A*B + 49*I*B^2)*a/d^2)*log((sqrt(2)*((4*I*A + 7*B)*e^(2*I*d*x + 2*I*c) + 4*I*A + 7*B)*sqrt(a/(e^(2*I*d*x + 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*d*sqrt((-16*I*A^2 - 56*A*B + 49*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(4*I*A + 7*B)) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((-16*I*A^2 - 56*A*B + 49*I*B^2)*a/d^2)*log((sqrt(2)*((4*I*A + 7*B)*e^(2*I*d*x + 2*I*c) + 4*I*A + 7*B)*sqrt(a/(e^(2*I*d*x + 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*d*sqrt((-16*I*A^2 - 56*A*B + 49*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(4*I*A + 7*B)) - 4*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 4*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
155,1,656,0,0.669362," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} B \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\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{{\left(4 i \, A^{2} + 4 \, A B - i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(2 i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, A + B\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 \, d \sqrt{\frac{{\left(4 i \, A^{2} + 4 \, A B - i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 i \, A + B}\right) - d \sqrt{\frac{{\left(4 i \, A^{2} + 4 \, A B - i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(2 i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, A + B\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 \, d \sqrt{\frac{{\left(4 i \, A^{2} + 4 \, A B - i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 i \, A + B}\right) - d \sqrt{\frac{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}} + d \sqrt{\frac{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + d \sqrt{\frac{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}} - d \sqrt{\frac{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right)}{2 \, d}"," ",0,"1/2*(2*sqrt(2)*B*sqrt(a/(e^(2*I*d*x + 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((4*I*A^2 + 4*A*B - I*B^2)*a/d^2)*log((sqrt(2)*((2*I*A + B)*e^(2*I*d*x + 2*I*c) + 2*I*A + B)*sqrt(a/(e^(2*I*d*x + 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*sqrt((4*I*A^2 + 4*A*B - I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(2*I*A + B)) - d*sqrt((4*I*A^2 + 4*A*B - I*B^2)*a/d^2)*log((sqrt(2)*((2*I*A + B)*e^(2*I*d*x + 2*I*c) + 2*I*A + B)*sqrt(a/(e^(2*I*d*x + 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*sqrt((4*I*A^2 + 4*A*B - I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(2*I*A + B)) - d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)))/d","B",0
156,1,523,0,0.718069," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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 \, d \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \frac{1}{2} \, \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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 \, d \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \frac{1}{2} \, \sqrt{\frac{4 i \, B^{2} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(B e^{\left(2 i \, d x + 2 i \, c\right)} + B\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 \, B^{2} a}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{B}\right) + \frac{1}{2} \, \sqrt{\frac{4 i \, B^{2} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(B e^{\left(2 i \, d x + 2 i \, c\right)} + B\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 \, B^{2} a}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{B}\right)"," ",0,"1/2*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 1/2*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 1/2*sqrt(4*I*B^2*a/d^2)*log((sqrt(2)*(B*e^(2*I*d*x + 2*I*c) + B)*sqrt(a/(e^(2*I*d*x + 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*B^2*a/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/B) + 1/2*sqrt(4*I*B^2*a/d^2)*log((sqrt(2)*(B*e^(2*I*d*x + 2*I*c) + B)*sqrt(a/(e^(2*I*d*x + 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*B^2*a/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/B)","B",0
157,1,417,0,1.563736," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/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{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}} + d \sqrt{\frac{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}} - d \sqrt{\frac{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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((2*I*A^2 + 4*A*B - 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - (d*e^(2*I*d*x + 2*I*c) - d)*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
158,1,467,0,0.677605," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(4 \, {\left(2 \, A - 3 i \, B\right)} e^{\left(5 i \, d x + 5 i \, c\right)} + 8 \, A e^{\left(3 i \, d x + 3 i \, c\right)} + 12 i \, B 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{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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 \, d \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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 \, d \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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*(sqrt(2)*(4*(2*A - 3*I*B)*e^(5*I*d*x + 5*I*c) + 8*A*e^(3*I*d*x + 3*I*c) + 12*I*B*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((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 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^2 - 4*A*B + 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
159,1,524,0,0.757202," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(68 i \, A + 40 \, B\right)} e^{\left(7 i \, d x + 7 i \, c\right)} - 12 i \, A e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(-20 i \, A - 40 \, B\right)} e^{\left(3 i \, d x + 3 i \, c\right)} + 60 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}} - 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{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}} + d \sqrt{\frac{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}} - d \sqrt{\frac{{\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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)*((68*I*A + 40*B)*e^(7*I*d*x + 7*I*c) - 12*I*A*e^(5*I*d*x + 5*I*c) + (-20*I*A - 40*B)*e^(3*I*d*x + 3*I*c) + 60*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)) - 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^2 + 4*A*B - 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 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^2 + 4*A*B - 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)))/(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
160,1,577,0,1.666505," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(4 \, {\left(92 \, A - 119 i \, B\right)} e^{\left(9 i \, d x + 9 i \, c\right)} - 80 \, {\left(A - 7 i \, B\right)} e^{\left(7 i \, d x + 7 i \, c\right)} + 56 \, {\left(2 \, A + i \, B\right)} e^{\left(5 i \, d x + 5 i \, c\right)} + 560 \, {\left(A - i \, B\right)} e^{\left(3 i \, d x + 3 i \, c\right)} + 420 i \, B 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{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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 \, d \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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 \, d \sqrt{\frac{{\left(-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}\right)} a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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*(sqrt(2)*(4*(92*A - 119*I*B)*e^(9*I*d*x + 9*I*c) - 80*(A - 7*I*B)*e^(7*I*d*x + 7*I*c) + 56*(2*A + I*B)*e^(5*I*d*x + 5*I*c) + 560*(A - I*B)*e^(3*I*d*x + 3*I*c) + 420*I*B*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((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 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((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*log((sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)))/(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
161,1,895,0,1.725073," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(7 \, {\left(6 \, A - 7 i \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, {\left(30 \, A - 19 i \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + 3 \, {\left(6 \, A - 7 i \, B\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}} + 3 \, \sqrt{\frac{{\left(-484 i \, A^{2} - 1012 \, A B + 529 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(22 i \, A + 23 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(22 i \, A + 23 \, B\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{{\left(-484 i \, A^{2} - 1012 \, A B + 529 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(22 i \, A + 23 \, B\right)} a}\right) - 3 \, \sqrt{\frac{{\left(-484 i \, A^{2} - 1012 \, A B + 529 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(22 i \, A + 23 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(22 i \, A + 23 \, B\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{{\left(-484 i \, A^{2} - 1012 \, A B + 529 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(22 i \, A + 23 \, B\right)} a}\right) - 24 \, \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 24 \, \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\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)}}"," ",0,"1/48*(2*sqrt(2)*(7*(6*A - 7*I*B)*a*e^(5*I*d*x + 5*I*c) + 2*(30*A - 19*I*B)*a*e^(3*I*d*x + 3*I*c) + 3*(6*A - 7*I*B)*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*sqrt((-484*I*A^2 - 1012*A*B + 529*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((22*I*A + 23*B)*a*e^(2*I*d*x + 2*I*c) + (22*I*A + 23*B)*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((-484*I*A^2 - 1012*A*B + 529*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((22*I*A + 23*B)*a)) - 3*sqrt((-484*I*A^2 - 1012*A*B + 529*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((22*I*A + 23*B)*a*e^(2*I*d*x + 2*I*c) + (22*I*A + 23*B)*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((-484*I*A^2 - 1012*A*B + 529*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((22*I*A + 23*B)*a)) - 24*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)) + 24*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
162,1,812,0,0.770766," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left({\left(4 i \, A + 7 \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(4 i \, A + 3 \, B\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}} + \sqrt{\frac{{\left(144 i \, A^{2} + 264 \, A B - 121 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(\sqrt{2} {\left({\left(12 i \, A + 11 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(12 i \, A + 11 \, B\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 \, \sqrt{\frac{{\left(144 i \, A^{2} + 264 \, A B - 121 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(12 i \, A + 11 \, B\right)} a}\right) - \sqrt{\frac{{\left(144 i \, A^{2} + 264 \, A B - 121 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(\sqrt{2} {\left({\left(12 i \, A + 11 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(12 i \, A + 11 \, B\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 \, \sqrt{\frac{{\left(144 i \, A^{2} + 264 \, A B - 121 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(12 i \, A + 11 \, B\right)} a}\right) - 4 \, \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 4 \, \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right)}{8 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/8*(2*sqrt(2)*((4*I*A + 7*B)*a*e^(3*I*d*x + 3*I*c) + (4*I*A + 3*B)*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)) + sqrt((144*I*A^2 + 264*A*B - 121*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((12*I*A + 11*B)*a*e^(2*I*d*x + 2*I*c) + (12*I*A + 11*B)*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*sqrt((144*I*A^2 + 264*A*B - 121*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((12*I*A + 11*B)*a)) - sqrt((144*I*A^2 + 264*A*B - 121*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((12*I*A + 11*B)*a*e^(2*I*d*x + 2*I*c) + (12*I*A + 11*B)*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*sqrt((144*I*A^2 + 264*A*B - 121*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((12*I*A + 11*B)*a)) - 4*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)) + 4*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
163,1,726,0,1.205522," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 i \, \sqrt{2} B 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{{\left(-4 i \, A^{2} - 12 \, A B + 9 i \, B^{2}\right)} a^{3}}{d^{2}}} d \log\left(\frac{{\left(\sqrt{2} {\left({\left(2 i \, A + 3 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 3 \, B\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{{\left(-4 i \, A^{2} - 12 \, A B + 9 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 3 \, B\right)} a}\right) + \sqrt{\frac{{\left(-4 i \, A^{2} - 12 \, A B + 9 i \, B^{2}\right)} a^{3}}{d^{2}}} d \log\left(\frac{{\left(\sqrt{2} {\left({\left(2 i \, A + 3 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 3 \, B\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{{\left(-4 i \, A^{2} - 12 \, A B + 9 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 3 \, B\right)} a}\right) + \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d \log\left(\frac{{\left(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d \log\left(\frac{{\left(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right)}{2 \, d}"," ",0,"1/2*(2*I*sqrt(2)*B*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((-4*I*A^2 - 12*A*B + 9*I*B^2)*a^3/d^2)*d*log((sqrt(2)*((2*I*A + 3*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 3*B)*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((-4*I*A^2 - 12*A*B + 9*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 3*B)*a)) + sqrt((-4*I*A^2 - 12*A*B + 9*I*B^2)*a^3/d^2)*d*log((sqrt(2)*((2*I*A + 3*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 3*B)*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((-4*I*A^2 - 12*A*B + 9*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 3*B)*a)) + sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*d*log((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)) - sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*d*log((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)))/d","B",0
164,1,729,0,0.706778," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-4 i \, A a e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, A 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}} + \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - \sqrt{-\frac{4 i \, B^{2} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(\sqrt{2} {\left(B a e^{\left(2 i \, d x + 2 i \, c\right)} + B 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 \, B^{2} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{B a}\right) + \sqrt{-\frac{4 i \, B^{2} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(\sqrt{2} {\left(B a e^{\left(2 i \, d x + 2 i \, c\right)} + B 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 \, B^{2} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{B 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*a*e^(3*I*d*x + 3*I*c) - 4*I*A*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)) + sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)) - sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)) - sqrt(-4*I*B^2*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((sqrt(2)*(B*a*e^(2*I*d*x + 2*I*c) + B*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*B^2*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(B*a)) + sqrt(-4*I*B^2*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((sqrt(2)*(B*a*e^(2*I*d*x + 2*I*c) + B*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*B^2*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(B*a)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
165,1,508,0,0.608384," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left({\left(5 \, A - 3 i \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, A a e^{\left(3 i \, d x + 3 i \, c\right)} - 3 \, {\left(A - i \, B\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}} - 3 \, \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 3 \, \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} 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 - 3*I*B)*a*e^(5*I*d*x + 5*I*c) + 2*A*a*e^(3*I*d*x + 3*I*c) - 3*(A - I*B)*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*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)) + 3*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
166,1,572,0,0.950133," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(108 i \, A + 100 \, B\right)} a e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(-12 i \, A - 60 \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(-60 i \, A - 100 \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(60 i \, A + 60 \, B\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}} - 15 \, \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 15 \, \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\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)*((108*I*A + 100*B)*a*e^(7*I*d*x + 7*I*c) + (-12*I*A - 60*B)*a*e^(5*I*d*x + 5*I*c) + (-60*I*A - 100*B)*a*e^(3*I*d*x + 3*I*c) + (60*I*A + 60*B)*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)) - 15*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a^3/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((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)) + 15*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a^3/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((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*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
167,1,622,0,0.577812," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left({\left(211 \, A - 189 i \, B\right)} a e^{\left(9 i \, d x + 9 i \, c\right)} - 10 \, {\left(16 \, A - 21 i \, B\right)} a e^{\left(7 i \, d x + 7 i \, c\right)} + 14 \, {\left(A + 6 i \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + 70 \, {\left(4 \, A - 3 i \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} - 105 \, {\left(A - i \, B\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}} - 105 \, \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 105 \, \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} 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 - 189*I*B)*a*e^(9*I*d*x + 9*I*c) - 10*(16*A - 21*I*B)*a*e^(7*I*d*x + 7*I*c) + 14*(A + 6*I*B)*a*e^(5*I*d*x + 5*I*c) + 70*(4*A - 3*I*B)*a*e^(3*I*d*x + 3*I*c) - 105*(A - I*B)*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*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a^3/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((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)) + 105*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a^3/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((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 - 16*A*B + 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*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
168,1,680,0,0.797542," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-2636 i \, A - 2532 \, B\right)} a e^{\left(11 i \, d x + 11 i \, c\right)} + {\left(3556 i \, A + 4452 \, B\right)} a e^{\left(9 i \, d x + 9 i \, c\right)} + {\left(-3384 i \, A - 2088 \, B\right)} a e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(-4536 i \, A - 3192 \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(3780 i \, A + 4620 \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-1260 i \, A - 1260 \, B\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}} + 315 \, \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - 315 \, \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{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(\sqrt{2} {\left({\left(2 i \, A + 2 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 2 \, B\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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 2 \, B\right)} a}\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)*((-2636*I*A - 2532*B)*a*e^(11*I*d*x + 11*I*c) + (3556*I*A + 4452*B)*a*e^(9*I*d*x + 9*I*c) + (-3384*I*A - 2088*B)*a*e^(7*I*d*x + 7*I*c) + (-4536*I*A - 3192*B)*a*e^(5*I*d*x + 5*I*c) + (3780*I*A + 4620*B)*a*e^(3*I*d*x + 3*I*c) + (-1260*I*A - 1260*B)*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)) + 315*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a^3/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((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*a)) - 315*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a^3/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((sqrt(2)*((2*I*A + 2*B)*a*e^(2*I*d*x + 2*I*c) + (2*I*A + 2*B)*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^2 + 16*A*B - 8*I*B^2)*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 2*B)*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
169,1,997,0,0.510200," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(13 \, {\left(56 \, A - 65 i \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + 3 \, {\left(504 \, A - 425 i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(1096 \, A - 1135 i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 3 \, {\left(104 \, A - 107 i \, B\right)} 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{{\left(-129600 i \, A^{2} - 261360 \, A B + 131769 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(360 i \, A + 363 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(360 i \, A + 363 \, B\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 i \, \sqrt{\frac{{\left(-129600 i \, A^{2} - 261360 \, A B + 131769 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(360 i \, A + 363 \, B\right)} a^{2}}\right) - 3 \, \sqrt{\frac{{\left(-129600 i \, A^{2} - 261360 \, A B + 131769 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(360 i \, A + 363 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(360 i \, A + 363 \, B\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 i \, \sqrt{\frac{{\left(-129600 i \, A^{2} - 261360 \, A B + 131769 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(360 i \, A + 363 \, B\right)} a^{2}}\right) - 192 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 192 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right)}{384 \, {\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,"1/384*(2*sqrt(2)*(13*(56*A - 65*I*B)*a^2*e^(7*I*d*x + 7*I*c) + 3*(504*A - 425*I*B)*a^2*e^(5*I*d*x + 5*I*c) + (1096*A - 1135*I*B)*a^2*e^(3*I*d*x + 3*I*c) + 3*(104*A - 107*I*B)*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((-129600*I*A^2 - 261360*A*B + 131769*I*B^2)*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((sqrt(2)*((360*I*A + 363*B)*a^2*e^(2*I*d*x + 2*I*c) + (360*I*A + 363*B)*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*I*sqrt((-129600*I*A^2 - 261360*A*B + 131769*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((360*I*A + 363*B)*a^2)) - 3*sqrt((-129600*I*A^2 - 261360*A*B + 131769*I*B^2)*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((sqrt(2)*((360*I*A + 363*B)*a^2*e^(2*I*d*x + 2*I*c) + (360*I*A + 363*B)*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*I*sqrt((-129600*I*A^2 - 261360*A*B + 131769*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((360*I*A + 363*B)*a^2)) - 192*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) + 192*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*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
170,1,913,0,0.823703," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left({\left(66 i \, A + 91 \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(108 i \, A + 98 \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(42 i \, A + 39 \, B\right)} 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{{\left(2116 i \, A^{2} + 4140 \, A B - 2025 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(46 i \, A + 45 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(46 i \, A + 45 \, B\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{{\left(2116 i \, A^{2} + 4140 \, A B - 2025 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(46 i \, A + 45 \, B\right)} a^{2}}\right) - 3 \, \sqrt{\frac{{\left(2116 i \, A^{2} + 4140 \, A B - 2025 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(46 i \, A + 45 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(46 i \, A + 45 \, B\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{{\left(2116 i \, A^{2} + 4140 \, A B - 2025 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(46 i \, A + 45 \, B\right)} a^{2}}\right) - 24 \, \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 24 \, \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\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)}}"," ",0,"1/48*(2*sqrt(2)*((66*I*A + 91*B)*a^2*e^(5*I*d*x + 5*I*c) + (108*I*A + 98*B)*a^2*e^(3*I*d*x + 3*I*c) + (42*I*A + 39*B)*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((2116*I*A^2 + 4140*A*B - 2025*I*B^2)*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((sqrt(2)*((46*I*A + 45*B)*a^2*e^(2*I*d*x + 2*I*c) + (46*I*A + 45*B)*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((2116*I*A^2 + 4140*A*B - 2025*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((46*I*A + 45*B)*a^2)) - 3*sqrt((2116*I*A^2 + 4140*A*B - 2025*I*B^2)*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((sqrt(2)*((46*I*A + 45*B)*a^2*e^(2*I*d*x + 2*I*c) + (46*I*A + 45*B)*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((2116*I*A^2 + 4140*A*B - 2025*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((46*I*A + 45*B)*a^2)) - 24*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 + 64*A*B - 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) + 24*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 + 64*A*B - 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
171,1,833,0,0.763349," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left({\left(4 \, A - 11 i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(4 \, A - 7 i \, B\right)} 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{{\left(-400 i \, A^{2} - 920 \, A B + 529 i \, B^{2}\right)} 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({\left(20 i \, A + 23 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(20 i \, A + 23 \, B\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 i \, \sqrt{\frac{{\left(-400 i \, A^{2} - 920 \, A B + 529 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(20 i \, A + 23 \, B\right)} a^{2}}\right) - \sqrt{\frac{{\left(-400 i \, A^{2} - 920 \, A B + 529 i \, B^{2}\right)} 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({\left(20 i \, A + 23 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(20 i \, A + 23 \, B\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 i \, \sqrt{\frac{{\left(-400 i \, A^{2} - 920 \, A B + 529 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(20 i \, A + 23 \, B\right)} a^{2}}\right) - 4 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} 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({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 4 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} 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({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right)}{8 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/8*(2*sqrt(2)*((4*A - 11*I*B)*a^2*e^(3*I*d*x + 3*I*c) + (4*A - 7*I*B)*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((-400*I*A^2 - 920*A*B + 529*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((20*I*A + 23*B)*a^2*e^(2*I*d*x + 2*I*c) + (20*I*A + 23*B)*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*I*sqrt((-400*I*A^2 - 920*A*B + 529*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((20*I*A + 23*B)*a^2)) - sqrt((-400*I*A^2 - 920*A*B + 529*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((20*I*A + 23*B)*a^2*e^(2*I*d*x + 2*I*c) + (20*I*A + 23*B)*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*I*sqrt((-400*I*A^2 - 920*A*B + 529*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((20*I*A + 23*B)*a^2)) - 4*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) + 4*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
172,1,840,0,0.699493," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-4 i \, A - 2 \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-4 i \, A + 2 \, B\right)} 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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} 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({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} 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({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - \sqrt{\frac{{\left(4 i \, A^{2} + 20 \, A B - 25 i \, B^{2}\right)} 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({\left(2 i \, A + 5 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 5 \, B\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{{\left(4 i \, A^{2} + 20 \, A B - 25 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 5 \, B\right)} a^{2}}\right) + \sqrt{\frac{{\left(4 i \, A^{2} + 20 \, A B - 25 i \, B^{2}\right)} 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({\left(2 i \, A + 5 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(2 i \, A + 5 \, B\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{{\left(4 i \, A^{2} + 20 \, A B - 25 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(2 i \, A + 5 \, B\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*B)*a^2*e^(3*I*d*x + 3*I*c) + (-4*I*A + 2*B)*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^2 + 64*A*B - 32*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 + 64*A*B - 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) - sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 + 64*A*B - 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) - sqrt((4*I*A^2 + 20*A*B - 25*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((sqrt(2)*((2*I*A + 5*B)*a^2*e^(2*I*d*x + 2*I*c) + (2*I*A + 5*B)*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((4*I*A^2 + 20*A*B - 25*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 5*B)*a^2)) + sqrt((4*I*A^2 + 20*A*B - 25*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((sqrt(2)*((2*I*A + 5*B)*a^2*e^(2*I*d*x + 2*I*c) + (2*I*A + 5*B)*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((4*I*A^2 + 20*A*B - 25*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((2*I*A + 5*B)*a^2)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
173,1,830,0,0.786876," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left({\left(8 \, A - 3 i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, A a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 3 \, {\left(2 \, A - i \, B\right)} 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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 3 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 3 \, \sqrt{\frac{4 i \, B^{2} 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(\sqrt{2} {\left(B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + B 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 \, B^{2} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{B a^{2}}\right) - 3 \, \sqrt{\frac{4 i \, B^{2} 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(\sqrt{2} {\left(B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + B 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 \, B^{2} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{B 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*(4*sqrt(2)*((8*A - 3*I*B)*a^2*e^(5*I*d*x + 5*I*c) + 2*A*a^2*e^(3*I*d*x + 3*I*c) - 3*(2*A - I*B)*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^2 - 64*A*B + 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) + 3*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) + 3*sqrt(4*I*B^2*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((sqrt(2)*(B*a^2*e^(2*I*d*x + 2*I*c) + B*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*B^2*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(B*a^2)) - 3*sqrt(4*I*B^2*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((sqrt(2)*(B*a^2*e^(2*I*d*x + 2*I*c) + B*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*B^2*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(B*a^2)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
174,1,588,0,1.047801," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(208 i \, A + 160 \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(-72 i \, A - 120 \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(-160 i \, A - 160 \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(120 i \, A + 120 \, B\right)} 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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 15 \, \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} 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 + 160*B)*a^2*e^(7*I*d*x + 7*I*c) + (-72*I*A - 120*B)*a^2*e^(5*I*d*x + 5*I*c) + (-160*I*A - 160*B)*a^2*e^(3*I*d*x + 3*I*c) + (120*I*A + 120*B)*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^2 + 64*A*B - 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 + 64*A*B - 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) + 15*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 + 64*A*B - 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*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
175,1,641,0,0.556465," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(2 \, {\left(100 \, A - 91 i \, B\right)} a^{2} e^{\left(9 i \, d x + 9 i \, c\right)} - 5 \, {\left(37 \, A - 49 i \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 7 \, {\left(5 \, A - 11 i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 245 \, {\left(A - i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 105 \, {\left(A - i \, B\right)} 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}} - 105 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 105 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\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*(8*sqrt(2)*(2*(100*A - 91*I*B)*a^2*e^(9*I*d*x + 9*I*c) - 5*(37*A - 49*I*B)*a^2*e^(7*I*d*x + 7*I*c) - 7*(5*A - 11*I*B)*a^2*e^(5*I*d*x + 5*I*c) + 245*(A - I*B)*a^2*e^(3*I*d*x + 3*I*c) - 105*(A - I*B)*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)) - 105*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) + 105*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*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
176,1,700,0,0.668743," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-5168 i \, A - 4800 \, B\right)} a^{2} e^{\left(11 i \, d x + 11 i \, c\right)} + {\left(8008 i \, A + 9240 \, B\right)} a^{2} e^{\left(9 i \, d x + 9 i \, c\right)} + {\left(-5472 i \, A - 3600 \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(-7728 i \, A - 6720 \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(8400 i \, A + 8400 \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-2520 i \, A - 2520 \, B\right)} 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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - 315 \, \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} 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(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} 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 - 4800*B)*a^2*e^(11*I*d*x + 11*I*c) + (8008*I*A + 9240*B)*a^2*e^(9*I*d*x + 9*I*c) + (-5472*I*A - 3600*B)*a^2*e^(7*I*d*x + 7*I*c) + (-7728*I*A - 6720*B)*a^2*e^(5*I*d*x + 5*I*c) + (8400*I*A + 8400*B)*a^2*e^(3*I*d*x + 3*I*c) + (-2520*I*A - 2520*B)*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^2 + 64*A*B - 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 + 64*A*B - 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) - 315*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*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((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 + 64*A*B - 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*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
177,1,755,0,1.274407," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} {\left(2 \, {\left(3730 \, A - 3553 i \, B\right)} a^{2} e^{\left(13 i \, d x + 13 i \, c\right)} - 9 \, {\left(1805 \, A - 2013 i \, B\right)} a^{2} e^{\left(11 i \, d x + 11 i \, c\right)} + 55 \, {\left(397 \, A - 337 i \, B\right)} a^{2} e^{\left(9 i \, d x + 9 i \, c\right)} + 66 \, {\left(95 \, A - 47 i \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 1386 \, {\left(15 \, A - 16 i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 15015 \, {\left(A - i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 3465 \, {\left(A - i \, B\right)} 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}} - 3465 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} {\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)} \log\left(\frac{{\left(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 3465 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} {\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)} \log\left(\frac{{\left(\sqrt{2} {\left({\left(4 i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, A + 4 \, B\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{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right)}{6930 \, {\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,"1/6930*(8*sqrt(2)*(2*(3730*A - 3553*I*B)*a^2*e^(13*I*d*x + 13*I*c) - 9*(1805*A - 2013*I*B)*a^2*e^(11*I*d*x + 11*I*c) + 55*(397*A - 337*I*B)*a^2*e^(9*I*d*x + 9*I*c) + 66*(95*A - 47*I*B)*a^2*e^(7*I*d*x + 7*I*c) - 1386*(15*A - 16*I*B)*a^2*e^(5*I*d*x + 5*I*c) + 15015*(A - I*B)*a^2*e^(3*I*d*x + 3*I*c) - 3465*(A - I*B)*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)) - 3465*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*(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)*log((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)) + 3465*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*(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)*log((sqrt(2)*((4*I*A + 4*B)*a^2*e^(2*I*d*x + 2*I*c) + (4*I*A + 4*B)*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^2 - 64*A*B + 32*I*B^2)*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/((4*I*A + 4*B)*a^2)))/(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)","B",0
178,1,880,0,0.650784," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(3/2*b*B/a+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(4 \, B a b e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-4 i \, B a^{2} + 16 \, B a b\right)} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(4 i \, B a^{2} - 12 \, B a b\right)} 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(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 \, B^{2} a^{5} - 96 \, B^{2} a^{4} b - 72 i \, B^{2} a^{3} b^{2}}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(-4 i \, B a^{2} + 6 \, B a b + {\left(-4 i \, B a^{2} + 6 \, B a b\right)} e^{\left(2 i \, d x + 2 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}} + d \sqrt{\frac{32 i \, B^{2} a^{5} - 96 \, B^{2} a^{4} b - 72 i \, B^{2} a^{3} b^{2}}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{-4 i \, B a^{2} + 6 \, B a b}\right) + {\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 \, B^{2} a^{5} - 96 \, B^{2} a^{4} b - 72 i \, B^{2} a^{3} b^{2}}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(-4 i \, B a^{2} + 6 \, B a b + {\left(-4 i \, B a^{2} + 6 \, B a b\right)} e^{\left(2 i \, d x + 2 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}} - d \sqrt{\frac{32 i \, B^{2} a^{5} - 96 \, B^{2} a^{4} b - 72 i \, B^{2} a^{3} b^{2}}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{-4 i \, B a^{2} + 6 \, B a b}\right) + \sqrt{\frac{4 i \, B^{2} 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(\sqrt{2} {\left(B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + B 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 \, B^{2} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{B a^{2}}\right) - \sqrt{\frac{4 i \, B^{2} 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(\sqrt{2} {\left(B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + B 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 \, B^{2} a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{B a^{2}}\right)}{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)}}"," ",0,"1/2*(sqrt(2)*(4*B*a*b*e^(3*I*d*x + 3*I*c) + (-4*I*B*a^2 + 16*B*a*b)*e^(5*I*d*x + 5*I*c) + (4*I*B*a^2 - 12*B*a*b)*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^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt((32*I*B^2*a^5 - 96*B^2*a^4*b - 72*I*B^2*a^3*b^2)/d^2)*log((sqrt(2)*(-4*I*B*a^2 + 6*B*a*b + (-4*I*B*a^2 + 6*B*a*b)*e^(2*I*d*x + 2*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*sqrt((32*I*B^2*a^5 - 96*B^2*a^4*b - 72*I*B^2*a^3*b^2)/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(-4*I*B*a^2 + 6*B*a*b)) + (d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt((32*I*B^2*a^5 - 96*B^2*a^4*b - 72*I*B^2*a^3*b^2)/d^2)*log((sqrt(2)*(-4*I*B*a^2 + 6*B*a*b + (-4*I*B*a^2 + 6*B*a*b)*e^(2*I*d*x + 2*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*sqrt((32*I*B^2*a^5 - 96*B^2*a^4*b - 72*I*B^2*a^3*b^2)/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(-4*I*B*a^2 + 6*B*a*b)) + sqrt(4*I*B^2*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((sqrt(2)*(B*a^2*e^(2*I*d*x + 2*I*c) + B*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*B^2*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(B*a^2)) - sqrt(4*I*B^2*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((sqrt(2)*(B*a^2*e^(2*I*d*x + 2*I*c) + B*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*B^2*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(B*a^2)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
179,1,789,0,0.748052," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{\frac{-4 i \, A^{2} + 4 \, A B + i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{\sqrt{2} {\left({\left(-416 i \, A + 208 \, B\right)} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-416 i \, A + 208 \, B\right)} 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(312 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 104 i \, a d\right)} \sqrt{\frac{-4 i \, A^{2} + 4 \, A B + i \, B^{2}}{a d^{2}}}}{{\left(-1210 i \, A + 605 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 1210 i \, A + 605 \, B}\right) - a d \sqrt{\frac{-4 i \, A^{2} + 4 \, A B + i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{\sqrt{2} {\left({\left(-416 i \, A + 208 \, B\right)} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-416 i \, A + 208 \, B\right)} 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(-312 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 104 i \, a d\right)} \sqrt{\frac{-4 i \, A^{2} + 4 \, A B + i \, B^{2}}{a d^{2}}}}{{\left(-1210 i \, A + 605 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 1210 i \, A + 605 \, B}\right) + a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{i \, a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{-i \, a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) + \sqrt{2} {\left(2 \, {\left(A + 3 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, A + 2 i \, B\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 d}"," ",0,"-1/4*(a*d*sqrt((-4*I*A^2 + 4*A*B + I*B^2)/(a*d^2))*e^(I*d*x + I*c)*log((sqrt(2)*((-416*I*A + 208*B)*e^(3*I*d*x + 3*I*c) + (-416*I*A + 208*B)*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)) + (312*I*a*d*e^(2*I*d*x + 2*I*c) - 104*I*a*d)*sqrt((-4*I*A^2 + 4*A*B + I*B^2)/(a*d^2)))/((-1210*I*A + 605*B)*e^(2*I*d*x + 2*I*c) - 1210*I*A + 605*B)) - a*d*sqrt((-4*I*A^2 + 4*A*B + I*B^2)/(a*d^2))*e^(I*d*x + I*c)*log((sqrt(2)*((-416*I*A + 208*B)*e^(3*I*d*x + 3*I*c) + (-416*I*A + 208*B)*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)) + (-312*I*a*d*e^(2*I*d*x + 2*I*c) + 104*I*a*d)*sqrt((-4*I*A^2 + 4*A*B + I*B^2)/(a*d^2)))/((-1210*I*A + 605*B)*e^(2*I*d*x + 2*I*c) - 1210*I*A + 605*B)) + a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c)*log((I*a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c)*log((-I*a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + sqrt(2)*(2*(A + 3*I*B)*e^(2*I*d*x + 2*I*c) + 2*A + 2*I*B)*sqrt(a/(e^(2*I*d*x + 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*d)","B",0
180,1,705,0,0.875988," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{-\frac{4 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{52 \, {\left(4 \, \sqrt{2} {\left(B e^{\left(3 i \, d x + 3 i \, c\right)} + B 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(3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{-\frac{4 i \, B^{2}}{a d^{2}}}\right)}}{605 \, {\left(B e^{\left(2 i \, d x + 2 i \, c\right)} + B\right)}}\right) - a d \sqrt{-\frac{4 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{52 \, {\left(4 \, \sqrt{2} {\left(B e^{\left(3 i \, d x + 3 i \, c\right)} + B 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(3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{-\frac{4 i \, B^{2}}{a d^{2}}}\right)}}{605 \, {\left(B e^{\left(2 i \, d x + 2 i \, c\right)} + B\right)}}\right) - a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) + a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) + \sqrt{2} {\left({\left(2 i \, A - 2 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, A - 2 \, B\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 d}"," ",0,"1/4*(a*d*sqrt(-4*I*B^2/(a*d^2))*e^(I*d*x + I*c)*log(52/605*(4*sqrt(2)*(B*e^(3*I*d*x + 3*I*c) + B*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*a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(-4*I*B^2/(a*d^2)))/(B*e^(2*I*d*x + 2*I*c) + B)) - a*d*sqrt(-4*I*B^2/(a*d^2))*e^(I*d*x + I*c)*log(52/605*(4*sqrt(2)*(B*e^(3*I*d*x + 3*I*c) + B*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*a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(-4*I*B^2/(a*d^2)))/(B*e^(2*I*d*x + 2*I*c) + B)) - a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c)*log((a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c)*log(-(a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) - sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + sqrt(2)*((2*I*A - 2*B)*e^(2*I*d*x + 2*I*c) + 2*I*A - 2*B)*sqrt(a/(e^(2*I*d*x + 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*d)","B",0
181,1,400,0,0.827041," ","integrate((A+B*tan(d*x+c))/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^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{i \, a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{-i \, a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) + 2 \, \sqrt{2} {\left({\left(A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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 d}"," ",0,"1/4*(a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c)*log((I*a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c)*log((-I*a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + 2*sqrt(2)*((A + I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*sqrt(a/(e^(2*I*d*x + 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*d)","B",0
182,1,458,0,0.595449," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-10 i \, A + 2 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 8 i \, A e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, A - 2 \, B\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(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^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} \log\left(\frac{a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\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^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} \log\left(-\frac{a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\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)*((-10*I*A + 2*B)*e^(4*I*d*x + 4*I*c) - 8*I*A*e^(2*I*d*x + 2*I*c) + 2*I*A - 2*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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^2 + 4*A*B - 2*I*B^2)/(a*d^2))*log((a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - (a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(a*d^2))*log(-(a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) - sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)))/(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))","B",0
183,1,518,0,0.727537," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(2 \, {\left(7 \, A + 15 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, {\left(11 \, A + 3 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 30 \, {\left(A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 \, A + 6 i \, B\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(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^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} \log\left(\frac{i \, a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\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^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} \log\left(\frac{-i \, a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\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*(sqrt(2)*(2*(7*A + 15*I*B)*e^(6*I*d*x + 6*I*c) - 2*(11*A + 3*I*B)*e^(4*I*d*x + 4*I*c) - 30*(A + I*B)*e^(2*I*d*x + 2*I*c) + 6*A + 6*I*B)*sqrt(a/(e^(2*I*d*x + 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*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^2 - 4*A*B + 2*I*B^2)/(a*d^2))*log((I*a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 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^2 - 4*A*B + 2*I*B^2)/(a*d^2))*log((-I*a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)))/(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
184,1,576,0,0.556805," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(206 i \, A - 70 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-204 i \, A + 180 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-80 i \, A + 40 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(300 i \, A - 180 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 30 i \, A + 30 \, B\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 \, {\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^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} \log\left(\frac{a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\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^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} \log\left(-\frac{a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\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)*((206*I*A - 70*B)*e^(8*I*d*x + 8*I*c) + (-204*I*A + 180*B)*e^(6*I*d*x + 6*I*c) + (-80*I*A + 40*B)*e^(4*I*d*x + 4*I*c) + (300*I*A - 180*B)*e^(2*I*d*x + 2*I*c) - 30*I*A + 30*B)*sqrt(a/(e^(2*I*d*x + 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*(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^2 + 4*A*B - 2*I*B^2)/(a*d^2))*log((a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + 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^2 + 4*A*B - 2*I*B^2)/(a*d^2))*log(-(a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(a*d^2))*e^(I*d*x + I*c) - sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)))/(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
185,1,756,0,0.865126," ","integrate(tan(d*x+c)^(3/2)*(A+B*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{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{2 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{-2 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 3 \, a^{2} d \sqrt{\frac{4 i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{208 \, \sqrt{2} {\left(B e^{\left(3 i \, d x + 3 i \, c\right)} + B 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(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 \, B^{2}}{a^{3} d^{2}}}}{605 \, {\left(B e^{\left(2 i \, d x + 2 i \, c\right)} + B\right)}}\right) + 3 \, a^{2} d \sqrt{\frac{4 i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{208 \, \sqrt{2} {\left(B e^{\left(3 i \, d x + 3 i \, c\right)} + B 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(-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 \, B^{2}}{a^{3} d^{2}}}}{605 \, {\left(B e^{\left(2 i \, d x + 2 i \, c\right)} + B\right)}}\right) - \sqrt{2} {\left(2 \, {\left(2 \, A + 5 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(A + 3 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"-1/12*(3*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((2*I*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 3*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((-2*I*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 3*a^2*d*sqrt(4*I*B^2/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(1/605*(208*sqrt(2)*(B*e^(3*I*d*x + 3*I*c) + B*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)) + (156*I*a^2*d*e^(2*I*d*x + 2*I*c) - 52*I*a^2*d)*sqrt(4*I*B^2/(a^3*d^2)))/(B*e^(2*I*d*x + 2*I*c) + B)) + 3*a^2*d*sqrt(4*I*B^2/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(1/605*(208*sqrt(2)*(B*e^(3*I*d*x + 3*I*c) + B*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)) + (-156*I*a^2*d*e^(2*I*d*x + 2*I*c) + 52*I*a^2*d)*sqrt(4*I*B^2/(a^3*d^2)))/(B*e^(2*I*d*x + 2*I*c) + B)) - sqrt(2)*(2*(2*A + 5*I*B)*e^(4*I*d*x + 4*I*c) + 3*(A + 3*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^2*d)","B",0
186,1,444,0,0.695868," ","integrate(tan(d*x+c)^(1/2)*(A+B*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{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{2 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - \sqrt{2} {\left({\left(2 i \, A + 4 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(3 i \, A + 3 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"-1/12*(3*sqrt(1/2)*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((2*sqrt(1/2)*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 3*sqrt(1/2)*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-(2*sqrt(1/2)*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*e^(I*d*x + I*c) - sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - sqrt(2)*((2*I*A + 4*B)*e^(4*I*d*x + 4*I*c) + (3*I*A + 3*B)*e^(2*I*d*x + 2*I*c) + I*A - B)*sqrt(a/(e^(2*I*d*x + 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)/(a^2*d)","B",0
187,1,441,0,0.796191," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{2 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{-2 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) + \sqrt{2} {\left(2 \, {\left(4 \, A + i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(3 \, A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((2*I*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 3*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((-2*I*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + sqrt(2)*(2*(4*A + I*B)*e^(4*I*d*x + 4*I*c) + 3*(3*A + I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^2*d)","B",0
188,1,509,0,1.429275," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} {\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 3 \, \sqrt{\frac{1}{2}} {\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} \log\left(-\frac{2 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) + \sqrt{2} {\left({\left(-38 i \, A + 8 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-25 i \, A + B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(14 i \, A - 8 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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(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*(3*sqrt(1/2)*(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*log((2*sqrt(1/2)*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 3*sqrt(1/2)*(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*log(-(2*sqrt(1/2)*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*e^(I*d*x + I*c) - sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + sqrt(2)*((-38*I*A + 8*B)*e^(6*I*d*x + 6*I*c) + (-25*I*A + B)*e^(4*I*d*x + 4*I*c) + (14*I*A - 8*B)*e^(2*I*d*x + 2*I*c) + I*A - B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
189,1,569,0,1.219721," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \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{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} \log\left(\frac{2 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 3 \, \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{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} \log\left(\frac{-2 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) + \sqrt{2} {\left(2 \, {\left(26 \, A + 19 i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(35 \, A + 13 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, {\left(23 \, A + 13 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(19 \, A + 13 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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(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*(3*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((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*log((2*I*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 3*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((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*log((-2*I*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + sqrt(2)*(2*(26*A + 19*I*B)*e^(8*I*d*x + 8*I*c) - (35*A + 13*I*B)*e^(6*I*d*x + 6*I*c) - 3*(23*A + 13*I*B)*e^(4*I*d*x + 4*I*c) + (19*A + 13*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
190,1,775,0,0.869088," ","integrate(tan(d*x+c)^(5/2)*(A+B*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{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-\frac{2 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 30 \, a^{3} d \sqrt{-\frac{4 i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{52 \, {\left(4 \, \sqrt{2} {\left(B e^{\left(3 i \, d x + 3 i \, c\right)} + B 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(3 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{-\frac{4 i \, B^{2}}{a^{5} d^{2}}}\right)}}{605 \, {\left(B e^{\left(2 i \, d x + 2 i \, c\right)} + B\right)}}\right) + 30 \, a^{3} d \sqrt{-\frac{4 i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{52 \, {\left(4 \, \sqrt{2} {\left(B e^{\left(3 i \, d x + 3 i \, c\right)} + B 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(3 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{-\frac{4 i \, B^{2}}{a^{5} d^{2}}}\right)}}{605 \, {\left(B e^{\left(2 i \, d x + 2 i \, c\right)} + B\right)}}\right) + \sqrt{2} {\left({\left(-23 i \, A + 123 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-12 i \, A + 102 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(8 i \, A - 18 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, A + 3 \, B\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(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(15*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((2*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 15*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-(2*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) - sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 30*a^3*d*sqrt(-4*I*B^2/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(52/605*(4*sqrt(2)*(B*e^(3*I*d*x + 3*I*c) + B*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*a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt(-4*I*B^2/(a^5*d^2)))/(B*e^(2*I*d*x + 2*I*c) + B)) + 30*a^3*d*sqrt(-4*I*B^2/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(52/605*(4*sqrt(2)*(B*e^(3*I*d*x + 3*I*c) + B*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*a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt(-4*I*B^2/(a^5*d^2)))/(B*e^(2*I*d*x + 2*I*c) + B)) + sqrt(2)*((-23*I*A + 123*B)*e^(6*I*d*x + 6*I*c) + (-12*I*A + 102*B)*e^(4*I*d*x + 4*I*c) + (8*I*A - 18*B)*e^(2*I*d*x + 2*I*c) - 3*I*A + 3*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^3*d)","B",0
191,1,459,0,0.708519," ","integrate(tan(d*x+c)^(3/2)*(A+B*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{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{2 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{-2 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - \sqrt{2} {\left({\left(17 \, A - 23 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, {\left(3 \, A - 2 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(A - 4 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, A - 3 i \, B\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(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"-1/120*(15*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((2*I*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 15*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((-2*I*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - sqrt(2)*((17*A - 23*I*B)*e^(6*I*d*x + 6*I*c) + 6*(3*A - 2*I*B)*e^(4*I*d*x + 4*I*c) - 2*(A - 4*I*B)*e^(2*I*d*x + 2*I*c) - 3*A - 3*I*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^3*d)","B",0
192,1,461,0,0.626323," ","integrate(tan(d*x+c)^(1/2)*(A+B*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{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-\frac{2 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - \sqrt{2} {\left({\left(3 i \, A + 17 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(12 i \, A + 18 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(12 i \, A - 2 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\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(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"-1/120*(15*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((2*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 15*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-(2*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) - sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - sqrt(2)*((3*I*A + 17*B)*e^(6*I*d*x + 6*I*c) + (12*I*A + 18*B)*e^(4*I*d*x + 4*I*c) + (12*I*A - 2*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^3*d)","B",0
193,1,460,0,0.810905," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{2 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{-2 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) + \sqrt{2} {\left({\left(83 \, A + 3 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, {\left(17 \, A + 2 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(11 \, A + 6 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, A + 3 i \, B\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(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(15*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((2*I*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 15*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((-2*I*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + sqrt(2)*((83*A + 3*I*B)*e^(6*I*d*x + 6*I*c) + 6*(17*A + 2*I*B)*e^(4*I*d*x + 4*I*c) + 2*(11*A + 6*I*B)*e^(2*I*d*x + 2*I*c) + 3*A + 3*I*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^3*d)","B",0
194,1,528,0,0.602489," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(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{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\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{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} \log\left(-\frac{2 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) + \sqrt{2} {\left({\left(-463 i \, A + 83 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-269 i \, A + 19 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(220 i \, A - 80 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(29 i \, A - 19 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\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}}}{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((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*log((2*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 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((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*log(-(2*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) - sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + sqrt(2)*((-463*I*A + 83*B)*e^(8*I*d*x + 8*I*c) + (-269*I*A + 19*B)*e^(6*I*d*x + 6*I*c) + (220*I*A - 80*B)*e^(4*I*d*x + 4*I*c) + (29*I*A - 19*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
195,1,588,0,0.889601," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{1}{2}} {\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} \log\left(\frac{2 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) - 15 \, \sqrt{\frac{1}{2}} {\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} \log\left(\frac{-2 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} {\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A + B\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}}}{4 i \, A + 4 \, B}\right) + \sqrt{2} {\left({\left(983 \, A + 463 i \, B\right)} e^{\left(10 i \, d x + 10 i \, c\right)} - 2 \, {\left(272 \, A + 97 i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - 3 \, {\left(393 \, A + 163 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(381 \, A + 191 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(18 \, A + 13 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, A + 3 i \, B\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}}}{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*(15*sqrt(1/2)*(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((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*log((2*I*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) - 15*sqrt(1/2)*(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((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*log((-2*I*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2))*e^(I*d*x + I*c) + sqrt(2)*((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A + B)*sqrt(a/(e^(2*I*d*x + 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*A + 4*B)) + sqrt(2)*((983*A + 463*I*B)*e^(10*I*d*x + 10*I*c) - 2*(272*A + 97*I*B)*e^(8*I*d*x + 8*I*c) - 3*(393*A + 163*I*B)*e^(6*I*d*x + 6*I*c) + (381*A + 191*I*B)*e^(4*I*d*x + 4*I*c) + 2*(18*A + 13*I*B)*e^(2*I*d*x + 2*I*c) + 3*A + 3*I*B)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(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
196,1,405,0,0.733251," ","integrate((a+I*a*tan(d*x+c))^(1/3)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \cdot 2^{\frac{1}{3}} B \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{1}{4}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} d - d\right)} \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(i \, A + B\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(\frac{1}{4}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} d + d\right)} \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a}{d^{3}}\right)^{\frac{1}{3}}}{i \, A + B}\right) + \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} d - d\right)} \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(i \, A + B\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(\frac{1}{4}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} d + d\right)} \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a}{d^{3}}\right)^{\frac{1}{3}}}{i \, A + B}\right) + 2 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} d \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(i \, A + B\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 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} d \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a}{d^{3}}\right)^{\frac{1}{3}}}{i \, A + B}\right)}{2 \, d}"," ",0,"1/2*(6*2^(1/3)*B*(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)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a/d^3)^(1/3)*log((2^(1/3)*(I*A + B)*(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)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a/d^3)^(1/3))/(I*A + B)) + (1/4)^(1/3)*(I*sqrt(3)*d - d)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a/d^3)^(1/3)*log((2^(1/3)*(I*A + B)*(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)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a/d^3)^(1/3))/(I*A + B)) + 2*(1/4)^(1/3)*d*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a/d^3)^(1/3)*log((2^(1/3)*(I*A + B)*(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*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a/d^3)^(1/3))/(I*A + B)))/d","B",0
197,1,665,0,1.518191," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} {\left({\left(-12 i \, A - 18 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-12 i \, A - 18 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 15 \, B\right)} \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)} + 10 \, \left(\frac{1}{2}\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{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} d^{2} \left(\frac{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(5 i \, \sqrt{3} d - 5 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(10 i \, \sqrt{3} d - 10 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, \sqrt{3} d - 5 \, d\right)} \left(\frac{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} d^{2} + d^{2}\right)} \left(\frac{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(-5 i \, \sqrt{3} d - 5 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-10 i \, \sqrt{3} d - 10 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 5 i \, \sqrt{3} d - 5 \, d\right)} \left(\frac{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} d^{2} + d^{2}\right)} \left(\frac{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right)}{10 \, {\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,"1/10*(2^(2/3)*((-12*I*A - 18*B)*e^(4*I*d*x + 4*I*c) + (-12*I*A - 18*B)*e^(2*I*d*x + 2*I*c) - 15*B)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*e^(4/3*I*d*x + 4/3*I*c) + 10*(1/2)^(1/3)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^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*(1/2)^(2/3)*d^2*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + (1/2)^(1/3)*((5*I*sqrt(3)*d - 5*d)*e^(4*I*d*x + 4*I*c) + (10*I*sqrt(3)*d - 10*d)*e^(2*I*d*x + 2*I*c) + 5*I*sqrt(3)*d - 5*d)*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (1/2)^(2/3)*(I*sqrt(3)*d^2 + d^2)*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + (1/2)^(1/3)*((-5*I*sqrt(3)*d - 5*d)*e^(4*I*d*x + 4*I*c) + (-10*I*sqrt(3)*d - 10*d)*e^(2*I*d*x + 2*I*c) - 5*I*sqrt(3)*d - 5*d)*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (1/2)^(2/3)*(-I*sqrt(3)*d^2 + d^2)*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
198,1,577,0,0.524447," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \cdot 2^{\frac{2}{3}} {\left({\left(5 \, A - 4 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 5 \, A\right)} \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)} + 10 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \left(\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} d^{2} \left(\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(-5 i \, \sqrt{3} d - 5 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 5 i \, \sqrt{3} d - 5 \, d\right)} \left(\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} d^{2} - d^{2}\right)} \left(\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(5 i \, \sqrt{3} d - 5 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, \sqrt{3} d - 5 \, d\right)} \left(\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} d^{2} - d^{2}\right)} \left(\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right)}{10 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/10*(3*2^(2/3)*((5*A - 4*I*B)*e^(2*I*d*x + 2*I*c) + 5*A)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*e^(4/3*I*d*x + 4/3*I*c) + 10*(1/2)^(1/3)*(d*e^(2*I*d*x + 2*I*c) + d)*((A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^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*(1/2)^(2/3)*d^2*((A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + (1/2)^(1/3)*((-5*I*sqrt(3)*d - 5*d)*e^(2*I*d*x + 2*I*c) - 5*I*sqrt(3)*d - 5*d)*((A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (1/2)^(2/3)*(I*sqrt(3)*d^2 - d^2)*((A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + (1/2)^(1/3)*((5*I*sqrt(3)*d - 5*d)*e^(2*I*d*x + 2*I*c) + 5*I*sqrt(3)*d - 5*d)*((A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (1/2)^(2/3)*(-I*sqrt(3)*d^2 - d^2)*((A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
199,1,489,0,0.819526," ","integrate((a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \cdot 2^{\frac{2}{3}} B \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)} + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} d \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} d^{2} \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} d - d\right)} \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} d^{2} + d^{2}\right)} \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} d - d\right)} \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} d^{2} + d^{2}\right)} \left(\frac{{\left(-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right)}{2 \, d}"," ",0,"1/2*(3*2^(2/3)*B*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*e^(4/3*I*d*x + 4/3*I*c) + 2*(1/2)^(1/3)*d*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^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*(1/2)^(2/3)*d^2*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + (1/2)^(1/3)*(I*sqrt(3)*d - d)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (1/2)^(2/3)*(I*sqrt(3)*d^2 + d^2)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + (1/2)^(1/3)*(-I*sqrt(3)*d - d)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (1/2)^(2/3)*(-I*sqrt(3)*d^2 + d^2)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)))/d","B",0
200,1,711,0,0.681302," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{1}{2} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)} \left(-\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} d^{2} - d^{2}\right)} \left(-\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + \frac{1}{2} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)} \left(-\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} d^{2} - d^{2}\right)} \left(-\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + \frac{1}{2} \, \left(\frac{A^{3} a^{2}}{d^{3}}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} A^{2} 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{A^{3} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{2 \, A^{2} a}\right) + \frac{1}{2} \, \left(\frac{A^{3} a^{2}}{d^{3}}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} A^{2} 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{A^{3} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{2 \, A^{2} a}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} d^{2} \left(-\frac{{\left(A^{3} - 3 i \, A^{2} B - 3 \, A B^{2} + i \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + \left(\frac{A^{3} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} A^{2} 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^{3} a^{2}}{d^{3}}\right)^{\frac{2}{3}} d^{2}}{A^{2} a}\right)"," ",0,"1/2*(1/2)^(1/3)*(-I*sqrt(3) - 1)*(-(A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (1/2)^(2/3)*(I*sqrt(3)*d^2 - d^2)*(-(A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + 1/2*(1/2)^(1/3)*(I*sqrt(3) - 1)*(-(A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (1/2)^(2/3)*(-I*sqrt(3)*d^2 - d^2)*(-(A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + 1/2*(A^3*a^2/d^3)^(1/3)*(I*sqrt(3) - 1)*log(1/2*(2*2^(1/3)*A^2*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)*(A^3*a^2/d^3)^(2/3))/(A^2*a)) + 1/2*(A^3*a^2/d^3)^(1/3)*(-I*sqrt(3) - 1)*log(1/2*(2*2^(1/3)*A^2*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)*(A^3*a^2/d^3)^(2/3))/(A^2*a)) + (1/2)^(1/3)*(-(A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^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*(1/2)^(2/3)*d^2*(-(A^3 - 3*I*A^2*B - 3*A*B^2 + I*B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + (A^3*a^2/d^3)^(1/3)*log((2^(1/3)*A^2*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (A^3*a^2/d^3)^(2/3)*d^2)/(A^2*a))","B",0
201,1,1096,0,1.669258," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \cdot 2^{\frac{2}{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{2}{3}} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} + 6 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \left(\frac{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} d^{2} \left(\frac{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + 3 \, \left(\frac{1}{2}\right)^{\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{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} d^{2} + d^{2}\right)} \left(\frac{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} a}\right) + 3 \, \left(\frac{1}{2}\right)^{\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{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} d^{2} + d^{2}\right)} \left(\frac{{\left(i \, A^{3} + 3 \, A^{2} B - 3 i \, A B^{2} - B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(A^{2} - 2 i \, A B - B^{2}\right)} 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{{\left(-8 i \, A^{3} - 36 \, A^{2} B + 54 i \, A B^{2} + 27 \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{9 \cdot 2^{\frac{1}{3}} {\left(8 \, A^{2} - 24 i \, A B - 18 \, B^{2}\right)} 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^{2} + 9 \, d^{2}\right)} \left(\frac{{\left(-8 i \, A^{3} - 36 \, A^{2} B + 54 i \, A B^{2} + 27 \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{9 \, {\left(8 \, A^{2} - 24 i \, A B - 18 \, B^{2}\right)} 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{{\left(-8 i \, A^{3} - 36 \, A^{2} B + 54 i \, A B^{2} + 27 \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{9 \cdot 2^{\frac{1}{3}} {\left(8 \, A^{2} - 24 i \, A B - 18 \, B^{2}\right)} 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^{2} + 9 \, d^{2}\right)} \left(\frac{{\left(-8 i \, A^{3} - 36 \, A^{2} B + 54 i \, A B^{2} + 27 \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{9 \, {\left(8 \, A^{2} - 24 i \, A B - 18 \, B^{2}\right)} a}\right) + 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \left(\frac{{\left(-8 i \, A^{3} - 36 \, A^{2} B + 54 i \, A B^{2} + 27 \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(4 \, A^{2} - 12 i \, A B - 9 \, B^{2}\right)} 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)} + d^{2} \left(\frac{{\left(-8 i \, A^{3} - 36 \, A^{2} B + 54 i \, A B^{2} + 27 \, B^{3}\right)} a^{2}}{d^{3}}\right)^{\frac{2}{3}}}{{\left(4 \, A^{2} - 12 i \, A B - 9 \, B^{2}\right)} a}\right)}{6 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/6*(3*2^(2/3)*(-2*I*A*e^(2*I*d*x + 2*I*c) - 2*I*A)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*e^(4/3*I*d*x + 4/3*I*c) + 6*(1/2)^(1/3)*(d*e^(2*I*d*x + 2*I*c) - d)*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^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*(1/2)^(2/3)*d^2*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + 3*(1/2)^(1/3)*((I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) - I*sqrt(3)*d + d)*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (1/2)^(2/3)*(I*sqrt(3)*d^2 + d^2)*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + 3*(1/2)^(1/3)*((-I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) + I*sqrt(3)*d + d)*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (1/2)^(2/3)*(-I*sqrt(3)*d^2 + d^2)*((I*A^3 + 3*A^2*B - 3*I*A*B^2 - B^3)*a^2/d^3)^(2/3))/((A^2 - 2*I*A*B - B^2)*a)) + ((I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) - I*sqrt(3)*d + d)*((-8*I*A^3 - 36*A^2*B + 54*I*A*B^2 + 27*B^3)*a^2/d^3)^(1/3)*log(1/9*(9*2^(1/3)*(8*A^2 - 24*I*A*B - 18*B^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*I*sqrt(3)*d^2 + 9*d^2)*((-8*I*A^3 - 36*A^2*B + 54*I*A*B^2 + 27*B^3)*a^2/d^3)^(2/3))/((8*A^2 - 24*I*A*B - 18*B^2)*a)) + ((-I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) + I*sqrt(3)*d + d)*((-8*I*A^3 - 36*A^2*B + 54*I*A*B^2 + 27*B^3)*a^2/d^3)^(1/3)*log(1/9*(9*2^(1/3)*(8*A^2 - 24*I*A*B - 18*B^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*I*sqrt(3)*d^2 + 9*d^2)*((-8*I*A^3 - 36*A^2*B + 54*I*A*B^2 + 27*B^3)*a^2/d^3)^(2/3))/((8*A^2 - 24*I*A*B - 18*B^2)*a)) + 2*(d*e^(2*I*d*x + 2*I*c) - d)*((-8*I*A^3 - 36*A^2*B + 54*I*A*B^2 + 27*B^3)*a^2/d^3)^(1/3)*log((2^(1/3)*(4*A^2 - 12*I*A*B - 9*B^2)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + d^2*((-8*I*A^3 - 36*A^2*B + 54*I*A*B^2 + 27*B^3)*a^2/d^3)^(2/3))/((4*A^2 - 12*I*A*B - 9*B^2)*a)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
202,1,550,0,0.667059," ","integrate((A+B*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{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d^{2} \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\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)}}{A^{2} - 2 i \, A B - B^{2}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} a d + a d\right)} \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\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(\frac{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} a d^{2} - a d^{2}\right)} \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a d^{3}}\right)^{\frac{2}{3}}}{A^{2} - 2 i \, A B - B^{2}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} a d + a d\right)} \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{2^{\frac{1}{3}} {\left(A^{2} - 2 i \, A B - B^{2}\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(\frac{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} a d^{2} - a d^{2}\right)} \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a d^{3}}\right)^{\frac{2}{3}}}{A^{2} - 2 i \, A B - B^{2}}\right) + 2^{\frac{2}{3}} {\left({\left(3 i \, A - 3 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\right)} \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)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(2*(1/2)^(1/3)*a*d*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log((2*(1/2)^(2/3)*a*d^2*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a*d^3))^(2/3) + 2^(1/3)*(A^2 - 2*I*A*B - B^2)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c))/(A^2 - 2*I*A*B - B^2)) - (1/2)^(1/3)*(I*sqrt(3)*a*d + a*d)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (1/2)^(2/3)*(I*sqrt(3)*a*d^2 - a*d^2)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a*d^3))^(2/3))/(A^2 - 2*I*A*B - B^2)) - (1/2)^(1/3)*(-I*sqrt(3)*a*d + a*d)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log((2^(1/3)*(A^2 - 2*I*A*B - B^2)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (1/2)^(2/3)*(-I*sqrt(3)*a*d^2 - a*d^2)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a*d^3))^(2/3))/(A^2 - 2*I*A*B - B^2)) + 2^(2/3)*((3*I*A - 3*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*e^(4/3*I*d*x + 4/3*I*c))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
203,1,496,0,0.696745," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(2/3),x, algorithm=""fricas"")","\frac{{\left(4 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} a d \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a^{2} d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{2 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} a d \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a^{2} d^{3}}\right)^{\frac{1}{3}} - 2^{\frac{1}{3}} {\left(i \, A + B\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)}}{i \, A + B}\right) - 2 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} a d + a d\right)} \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a^{2} d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{2^{\frac{1}{3}} {\left(i \, A + B\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(\frac{1}{4}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} a d - a d\right)} \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a^{2} d^{3}}\right)^{\frac{1}{3}}}{i \, A + B}\right) - 2 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} a d + a d\right)} \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a^{2} d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{2^{\frac{1}{3}} {\left(i \, A + B\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(\frac{1}{4}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} a d - a d\right)} \left(\frac{-i \, A^{3} - 3 \, A^{2} B + 3 i \, A B^{2} + B^{3}}{a^{2} d^{3}}\right)^{\frac{1}{3}}}{i \, A + B}\right) + 2^{\frac{1}{3}} {\left({\left(3 i \, A - 3 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\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)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a d}"," ",0,"1/8*(4*(1/4)^(1/3)*a*d*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a^2*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-(2*(1/4)^(1/3)*a*d*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a^2*d^3))^(1/3) - 2^(1/3)*(I*A + B)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c))/(I*A + B)) - 2*(1/4)^(1/3)*(-I*sqrt(3)*a*d + a*d)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a^2*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log((2^(1/3)*(I*A + B)*(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)*a*d - a*d)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a^2*d^3))^(1/3))/(I*A + B)) - 2*(1/4)^(1/3)*(I*sqrt(3)*a*d + a*d)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a^2*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log((2^(1/3)*(I*A + B)*(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)*a*d - a*d)*((-I*A^3 - 3*A^2*B + 3*I*A*B^2 + B^3)/(a^2*d^3))^(1/3))/(I*A + B)) + 2^(1/3)*((3*I*A - 3*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*(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
204,0,0,0,0.763183," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{16 \, {\left({\left(A - i \, B\right)} a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(A + i \, B\right)} a^{4} e^{\left(8 i \, d x + 8 i \, c\right)}\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)^{m}}{e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(16*((A - I*B)*a^4*e^(10*I*d*x + 10*I*c) + (A + I*B)*a^4*e^(8*I*d*x + 8*I*c))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m/(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
205,0,0,0,0.713848," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{8 \, {\left({\left(A - i \, B\right)} a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(A + i \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)}\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)^{m}}{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(8*((A - I*B)*a^3*e^(8*I*d*x + 8*I*c) + (A + I*B)*a^3*e^(6*I*d*x + 6*I*c))*((-I*e^(2*I*d*x + 2*I*c) + I)/(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), x)","F",0
206,0,0,0,0.542374," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, {\left({\left(A - i \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(A + i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)}\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)^{m}}{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(4*((A - I*B)*a^2*e^(6*I*d*x + 6*I*c) + (A + I*B)*a^2*e^(4*I*d*x + 4*I*c))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m/(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
207,0,0,0,0.577648," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, {\left({\left(A - i \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(A + i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)}\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)^{m}}{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 - I*B)*a*e^(4*I*d*x + 4*I*c) + (A + I*B)*a*e^(2*I*d*x + 2*I*c))*((-I*e^(2*I*d*x + 2*I*c) + I)/(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), x)","F",0
208,0,0,0,1.050460," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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)^{m} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*((A - I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*e^(-2*I*d*x - 2*I*c)/a, x)","F",0
209,0,0,0,0.644622," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, A e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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)^{m} e^{\left(-4 i \, d x - 4 i \, c\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*((A - I*B)*e^(4*I*d*x + 4*I*c) + 2*A*e^(2*I*d*x + 2*I*c) + A + I*B)*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*e^(-4*I*d*x - 4*I*c)/a^2, x)","F",0
210,0,0,0,0.689541," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(3 \, A - i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(3 \, A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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)^{m} e^{\left(-6 i \, d x - 6 i \, c\right)}}{8 \, a^{3}}, x\right)"," ",0,"integral(1/8*((A - I*B)*e^(6*I*d*x + 6*I*c) + (3*A - I*B)*e^(4*I*d*x + 4*I*c) + (3*A + I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*e^(-6*I*d*x - 6*I*c)/a^3, x)","F",0
211,0,0,0,0.617089," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + 2 \, {\left(2 \, A - i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, A e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(2 \, A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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)^{m} e^{\left(-8 i \, d x - 8 i \, c\right)}}{16 \, a^{4}}, x\right)"," ",0,"integral(1/16*((A - I*B)*e^(8*I*d*x + 8*I*c) + 2*(2*A - I*B)*e^(6*I*d*x + 6*I*c) + 6*A*e^(4*I*d*x + 4*I*c) + 2*(2*A + I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*e^(-8*I*d*x - 8*I*c)/a^4, x)","F",0
212,0,0,0,0.650087," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, \sqrt{2} {\left({\left(A - i \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(A + i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)}\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)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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(4*sqrt(2)*((A - I*B)*a^2*e^(7*I*d*x + 7*I*c) + (A + I*B)*a^2*e^(5*I*d*x + 5*I*c))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(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
213,0,0,0,0.586656," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, \sqrt{2} {\left({\left(A - i \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(A + i \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)}\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)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{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*sqrt(2)*((A - I*B)*a*e^(5*I*d*x + 5*I*c) + (A + I*B)*a*e^(3*I*d*x + 3*I*c))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(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
214,0,0,0,0.709515," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} {\left({\left(A - i \, B\right)} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(A + i \, B\right)} e^{\left(i \, d x + i \, c\right)}\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)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(sqrt(2)*((A - I*B)*e^(3*I*d*x + 3*I*c) + (A + I*B)*e^(I*d*x + I*c))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
215,0,0,0,0.630116," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} {\left({\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*sqrt(2)*((A - I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-I*d*x - I*c)/a, x)","F",0
216,0,0,0,0.742573," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} {\left({\left(A - i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, A e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-3 i \, d x - 3 i \, c\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*sqrt(2)*((A - I*B)*e^(4*I*d*x + 4*I*c) + 2*A*e^(2*I*d*x + 2*I*c) + A + I*B)*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-3*I*d*x - 3*I*c)/a^2, x)","F",0
217,0,0,0,0.849476," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} {\left({\left(A - i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(3 \, A - i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(3 \, A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-5 i \, d x - 5 i \, c\right)}}{8 \, a^{3}}, x\right)"," ",0,"integral(1/8*sqrt(2)*((A - I*B)*e^(6*I*d*x + 6*I*c) + (3*A - I*B)*e^(4*I*d*x + 4*I*c) + (3*A + I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-5*I*d*x - 5*I*c)/a^3, x)","F",0
218,0,0,0,1.609510," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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} \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}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(((A - I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
219,0,0,0,1.403842," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(i \, A + B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-2 i \, A - 4 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, B e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(2 i \, A - 4 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\right)} \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}}{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(((I*A + B)*e^(8*I*d*x + 8*I*c) + (-2*I*A - 4*B)*e^(6*I*d*x + 6*I*c) + 6*B*e^(4*I*d*x + 4*I*c) + (2*I*A - 4*B)*e^(2*I*d*x + 2*I*c) - I*A + B)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n/(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
220,0,0,0,0.661935," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left({\left(A - i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(A - 3 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(A + 3 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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}}{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(-((A - I*B)*e^(6*I*d*x + 6*I*c) - (A - 3*I*B)*e^(4*I*d*x + 4*I*c) - (A + 3*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n/(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
221,0,0,0,0.578177," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(-i \, A - B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, B e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} \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}}{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(((-I*A - B)*e^(4*I*d*x + 4*I*c) + 2*B*e^(2*I*d*x + 2*I*c) + I*A - B)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n/(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
222,0,0,0,0.629206," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(((A - I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
223,0,0,0,0.993314," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} \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}}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}, x\right)"," ",0,"integral(((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A - B)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n/(e^(2*I*d*x + 2*I*c) - 1), x)","F",0
224,0,0,0,0.569791," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left({\left(A - i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, A e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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}}{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(-((A - I*B)*e^(4*I*d*x + 4*I*c) + 2*A*e^(2*I*d*x + 2*I*c) + A + I*B)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n/(e^(4*I*d*x + 4*I*c) - 2*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
225,0,0,0,1.640300," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(-i \, A - B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-3 i \, A - B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-3 i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\right)} \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}}{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(((-I*A - B)*e^(6*I*d*x + 6*I*c) + (-3*I*A - B)*e^(4*I*d*x + 4*I*c) + (-3*I*A + B)*e^(2*I*d*x + 2*I*c) - I*A + B)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n/(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
226,0,0,0,1.201963," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left({\left(A - i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(A - 3 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(A + 3 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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}}}{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(-((A - I*B)*e^(6*I*d*x + 6*I*c) - (A - 3*I*B)*e^(4*I*d*x + 4*I*c) - (A + 3*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*(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^(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
227,0,0,0,0.660361," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(-i \, A - B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, B e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} \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}}}{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(((-I*A - B)*e^(4*I*d*x + 4*I*c) + 2*B*e^(2*I*d*x + 2*I*c) + I*A - B)*(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), x)","F",0
228,0,0,0,0.544369," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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}}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(((A - I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*(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^(2*I*d*x + 2*I*c) + 1), x)","F",0
229,0,0,0,0.585692," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} \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}}}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}, x\right)"," ",0,"integral(((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A - B)*(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^(2*I*d*x + 2*I*c) - 1), x)","F",0
230,0,0,0,0.746012," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left({\left(A - i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, A e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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}}}{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(-((A - I*B)*e^(4*I*d*x + 4*I*c) + 2*A*e^(2*I*d*x + 2*I*c) + A + I*B)*(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), x)","F",0
231,0,0,0,0.862326," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(-i \, A - B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-3 i \, A - B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-3 i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\right)} \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}}}{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(((-I*A - B)*e^(6*I*d*x + 6*I*c) + (-3*I*A - B)*e^(4*I*d*x + 4*I*c) + (-3*I*A + B)*e^(2*I*d*x + 2*I*c) - I*A + B)*(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^(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
232,1,85,0,0.545648," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, B b \tan\left(d x + c\right)^{3} - 6 \, {\left(A a - B b\right)} d x + 3 \, {\left(B a + A b\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a + A b\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 6 \, {\left(A a - B b\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*b*tan(d*x + c)^3 - 6*(A*a - B*b)*d*x + 3*(B*a + A*b)*tan(d*x + c)^2 + 3*(B*a + A*b)*log(1/(tan(d*x + c)^2 + 1)) + 6*(A*a - B*b)*tan(d*x + c))/d","A",0
233,1,66,0,0.604829," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{B b \tan\left(d x + c\right)^{2} - 2 \, {\left(B a + A b\right)} d x - {\left(A a - B b\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(B a + A b\right)} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*b*tan(d*x + c)^2 - 2*(B*a + A*b)*d*x - (A*a - B*b)*log(1/(tan(d*x + c)^2 + 1)) + 2*(B*a + A*b)*tan(d*x + c))/d","A",0
234,1,50,0,0.657419," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(A a - B b\right)} d x + 2 \, B b \tan\left(d x + c\right) - {\left(B a + A b\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(2*(A*a - B*b)*d*x + 2*B*b*tan(d*x + c) - (B*a + A*b)*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
235,1,59,0,0.698101," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(B a + A b\right)} d x + A a \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - B b \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(2*(B*a + A*b)*d*x + A*a*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - B*b*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
236,1,73,0,1.458276," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(A a - B b\right)} d x \tan\left(d x + c\right) - {\left(B a + A b\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 a}{2 \, d \tan\left(d x + c\right)}"," ",0,"-1/2*(2*(A*a - B*b)*d*x*tan(d*x + c) - (B*a + A*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) + 2*A*a)/(d*tan(d*x + c))","A",0
237,1,95,0,0.556370," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(A a - B b\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 \, {\left(B a + A b\right)} d x + A a\right)} \tan\left(d x + c\right)^{2} + A a + 2 \, {\left(B a + A b\right)} \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*((A*a - B*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + (2*(B*a + A*b)*d*x + A*a)*tan(d*x + c)^2 + A*a + 2*(B*a + A*b)*tan(d*x + c))/(d*tan(d*x + c)^2)","A",0
238,1,121,0,0.970608," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(B a + A b\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 \, {\left(A a - B b\right)} d x - B a - A b\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(A a - B b\right)} \tan\left(d x + c\right)^{2} + 2 \, A a + 3 \, {\left(B a + A b\right)} \tan\left(d x + c\right)}{6 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*(B*a + A*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 - 3*(2*(A*a - B*b)*d*x - B*a - A*b)*tan(d*x + c)^3 - 6*(A*a - B*b)*tan(d*x + c)^2 + 2*A*a + 3*(B*a + A*b)*tan(d*x + c))/(d*tan(d*x + c)^3)","A",0
239,1,138,0,0.594672," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(A a - B b\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} + 3 \, {\left(4 \, {\left(B a + A b\right)} d x + 3 \, A a - 2 \, B b\right)} \tan\left(d x + c\right)^{4} + 12 \, {\left(B a + A b\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(A a - B b\right)} \tan\left(d x + c\right)^{2} - 3 \, A a - 4 \, {\left(B a + A b\right)} \tan\left(d x + c\right)}{12 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(A*a - B*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 + 3*(4*(B*a + A*b)*d*x + 3*A*a - 2*B*b)*tan(d*x + c)^4 + 12*(B*a + A*b)*tan(d*x + c)^3 + 6*(A*a - B*b)*tan(d*x + c)^2 - 3*A*a - 4*(B*a + A*b)*tan(d*x + c))/(d*tan(d*x + c)^4)","A",0
240,1,146,0,1.431130," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, B b^{2} \tan\left(d x + c\right)^{4} + 4 \, {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)^{3} - 12 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} d x + 6 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 12 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*b^2*tan(d*x + c)^4 + 4*(2*B*a*b + A*b^2)*tan(d*x + c)^3 - 12*(A*a^2 - 2*B*a*b - A*b^2)*d*x + 6*(B*a^2 + 2*A*a*b - B*b^2)*tan(d*x + c)^2 + 6*(B*a^2 + 2*A*a*b - B*b^2)*log(1/(tan(d*x + c)^2 + 1)) + 12*(A*a^2 - 2*B*a*b - A*b^2)*tan(d*x + c))/d","A",0
241,1,119,0,0.717767," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, B b^{2} \tan\left(d x + c\right)^{3} - 6 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} d x + 3 \, {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 6 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*b^2*tan(d*x + c)^3 - 6*(B*a^2 + 2*A*a*b - B*b^2)*d*x + 3*(2*B*a*b + A*b^2)*tan(d*x + c)^2 - 3*(A*a^2 - 2*B*a*b - A*b^2)*log(1/(tan(d*x + c)^2 + 1)) + 6*(B*a^2 + 2*A*a*b - B*b^2)*tan(d*x + c))/d","A",0
242,1,91,0,1.141039," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{B b^{2} \tan\left(d x + c\right)^{2} + 2 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} d x - {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*b^2*tan(d*x + c)^2 + 2*(A*a^2 - 2*B*a*b - A*b^2)*d*x - (B*a^2 + 2*A*a*b - B*b^2)*log(1/(tan(d*x + c)^2 + 1)) + 2*(2*B*a*b + A*b^2)*tan(d*x + c))/d","A",0
243,1,92,0,0.625790," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{A a^{2} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, B b^{2} \tan\left(d x + c\right) + 2 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} d x - {\left(2 \, B a b + A b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(A*a^2*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + 2*B*b^2*tan(d*x + c) + 2*(B*a^2 + 2*A*a*b - B*b^2)*d*x - (2*B*a*b + A*b^2)*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
244,1,112,0,1.449868," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{B b^{2} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) + 2 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} d x \tan\left(d x + c\right) + 2 \, A a^{2} - {\left(B a^{2} + 2 \, A a b\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 \, d \tan\left(d x + c\right)}"," ",0,"-1/2*(B*b^2*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c) + 2*(A*a^2 - 2*B*a*b - A*b^2)*d*x*tan(d*x + c) + 2*A*a^2 - (B*a^2 + 2*A*a*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c))/(d*tan(d*x + c))","A",0
245,1,122,0,0.626918," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(A a^{2} - 2 \, B a b - 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 a^{2} + {\left(A a^{2} + 2 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*((A*a^2 - 2*B*a*b - A*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + A*a^2 + (A*a^2 + 2*(B*a^2 + 2*A*a*b - B*b^2)*d*x)*tan(d*x + c)^2 + 2*(B*a^2 + 2*A*a*b)*tan(d*x + c))/(d*tan(d*x + c)^2)","A",0
246,1,157,0,0.532539," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(B a^{2} + 2 \, A a b - B 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)^{3} + 3 \, {\left(B a^{2} + 2 \, A a b - 2 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 2 \, A a^{2} - 6 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} \tan\left(d x + c\right)}{6 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*(B*a^2 + 2*A*a*b - B*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 + 3*(B*a^2 + 2*A*a*b - 2*(A*a^2 - 2*B*a*b - A*b^2)*d*x)*tan(d*x + c)^3 + 2*A*a^2 - 6*(A*a^2 - 2*B*a*b - A*b^2)*tan(d*x + c)^2 + 3*(B*a^2 + 2*A*a*b)*tan(d*x + c))/(d*tan(d*x + c)^3)","A",0
247,1,191,0,0.520545," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(A a^{2} - 2 \, B a b - 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} + 3 \, {\left(3 \, A a^{2} - 4 \, B a b - 2 \, A b^{2} + 4 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} d x\right)} \tan\left(d x + c\right)^{4} + 12 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \tan\left(d x + c\right)^{3} - 3 \, A a^{2} + 6 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \tan\left(d x + c\right)^{2} - 4 \, {\left(B a^{2} + 2 \, A a b\right)} \tan\left(d x + c\right)}{12 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(A*a^2 - 2*B*a*b - A*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 + 3*(3*A*a^2 - 4*B*a*b - 2*A*b^2 + 4*(B*a^2 + 2*A*a*b - B*b^2)*d*x)*tan(d*x + c)^4 + 12*(B*a^2 + 2*A*a*b - B*b^2)*tan(d*x + c)^3 - 3*A*a^2 + 6*(A*a^2 - 2*B*a*b - A*b^2)*tan(d*x + c)^2 - 4*(B*a^2 + 2*A*a*b)*tan(d*x + c))/(d*tan(d*x + c)^4)","A",0
248,1,213,0,0.669113," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, B b^{3} \tan\left(d x + c\right)^{5} + 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)^{4} + 20 \, {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)^{3} - 60 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} d x + 30 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \tan\left(d x + c\right)^{2} + 30 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 60 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*B*b^3*tan(d*x + c)^5 + 15*(3*B*a*b^2 + A*b^3)*tan(d*x + c)^4 + 20*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)*tan(d*x + c)^3 - 60*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*d*x + 30*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*tan(d*x + c)^2 + 30*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(1/(tan(d*x + c)^2 + 1)) + 60*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*tan(d*x + c))/d","A",0
249,1,178,0,0.650694," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, B b^{3} \tan\left(d x + c\right)^{4} + 4 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)^{3} - 12 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} d x + 6 \, {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)^{2} - 6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 12 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*b^3*tan(d*x + c)^4 + 4*(3*B*a*b^2 + A*b^3)*tan(d*x + c)^3 - 12*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*d*x + 6*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)*tan(d*x + c)^2 - 6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*log(1/(tan(d*x + c)^2 + 1)) + 12*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*tan(d*x + c))/d","A",0
250,1,142,0,0.561515," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, B b^{3} \tan\left(d x + c\right)^{3} + 6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} d x + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 6 \, {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*b^3*tan(d*x + c)^3 + 6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*d*x + 3*(3*B*a*b^2 + A*b^3)*tan(d*x + c)^2 - 3*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(1/(tan(d*x + c)^2 + 1)) + 6*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)*tan(d*x + c))/d","A",0
251,1,133,0,1.122676," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{B b^{3} \tan\left(d x + c\right)^{2} + A a^{3} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} d x - {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*b^3*tan(d*x + c)^2 + A*a^3*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + 2*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*d*x - (3*B*a^2*b + 3*A*a*b^2 - B*b^3)*log(1/(tan(d*x + c)^2 + 1)) + 2*(3*B*a*b^2 + A*b^3)*tan(d*x + c))/d","A",0
252,1,145,0,0.670715," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, B b^{3} \tan\left(d x + c\right)^{2} - 2 \, A a^{3} - 2 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} d x \tan\left(d x + c\right) + {\left(B a^{3} + 3 \, A a^{2} b\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) - {\left(3 \, B a b^{2} + A b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)}"," ",0,"1/2*(2*B*b^3*tan(d*x + c)^2 - 2*A*a^3 - 2*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*d*x*tan(d*x + c) + (B*a^3 + 3*A*a^2*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) - (3*B*a*b^2 + A*b^3)*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c))/(d*tan(d*x + c))","A",0
253,1,162,0,0.584099," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{B b^{3} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + A a^{3} + {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A 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} + {\left(A a^{3} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*(B*b^3*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + A*a^3 + (A*a^3 - 3*B*a^2*b - 3*A*a*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + (A*a^3 + 2*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*d*x)*tan(d*x + c)^2 + 2*(B*a^3 + 3*A*a^2*b)*tan(d*x + c))/(d*tan(d*x + c)^2)","A",0
254,1,181,0,0.598365," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - 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} + 2 \, A a^{3} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b - 2 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)}{6 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 + 2*A*a^3 + 3*(B*a^3 + 3*A*a^2*b - 2*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*d*x)*tan(d*x + c)^3 - 6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2)*tan(d*x + c)^2 + 3*(B*a^3 + 3*A*a^2*b)*tan(d*x + c))/(d*tan(d*x + c)^3)","A",0
255,1,225,0,0.495612," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{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)^{4} + 3 \, {\left(3 \, A a^{3} - 6 \, B a^{2} b - 6 \, A a b^{2} + 4 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{4} - 3 \, A a^{3} + 12 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} \tan\left(d x + c\right)^{2} - 4 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)}{12 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 + 3*(3*A*a^3 - 6*B*a^2*b - 6*A*a*b^2 + 4*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*d*x)*tan(d*x + c)^4 - 3*A*a^3 + 12*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*tan(d*x + c)^3 + 6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2)*tan(d*x + c)^2 - 4*(B*a^3 + 3*A*a^2*b)*tan(d*x + c))/(d*tan(d*x + c)^4)","A",0
256,1,266,0,0.548159," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - 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 \, B a^{3} + 9 \, A a^{2} b - 6 \, B a b^{2} - 2 \, A b^{3} - 4 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{5} - 60 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \tan\left(d x + c\right)^{4} - 12 \, A a^{3} + 30 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \tan\left(d x + c\right)^{3} + 20 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} \tan\left(d x + c\right)^{2} - 15 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)}{60 \, d \tan\left(d x + c\right)^{5}}"," ",0,"1/60*(30*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^5 + 15*(3*B*a^3 + 9*A*a^2*b - 6*B*a*b^2 - 2*A*b^3 - 4*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*d*x)*tan(d*x + c)^5 - 60*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*tan(d*x + c)^4 - 12*A*a^3 + 30*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*tan(d*x + c)^3 + 20*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2)*tan(d*x + c)^2 - 15*(B*a^3 + 3*A*a^2*b)*tan(d*x + c))/(d*tan(d*x + c)^5)","A",0
257,1,289,0,1.085657," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{10 \, B b^{4} \tan\left(d x + c\right)^{6} + 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{5} + 15 \, {\left(6 \, B a^{2} b^{2} + 4 \, A a b^{3} - B b^{4}\right)} \tan\left(d x + c\right)^{4} + 20 \, {\left(4 \, B a^{3} b + 6 \, A a^{2} b^{2} - 4 \, B a b^{3} - A b^{4}\right)} \tan\left(d x + c\right)^{3} - 60 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} d x + 30 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \tan\left(d x + c\right)^{2} + 30 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 60 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*B*b^4*tan(d*x + c)^6 + 12*(4*B*a*b^3 + A*b^4)*tan(d*x + c)^5 + 15*(6*B*a^2*b^2 + 4*A*a*b^3 - B*b^4)*tan(d*x + c)^4 + 20*(4*B*a^3*b + 6*A*a^2*b^2 - 4*B*a*b^3 - A*b^4)*tan(d*x + c)^3 - 60*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*d*x + 30*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*tan(d*x + c)^2 + 30*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*log(1/(tan(d*x + c)^2 + 1)) + 60*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*tan(d*x + c))/d","A",0
258,1,245,0,0.546492," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, B b^{4} \tan\left(d x + c\right)^{5} + 15 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{4} + 20 \, {\left(6 \, B a^{2} b^{2} + 4 \, A a b^{3} - B b^{4}\right)} \tan\left(d x + c\right)^{3} - 60 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} d x + 30 \, {\left(4 \, B a^{3} b + 6 \, A a^{2} b^{2} - 4 \, B a b^{3} - A b^{4}\right)} \tan\left(d x + c\right)^{2} - 30 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 60 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*B*b^4*tan(d*x + c)^5 + 15*(4*B*a*b^3 + A*b^4)*tan(d*x + c)^4 + 20*(6*B*a^2*b^2 + 4*A*a*b^3 - B*b^4)*tan(d*x + c)^3 - 60*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*d*x + 30*(4*B*a^3*b + 6*A*a^2*b^2 - 4*B*a*b^3 - A*b^4)*tan(d*x + c)^2 - 30*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(1/(tan(d*x + c)^2 + 1)) + 60*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*tan(d*x + c))/d","A",0
259,1,201,0,0.756502," ","integrate((a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, B b^{4} \tan\left(d x + c\right)^{4} + 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{3} + 12 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} d x + 6 \, {\left(6 \, B a^{2} b^{2} + 4 \, A a b^{3} - B b^{4}\right)} \tan\left(d x + c\right)^{2} - 6 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 12 \, {\left(4 \, B a^{3} b + 6 \, A a^{2} b^{2} - 4 \, B a b^{3} - A b^{4}\right)} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*b^4*tan(d*x + c)^4 + 4*(4*B*a*b^3 + A*b^4)*tan(d*x + c)^3 + 12*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*d*x + 6*(6*B*a^2*b^2 + 4*A*a*b^3 - B*b^4)*tan(d*x + c)^2 - 6*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*log(1/(tan(d*x + c)^2 + 1)) + 12*(4*B*a^3*b + 6*A*a^2*b^2 - 4*B*a*b^3 - A*b^4)*tan(d*x + c))/d","A",0
260,1,185,0,0.741633," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, B b^{4} \tan\left(d x + c\right)^{3} + 3 \, A a^{4} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 6 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} d x + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(4 \, B a^{3} b + 6 \, A a^{2} b^{2} - 4 \, B a b^{3} - A b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 6 \, {\left(6 \, B a^{2} b^{2} + 4 \, A a b^{3} - B b^{4}\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*b^4*tan(d*x + c)^3 + 3*A*a^4*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + 6*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*d*x + 3*(4*B*a*b^3 + A*b^4)*tan(d*x + c)^2 - 3*(4*B*a^3*b + 6*A*a^2*b^2 - 4*B*a*b^3 - A*b^4)*log(1/(tan(d*x + c)^2 + 1)) + 6*(6*B*a^2*b^2 + 4*A*a*b^3 - B*b^4)*tan(d*x + c))/d","A",0
261,1,193,0,0.631584," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{B b^{4} \tan\left(d x + c\right)^{3} - 2 \, A a^{4} + {\left(B a^{4} + 4 \, A a^{3} b\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) - {\left(6 \, B a^{2} b^{2} + 4 \, A a b^{3} - B b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) + 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{2} + {\left(B b^{4} - 2 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)}"," ",0,"1/2*(B*b^4*tan(d*x + c)^3 - 2*A*a^4 + (B*a^4 + 4*A*a^3*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) - (6*B*a^2*b^2 + 4*A*a*b^3 - B*b^4)*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c) + 2*(4*B*a*b^3 + A*b^4)*tan(d*x + c)^2 + (B*b^4 - 2*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*d*x)*tan(d*x + c))/(d*tan(d*x + c))","A",0
262,1,199,0,0.703353," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, B b^{4} \tan\left(d x + c\right)^{3} - A a^{4} - {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A 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(4 \, B a b^{3} + A b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} - {\left(A a^{4} + 2 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{2} - 2 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"1/2*(2*B*b^4*tan(d*x + c)^3 - A*a^4 - (A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 - (4*B*a*b^3 + A*b^4)*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 - (A*a^4 + 2*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*d*x)*tan(d*x + c)^2 - 2*(B*a^4 + 4*A*a^3*b)*tan(d*x + c))/(d*tan(d*x + c)^2)","A",0
263,1,222,0,0.764345," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, B b^{4} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{3} + 2 \, A a^{4} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A 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} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b - 2 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)}{6 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*B*b^4*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 + 2*A*a^4 + 3*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 + 3*(B*a^4 + 4*A*a^3*b - 2*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*d*x)*tan(d*x + c)^3 - 6*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2)*tan(d*x + c)^2 + 3*(B*a^4 + 4*A*a^3*b)*tan(d*x + c))/(d*tan(d*x + c)^3)","A",0
264,1,249,0,0.545709," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A 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} - 3 \, A a^{4} + 3 \, {\left(3 \, A a^{4} - 8 \, B a^{3} b - 12 \, A a^{2} b^{2} + 4 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{4} + 12 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} - 4 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)}{12 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 - 3*A*a^4 + 3*(3*A*a^4 - 8*B*a^3*b - 12*A*a^2*b^2 + 4*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*d*x)*tan(d*x + c)^4 + 12*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3)*tan(d*x + c)^3 + 6*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2)*tan(d*x + c)^2 - 4*(B*a^4 + 4*A*a^3*b)*tan(d*x + c))/(d*tan(d*x + c)^4)","A",0
265,1,300,0,0.559775," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B 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)^{5} + 15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b - 12 \, B a^{2} b^{2} - 8 \, A a b^{3} - 4 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{5} - 12 \, A a^{4} - 60 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{4} + 30 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} \tan\left(d x + c\right)^{3} + 20 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} - 15 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)}{60 \, d \tan\left(d x + c\right)^{5}}"," ",0,"1/60*(30*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^5 + 15*(3*B*a^4 + 12*A*a^3*b - 12*B*a^2*b^2 - 8*A*a*b^3 - 4*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*d*x)*tan(d*x + c)^5 - 12*A*a^4 - 60*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*tan(d*x + c)^4 + 30*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3)*tan(d*x + c)^3 + 20*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2)*tan(d*x + c)^2 - 15*(B*a^4 + 4*A*a^3*b)*tan(d*x + c))/(d*tan(d*x + c)^5)","A",0
266,1,350,0,0.721653," ","integrate(cot(d*x+c)^7*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{30 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A 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 a^{4} - 36 \, B a^{3} b - 54 \, A a^{2} b^{2} + 24 \, B a b^{3} + 6 \, A b^{4} + 12 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{6} + 60 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \tan\left(d x + c\right)^{5} + 10 \, A a^{4} + 30 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{4} - 20 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} \tan\left(d x + c\right)^{3} - 15 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} + 12 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)}{60 \, d \tan\left(d x + c\right)^{6}}"," ",0,"-1/60*(30*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^6 + 5*(11*A*a^4 - 36*B*a^3*b - 54*A*a^2*b^2 + 24*B*a*b^3 + 6*A*b^4 + 12*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*d*x)*tan(d*x + c)^6 + 60*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*tan(d*x + c)^5 + 10*A*a^4 + 30*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*tan(d*x + c)^4 - 20*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3)*tan(d*x + c)^3 - 15*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2)*tan(d*x + c)^2 + 12*(B*a^4 + 4*A*a^3*b)*tan(d*x + c))/(d*tan(d*x + c)^6)","A",0
267,1,190,0,0.586309," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(B a b^{3} - A b^{4}\right)} d x + {\left(B a^{2} b^{2} + B b^{4}\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{4} - A a^{3} 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(B a^{4} - A a^{3} b - A a b^{3} - B b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(B a^{3} b - A a^{2} b^{2} + B a b^{3} - A b^{4}\right)} \tan\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} + b^{5}\right)} d}"," ",0,"1/2*(2*(B*a*b^3 - A*b^4)*d*x + (B*a^2*b^2 + B*b^4)*tan(d*x + c)^2 + (B*a^4 - A*a^3*b)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (B*a^4 - A*a^3*b - A*a*b^3 - B*b^4)*log(1/(tan(d*x + c)^2 + 1)) - 2*(B*a^3*b - A*a^2*b^2 + B*a*b^3 - A*b^4)*tan(d*x + c))/((a^2*b^3 + b^5)*d)","A",0
268,1,149,0,0.836525," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(A a b^{2} + B b^{3}\right)} d x + {\left(B a^{3} - A 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(B a^{3} - A a^{2} b + B a b^{2} - A b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(B a^{2} b + B b^{3}\right)} \tan\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} + b^{4}\right)} d}"," ",0,"-1/2*(2*(A*a*b^2 + B*b^3)*d*x + (B*a^3 - A*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)) - (B*a^3 - A*a^2*b + B*a*b^2 - A*b^3)*log(1/(tan(d*x + c)^2 + 1)) - 2*(B*a^2*b + B*b^3)*tan(d*x + c))/((a^2*b^2 + b^4)*d)","A",0
269,1,110,0,0.713551," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(B a b - A b^{2}\right)} d x - {\left(B a^{2} - A a 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(B a^{2} + B 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*(B*a*b - A*b^2)*d*x - (B*a^2 - A*a*b)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + (B*a^2 + B*b^2)*log(1/(tan(d*x + c)^2 + 1)))/((a^2*b + b^3)*d)","A",0
270,1,76,0,0.628030," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(A a + B b\right)} d x - {\left(B a - A 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)}{2 \, {\left(a^{2} + b^{2}\right)} d}"," ",0,"1/2*(2*(A*a + B*b)*d*x - (B*a - A*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
271,1,118,0,1.331031," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(B a^{2} - A a b\right)} d x + {\left(A a^{2} + A b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(B a b - A b^{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)}{2 \, {\left(a^{3} + a b^{2}\right)} d}"," ",0,"1/2*(2*(B*a^2 - A*a*b)*d*x + (A*a^2 + A*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + (B*a*b - A*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^3 + a*b^2)*d)","A",0
272,1,177,0,0.588685," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, A a^{3} + 2 \, A a b^{2} + 2 \, {\left(A a^{3} + B a^{2} b\right)} d x \tan\left(d x + c\right) - {\left(B a^{3} - A a^{2} b + B a b^{2} - 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) + {\left(B a b^{2} - A b^{3}\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) \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*a^3 + 2*A*a*b^2 + 2*(A*a^3 + B*a^2*b)*d*x*tan(d*x + c) - (B*a^3 - A*a^2*b + B*a*b^2 - A*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) + (B*a*b^2 - A*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))/((a^4 + a^2*b^2)*d*tan(d*x + c))","A",0
273,1,234,0,0.698203," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{A a^{4} + A a^{2} b^{2} + {\left(A a^{4} + B a^{3} b + B a b^{3} - A 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(B a b^{3} - A b^{4}\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) \tan\left(d x + c\right)^{2} + {\left(A a^{4} + A a^{2} b^{2} + 2 \, {\left(B a^{4} - A a^{3} b\right)} d x\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{4} - A a^{3} b + B a^{2} b^{2} - A 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*(A*a^4 + A*a^2*b^2 + (A*a^4 + B*a^3*b + B*a*b^3 - A*b^4)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 - (B*a*b^3 - A*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*a^4 + A*a^2*b^2 + 2*(B*a^4 - A*a^3*b)*d*x)*tan(d*x + c)^2 + 2*(B*a^4 - A*a^3*b + B*a^2*b^2 - A*a*b^3)*tan(d*x + c))/((a^5 + a^3*b^2)*d*tan(d*x + c)^2)","A",0
274,1,293,0,0.759273," ","integrate(cot(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, A a^{5} + 2 \, A a^{3} b^{2} + 3 \, {\left(B a^{5} - A a^{4} b - B a b^{4} + A 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(B a b^{4} - A b^{5}\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) \tan\left(d x + c\right)^{3} + 3 \, {\left(B a^{5} - A a^{4} b + B a^{3} b^{2} - A a^{2} b^{3} - 2 \, {\left(A a^{5} + B a^{4} b\right)} d x\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(A a^{5} + B a^{4} b + B a^{2} b^{3} - A a b^{4}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{5} - A a^{4} b + B a^{3} b^{2} - A 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*(2*A*a^5 + 2*A*a^3*b^2 + 3*(B*a^5 - A*a^4*b - B*a*b^4 + A*b^5)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 + 3*(B*a*b^4 - A*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 + 3*(B*a^5 - A*a^4*b + B*a^3*b^2 - A*a^2*b^3 - 2*(A*a^5 + B*a^4*b)*d*x)*tan(d*x + c)^3 - 6*(A*a^5 + B*a^4*b + B*a^2*b^3 - A*a*b^4)*tan(d*x + c)^2 + 3*(B*a^5 - A*a^4*b + B*a^3*b^2 - A*a^2*b^3)*tan(d*x + c))/((a^6 + a^4*b^2)*d*tan(d*x + c)^3)","A",0
275,1,434,0,0.795868," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, B a^{4} b^{2} - 2 \, A a^{3} b^{3} - 2 \, {\left(B a^{3} b^{3} - 2 \, A a^{2} b^{4} - B a b^{5}\right)} d x - 2 \, {\left(B a^{4} b^{2} + 2 \, B a^{2} b^{4} + B b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(2 \, B a^{6} - A a^{5} b + 4 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3} + {\left(2 \, B a^{5} b - A a^{4} b^{2} + 4 \, B a^{3} b^{3} - 3 \, A a^{2} 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) - {\left(2 \, B a^{6} - A a^{5} b + 4 \, B a^{4} b^{2} - 2 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - A a b^{5} + {\left(2 \, B a^{5} b - A a^{4} b^{2} + 4 \, B a^{3} b^{3} - 2 \, A a^{2} b^{4} + 2 \, B a b^{5} - A b^{6}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(2 \, B a^{5} b - A a^{4} b^{2} + 2 \, B a^{3} b^{3} + B a b^{5} + {\left(B a^{2} b^{4} - 2 \, A a b^{5} - B b^{6}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\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\right)}}"," ",0,"-1/2*(2*B*a^4*b^2 - 2*A*a^3*b^3 - 2*(B*a^3*b^3 - 2*A*a^2*b^4 - B*a*b^5)*d*x - 2*(B*a^4*b^2 + 2*B*a^2*b^4 + B*b^6)*tan(d*x + c)^2 + (2*B*a^6 - A*a^5*b + 4*B*a^4*b^2 - 3*A*a^3*b^3 + (2*B*a^5*b - A*a^4*b^2 + 4*B*a^3*b^3 - 3*A*a^2*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*B*a^6 - A*a^5*b + 4*B*a^4*b^2 - 2*A*a^3*b^3 + 2*B*a^2*b^4 - A*a*b^5 + (2*B*a^5*b - A*a^4*b^2 + 4*B*a^3*b^3 - 2*A*a^2*b^4 + 2*B*a*b^5 - A*b^6)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(2*B*a^5*b - A*a^4*b^2 + 2*B*a^3*b^3 + B*a*b^5 + (B*a^2*b^4 - 2*A*a*b^5 - B*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)","B",0
276,1,311,0,0.803232," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3} - 2 \, {\left(A a^{3} b^{2} + 2 \, B a^{2} b^{3} - A a b^{4}\right)} d x + {\left(B a^{5} + 3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3} + {\left(B a^{4} b + 3 \, B a^{2} b^{3} - 2 \, A 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) - {\left(B a^{5} + 2 \, B a^{3} b^{2} + B a b^{4} + {\left(B a^{4} b + 2 \, B a^{2} b^{3} + B 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(B a^{4} b - A a^{3} b^{2} + {\left(A a^{2} b^{3} + 2 \, B a b^{4} - A b^{5}\right)} d x\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*(2*B*a^3*b^2 - 2*A*a^2*b^3 - 2*(A*a^3*b^2 + 2*B*a^2*b^3 - A*a*b^4)*d*x + (B*a^5 + 3*B*a^3*b^2 - 2*A*a^2*b^3 + (B*a^4*b + 3*B*a^2*b^3 - 2*A*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)) - (B*a^5 + 2*B*a^3*b^2 + B*a*b^4 + (B*a^4*b + 2*B*a^2*b^3 + B*b^5)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(B*a^4*b - A*a^3*b^2 + (A*a^2*b^3 + 2*B*a*b^4 - A*b^5)*d*x)*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)","B",0
277,1,221,0,0.645403," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, B a^{2} b - 2 \, A a b^{2} + 2 \, {\left(B a^{3} - 2 \, A a^{2} b - B a b^{2}\right)} d x + {\left(A a^{3} + 2 \, B a^{2} b - A a b^{2} + {\left(A a^{2} b + 2 \, B a b^{2} - A 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(B a^{3} - A a^{2} b - {\left(B a^{2} b - 2 \, A a b^{2} - B b^{3}\right)} d x\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*(2*B*a^2*b - 2*A*a*b^2 + 2*(B*a^3 - 2*A*a^2*b - B*a*b^2)*d*x + (A*a^3 + 2*B*a^2*b - A*a*b^2 + (A*a^2*b + 2*B*a*b^2 - A*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*(B*a^3 - A*a^2*b - (B*a^2*b - 2*A*a*b^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
278,1,222,0,0.794845," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, B a b^{2} - 2 \, A b^{3} + 2 \, {\left(A a^{3} + 2 \, B a^{2} b - A a b^{2}\right)} d x - {\left(B a^{3} - 2 \, A a^{2} b - B a b^{2} + {\left(B a^{2} b - 2 \, A a b^{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(B a^{2} b - A a b^{2} - {\left(A a^{2} b + 2 \, B a b^{2} - A b^{3}\right)} d x\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*(2*B*a*b^2 - 2*A*b^3 + 2*(A*a^3 + 2*B*a^2*b - A*a*b^2)*d*x - (B*a^3 - 2*A*a^2*b - B*a*b^2 + (B*a^2*b - 2*A*a*b^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*(B*a^2*b - A*a*b^2 - (A*a^2*b + 2*B*a*b^2 - A*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
279,1,323,0,0.778060," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, B a^{2} b^{3} - 2 \, A a b^{4} - 2 \, {\left(B a^{5} - 2 \, A a^{4} b - B a^{3} b^{2}\right)} d x - {\left(A a^{5} + 2 \, A a^{3} b^{2} + A a b^{4} + {\left(A a^{4} b + 2 \, A a^{2} 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(2 \, B a^{4} b - 3 \, A a^{3} b^{2} - A a b^{4} + {\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} 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) - 2 \, {\left(B a^{3} b^{2} - A a^{2} b^{3} + {\left(B a^{4} b - 2 \, A a^{3} b^{2} - B a^{2} b^{3}\right)} d x\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*(2*B*a^2*b^3 - 2*A*a*b^4 - 2*(B*a^5 - 2*A*a^4*b - B*a^3*b^2)*d*x - (A*a^5 + 2*A*a^3*b^2 + A*a*b^4 + (A*a^4*b + 2*A*a^2*b^3 + A*b^5)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - (2*B*a^4*b - 3*A*a^3*b^2 - A*a*b^4 + (2*B*a^3*b^2 - 3*A*a^2*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)) - 2*(B*a^3*b^2 - A*a^2*b^3 + (B*a^4*b - 2*A*a^3*b^2 - B*a^2*b^3)*d*x)*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
280,1,465,0,0.912668," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, A a^{6} + 4 \, A a^{4} b^{2} + 2 \, A a^{2} b^{4} + 2 \, {\left(B a^{3} b^{3} - A a^{2} b^{4} + {\left(A a^{5} b + 2 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{2} - {\left({\left(B a^{5} b - 2 \, A a^{4} b^{2} + 2 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4} + B a b^{5} - 2 \, A b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{6} - 2 \, A a^{5} b + 2 \, B a^{4} b^{2} - 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, A 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(3 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4} + B a b^{5} - 2 \, A b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(3 \, B a^{4} b^{2} - 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, A 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) + 2 \, {\left(A a^{5} b + 2 \, A a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5} + {\left(A a^{6} + 2 \, B a^{5} b - A a^{4} b^{2}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\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)\right)}}"," ",0,"-1/2*(2*A*a^6 + 4*A*a^4*b^2 + 2*A*a^2*b^4 + 2*(B*a^3*b^3 - A*a^2*b^4 + (A*a^5*b + 2*B*a^4*b^2 - A*a^3*b^3)*d*x)*tan(d*x + c)^2 - ((B*a^5*b - 2*A*a^4*b^2 + 2*B*a^3*b^3 - 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*tan(d*x + c)^2 + (B*a^6 - 2*A*a^5*b + 2*B*a^4*b^2 - 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + ((3*B*a^3*b^3 - 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*tan(d*x + c)^2 + (3*B*a^4*b^2 - 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*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)) + 2*(A*a^5*b + 2*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5 + (A*a^6 + 2*B*a^5*b - A*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
281,1,590,0,0.666785," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{A a^{7} + 2 \, A a^{5} b^{2} + A a^{3} b^{4} + {\left(A a^{6} b + 2 \, A a^{4} b^{3} - 2 \, B a^{3} b^{4} + 3 \, A a^{2} b^{5} + 2 \, {\left(B a^{6} b - 2 \, A a^{5} b^{2} - B a^{4} b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{3} + {\left(A a^{7} + 2 \, B a^{6} b - 2 \, A a^{5} b^{2} + 4 \, B a^{4} b^{3} - 7 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 6 \, A a b^{6} + 2 \, {\left(B a^{7} - 2 \, A a^{6} b - B a^{5} b^{2}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left({\left(A a^{6} b + 2 \, B a^{5} b^{2} - A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 2 \, B a b^{6} - 3 \, A b^{7}\right)} \tan\left(d x + c\right)^{3} + {\left(A a^{7} + 2 \, B a^{6} b - A a^{5} b^{2} + 4 \, B a^{4} b^{3} - 5 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} - 3 \, A 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(4 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 2 \, B a b^{6} - 3 \, A b^{7}\right)} \tan\left(d x + c\right)^{3} + {\left(4 \, B a^{4} b^{3} - 5 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} - 3 \, A 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) + {\left(2 \, B a^{7} - 3 \, A a^{6} b + 4 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} + 2 \, B a^{3} b^{4} - 3 \, A 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*a^7 + 2*A*a^5*b^2 + A*a^3*b^4 + (A*a^6*b + 2*A*a^4*b^3 - 2*B*a^3*b^4 + 3*A*a^2*b^5 + 2*(B*a^6*b - 2*A*a^5*b^2 - B*a^4*b^3)*d*x)*tan(d*x + c)^3 + (A*a^7 + 2*B*a^6*b - 2*A*a^5*b^2 + 4*B*a^4*b^3 - 7*A*a^3*b^4 + 4*B*a^2*b^5 - 6*A*a*b^6 + 2*(B*a^7 - 2*A*a^6*b - B*a^5*b^2)*d*x)*tan(d*x + c)^2 + ((A*a^6*b + 2*B*a^5*b^2 - A*a^4*b^3 + 4*B*a^3*b^4 - 5*A*a^2*b^5 + 2*B*a*b^6 - 3*A*b^7)*tan(d*x + c)^3 + (A*a^7 + 2*B*a^6*b - A*a^5*b^2 + 4*B*a^4*b^3 - 5*A*a^3*b^4 + 2*B*a^2*b^5 - 3*A*a*b^6)*tan(d*x + c)^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - ((4*B*a^3*b^4 - 5*A*a^2*b^5 + 2*B*a*b^6 - 3*A*b^7)*tan(d*x + c)^3 + (4*B*a^4*b^3 - 5*A*a^3*b^4 + 2*B*a^2*b^5 - 3*A*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)) + (2*B*a^7 - 3*A*a^6*b + 4*B*a^5*b^2 - 6*A*a^4*b^3 + 2*B*a^3*b^4 - 3*A*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
282,1,890,0,0.937625," ","integrate(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, B a^{7} b^{2} - A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 7 \, A a^{4} b^{5} - 2 \, {\left(B a^{6} b^{3} + 3 \, B a^{4} b^{5} + 3 \, B a^{2} b^{7} + B b^{9}\right)} \tan\left(d x + c\right)^{3} - 2 \, {\left(A a^{5} b^{4} + 3 \, B a^{4} b^{5} - 3 \, A a^{3} b^{6} - B a^{2} b^{7}\right)} d x - {\left(9 \, B a^{7} b^{2} - 3 \, A a^{6} b^{3} + 23 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} + 12 \, B a^{3} b^{6} + 4 \, B a b^{8} + 2 \, {\left(A a^{3} b^{6} + 3 \, B a^{2} b^{7} - 3 \, A a b^{8} - B b^{9}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(3 \, B a^{9} - A a^{8} b + 9 \, B a^{7} b^{2} - 3 \, A a^{6} b^{3} + 10 \, B a^{5} b^{4} - 6 \, A a^{4} b^{5} + {\left(3 \, B a^{7} b^{2} - A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 3 \, A a^{4} b^{5} + 10 \, B a^{3} b^{6} - 6 \, A a^{2} b^{7}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, B a^{8} b - A a^{7} b^{2} + 9 \, B a^{6} b^{3} - 3 \, A a^{5} b^{4} + 10 \, B a^{4} b^{5} - 6 \, A a^{3} b^{6}\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 \, B a^{9} - A a^{8} b + 9 \, B a^{7} b^{2} - 3 \, A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 3 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - A a^{2} b^{7} + {\left(3 \, B a^{7} b^{2} - A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 3 \, A a^{4} b^{5} + 9 \, B a^{3} b^{6} - 3 \, A a^{2} b^{7} + 3 \, B a b^{8} - A b^{9}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, B a^{8} b - A a^{7} b^{2} + 9 \, B a^{6} b^{3} - 3 \, A a^{5} b^{4} + 9 \, B a^{4} b^{5} - 3 \, A a^{3} b^{6} + 3 \, B a^{2} b^{7} - A a b^{8}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(3 \, B a^{8} b - A a^{7} b^{2} + 6 \, B a^{6} b^{3} - 3 \, A a^{5} b^{4} - 2 \, B a^{4} b^{5} + 4 \, A a^{3} b^{6} + B a^{2} b^{7} + 2 \, {\left(A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 3 \, A a^{2} b^{7} - B 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*B*a^7*b^2 - A*a^6*b^3 + 9*B*a^5*b^4 - 7*A*a^4*b^5 - 2*(B*a^6*b^3 + 3*B*a^4*b^5 + 3*B*a^2*b^7 + B*b^9)*tan(d*x + c)^3 - 2*(A*a^5*b^4 + 3*B*a^4*b^5 - 3*A*a^3*b^6 - B*a^2*b^7)*d*x - (9*B*a^7*b^2 - 3*A*a^6*b^3 + 23*B*a^5*b^4 - 9*A*a^4*b^5 + 12*B*a^3*b^6 + 4*B*a*b^8 + 2*(A*a^3*b^6 + 3*B*a^2*b^7 - 3*A*a*b^8 - B*b^9)*d*x)*tan(d*x + c)^2 + (3*B*a^9 - A*a^8*b + 9*B*a^7*b^2 - 3*A*a^6*b^3 + 10*B*a^5*b^4 - 6*A*a^4*b^5 + (3*B*a^7*b^2 - A*a^6*b^3 + 9*B*a^5*b^4 - 3*A*a^4*b^5 + 10*B*a^3*b^6 - 6*A*a^2*b^7)*tan(d*x + c)^2 + 2*(3*B*a^8*b - A*a^7*b^2 + 9*B*a^6*b^3 - 3*A*a^5*b^4 + 10*B*a^4*b^5 - 6*A*a^3*b^6)*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*B*a^9 - A*a^8*b + 9*B*a^7*b^2 - 3*A*a^6*b^3 + 9*B*a^5*b^4 - 3*A*a^4*b^5 + 3*B*a^3*b^6 - A*a^2*b^7 + (3*B*a^7*b^2 - A*a^6*b^3 + 9*B*a^5*b^4 - 3*A*a^4*b^5 + 9*B*a^3*b^6 - 3*A*a^2*b^7 + 3*B*a*b^8 - A*b^9)*tan(d*x + c)^2 + 2*(3*B*a^8*b - A*a^7*b^2 + 9*B*a^6*b^3 - 3*A*a^5*b^4 + 9*B*a^4*b^5 - 3*A*a^3*b^6 + 3*B*a^2*b^7 - A*a*b^8)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(3*B*a^8*b - A*a^7*b^2 + 6*B*a^6*b^3 - 3*A*a^5*b^4 - 2*B*a^4*b^5 + 4*A*a^3*b^6 + B*a^2*b^7 + 2*(A*a^4*b^5 + 3*B*a^3*b^6 - 3*A*a^2*b^7 - B*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
283,1,666,0,0.887395," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{B a^{6} b^{2} + A a^{5} b^{3} + 7 \, B a^{4} b^{4} - 5 \, A a^{3} b^{5} + 2 \, {\left(B a^{5} b^{3} - 3 \, A a^{4} b^{4} - 3 \, B a^{3} b^{5} + A a^{2} b^{6}\right)} d x - {\left(3 \, B a^{6} b^{2} - A a^{5} b^{3} + 9 \, B a^{4} b^{4} - 7 \, A a^{3} b^{5} - 2 \, {\left(B a^{3} b^{5} - 3 \, A a^{2} b^{6} - 3 \, B a b^{7} + A b^{8}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{8} + 3 \, B a^{6} b^{2} + A a^{5} b^{3} + 6 \, B a^{4} b^{4} - 3 \, A a^{3} b^{5} + {\left(B a^{6} b^{2} + 3 \, B a^{4} b^{4} + A a^{3} b^{5} + 6 \, B a^{2} b^{6} - 3 \, A a b^{7}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b + 3 \, B a^{5} b^{3} + A a^{4} b^{4} + 6 \, B a^{3} b^{5} - 3 \, A a^{2} b^{6}\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(B a^{8} + 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} + B a^{2} b^{6} + {\left(B a^{6} b^{2} + 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} + B b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b + 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} + B 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(B a^{7} b + 3 \, B a^{5} b^{3} - 3 \, A a^{4} b^{4} - 4 \, B a^{3} b^{5} + 3 \, A a^{2} b^{6} - 2 \, {\left(B a^{4} b^{4} - 3 \, A a^{3} b^{5} - 3 \, B a^{2} b^{6} + A a b^{7}\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*(B*a^6*b^2 + A*a^5*b^3 + 7*B*a^4*b^4 - 5*A*a^3*b^5 + 2*(B*a^5*b^3 - 3*A*a^4*b^4 - 3*B*a^3*b^5 + A*a^2*b^6)*d*x - (3*B*a^6*b^2 - A*a^5*b^3 + 9*B*a^4*b^4 - 7*A*a^3*b^5 - 2*(B*a^3*b^5 - 3*A*a^2*b^6 - 3*B*a*b^7 + A*b^8)*d*x)*tan(d*x + c)^2 + (B*a^8 + 3*B*a^6*b^2 + A*a^5*b^3 + 6*B*a^4*b^4 - 3*A*a^3*b^5 + (B*a^6*b^2 + 3*B*a^4*b^4 + A*a^3*b^5 + 6*B*a^2*b^6 - 3*A*a*b^7)*tan(d*x + c)^2 + 2*(B*a^7*b + 3*B*a^5*b^3 + A*a^4*b^4 + 6*B*a^3*b^5 - 3*A*a^2*b^6)*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)) - (B*a^8 + 3*B*a^6*b^2 + 3*B*a^4*b^4 + B*a^2*b^6 + (B*a^6*b^2 + 3*B*a^4*b^4 + 3*B*a^2*b^6 + B*b^8)*tan(d*x + c)^2 + 2*(B*a^7*b + 3*B*a^5*b^3 + 3*B*a^3*b^5 + B*a*b^7)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(B*a^7*b + 3*B*a^5*b^3 - 3*A*a^4*b^4 - 4*B*a^3*b^5 + 3*A*a^2*b^6 - 2*(B*a^4*b^4 - 3*A*a^3*b^5 - 3*B*a^2*b^6 + A*a*b^7)*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
284,1,478,0,0.588766," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{B a^{5} - 3 \, A a^{4} b - 5 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3} - 2 \, {\left(A a^{5} + 3 \, B a^{4} b - 3 \, A a^{3} b^{2} - B a^{2} b^{3}\right)} d x + {\left(B a^{5} + A a^{4} b + 7 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3} - 2 \, {\left(A a^{3} b^{2} + 3 \, B a^{2} b^{3} - 3 \, A a b^{4} - B b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{5} - 3 \, A a^{4} b - 3 \, B a^{3} b^{2} + A a^{2} b^{3} + {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3} - 3 \, B a b^{4} + A b^{5}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + A 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 a^{5} + 3 \, B a^{4} b - 3 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + 2 \, A a b^{4} - 2 \, {\left(A a^{4} b + 3 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - B 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*(B*a^5 - 3*A*a^4*b - 5*B*a^3*b^2 + 3*A*a^2*b^3 - 2*(A*a^5 + 3*B*a^4*b - 3*A*a^3*b^2 - B*a^2*b^3)*d*x + (B*a^5 + A*a^4*b + 7*B*a^3*b^2 - 5*A*a^2*b^3 - 2*(A*a^3*b^2 + 3*B*a^2*b^3 - 3*A*a*b^4 - B*b^5)*d*x)*tan(d*x + c)^2 + (B*a^5 - 3*A*a^4*b - 3*B*a^3*b^2 + A*a^2*b^3 + (B*a^3*b^2 - 3*A*a^2*b^3 - 3*B*a*b^4 + A*b^5)*tan(d*x + c)^2 + 2*(B*a^4*b - 3*A*a^3*b^2 - 3*B*a^2*b^3 + A*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*a^5 + 3*B*a^4*b - 3*A*a^3*b^2 - 3*B*a^2*b^3 + 2*A*a*b^4 - 2*(A*a^4*b + 3*B*a^3*b^2 - 3*A*a^2*b^3 - B*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
285,1,488,0,0.828915," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, B a^{4} b - 5 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + A a b^{4} + 2 \, {\left(B a^{5} - 3 \, A a^{4} b - 3 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} d x - {\left(B a^{4} b - 3 \, A a^{3} b^{2} - 5 \, B a^{2} b^{3} + 3 \, A a b^{4} - 2 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3} - 3 \, B a b^{4} + A b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(A a^{5} + 3 \, B a^{4} b - 3 \, A a^{3} b^{2} - B a^{2} b^{3} + {\left(A a^{3} b^{2} + 3 \, B a^{2} b^{3} - 3 \, A a b^{4} - B b^{5}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(A a^{4} b + 3 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - B 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(B a^{5} - 2 \, A a^{4} b - 3 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3} + 2 \, B a b^{4} - A b^{5} - 2 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + A 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*(3*B*a^4*b - 5*A*a^3*b^2 - 3*B*a^2*b^3 + A*a*b^4 + 2*(B*a^5 - 3*A*a^4*b - 3*B*a^3*b^2 + A*a^2*b^3)*d*x - (B*a^4*b - 3*A*a^3*b^2 - 5*B*a^2*b^3 + 3*A*a*b^4 - 2*(B*a^3*b^2 - 3*A*a^2*b^3 - 3*B*a*b^4 + A*b^5)*d*x)*tan(d*x + c)^2 + (A*a^5 + 3*B*a^4*b - 3*A*a^3*b^2 - B*a^2*b^3 + (A*a^3*b^2 + 3*B*a^2*b^3 - 3*A*a*b^4 - B*b^5)*tan(d*x + c)^2 + 2*(A*a^4*b + 3*B*a^3*b^2 - 3*A*a^2*b^3 - B*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*(B*a^5 - 2*A*a^4*b - 3*B*a^3*b^2 + 3*A*a^2*b^3 + 2*B*a*b^4 - A*b^5 - 2*(B*a^4*b - 3*A*a^3*b^2 - 3*B*a^2*b^3 + A*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
286,1,482,0,0.620131," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{5 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3} - B a b^{4} - A b^{5} + 2 \, {\left(A a^{5} + 3 \, B a^{4} b - 3 \, A a^{3} b^{2} - B a^{2} b^{3}\right)} d x - {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3} - 3 \, B a b^{4} + A b^{5} - 2 \, {\left(A a^{3} b^{2} + 3 \, B a^{2} b^{3} - 3 \, A a b^{4} - B b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} - {\left(B a^{5} - 3 \, A a^{4} b - 3 \, B a^{3} b^{2} + A a^{2} b^{3} + {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3} - 3 \, B a b^{4} + A b^{5}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + A 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(2 \, B a^{4} b - 3 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + 3 \, A a b^{4} + B b^{5} - 2 \, {\left(A a^{4} b + 3 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - B 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*B*a^3*b^2 - 7*A*a^2*b^3 - B*a*b^4 - A*b^5 + 2*(A*a^5 + 3*B*a^4*b - 3*A*a^3*b^2 - B*a^2*b^3)*d*x - (3*B*a^3*b^2 - 5*A*a^2*b^3 - 3*B*a*b^4 + A*b^5 - 2*(A*a^3*b^2 + 3*B*a^2*b^3 - 3*A*a*b^4 - B*b^5)*d*x)*tan(d*x + c)^2 - (B*a^5 - 3*A*a^4*b - 3*B*a^3*b^2 + A*a^2*b^3 + (B*a^3*b^2 - 3*A*a^2*b^3 - 3*B*a*b^4 + A*b^5)*tan(d*x + c)^2 + 2*(B*a^4*b - 3*A*a^3*b^2 - 3*B*a^2*b^3 + A*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*(2*B*a^4*b - 3*A*a^3*b^2 - 3*B*a^2*b^3 + 3*A*a*b^4 + B*b^5 - 2*(A*a^4*b + 3*B*a^3*b^2 - 3*A*a^2*b^3 - B*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
287,1,683,0,0.942204," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{7 \, B a^{5} b^{3} - 9 \, A a^{4} b^{4} + B a^{3} b^{5} - 3 \, A a^{2} b^{6} - 2 \, {\left(B a^{8} - 3 \, A a^{7} b - 3 \, B a^{6} b^{2} + A a^{5} b^{3}\right)} d x - {\left(5 \, B a^{5} b^{3} - 7 \, A a^{4} b^{4} - B a^{3} b^{5} - A a^{2} b^{6} + 2 \, {\left(B a^{6} b^{2} - 3 \, A a^{5} b^{3} - 3 \, B a^{4} b^{4} + A a^{3} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} - {\left(A a^{8} + 3 \, A a^{6} b^{2} + 3 \, A a^{4} b^{4} + A a^{2} b^{6} + {\left(A a^{6} b^{2} + 3 \, A a^{4} b^{4} + 3 \, A a^{2} b^{6} + A b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(A a^{7} b + 3 \, A a^{5} b^{3} + 3 \, A a^{3} b^{5} + A 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(3 \, B a^{7} b - 6 \, A a^{6} b^{2} - B a^{5} b^{3} - 3 \, A a^{4} b^{4} - A a^{2} b^{6} + {\left(3 \, B a^{5} b^{3} - 6 \, A a^{4} b^{4} - B a^{3} b^{5} - 3 \, A a^{2} b^{6} - A b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, B a^{6} b^{2} - 6 \, A a^{5} b^{3} - B a^{4} b^{4} - 3 \, A a^{3} b^{5} - A 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(3 \, B a^{6} b^{2} - 4 \, A a^{5} b^{3} - 3 \, B a^{4} b^{4} + 3 \, A a^{3} b^{5} + A a b^{7} + 2 \, {\left(B a^{7} b - 3 \, A a^{6} b^{2} - 3 \, B a^{5} b^{3} + A 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*(7*B*a^5*b^3 - 9*A*a^4*b^4 + B*a^3*b^5 - 3*A*a^2*b^6 - 2*(B*a^8 - 3*A*a^7*b - 3*B*a^6*b^2 + A*a^5*b^3)*d*x - (5*B*a^5*b^3 - 7*A*a^4*b^4 - B*a^3*b^5 - A*a^2*b^6 + 2*(B*a^6*b^2 - 3*A*a^5*b^3 - 3*B*a^4*b^4 + A*a^3*b^5)*d*x)*tan(d*x + c)^2 - (A*a^8 + 3*A*a^6*b^2 + 3*A*a^4*b^4 + A*a^2*b^6 + (A*a^6*b^2 + 3*A*a^4*b^4 + 3*A*a^2*b^6 + A*b^8)*tan(d*x + c)^2 + 2*(A*a^7*b + 3*A*a^5*b^3 + 3*A*a^3*b^5 + A*a*b^7)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - (3*B*a^7*b - 6*A*a^6*b^2 - B*a^5*b^3 - 3*A*a^4*b^4 - A*a^2*b^6 + (3*B*a^5*b^3 - 6*A*a^4*b^4 - B*a^3*b^5 - 3*A*a^2*b^6 - A*b^8)*tan(d*x + c)^2 + 2*(3*B*a^6*b^2 - 6*A*a^5*b^3 - B*a^4*b^4 - 3*A*a^3*b^5 - A*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*(3*B*a^6*b^2 - 4*A*a^5*b^3 - 3*B*a^4*b^4 + 3*A*a^3*b^5 + A*a*b^7 + 2*(B*a^7*b - 3*A*a^6*b^2 - 3*B*a^5*b^3 + A*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
288,1,917,0,1.088728," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, A a^{9} + 6 \, A a^{7} b^{2} + 6 \, A a^{5} b^{4} + 2 \, A a^{3} b^{6} + {\left(7 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} + B a^{3} b^{6} - 3 \, A a^{2} b^{7} + 2 \, {\left(A a^{7} b^{2} + 3 \, B a^{6} b^{3} - 3 \, A a^{5} b^{4} - B a^{4} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(A a^{7} b^{2} + 4 \, B a^{6} b^{3} - 2 \, A a^{5} b^{4} - 3 \, B a^{4} b^{5} + 6 \, A a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8} + 2 \, {\left(A a^{8} b + 3 \, B a^{7} b^{2} - 3 \, A a^{6} b^{3} - B a^{5} b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{2} - {\left({\left(B a^{7} b^{2} - 3 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} + B a b^{8} - 3 \, A b^{9}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(B a^{8} b - 3 \, A a^{7} b^{2} + 3 \, B a^{6} b^{3} - 9 \, A a^{5} b^{4} + 3 \, B a^{4} b^{5} - 9 \, A a^{3} b^{6} + B a^{2} b^{7} - 3 \, A a b^{8}\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{9} - 3 \, A a^{8} b + 3 \, B a^{7} b^{2} - 9 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} + B a^{3} b^{6} - 3 \, A 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(6 \, B a^{5} b^{4} - 10 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} + B a b^{8} - 3 \, A b^{9}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(6 \, B a^{6} b^{3} - 10 \, A a^{5} b^{4} + 3 \, B a^{4} b^{5} - 9 \, A a^{3} b^{6} + B a^{2} b^{7} - 3 \, A a b^{8}\right)} \tan\left(d x + c\right)^{2} + {\left(6 \, B a^{7} b^{2} - 10 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} + B a^{3} b^{6} - 3 \, A 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 a^{8} b + 12 \, A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 23 \, A a^{4} b^{5} - 3 \, B a^{3} b^{6} + 9 \, A a^{2} b^{7} + 2 \, {\left(A a^{9} + 3 \, B a^{8} b - 3 \, A a^{7} b^{2} - B a^{6} b^{3}\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*a^9 + 6*A*a^7*b^2 + 6*A*a^5*b^4 + 2*A*a^3*b^6 + (7*B*a^5*b^4 - 9*A*a^4*b^5 + B*a^3*b^6 - 3*A*a^2*b^7 + 2*(A*a^7*b^2 + 3*B*a^6*b^3 - 3*A*a^5*b^4 - B*a^4*b^5)*d*x)*tan(d*x + c)^3 + 2*(A*a^7*b^2 + 4*B*a^6*b^3 - 2*A*a^5*b^4 - 3*B*a^4*b^5 + 6*A*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8 + 2*(A*a^8*b + 3*B*a^7*b^2 - 3*A*a^6*b^3 - B*a^5*b^4)*d*x)*tan(d*x + c)^2 - ((B*a^7*b^2 - 3*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7 + B*a*b^8 - 3*A*b^9)*tan(d*x + c)^3 + 2*(B*a^8*b - 3*A*a^7*b^2 + 3*B*a^6*b^3 - 9*A*a^5*b^4 + 3*B*a^4*b^5 - 9*A*a^3*b^6 + B*a^2*b^7 - 3*A*a*b^8)*tan(d*x + c)^2 + (B*a^9 - 3*A*a^8*b + 3*B*a^7*b^2 - 9*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 + B*a^3*b^6 - 3*A*a^2*b^7)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + ((6*B*a^5*b^4 - 10*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7 + B*a*b^8 - 3*A*b^9)*tan(d*x + c)^3 + 2*(6*B*a^6*b^3 - 10*A*a^5*b^4 + 3*B*a^4*b^5 - 9*A*a^3*b^6 + B*a^2*b^7 - 3*A*a*b^8)*tan(d*x + c)^2 + (6*B*a^7*b^2 - 10*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 + B*a^3*b^6 - 3*A*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*a^8*b + 12*A*a^6*b^3 - 9*B*a^5*b^4 + 23*A*a^4*b^5 - 3*B*a^3*b^6 + 9*A*a^2*b^7 + 2*(A*a^9 + 3*B*a^8*b - 3*A*a^7*b^2 - B*a^6*b^3)*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
289,1,1065,0,1.152958," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{A a^{10} + 3 \, A a^{8} b^{2} + 3 \, A a^{6} b^{4} + A a^{4} b^{6} + {\left(A a^{8} b^{2} + 3 \, A a^{6} b^{4} - 9 \, B a^{5} b^{5} + 14 \, A a^{4} b^{6} - 3 \, B a^{3} b^{7} + 6 \, A a^{2} b^{8} + 2 \, {\left(B a^{8} b^{2} - 3 \, A a^{7} b^{3} - 3 \, B a^{6} b^{4} + A a^{5} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(A a^{9} b + B a^{8} b^{2} - 2 \, B a^{6} b^{4} + 6 \, B a^{4} b^{6} - 11 \, A a^{3} b^{7} + 3 \, B a^{2} b^{8} - 6 \, A a b^{9} + 2 \, {\left(B a^{9} b - 3 \, A a^{8} b^{2} - 3 \, B a^{7} b^{3} + A a^{6} b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{3} + {\left(A a^{10} + 4 \, B a^{9} b - 8 \, A a^{8} b^{2} + 12 \, B a^{7} b^{3} - 30 \, A a^{6} b^{4} + 23 \, B a^{5} b^{5} - 45 \, A a^{4} b^{6} + 9 \, B a^{3} b^{7} - 18 \, A a^{2} b^{8} + 2 \, {\left(B a^{10} - 3 \, A a^{9} b - 3 \, B a^{8} b^{2} + A a^{7} b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left({\left(A a^{8} b^{2} + 3 \, B a^{7} b^{3} - 3 \, A a^{6} b^{4} + 9 \, B a^{5} b^{5} - 15 \, A a^{4} b^{6} + 9 \, B a^{3} b^{7} - 17 \, A a^{2} b^{8} + 3 \, B a b^{9} - 6 \, A b^{10}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(A a^{9} b + 3 \, B a^{8} b^{2} - 3 \, A a^{7} b^{3} + 9 \, B a^{6} b^{4} - 15 \, A a^{5} b^{5} + 9 \, B a^{4} b^{6} - 17 \, A a^{3} b^{7} + 3 \, B a^{2} b^{8} - 6 \, A a b^{9}\right)} \tan\left(d x + c\right)^{3} + {\left(A a^{10} + 3 \, B a^{9} b - 3 \, A a^{8} b^{2} + 9 \, B a^{7} b^{3} - 15 \, A a^{6} b^{4} + 9 \, B a^{5} b^{5} - 17 \, A a^{4} b^{6} + 3 \, B a^{3} b^{7} - 6 \, A a^{2} b^{8}\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(10 \, B a^{5} b^{5} - 15 \, A a^{4} b^{6} + 9 \, B a^{3} b^{7} - 17 \, A a^{2} b^{8} + 3 \, B a b^{9} - 6 \, A b^{10}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(10 \, B a^{6} b^{4} - 15 \, A a^{5} b^{5} + 9 \, B a^{4} b^{6} - 17 \, A a^{3} b^{7} + 3 \, B a^{2} b^{8} - 6 \, A a b^{9}\right)} \tan\left(d x + c\right)^{3} + {\left(10 \, B a^{7} b^{3} - 15 \, A a^{6} b^{4} + 9 \, B a^{5} b^{5} - 17 \, A a^{4} b^{6} + 3 \, B a^{3} b^{7} - 6 \, A a^{2} b^{8}\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) + 2 \, {\left(B a^{10} - 2 \, A a^{9} b + 3 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} + 3 \, B a^{6} b^{4} - 6 \, A a^{5} b^{5} + B a^{4} b^{6} - 2 \, A a^{3} b^{7}\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{11} b^{2} + 3 \, a^{9} b^{4} + 3 \, a^{7} b^{6} + a^{5} b^{8}\right)} d \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{12} b + 3 \, a^{10} b^{3} + 3 \, a^{8} b^{5} + a^{6} b^{7}\right)} d \tan\left(d x + c\right)^{3} + {\left(a^{13} + 3 \, a^{11} b^{2} + 3 \, a^{9} b^{4} + a^{7} b^{6}\right)} d \tan\left(d x + c\right)^{2}\right)}}"," ",0,"-1/2*(A*a^10 + 3*A*a^8*b^2 + 3*A*a^6*b^4 + A*a^4*b^6 + (A*a^8*b^2 + 3*A*a^6*b^4 - 9*B*a^5*b^5 + 14*A*a^4*b^6 - 3*B*a^3*b^7 + 6*A*a^2*b^8 + 2*(B*a^8*b^2 - 3*A*a^7*b^3 - 3*B*a^6*b^4 + A*a^5*b^5)*d*x)*tan(d*x + c)^4 + 2*(A*a^9*b + B*a^8*b^2 - 2*B*a^6*b^4 + 6*B*a^4*b^6 - 11*A*a^3*b^7 + 3*B*a^2*b^8 - 6*A*a*b^9 + 2*(B*a^9*b - 3*A*a^8*b^2 - 3*B*a^7*b^3 + A*a^6*b^4)*d*x)*tan(d*x + c)^3 + (A*a^10 + 4*B*a^9*b - 8*A*a^8*b^2 + 12*B*a^7*b^3 - 30*A*a^6*b^4 + 23*B*a^5*b^5 - 45*A*a^4*b^6 + 9*B*a^3*b^7 - 18*A*a^2*b^8 + 2*(B*a^10 - 3*A*a^9*b - 3*B*a^8*b^2 + A*a^7*b^3)*d*x)*tan(d*x + c)^2 + ((A*a^8*b^2 + 3*B*a^7*b^3 - 3*A*a^6*b^4 + 9*B*a^5*b^5 - 15*A*a^4*b^6 + 9*B*a^3*b^7 - 17*A*a^2*b^8 + 3*B*a*b^9 - 6*A*b^10)*tan(d*x + c)^4 + 2*(A*a^9*b + 3*B*a^8*b^2 - 3*A*a^7*b^3 + 9*B*a^6*b^4 - 15*A*a^5*b^5 + 9*B*a^4*b^6 - 17*A*a^3*b^7 + 3*B*a^2*b^8 - 6*A*a*b^9)*tan(d*x + c)^3 + (A*a^10 + 3*B*a^9*b - 3*A*a^8*b^2 + 9*B*a^7*b^3 - 15*A*a^6*b^4 + 9*B*a^5*b^5 - 17*A*a^4*b^6 + 3*B*a^3*b^7 - 6*A*a^2*b^8)*tan(d*x + c)^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - ((10*B*a^5*b^5 - 15*A*a^4*b^6 + 9*B*a^3*b^7 - 17*A*a^2*b^8 + 3*B*a*b^9 - 6*A*b^10)*tan(d*x + c)^4 + 2*(10*B*a^6*b^4 - 15*A*a^5*b^5 + 9*B*a^4*b^6 - 17*A*a^3*b^7 + 3*B*a^2*b^8 - 6*A*a*b^9)*tan(d*x + c)^3 + (10*B*a^7*b^3 - 15*A*a^6*b^4 + 9*B*a^5*b^5 - 17*A*a^4*b^6 + 3*B*a^3*b^7 - 6*A*a^2*b^8)*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)) + 2*(B*a^10 - 2*A*a^9*b + 3*B*a^8*b^2 - 6*A*a^7*b^3 + 3*B*a^6*b^4 - 6*A*a^5*b^5 + B*a^4*b^6 - 2*A*a^3*b^7)*tan(d*x + c))/((a^11*b^2 + 3*a^9*b^4 + 3*a^7*b^6 + a^5*b^8)*d*tan(d*x + c)^4 + 2*(a^12*b + 3*a^10*b^3 + 3*a^8*b^5 + a^6*b^7)*d*tan(d*x + c)^3 + (a^13 + 3*a^11*b^2 + 3*a^9*b^4 + a^7*b^6)*d*tan(d*x + c)^2)","B",0
290,1,1113,0,0.863735," ","integrate(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, B a^{9} b^{2} + 6 \, B a^{7} b^{4} + 18 \, A a^{6} b^{5} + 47 \, B a^{5} b^{6} - 26 \, A a^{4} b^{7} - {\left(11 \, B a^{8} b^{3} - 2 \, A a^{7} b^{4} + 42 \, B a^{6} b^{5} - 6 \, A a^{5} b^{6} + 75 \, B a^{4} b^{7} - 48 \, A a^{3} b^{8} - 6 \, {\left(A a^{4} b^{7} + 4 \, B a^{3} b^{8} - 6 \, A a^{2} b^{9} - 4 \, B a b^{10} + A b^{11}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(A a^{7} b^{4} + 4 \, B a^{6} b^{5} - 6 \, A a^{5} b^{6} - 4 \, B a^{4} b^{7} + A a^{3} b^{8}\right)} d x - 3 \, {\left(5 \, B a^{9} b^{2} + 18 \, B a^{7} b^{4} + 2 \, A a^{6} b^{5} + 37 \, B a^{5} b^{6} - 30 \, A a^{4} b^{7} - 20 \, B a^{3} b^{8} + 12 \, A a^{2} b^{9} - 6 \, {\left(A a^{5} b^{6} + 4 \, B a^{4} b^{7} - 6 \, A a^{3} b^{8} - 4 \, B a^{2} b^{9} + A a b^{10}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{11} + 4 \, B a^{9} b^{2} + 5 \, B a^{7} b^{4} + 4 \, A a^{6} b^{5} + 10 \, B a^{5} b^{6} - 4 \, A a^{4} b^{7} + {\left(B a^{8} b^{3} + 4 \, B a^{6} b^{5} + 5 \, B a^{4} b^{7} + 4 \, A a^{3} b^{8} + 10 \, B a^{2} b^{9} - 4 \, A a b^{10}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(B a^{9} b^{2} + 4 \, B a^{7} b^{4} + 5 \, B a^{5} b^{6} + 4 \, A a^{4} b^{7} + 10 \, B a^{3} b^{8} - 4 \, A a^{2} b^{9}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{10} b + 4 \, B a^{8} b^{3} + 5 \, B a^{6} b^{5} + 4 \, A a^{5} b^{6} + 10 \, B a^{4} b^{7} - 4 \, A a^{3} b^{8}\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(B a^{11} + 4 \, B a^{9} b^{2} + 6 \, B a^{7} b^{4} + 4 \, B a^{5} b^{6} + B a^{3} b^{8} + {\left(B a^{8} b^{3} + 4 \, B a^{6} b^{5} + 6 \, B a^{4} b^{7} + 4 \, B a^{2} b^{9} + B b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(B a^{9} b^{2} + 4 \, B a^{7} b^{4} + 6 \, B a^{5} b^{6} + 4 \, B a^{3} b^{8} + B a b^{10}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{10} b + 4 \, B a^{8} b^{3} + 6 \, B a^{6} b^{5} + 4 \, B a^{4} b^{7} + B 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 \, B a^{10} b + 5 \, B a^{8} b^{3} + 2 \, A a^{7} b^{4} + 12 \, B a^{6} b^{5} - 22 \, A a^{5} b^{6} - 35 \, B a^{4} b^{7} + 20 \, A a^{3} b^{8} - 6 \, {\left(A a^{6} b^{5} + 4 \, B a^{5} b^{6} - 6 \, A a^{4} b^{7} - 4 \, B a^{3} b^{8} + A a^{2} b^{9}\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*B*a^9*b^2 + 6*B*a^7*b^4 + 18*A*a^6*b^5 + 47*B*a^5*b^6 - 26*A*a^4*b^7 - (11*B*a^8*b^3 - 2*A*a^7*b^4 + 42*B*a^6*b^5 - 6*A*a^5*b^6 + 75*B*a^4*b^7 - 48*A*a^3*b^8 - 6*(A*a^4*b^7 + 4*B*a^3*b^8 - 6*A*a^2*b^9 - 4*B*a*b^10 + A*b^11)*d*x)*tan(d*x + c)^3 + 6*(A*a^7*b^4 + 4*B*a^6*b^5 - 6*A*a^5*b^6 - 4*B*a^4*b^7 + A*a^3*b^8)*d*x - 3*(5*B*a^9*b^2 + 18*B*a^7*b^4 + 2*A*a^6*b^5 + 37*B*a^5*b^6 - 30*A*a^4*b^7 - 20*B*a^3*b^8 + 12*A*a^2*b^9 - 6*(A*a^5*b^6 + 4*B*a^4*b^7 - 6*A*a^3*b^8 - 4*B*a^2*b^9 + A*a*b^10)*d*x)*tan(d*x + c)^2 + 3*(B*a^11 + 4*B*a^9*b^2 + 5*B*a^7*b^4 + 4*A*a^6*b^5 + 10*B*a^5*b^6 - 4*A*a^4*b^7 + (B*a^8*b^3 + 4*B*a^6*b^5 + 5*B*a^4*b^7 + 4*A*a^3*b^8 + 10*B*a^2*b^9 - 4*A*a*b^10)*tan(d*x + c)^3 + 3*(B*a^9*b^2 + 4*B*a^7*b^4 + 5*B*a^5*b^6 + 4*A*a^4*b^7 + 10*B*a^3*b^8 - 4*A*a^2*b^9)*tan(d*x + c)^2 + 3*(B*a^10*b + 4*B*a^8*b^3 + 5*B*a^6*b^5 + 4*A*a^5*b^6 + 10*B*a^4*b^7 - 4*A*a^3*b^8)*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*(B*a^11 + 4*B*a^9*b^2 + 6*B*a^7*b^4 + 4*B*a^5*b^6 + B*a^3*b^8 + (B*a^8*b^3 + 4*B*a^6*b^5 + 6*B*a^4*b^7 + 4*B*a^2*b^9 + B*b^11)*tan(d*x + c)^3 + 3*(B*a^9*b^2 + 4*B*a^7*b^4 + 6*B*a^5*b^6 + 4*B*a^3*b^8 + B*a*b^10)*tan(d*x + c)^2 + 3*(B*a^10*b + 4*B*a^8*b^3 + 6*B*a^6*b^5 + 4*B*a^4*b^7 + B*a^2*b^9)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 3*(2*B*a^10*b + 5*B*a^8*b^3 + 2*A*a^7*b^4 + 12*B*a^6*b^5 - 22*A*a^5*b^6 - 35*B*a^4*b^7 + 20*A*a^3*b^8 - 6*(A*a^6*b^5 + 4*B*a^5*b^6 - 6*A*a^4*b^7 - 4*B*a^3*b^8 + A*a^2*b^9)*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
291,1,813,0,0.766857," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, A a^{7} + 18 \, B a^{6} b - 30 \, A a^{5} b^{2} - 26 \, B a^{4} b^{3} + 11 \, A a^{3} b^{4} + {\left(2 \, B a^{7} + A a^{6} b + 6 \, B a^{5} b^{2} + 18 \, A a^{4} b^{3} + 48 \, B a^{3} b^{4} - 27 \, A a^{2} b^{5} + 6 \, {\left(B a^{4} b^{3} - 4 \, A a^{3} b^{4} - 6 \, B a^{2} b^{5} + 4 \, A a b^{6} + B b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(B a^{7} - 4 \, A a^{6} b - 6 \, B a^{5} b^{2} + 4 \, A a^{4} b^{3} + B a^{3} b^{4}\right)} d x + 3 \, {\left(A a^{7} - 2 \, B a^{6} b + 16 \, A a^{5} b^{2} + 30 \, B a^{4} b^{3} - 23 \, A a^{3} b^{4} - 12 \, B a^{2} b^{5} + 6 \, A a b^{6} + 6 \, {\left(B a^{5} b^{2} - 4 \, A a^{4} b^{3} - 6 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} + B a b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(A a^{7} + 4 \, B a^{6} b - 6 \, A a^{5} b^{2} - 4 \, B a^{4} b^{3} + A a^{3} b^{4} + {\left(A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 6 \, A a^{2} b^{5} - 4 \, B a b^{6} + A b^{7}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(A a^{5} b^{2} + 4 \, B a^{4} b^{3} - 6 \, A a^{3} b^{4} - 4 \, B a^{2} b^{5} + A a b^{6}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(A a^{6} b + 4 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} - 4 \, B a^{3} b^{4} + A 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(2 \, B a^{7} - 9 \, A a^{6} b - 22 \, B a^{5} b^{2} + 26 \, A a^{4} b^{3} + 20 \, B a^{3} b^{4} - 9 \, A a^{2} b^{5} - 6 \, {\left(B a^{6} b - 4 \, A a^{5} b^{2} - 6 \, B a^{4} b^{3} + 4 \, A a^{3} b^{4} + B a^{2} b^{5}\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*a^7 + 18*B*a^6*b - 30*A*a^5*b^2 - 26*B*a^4*b^3 + 11*A*a^3*b^4 + (2*B*a^7 + A*a^6*b + 6*B*a^5*b^2 + 18*A*a^4*b^3 + 48*B*a^3*b^4 - 27*A*a^2*b^5 + 6*(B*a^4*b^3 - 4*A*a^3*b^4 - 6*B*a^2*b^5 + 4*A*a*b^6 + B*b^7)*d*x)*tan(d*x + c)^3 + 6*(B*a^7 - 4*A*a^6*b - 6*B*a^5*b^2 + 4*A*a^4*b^3 + B*a^3*b^4)*d*x + 3*(A*a^7 - 2*B*a^6*b + 16*A*a^5*b^2 + 30*B*a^4*b^3 - 23*A*a^3*b^4 - 12*B*a^2*b^5 + 6*A*a*b^6 + 6*(B*a^5*b^2 - 4*A*a^4*b^3 - 6*B*a^3*b^4 + 4*A*a^2*b^5 + B*a*b^6)*d*x)*tan(d*x + c)^2 + 3*(A*a^7 + 4*B*a^6*b - 6*A*a^5*b^2 - 4*B*a^4*b^3 + A*a^3*b^4 + (A*a^4*b^3 + 4*B*a^3*b^4 - 6*A*a^2*b^5 - 4*B*a*b^6 + A*b^7)*tan(d*x + c)^3 + 3*(A*a^5*b^2 + 4*B*a^4*b^3 - 6*A*a^3*b^4 - 4*B*a^2*b^5 + A*a*b^6)*tan(d*x + c)^2 + 3*(A*a^6*b + 4*B*a^5*b^2 - 6*A*a^4*b^3 - 4*B*a^3*b^4 + A*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*(2*B*a^7 - 9*A*a^6*b - 22*B*a^5*b^2 + 26*A*a^4*b^3 + 20*B*a^3*b^4 - 9*A*a^2*b^5 - 6*(B*a^6*b - 4*A*a^5*b^2 - 6*B*a^4*b^3 + 4*A*a^3*b^4 + B*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
292,1,836,0,0.846199," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, B a^{7} - 12 \, A a^{6} b - 30 \, B a^{5} b^{2} + 30 \, A a^{4} b^{3} + 11 \, B a^{3} b^{4} - 2 \, A a^{2} b^{5} + {\left(B a^{6} b + 2 \, A a^{5} b^{2} + 18 \, B a^{4} b^{3} - 30 \, A a^{3} b^{4} - 27 \, B a^{2} b^{5} + 12 \, A a b^{6} - 6 \, {\left(A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 6 \, A a^{2} b^{5} - 4 \, B a b^{6} + A b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(A a^{7} + 4 \, B a^{6} b - 6 \, A a^{5} b^{2} - 4 \, B a^{4} b^{3} + A a^{3} b^{4}\right)} d x + 3 \, {\left(B a^{7} + 2 \, A a^{6} b + 16 \, B a^{5} b^{2} - 24 \, A a^{4} b^{3} - 23 \, B a^{3} b^{4} + 16 \, A a^{2} b^{5} + 6 \, B a b^{6} - 2 \, A b^{7} - 6 \, {\left(A a^{5} b^{2} + 4 \, B a^{4} b^{3} - 6 \, A a^{3} b^{4} - 4 \, B a^{2} b^{5} + A a b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{7} - 4 \, A a^{6} b - 6 \, B a^{5} b^{2} + 4 \, A a^{4} b^{3} + B a^{3} b^{4} + {\left(B a^{4} b^{3} - 4 \, A a^{3} b^{4} - 6 \, B a^{2} b^{5} + 4 \, A a b^{6} + B b^{7}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(B a^{5} b^{2} - 4 \, A a^{4} b^{3} - 6 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} + B a b^{6}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{6} b - 4 \, A a^{5} b^{2} - 6 \, B a^{4} b^{3} + 4 \, A a^{3} b^{4} + B 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(2 \, A a^{7} + 9 \, B a^{6} b - 16 \, A a^{5} b^{2} - 26 \, B a^{4} b^{3} + 24 \, A a^{3} b^{4} + 9 \, B a^{2} b^{5} - 2 \, A a b^{6} - 6 \, {\left(A a^{6} b + 4 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} - 4 \, B a^{3} b^{4} + A a^{2} b^{5}\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*B*a^7 - 12*A*a^6*b - 30*B*a^5*b^2 + 30*A*a^4*b^3 + 11*B*a^3*b^4 - 2*A*a^2*b^5 + (B*a^6*b + 2*A*a^5*b^2 + 18*B*a^4*b^3 - 30*A*a^3*b^4 - 27*B*a^2*b^5 + 12*A*a*b^6 - 6*(A*a^4*b^3 + 4*B*a^3*b^4 - 6*A*a^2*b^5 - 4*B*a*b^6 + A*b^7)*d*x)*tan(d*x + c)^3 - 6*(A*a^7 + 4*B*a^6*b - 6*A*a^5*b^2 - 4*B*a^4*b^3 + A*a^3*b^4)*d*x + 3*(B*a^7 + 2*A*a^6*b + 16*B*a^5*b^2 - 24*A*a^4*b^3 - 23*B*a^3*b^4 + 16*A*a^2*b^5 + 6*B*a*b^6 - 2*A*b^7 - 6*(A*a^5*b^2 + 4*B*a^4*b^3 - 6*A*a^3*b^4 - 4*B*a^2*b^5 + A*a*b^6)*d*x)*tan(d*x + c)^2 + 3*(B*a^7 - 4*A*a^6*b - 6*B*a^5*b^2 + 4*A*a^4*b^3 + B*a^3*b^4 + (B*a^4*b^3 - 4*A*a^3*b^4 - 6*B*a^2*b^5 + 4*A*a*b^6 + B*b^7)*tan(d*x + c)^3 + 3*(B*a^5*b^2 - 4*A*a^4*b^3 - 6*B*a^3*b^4 + 4*A*a^2*b^5 + B*a*b^6)*tan(d*x + c)^2 + 3*(B*a^6*b - 4*A*a^5*b^2 - 6*B*a^4*b^3 + 4*A*a^3*b^4 + B*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*(2*A*a^7 + 9*B*a^6*b - 16*A*a^5*b^2 - 26*B*a^4*b^3 + 24*A*a^3*b^4 + 9*B*a^2*b^5 - 2*A*a*b^6 - 6*(A*a^6*b + 4*B*a^5*b^2 - 6*A*a^4*b^3 - 4*B*a^3*b^4 + A*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
293,1,838,0,0.832479," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{12 \, B a^{6} b - 27 \, A a^{5} b^{2} - 30 \, B a^{4} b^{3} + 18 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} + A a b^{6} - {\left(2 \, B a^{5} b^{2} - 11 \, A a^{4} b^{3} - 30 \, B a^{3} b^{4} + 30 \, A a^{2} b^{5} + 12 \, B a b^{6} - 3 \, A b^{7} - 6 \, {\left(B a^{4} b^{3} - 4 \, A a^{3} b^{4} - 6 \, B a^{2} b^{5} + 4 \, A a b^{6} + B b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(B a^{7} - 4 \, A a^{6} b - 6 \, B a^{5} b^{2} + 4 \, A a^{4} b^{3} + B a^{3} b^{4}\right)} d x - 3 \, {\left(2 \, B a^{6} b - 9 \, A a^{5} b^{2} - 24 \, B a^{4} b^{3} + 26 \, A a^{3} b^{4} + 16 \, B a^{2} b^{5} - 9 \, A a b^{6} - 2 \, B b^{7} - 6 \, {\left(B a^{5} b^{2} - 4 \, A a^{4} b^{3} - 6 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} + B a b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(A a^{7} + 4 \, B a^{6} b - 6 \, A a^{5} b^{2} - 4 \, B a^{4} b^{3} + A a^{3} b^{4} + {\left(A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 6 \, A a^{2} b^{5} - 4 \, B a b^{6} + A b^{7}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(A a^{5} b^{2} + 4 \, B a^{4} b^{3} - 6 \, A a^{3} b^{4} - 4 \, B a^{2} b^{5} + A a b^{6}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(A a^{6} b + 4 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} - 4 \, B a^{3} b^{4} + A 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(2 \, B a^{7} - 6 \, A a^{6} b - 16 \, B a^{5} b^{2} + 23 \, A a^{4} b^{3} + 24 \, B a^{3} b^{4} - 16 \, A a^{2} b^{5} - 2 \, B a b^{6} - A b^{7} - 6 \, {\left(B a^{6} b - 4 \, A a^{5} b^{2} - 6 \, B a^{4} b^{3} + 4 \, A a^{3} b^{4} + B a^{2} b^{5}\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*(12*B*a^6*b - 27*A*a^5*b^2 - 30*B*a^4*b^3 + 18*A*a^3*b^4 + 2*B*a^2*b^5 + A*a*b^6 - (2*B*a^5*b^2 - 11*A*a^4*b^3 - 30*B*a^3*b^4 + 30*A*a^2*b^5 + 12*B*a*b^6 - 3*A*b^7 - 6*(B*a^4*b^3 - 4*A*a^3*b^4 - 6*B*a^2*b^5 + 4*A*a*b^6 + B*b^7)*d*x)*tan(d*x + c)^3 + 6*(B*a^7 - 4*A*a^6*b - 6*B*a^5*b^2 + 4*A*a^4*b^3 + B*a^3*b^4)*d*x - 3*(2*B*a^6*b - 9*A*a^5*b^2 - 24*B*a^4*b^3 + 26*A*a^3*b^4 + 16*B*a^2*b^5 - 9*A*a*b^6 - 2*B*b^7 - 6*(B*a^5*b^2 - 4*A*a^4*b^3 - 6*B*a^3*b^4 + 4*A*a^2*b^5 + B*a*b^6)*d*x)*tan(d*x + c)^2 + 3*(A*a^7 + 4*B*a^6*b - 6*A*a^5*b^2 - 4*B*a^4*b^3 + A*a^3*b^4 + (A*a^4*b^3 + 4*B*a^3*b^4 - 6*A*a^2*b^5 - 4*B*a*b^6 + A*b^7)*tan(d*x + c)^3 + 3*(A*a^5*b^2 + 4*B*a^4*b^3 - 6*A*a^3*b^4 - 4*B*a^2*b^5 + A*a*b^6)*tan(d*x + c)^2 + 3*(A*a^6*b + 4*B*a^5*b^2 - 6*A*a^4*b^3 - 4*B*a^3*b^4 + A*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*(2*B*a^7 - 6*A*a^6*b - 16*B*a^5*b^2 + 23*A*a^4*b^3 + 24*B*a^3*b^4 - 16*A*a^2*b^5 - 2*B*a*b^6 - A*b^7 - 6*(B*a^6*b - 4*A*a^5*b^2 - 6*B*a^4*b^3 + 4*A*a^3*b^4 + B*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
294,1,815,0,0.618427," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{27 \, B a^{5} b^{2} - 48 \, A a^{4} b^{3} - 18 \, B a^{3} b^{4} - 6 \, A a^{2} b^{5} - B a b^{6} - 2 \, A b^{7} - {\left(11 \, B a^{4} b^{3} - 26 \, A a^{3} b^{4} - 30 \, B a^{2} b^{5} + 18 \, A a b^{6} + 3 \, B b^{7} - 6 \, {\left(A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 6 \, A a^{2} b^{5} - 4 \, B a b^{6} + A b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(A a^{7} + 4 \, B a^{6} b - 6 \, A a^{5} b^{2} - 4 \, B a^{4} b^{3} + A a^{3} b^{4}\right)} d x - 3 \, {\left(9 \, B a^{5} b^{2} - 20 \, A a^{4} b^{3} - 26 \, B a^{3} b^{4} + 22 \, A a^{2} b^{5} + 9 \, B a b^{6} - 2 \, A b^{7} - 6 \, {\left(A a^{5} b^{2} + 4 \, B a^{4} b^{3} - 6 \, A a^{3} b^{4} - 4 \, B a^{2} b^{5} + A a b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(B a^{7} - 4 \, A a^{6} b - 6 \, B a^{5} b^{2} + 4 \, A a^{4} b^{3} + B a^{3} b^{4} + {\left(B a^{4} b^{3} - 4 \, A a^{3} b^{4} - 6 \, B a^{2} b^{5} + 4 \, A a b^{6} + B b^{7}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(B a^{5} b^{2} - 4 \, A a^{4} b^{3} - 6 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} + B a b^{6}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{6} b - 4 \, A a^{5} b^{2} - 6 \, B a^{4} b^{3} + 4 \, A a^{3} b^{4} + B 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 \, B a^{6} b - 12 \, A a^{5} b^{2} - 23 \, B a^{4} b^{3} + 30 \, A a^{3} b^{4} + 16 \, B a^{2} b^{5} - 2 \, A a b^{6} + B b^{7} - 6 \, {\left(A a^{6} b + 4 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} - 4 \, B a^{3} b^{4} + A a^{2} b^{5}\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*B*a^5*b^2 - 48*A*a^4*b^3 - 18*B*a^3*b^4 - 6*A*a^2*b^5 - B*a*b^6 - 2*A*b^7 - (11*B*a^4*b^3 - 26*A*a^3*b^4 - 30*B*a^2*b^5 + 18*A*a*b^6 + 3*B*b^7 - 6*(A*a^4*b^3 + 4*B*a^3*b^4 - 6*A*a^2*b^5 - 4*B*a*b^6 + A*b^7)*d*x)*tan(d*x + c)^3 + 6*(A*a^7 + 4*B*a^6*b - 6*A*a^5*b^2 - 4*B*a^4*b^3 + A*a^3*b^4)*d*x - 3*(9*B*a^5*b^2 - 20*A*a^4*b^3 - 26*B*a^3*b^4 + 22*A*a^2*b^5 + 9*B*a*b^6 - 2*A*b^7 - 6*(A*a^5*b^2 + 4*B*a^4*b^3 - 6*A*a^3*b^4 - 4*B*a^2*b^5 + A*a*b^6)*d*x)*tan(d*x + c)^2 - 3*(B*a^7 - 4*A*a^6*b - 6*B*a^5*b^2 + 4*A*a^4*b^3 + B*a^3*b^4 + (B*a^4*b^3 - 4*A*a^3*b^4 - 6*B*a^2*b^5 + 4*A*a*b^6 + B*b^7)*tan(d*x + c)^3 + 3*(B*a^5*b^2 - 4*A*a^4*b^3 - 6*B*a^3*b^4 + 4*A*a^2*b^5 + B*a*b^6)*tan(d*x + c)^2 + 3*(B*a^6*b - 4*A*a^5*b^2 - 6*B*a^4*b^3 + 4*A*a^3*b^4 + B*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*B*a^6*b - 12*A*a^5*b^2 - 23*B*a^4*b^3 + 30*A*a^3*b^4 + 16*B*a^2*b^5 - 2*A*a*b^6 + B*b^7 - 6*(A*a^6*b + 4*B*a^5*b^2 - 6*A*a^4*b^3 - 4*B*a^3*b^4 + A*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
295,1,1126,0,0.949044," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{48 \, B a^{8} b^{3} - 75 \, A a^{7} b^{4} + 6 \, B a^{6} b^{5} - 42 \, A a^{5} b^{6} + 2 \, B a^{4} b^{7} - 11 \, A a^{3} b^{8} - {\left(26 \, B a^{7} b^{4} - 47 \, A a^{6} b^{5} - 18 \, B a^{5} b^{6} - 6 \, A a^{4} b^{7} - 3 \, A a^{2} b^{9} + 6 \, {\left(B a^{8} b^{3} - 4 \, A a^{7} b^{4} - 6 \, B a^{6} b^{5} + 4 \, A a^{5} b^{6} + B a^{4} b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(B a^{11} - 4 \, A a^{10} b - 6 \, B a^{9} b^{2} + 4 \, A a^{8} b^{3} + B a^{7} b^{4}\right)} d x - 3 \, {\left(20 \, B a^{8} b^{3} - 35 \, A a^{7} b^{4} - 22 \, B a^{6} b^{5} + 12 \, A a^{5} b^{6} + 2 \, B a^{4} b^{7} + 5 \, A a^{3} b^{8} + 2 \, A a b^{10} + 6 \, {\left(B a^{9} b^{2} - 4 \, A a^{8} b^{3} - 6 \, B a^{7} b^{4} + 4 \, A a^{6} b^{5} + B a^{5} b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(A a^{11} + 4 \, A a^{9} b^{2} + 6 \, A a^{7} b^{4} + 4 \, A a^{5} b^{6} + A a^{3} b^{8} + {\left(A a^{8} b^{3} + 4 \, A a^{6} b^{5} + 6 \, A a^{4} b^{7} + 4 \, A a^{2} b^{9} + A b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(A a^{9} b^{2} + 4 \, A a^{7} b^{4} + 6 \, A a^{5} b^{6} + 4 \, A a^{3} b^{8} + A a b^{10}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(A a^{10} b + 4 \, A a^{8} b^{3} + 6 \, A a^{6} b^{5} + 4 \, A a^{4} b^{7} + A 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(4 \, B a^{10} b - 10 \, A a^{9} b^{2} - 4 \, B a^{8} b^{3} - 5 \, A a^{7} b^{4} - 4 \, A a^{5} b^{6} - A a^{3} b^{8} + {\left(4 \, B a^{7} b^{4} - 10 \, A a^{6} b^{5} - 4 \, B a^{5} b^{6} - 5 \, A a^{4} b^{7} - 4 \, A a^{2} b^{9} - A b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(4 \, B a^{8} b^{3} - 10 \, A a^{7} b^{4} - 4 \, B a^{6} b^{5} - 5 \, A a^{5} b^{6} - 4 \, A a^{3} b^{8} - A a b^{10}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(4 \, B a^{9} b^{2} - 10 \, A a^{8} b^{3} - 4 \, B a^{7} b^{4} - 5 \, A a^{6} b^{5} - 4 \, A a^{4} b^{7} - A 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(12 \, B a^{9} b^{2} - 20 \, A a^{8} b^{3} - 30 \, B a^{7} b^{4} + 37 \, A a^{6} b^{5} + 2 \, B a^{5} b^{6} + 18 \, A a^{4} b^{7} + 5 \, A a^{2} b^{9} + 6 \, {\left(B a^{10} b - 4 \, A a^{9} b^{2} - 6 \, B a^{8} b^{3} + 4 \, A a^{7} b^{4} + B a^{6} b^{5}\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*(48*B*a^8*b^3 - 75*A*a^7*b^4 + 6*B*a^6*b^5 - 42*A*a^5*b^6 + 2*B*a^4*b^7 - 11*A*a^3*b^8 - (26*B*a^7*b^4 - 47*A*a^6*b^5 - 18*B*a^5*b^6 - 6*A*a^4*b^7 - 3*A*a^2*b^9 + 6*(B*a^8*b^3 - 4*A*a^7*b^4 - 6*B*a^6*b^5 + 4*A*a^5*b^6 + B*a^4*b^7)*d*x)*tan(d*x + c)^3 - 6*(B*a^11 - 4*A*a^10*b - 6*B*a^9*b^2 + 4*A*a^8*b^3 + B*a^7*b^4)*d*x - 3*(20*B*a^8*b^3 - 35*A*a^7*b^4 - 22*B*a^6*b^5 + 12*A*a^5*b^6 + 2*B*a^4*b^7 + 5*A*a^3*b^8 + 2*A*a*b^10 + 6*(B*a^9*b^2 - 4*A*a^8*b^3 - 6*B*a^7*b^4 + 4*A*a^6*b^5 + B*a^5*b^6)*d*x)*tan(d*x + c)^2 - 3*(A*a^11 + 4*A*a^9*b^2 + 6*A*a^7*b^4 + 4*A*a^5*b^6 + A*a^3*b^8 + (A*a^8*b^3 + 4*A*a^6*b^5 + 6*A*a^4*b^7 + 4*A*a^2*b^9 + A*b^11)*tan(d*x + c)^3 + 3*(A*a^9*b^2 + 4*A*a^7*b^4 + 6*A*a^5*b^6 + 4*A*a^3*b^8 + A*a*b^10)*tan(d*x + c)^2 + 3*(A*a^10*b + 4*A*a^8*b^3 + 6*A*a^6*b^5 + 4*A*a^4*b^7 + A*a^2*b^9)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - 3*(4*B*a^10*b - 10*A*a^9*b^2 - 4*B*a^8*b^3 - 5*A*a^7*b^4 - 4*A*a^5*b^6 - A*a^3*b^8 + (4*B*a^7*b^4 - 10*A*a^6*b^5 - 4*B*a^5*b^6 - 5*A*a^4*b^7 - 4*A*a^2*b^9 - A*b^11)*tan(d*x + c)^3 + 3*(4*B*a^8*b^3 - 10*A*a^7*b^4 - 4*B*a^6*b^5 - 5*A*a^5*b^6 - 4*A*a^3*b^8 - A*a*b^10)*tan(d*x + c)^2 + 3*(4*B*a^9*b^2 - 10*A*a^8*b^3 - 4*B*a^7*b^4 - 5*A*a^6*b^5 - 4*A*a^4*b^7 - A*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*(12*B*a^9*b^2 - 20*A*a^8*b^3 - 30*B*a^7*b^4 + 37*A*a^6*b^5 + 2*B*a^5*b^6 + 18*A*a^4*b^7 + 5*A*a^2*b^9 + 6*(B*a^10*b - 4*A*a^9*b^2 - 6*B*a^8*b^3 + 4*A*a^7*b^4 + B*a^6*b^5)*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
296,1,1510,0,1.300607," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{6 \, A a^{12} + 24 \, A a^{10} b^{2} + 36 \, A a^{8} b^{4} + 24 \, A a^{6} b^{6} + 6 \, A a^{4} b^{8} + {\left(47 \, B a^{7} b^{5} - 74 \, A a^{6} b^{6} + 6 \, B a^{5} b^{7} - 42 \, A a^{4} b^{8} + 3 \, B a^{3} b^{9} - 12 \, A a^{2} b^{10} + 6 \, {\left(A a^{9} b^{3} + 4 \, B a^{8} b^{4} - 6 \, A a^{7} b^{5} - 4 \, B a^{6} b^{6} + A a^{5} b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(2 \, A a^{9} b^{3} + 35 \, B a^{8} b^{4} - 46 \, A a^{7} b^{5} - 12 \, B a^{6} b^{6} + 8 \, A a^{5} b^{7} - 5 \, B a^{4} b^{8} + 20 \, A a^{3} b^{9} - 2 \, B a^{2} b^{10} + 8 \, A a b^{11} + 6 \, {\left(A a^{10} b^{2} + 4 \, B a^{9} b^{3} - 6 \, A a^{8} b^{4} - 4 \, B a^{7} b^{5} + A a^{6} b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(6 \, A a^{10} b^{2} + 20 \, B a^{9} b^{3} - 6 \, A a^{8} b^{4} - 37 \, B a^{7} b^{5} + 80 \, A a^{6} b^{6} - 18 \, B a^{5} b^{7} + 68 \, A a^{4} b^{8} - 5 \, B a^{3} b^{9} + 20 \, A a^{2} b^{10} + 6 \, {\left(A a^{11} b + 4 \, B a^{10} b^{2} - 6 \, A a^{9} b^{3} - 4 \, B a^{8} b^{4} + A a^{7} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left({\left(B a^{9} b^{3} - 4 \, A a^{8} b^{4} + 4 \, B a^{7} b^{5} - 16 \, A a^{6} b^{6} + 6 \, B a^{5} b^{7} - 24 \, A a^{4} b^{8} + 4 \, B a^{3} b^{9} - 16 \, A a^{2} b^{10} + B a b^{11} - 4 \, A b^{12}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(B a^{10} b^{2} - 4 \, A a^{9} b^{3} + 4 \, B a^{8} b^{4} - 16 \, A a^{7} b^{5} + 6 \, B a^{6} b^{6} - 24 \, A a^{5} b^{7} + 4 \, B a^{4} b^{8} - 16 \, A a^{3} b^{9} + B a^{2} b^{10} - 4 \, A a b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(B a^{11} b - 4 \, A a^{10} b^{2} + 4 \, B a^{9} b^{3} - 16 \, A a^{8} b^{4} + 6 \, B a^{7} b^{5} - 24 \, A a^{6} b^{6} + 4 \, B a^{5} b^{7} - 16 \, A a^{4} b^{8} + B a^{3} b^{9} - 4 \, A a^{2} b^{10}\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{12} - 4 \, A a^{11} b + 4 \, B a^{10} b^{2} - 16 \, A a^{9} b^{3} + 6 \, B a^{8} b^{4} - 24 \, A a^{7} b^{5} + 4 \, B a^{6} b^{6} - 16 \, A a^{5} b^{7} + B a^{4} b^{8} - 4 \, A 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) + 3 \, {\left({\left(10 \, B a^{7} b^{5} - 20 \, A a^{6} b^{6} + 5 \, B a^{5} b^{7} - 24 \, A a^{4} b^{8} + 4 \, B a^{3} b^{9} - 16 \, A a^{2} b^{10} + B a b^{11} - 4 \, A b^{12}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(10 \, B a^{8} b^{4} - 20 \, A a^{7} b^{5} + 5 \, B a^{6} b^{6} - 24 \, A a^{5} b^{7} + 4 \, B a^{4} b^{8} - 16 \, A a^{3} b^{9} + B a^{2} b^{10} - 4 \, A a b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(10 \, B a^{9} b^{3} - 20 \, A a^{8} b^{4} + 5 \, B a^{7} b^{5} - 24 \, A a^{6} b^{6} + 4 \, B a^{5} b^{7} - 16 \, A a^{4} b^{8} + B a^{3} b^{9} - 4 \, A a^{2} b^{10}\right)} \tan\left(d x + c\right)^{2} + {\left(10 \, B a^{10} b^{2} - 20 \, A a^{9} b^{3} + 5 \, B a^{8} b^{4} - 24 \, A a^{7} b^{5} + 4 \, B a^{6} b^{6} - 16 \, A a^{5} b^{7} + B a^{4} b^{8} - 4 \, A 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(18 \, A a^{11} b + 72 \, A a^{9} b^{3} - 75 \, B a^{8} b^{4} + 216 \, A a^{7} b^{5} - 42 \, B a^{6} b^{6} + 162 \, A a^{5} b^{7} - 11 \, B a^{4} b^{8} + 44 \, A a^{3} b^{9} + 6 \, {\left(A a^{12} + 4 \, B a^{11} b - 6 \, A a^{10} b^{2} - 4 \, B a^{9} b^{3} + A a^{8} b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{6 \, {\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,"-1/6*(6*A*a^12 + 24*A*a^10*b^2 + 36*A*a^8*b^4 + 24*A*a^6*b^6 + 6*A*a^4*b^8 + (47*B*a^7*b^5 - 74*A*a^6*b^6 + 6*B*a^5*b^7 - 42*A*a^4*b^8 + 3*B*a^3*b^9 - 12*A*a^2*b^10 + 6*(A*a^9*b^3 + 4*B*a^8*b^4 - 6*A*a^7*b^5 - 4*B*a^6*b^6 + A*a^5*b^7)*d*x)*tan(d*x + c)^4 + 3*(2*A*a^9*b^3 + 35*B*a^8*b^4 - 46*A*a^7*b^5 - 12*B*a^6*b^6 + 8*A*a^5*b^7 - 5*B*a^4*b^8 + 20*A*a^3*b^9 - 2*B*a^2*b^10 + 8*A*a*b^11 + 6*(A*a^10*b^2 + 4*B*a^9*b^3 - 6*A*a^8*b^4 - 4*B*a^7*b^5 + A*a^6*b^6)*d*x)*tan(d*x + c)^3 + 3*(6*A*a^10*b^2 + 20*B*a^9*b^3 - 6*A*a^8*b^4 - 37*B*a^7*b^5 + 80*A*a^6*b^6 - 18*B*a^5*b^7 + 68*A*a^4*b^8 - 5*B*a^3*b^9 + 20*A*a^2*b^10 + 6*(A*a^11*b + 4*B*a^10*b^2 - 6*A*a^9*b^3 - 4*B*a^8*b^4 + A*a^7*b^5)*d*x)*tan(d*x + c)^2 - 3*((B*a^9*b^3 - 4*A*a^8*b^4 + 4*B*a^7*b^5 - 16*A*a^6*b^6 + 6*B*a^5*b^7 - 24*A*a^4*b^8 + 4*B*a^3*b^9 - 16*A*a^2*b^10 + B*a*b^11 - 4*A*b^12)*tan(d*x + c)^4 + 3*(B*a^10*b^2 - 4*A*a^9*b^3 + 4*B*a^8*b^4 - 16*A*a^7*b^5 + 6*B*a^6*b^6 - 24*A*a^5*b^7 + 4*B*a^4*b^8 - 16*A*a^3*b^9 + B*a^2*b^10 - 4*A*a*b^11)*tan(d*x + c)^3 + 3*(B*a^11*b - 4*A*a^10*b^2 + 4*B*a^9*b^3 - 16*A*a^8*b^4 + 6*B*a^7*b^5 - 24*A*a^6*b^6 + 4*B*a^5*b^7 - 16*A*a^4*b^8 + B*a^3*b^9 - 4*A*a^2*b^10)*tan(d*x + c)^2 + (B*a^12 - 4*A*a^11*b + 4*B*a^10*b^2 - 16*A*a^9*b^3 + 6*B*a^8*b^4 - 24*A*a^7*b^5 + 4*B*a^6*b^6 - 16*A*a^5*b^7 + B*a^4*b^8 - 4*A*a^3*b^9)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + 3*((10*B*a^7*b^5 - 20*A*a^6*b^6 + 5*B*a^5*b^7 - 24*A*a^4*b^8 + 4*B*a^3*b^9 - 16*A*a^2*b^10 + B*a*b^11 - 4*A*b^12)*tan(d*x + c)^4 + 3*(10*B*a^8*b^4 - 20*A*a^7*b^5 + 5*B*a^6*b^6 - 24*A*a^5*b^7 + 4*B*a^4*b^8 - 16*A*a^3*b^9 + B*a^2*b^10 - 4*A*a*b^11)*tan(d*x + c)^3 + 3*(10*B*a^9*b^3 - 20*A*a^8*b^4 + 5*B*a^7*b^5 - 24*A*a^6*b^6 + 4*B*a^5*b^7 - 16*A*a^4*b^8 + B*a^3*b^9 - 4*A*a^2*b^10)*tan(d*x + c)^2 + (10*B*a^10*b^2 - 20*A*a^9*b^3 + 5*B*a^8*b^4 - 24*A*a^7*b^5 + 4*B*a^6*b^6 - 16*A*a^5*b^7 + B*a^4*b^8 - 4*A*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)) + (18*A*a^11*b + 72*A*a^9*b^3 - 75*B*a^8*b^4 + 216*A*a^7*b^5 - 42*B*a^6*b^6 + 162*A*a^5*b^7 - 11*B*a^4*b^8 + 44*A*a^3*b^9 + 6*(A*a^12 + 4*B*a^11*b - 6*A*a^10*b^2 - 4*B*a^9*b^3 + A*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
297,1,1732,0,1.380263," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{3 \, A a^{13} + 12 \, A a^{11} b^{2} + 18 \, A a^{9} b^{4} + 12 \, A a^{7} b^{6} + 3 \, A a^{5} b^{8} + {\left(3 \, A a^{10} b^{3} + 12 \, A a^{8} b^{5} - 74 \, B a^{7} b^{6} + 125 \, A a^{6} b^{7} - 42 \, B a^{5} b^{8} + 102 \, A a^{4} b^{9} - 12 \, B a^{3} b^{10} + 30 \, A a^{2} b^{11} + 6 \, {\left(B a^{10} b^{3} - 4 \, A a^{9} b^{4} - 6 \, B a^{8} b^{5} + 4 \, A a^{7} b^{6} + B a^{6} b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{5} + 3 \, {\left(3 \, A a^{11} b^{2} + 2 \, B a^{10} b^{3} + 4 \, A a^{9} b^{4} - 46 \, B a^{8} b^{5} + 63 \, A a^{7} b^{6} + 8 \, B a^{6} b^{7} - 10 \, A a^{5} b^{8} + 20 \, B a^{4} b^{9} - 48 \, A a^{3} b^{10} + 8 \, B a^{2} b^{11} - 20 \, A a b^{12} + 6 \, {\left(B a^{11} b^{2} - 4 \, A a^{10} b^{3} - 6 \, B a^{9} b^{4} + 4 \, A a^{8} b^{5} + B a^{7} b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(3 \, A a^{12} b + 6 \, B a^{11} b^{2} - 11 \, A a^{10} b^{3} - 6 \, B a^{9} b^{4} - 32 \, A a^{8} b^{5} + 80 \, B a^{7} b^{6} - 177 \, A a^{6} b^{7} + 68 \, B a^{5} b^{8} - 165 \, A a^{4} b^{9} + 20 \, B a^{3} b^{10} - 50 \, A a^{2} b^{11} + 6 \, {\left(B a^{12} b - 4 \, A a^{11} b^{2} - 6 \, B a^{10} b^{3} + 4 \, A a^{9} b^{4} + B a^{8} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{3} + {\left(3 \, A a^{13} + 18 \, B a^{12} b - 51 \, A a^{11} b^{2} + 72 \, B a^{10} b^{3} - 234 \, A a^{9} b^{4} + 216 \, B a^{8} b^{5} - 513 \, A a^{7} b^{6} + 162 \, B a^{6} b^{7} - 399 \, A a^{5} b^{8} + 44 \, B a^{4} b^{9} - 110 \, A a^{3} b^{10} + 6 \, {\left(B a^{13} - 4 \, A a^{12} b - 6 \, B a^{11} b^{2} + 4 \, A a^{10} b^{3} + B a^{9} b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left({\left(A a^{10} b^{3} + 4 \, B a^{9} b^{4} - 6 \, A a^{8} b^{5} + 16 \, B a^{7} b^{6} - 34 \, A a^{6} b^{7} + 24 \, B a^{5} b^{8} - 56 \, A a^{4} b^{9} + 16 \, B a^{3} b^{10} - 39 \, A a^{2} b^{11} + 4 \, B a b^{12} - 10 \, A b^{13}\right)} \tan\left(d x + c\right)^{5} + 3 \, {\left(A a^{11} b^{2} + 4 \, B a^{10} b^{3} - 6 \, A a^{9} b^{4} + 16 \, B a^{8} b^{5} - 34 \, A a^{7} b^{6} + 24 \, B a^{6} b^{7} - 56 \, A a^{5} b^{8} + 16 \, B a^{4} b^{9} - 39 \, A a^{3} b^{10} + 4 \, B a^{2} b^{11} - 10 \, A a b^{12}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(A a^{12} b + 4 \, B a^{11} b^{2} - 6 \, A a^{10} b^{3} + 16 \, B a^{9} b^{4} - 34 \, A a^{8} b^{5} + 24 \, B a^{7} b^{6} - 56 \, A a^{6} b^{7} + 16 \, B a^{5} b^{8} - 39 \, A a^{4} b^{9} + 4 \, B a^{3} b^{10} - 10 \, A a^{2} b^{11}\right)} \tan\left(d x + c\right)^{3} + {\left(A a^{13} + 4 \, B a^{12} b - 6 \, A a^{11} b^{2} + 16 \, B a^{10} b^{3} - 34 \, A a^{9} b^{4} + 24 \, B a^{8} b^{5} - 56 \, A a^{7} b^{6} + 16 \, B a^{6} b^{7} - 39 \, A a^{5} b^{8} + 4 \, B a^{4} b^{9} - 10 \, A a^{3} b^{10}\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) - 3 \, {\left({\left(20 \, B a^{7} b^{6} - 35 \, A a^{6} b^{7} + 24 \, B a^{5} b^{8} - 56 \, A a^{4} b^{9} + 16 \, B a^{3} b^{10} - 39 \, A a^{2} b^{11} + 4 \, B a b^{12} - 10 \, A b^{13}\right)} \tan\left(d x + c\right)^{5} + 3 \, {\left(20 \, B a^{8} b^{5} - 35 \, A a^{7} b^{6} + 24 \, B a^{6} b^{7} - 56 \, A a^{5} b^{8} + 16 \, B a^{4} b^{9} - 39 \, A a^{3} b^{10} + 4 \, B a^{2} b^{11} - 10 \, A a b^{12}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(20 \, B a^{9} b^{4} - 35 \, A a^{8} b^{5} + 24 \, B a^{7} b^{6} - 56 \, A a^{6} b^{7} + 16 \, B a^{5} b^{8} - 39 \, A a^{4} b^{9} + 4 \, B a^{3} b^{10} - 10 \, A a^{2} b^{11}\right)} \tan\left(d x + c\right)^{3} + {\left(20 \, B a^{10} b^{3} - 35 \, A a^{9} b^{4} + 24 \, B a^{8} b^{5} - 56 \, A a^{7} b^{6} + 16 \, B a^{6} b^{7} - 39 \, A a^{5} b^{8} + 4 \, B a^{4} b^{9} - 10 \, A a^{3} b^{10}\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(2 \, B a^{13} - 5 \, A a^{12} b + 8 \, B a^{11} b^{2} - 20 \, A a^{10} b^{3} + 12 \, B a^{9} b^{4} - 30 \, A a^{8} b^{5} + 8 \, B a^{7} b^{6} - 20 \, A a^{6} b^{7} + 2 \, B a^{5} b^{8} - 5 \, A a^{4} b^{9}\right)} \tan\left(d x + c\right)}{6 \, {\left({\left(a^{14} b^{3} + 4 \, a^{12} b^{5} + 6 \, a^{10} b^{7} + 4 \, a^{8} b^{9} + a^{6} b^{11}\right)} d \tan\left(d x + c\right)^{5} + 3 \, {\left(a^{15} b^{2} + 4 \, a^{13} b^{4} + 6 \, a^{11} b^{6} + 4 \, a^{9} b^{8} + a^{7} b^{10}\right)} d \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{16} b + 4 \, a^{14} b^{3} + 6 \, a^{12} b^{5} + 4 \, a^{10} b^{7} + a^{8} b^{9}\right)} d \tan\left(d x + c\right)^{3} + {\left(a^{17} + 4 \, a^{15} b^{2} + 6 \, a^{13} b^{4} + 4 \, a^{11} b^{6} + a^{9} b^{8}\right)} d \tan\left(d x + c\right)^{2}\right)}}"," ",0,"-1/6*(3*A*a^13 + 12*A*a^11*b^2 + 18*A*a^9*b^4 + 12*A*a^7*b^6 + 3*A*a^5*b^8 + (3*A*a^10*b^3 + 12*A*a^8*b^5 - 74*B*a^7*b^6 + 125*A*a^6*b^7 - 42*B*a^5*b^8 + 102*A*a^4*b^9 - 12*B*a^3*b^10 + 30*A*a^2*b^11 + 6*(B*a^10*b^3 - 4*A*a^9*b^4 - 6*B*a^8*b^5 + 4*A*a^7*b^6 + B*a^6*b^7)*d*x)*tan(d*x + c)^5 + 3*(3*A*a^11*b^2 + 2*B*a^10*b^3 + 4*A*a^9*b^4 - 46*B*a^8*b^5 + 63*A*a^7*b^6 + 8*B*a^6*b^7 - 10*A*a^5*b^8 + 20*B*a^4*b^9 - 48*A*a^3*b^10 + 8*B*a^2*b^11 - 20*A*a*b^12 + 6*(B*a^11*b^2 - 4*A*a^10*b^3 - 6*B*a^9*b^4 + 4*A*a^8*b^5 + B*a^7*b^6)*d*x)*tan(d*x + c)^4 + 3*(3*A*a^12*b + 6*B*a^11*b^2 - 11*A*a^10*b^3 - 6*B*a^9*b^4 - 32*A*a^8*b^5 + 80*B*a^7*b^6 - 177*A*a^6*b^7 + 68*B*a^5*b^8 - 165*A*a^4*b^9 + 20*B*a^3*b^10 - 50*A*a^2*b^11 + 6*(B*a^12*b - 4*A*a^11*b^2 - 6*B*a^10*b^3 + 4*A*a^9*b^4 + B*a^8*b^5)*d*x)*tan(d*x + c)^3 + (3*A*a^13 + 18*B*a^12*b - 51*A*a^11*b^2 + 72*B*a^10*b^3 - 234*A*a^9*b^4 + 216*B*a^8*b^5 - 513*A*a^7*b^6 + 162*B*a^6*b^7 - 399*A*a^5*b^8 + 44*B*a^4*b^9 - 110*A*a^3*b^10 + 6*(B*a^13 - 4*A*a^12*b - 6*B*a^11*b^2 + 4*A*a^10*b^3 + B*a^9*b^4)*d*x)*tan(d*x + c)^2 + 3*((A*a^10*b^3 + 4*B*a^9*b^4 - 6*A*a^8*b^5 + 16*B*a^7*b^6 - 34*A*a^6*b^7 + 24*B*a^5*b^8 - 56*A*a^4*b^9 + 16*B*a^3*b^10 - 39*A*a^2*b^11 + 4*B*a*b^12 - 10*A*b^13)*tan(d*x + c)^5 + 3*(A*a^11*b^2 + 4*B*a^10*b^3 - 6*A*a^9*b^4 + 16*B*a^8*b^5 - 34*A*a^7*b^6 + 24*B*a^6*b^7 - 56*A*a^5*b^8 + 16*B*a^4*b^9 - 39*A*a^3*b^10 + 4*B*a^2*b^11 - 10*A*a*b^12)*tan(d*x + c)^4 + 3*(A*a^12*b + 4*B*a^11*b^2 - 6*A*a^10*b^3 + 16*B*a^9*b^4 - 34*A*a^8*b^5 + 24*B*a^7*b^6 - 56*A*a^6*b^7 + 16*B*a^5*b^8 - 39*A*a^4*b^9 + 4*B*a^3*b^10 - 10*A*a^2*b^11)*tan(d*x + c)^3 + (A*a^13 + 4*B*a^12*b - 6*A*a^11*b^2 + 16*B*a^10*b^3 - 34*A*a^9*b^4 + 24*B*a^8*b^5 - 56*A*a^7*b^6 + 16*B*a^6*b^7 - 39*A*a^5*b^8 + 4*B*a^4*b^9 - 10*A*a^3*b^10)*tan(d*x + c)^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - 3*((20*B*a^7*b^6 - 35*A*a^6*b^7 + 24*B*a^5*b^8 - 56*A*a^4*b^9 + 16*B*a^3*b^10 - 39*A*a^2*b^11 + 4*B*a*b^12 - 10*A*b^13)*tan(d*x + c)^5 + 3*(20*B*a^8*b^5 - 35*A*a^7*b^6 + 24*B*a^6*b^7 - 56*A*a^5*b^8 + 16*B*a^4*b^9 - 39*A*a^3*b^10 + 4*B*a^2*b^11 - 10*A*a*b^12)*tan(d*x + c)^4 + 3*(20*B*a^9*b^4 - 35*A*a^8*b^5 + 24*B*a^7*b^6 - 56*A*a^6*b^7 + 16*B*a^5*b^8 - 39*A*a^4*b^9 + 4*B*a^3*b^10 - 10*A*a^2*b^11)*tan(d*x + c)^3 + (20*B*a^10*b^3 - 35*A*a^9*b^4 + 24*B*a^8*b^5 - 56*A*a^7*b^6 + 16*B*a^6*b^7 - 39*A*a^5*b^8 + 4*B*a^4*b^9 - 10*A*a^3*b^10)*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*(2*B*a^13 - 5*A*a^12*b + 8*B*a^11*b^2 - 20*A*a^10*b^3 + 12*B*a^9*b^4 - 30*A*a^8*b^5 + 8*B*a^7*b^6 - 20*A*a^6*b^7 + 2*B*a^5*b^8 - 5*A*a^4*b^9)*tan(d*x + c))/((a^14*b^3 + 4*a^12*b^5 + 6*a^10*b^7 + 4*a^8*b^9 + a^6*b^11)*d*tan(d*x + c)^5 + 3*(a^15*b^2 + 4*a^13*b^4 + 6*a^11*b^6 + 4*a^9*b^8 + a^7*b^10)*d*tan(d*x + c)^4 + 3*(a^16*b + 4*a^14*b^3 + 6*a^12*b^5 + 4*a^10*b^7 + a^8*b^9)*d*tan(d*x + c)^3 + (a^17 + 4*a^15*b^2 + 6*a^13*b^4 + 4*a^11*b^6 + a^9*b^8)*d*tan(d*x + c)^2)","B",0
298,1,31,0,0.756377," ","integrate(tan(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{B \tan\left(d x + c\right)^{2} + B \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(B*tan(d*x + c)^2 + B*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
299,1,19,0,0.584422," ","integrate(tan(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{B d x - B \tan\left(d x + c\right)}{d}"," ",0,"-(B*d*x - B*tan(d*x + c))/d","A",0
300,1,19,0,0.535620," ","integrate(tan(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{B \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"-1/2*B*log(1/(tan(d*x + c)^2 + 1))/d","A",0
301,1,3,0,0.535287," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","B x"," ",0,"B*x","A",0
302,1,20,0,0.668290," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{B \log\left(-\frac{1}{2} \, \cos\left(2 \, d x + 2 \, c\right) + \frac{1}{2}\right)}{2 \, d}"," ",0,"1/2*B*log(-1/2*cos(2*d*x + 2*c) + 1/2)/d","A",0
303,1,42,0,0.788220," ","integrate(cot(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{B d x \sin\left(2 \, d x + 2 \, c\right) + B \cos\left(2 \, d x + 2 \, c\right) + B}{d \sin\left(2 \, d x + 2 \, c\right)}"," ",0,"-(B*d*x*sin(2*d*x + 2*c) + B*cos(2*d*x + 2*c) + B)/(d*sin(2*d*x + 2*c))","B",0
304,1,53,0,0.656792," ","integrate(cot(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(B \cos\left(2 \, d x + 2 \, c\right) - B\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, d x + 2 \, c\right) + \frac{1}{2}\right) - 2 \, B}{2 \, {\left(d \cos\left(2 \, d x + 2 \, c\right) - d\right)}}"," ",0,"-1/2*((B*cos(2*d*x + 2*c) - B)*log(-1/2*cos(2*d*x + 2*c) + 1/2) - 2*B)/(d*cos(2*d*x + 2*c) - d)","A",0
305,1,90,0,0.677438," ","integrate(cot(d*x+c)^4*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, B \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, B \cos\left(2 \, d x + 2 \, c\right) + 3 \, {\left(B d x \cos\left(2 \, d x + 2 \, c\right) - B d x\right)} \sin\left(2 \, d x + 2 \, c\right) - 2 \, B}{3 \, {\left(d \cos\left(2 \, d x + 2 \, c\right) - d\right)} \sin\left(2 \, d x + 2 \, c\right)}"," ",0,"1/3*(4*B*cos(2*d*x + 2*c)^2 + 2*B*cos(2*d*x + 2*c) + 3*(B*d*x*cos(2*d*x + 2*c) - B*d*x)*sin(2*d*x + 2*c) - 2*B)/((d*cos(2*d*x + 2*c) - d)*sin(2*d*x + 2*c))","B",0
306,1,144,0,0.751432," ","integrate(tan(d*x+c)^4*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, B a b^{3} d x + B 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(B a^{2} b^{2} + B b^{4}\right)} \tan\left(d x + c\right)^{2} - {\left(B a^{4} - B b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(B a^{3} b + 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*B*a*b^3*d*x + B*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)) + (B*a^2*b^2 + B*b^4)*tan(d*x + c)^2 - (B*a^4 - B*b^4)*log(1/(tan(d*x + c)^2 + 1)) - 2*(B*a^3*b + B*a*b^3)*tan(d*x + c))/((a^2*b^3 + b^5)*d)","A",0
307,1,119,0,0.544993," ","integrate(tan(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, B b^{3} d x + B 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(B a^{3} + B a b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(B a^{2} b + 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*b^3*d*x + B*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)) - (B*a^3 + B*a*b^2)*log(1/(tan(d*x + c)^2 + 1)) - 2*(B*a^2*b + B*b^3)*tan(d*x + c))/((a^2*b^2 + b^4)*d)","A",0
308,1,95,0,0.797998," ","integrate(tan(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, B a b d x - B 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(B a^{2} + B 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*B*a*b*d*x - B*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)) + (B*a^2 + B*b^2)*log(1/(tan(d*x + c)^2 + 1)))/((a^2*b + b^3)*d)","A",0
309,1,65,0,0.699087," ","integrate(tan(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, B b d x - B 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*b*d*x - B*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
310,1,64,0,0.685526," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, B a d x + B 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*B*a*d*x + B*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
311,1,104,0,0.723642," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, B a b d x + B 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(B a^{2} + B 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*B*a*b*d*x + B*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)) - (B*a^2 + B*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)))/((a^3 + a*b^2)*d)","A",0
312,1,147,0,0.728619," ","integrate(cot(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, B a^{3} d x \tan\left(d x + c\right) - B 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 \, B a^{3} + 2 \, B a b^{2} + {\left(B a^{2} b + 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*B*a^3*d*x*tan(d*x + c) - B*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*B*a^3 + 2*B*a*b^2 + (B*a^2*b + 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
313,1,192,0,0.572077," ","integrate(cot(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{B 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} + B a^{4} + B a^{2} b^{2} + {\left(B a^{4} - B 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 \, B a^{3} b d x - B a^{4} - B a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} - 2 \, {\left(B a^{3} b + 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*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 + B*a^4 + B*a^2*b^2 + (B*a^4 - B*b^4)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 - (2*B*a^3*b*d*x - B*a^4 - B*a^2*b^2)*tan(d*x + c)^2 - 2*(B*a^3*b + B*a*b^3)*tan(d*x + c))/((a^5 + a^3*b^2)*d*tan(d*x + c)^2)","A",0
314,1,44,0,0.777019," ","integrate((3+tan(d*x+c))/(2-tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d x - \log\left(\frac{\tan\left(d x + c\right)^{2} - 4 \, \tan\left(d x + c\right) + 4}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(2*d*x - log((tan(d*x + c)^2 - 4*tan(d*x + c) + 4)/(tan(d*x + c)^2 + 1)))/d","A",0
315,1,78,0,0.587634," ","integrate((b*B/a+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, B a b d x - {\left(B a^{2} - B b^{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)}{2 \, {\left(a^{3} + a b^{2}\right)} d}"," ",0,"1/2*(4*B*a*b*d*x - (B*a^2 - B*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^3 + a*b^2)*d)","A",0
316,1,191,0,1.009730," ","integrate((a+b*tan(d*x+c))/(b+a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{4} - 2 \, a^{2} b^{2} + 2 \, {\left(a^{3} b - 3 \, a b^{3}\right)} d x - {\left(3 \, a^{2} b^{2} - b^{4} + {\left(3 \, a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{a^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + b^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(a^{3} b - a b^{3} - {\left(a^{4} - 3 \, a^{2} b^{2}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \tan\left(d x + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d\right)}}"," ",0,"-1/2*(2*a^4 - 2*a^2*b^2 + 2*(a^3*b - 3*a*b^3)*d*x - (3*a^2*b^2 - b^4 + (3*a^3*b - a*b^3)*tan(d*x + c))*log((a^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + b^2)/(tan(d*x + c)^2 + 1)) - 2*(a^3*b - a*b^3 - (a^4 - 3*a^2*b^2)*d*x)*tan(d*x + c))/((a^5 + 2*a^3*b^2 + a*b^4)*d*tan(d*x + c) + (a^4*b + 2*a^2*b^3 + b^5)*d)","A",0
317,1,9053,0,12.579358," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{420 \, \sqrt{2} b^{3} d^{5} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{3} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{2} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{3}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + \sqrt{2} {\left({\left(2 \, {\left(A^{4} B + A^{2} B^{3}\right)} a + {\left(A^{5} - A B^{4}\right)} b\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{2} + {\left(A^{7} - A^{5} B^{2} - 5 \, A^{3} B^{4} - 3 \, A B^{6}\right)} a b - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{2}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(A d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a - {\left(A^{2} B + B^{3}\right)} b\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{3} + 4 \, {\left(A^{4} B - 2 \, A^{2} B^{3}\right)} a^{2} b + {\left(A^{5} - 6 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a b^{2} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{4} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a^{3} b + {\left(A^{7} + 3 \, A^{5} B^{2} + 3 \, A^{3} B^{4} + A B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a b^{3} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{4} b + 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)} a^{3} b^{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)} a^{2} b^{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)} a b^{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)} b^{5}}\right) \cos\left(d x + c\right)^{3} + 420 \, \sqrt{2} b^{3} d^{5} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{3} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{2} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{3}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - \sqrt{2} {\left({\left(2 \, {\left(A^{4} B + A^{2} B^{3}\right)} a + {\left(A^{5} - A B^{4}\right)} b\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{2} + {\left(A^{7} - A^{5} B^{2} - 5 \, A^{3} B^{4} - 3 \, A B^{6}\right)} a b - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{2}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(A d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a - {\left(A^{2} B + B^{3}\right)} b\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{3} + 4 \, {\left(A^{4} B - 2 \, A^{2} B^{3}\right)} a^{2} b + {\left(A^{5} - 6 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a b^{2} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{4} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a^{3} b + {\left(A^{7} + 3 \, A^{5} B^{2} + 3 \, A^{3} B^{4} + A B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a b^{3} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{4} b + 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)} a^{3} b^{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)} a^{2} b^{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)} a b^{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)} b^{5}}\right) \cos\left(d x + c\right)^{3} - 105 \, \sqrt{2} {\left({\left(2 \, A B b^{4} - {\left(A^{2} - B^{2}\right)} a b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right)^{3} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{3} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{5}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{3} + 4 \, {\left(A^{4} B - 2 \, A^{2} B^{3}\right)} a^{2} b + {\left(A^{5} - 6 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a b^{2} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{4} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a^{3} b + {\left(A^{7} + 3 \, A^{5} B^{2} + 3 \, A^{3} B^{4} + A B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a b^{3} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} 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({\left(2 \, A B b^{4} - {\left(A^{2} - B^{2}\right)} a b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right)^{3} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{3} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{5}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{3} + 4 \, {\left(A^{4} B - 2 \, A^{2} B^{3}\right)} a^{2} b + {\left(A^{5} - 6 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a b^{2} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{4} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a^{3} b + {\left(A^{7} + 3 \, A^{5} B^{2} + 3 \, A^{3} B^{4} + A B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a b^{3} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} 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 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} - 7 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{4} b - 15 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 70 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} - 19 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{4} - 63 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} + 7 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + 7 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} \cos\left(d x + c\right) + {\left(15 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + 15 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{5} - {\left(4 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 7 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} + 54 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} - 7 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a b^{4} + 50 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} 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({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{3} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{5}\right)} d \cos\left(d x + c\right)^{3}}"," ",0,"1/420*(420*sqrt(2)*b^3*d^5*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4)*arctan(((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^2 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^3)*d^4*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4) + sqrt(2)*((2*(A^4*B + A^2*B^3)*a + (A^5 - A*B^4)*b)*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^2 + (A^7 - A^5*B^2 - 5*A^3*B^4 - 3*A*B^6)*a*b - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^2)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4) + sqrt(2)*(A*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + ((A^3 + A*B^2)*a - (A^2*B + B^3)*b)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + sqrt(2)*((4*A^3*B^2*a^3 + 4*(A^4*B - 2*A^2*B^3)*a^2*b + (A^5 - 6*A^3*B^2 + 5*A*B^4)*a*b^2 - (A^4*B - 2*A^2*B^3 + B^5)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^4 + 4*(A^6*B - A^2*B^5)*a^3*b + (A^7 + 3*A^5*B^2 + 3*A^3*B^4 + A*B^6)*a^2*b^2 + 4*(A^6*B - A^2*B^5)*a*b^3 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^4)*d*cos(d*x + c))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^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)*a^4*b + 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)*a^3*b^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)*a^2*b^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)*a*b^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)*b^5))*cos(d*x + c)^3 + 420*sqrt(2)*b^3*d^5*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4)*arctan(-((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^2 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^3)*d^4*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4) - sqrt(2)*((2*(A^4*B + A^2*B^3)*a + (A^5 - A*B^4)*b)*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^2 + (A^7 - A^5*B^2 - 5*A^3*B^4 - 3*A*B^6)*a*b - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^2)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4) - sqrt(2)*(A*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + ((A^3 + A*B^2)*a - (A^2*B + B^3)*b)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) - sqrt(2)*((4*A^3*B^2*a^3 + 4*(A^4*B - 2*A^2*B^3)*a^2*b + (A^5 - 6*A^3*B^2 + 5*A*B^4)*a*b^2 - (A^4*B - 2*A^2*B^3 + B^5)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^4 + 4*(A^6*B - A^2*B^5)*a^3*b + (A^7 + 3*A^5*B^2 + 3*A^3*B^4 + A*B^6)*a^2*b^2 + 4*(A^6*B - A^2*B^5)*a*b^3 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^4)*d*cos(d*x + c))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^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)*a^4*b + 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)*a^3*b^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)*a^2*b^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)*a*b^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)*b^5))*cos(d*x + c)^3 - 105*sqrt(2)*((2*A*B*b^4 - (A^2 - B^2)*a*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c)^3 - ((A^4 + 2*A^2*B^2 + B^4)*a^2*b^3 + (A^4 + 2*A^2*B^2 + B^4)*b^5)*d*cos(d*x + c)^3)*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + sqrt(2)*((4*A^3*B^2*a^3 + 4*(A^4*B - 2*A^2*B^3)*a^2*b + (A^5 - 6*A^3*B^2 + 5*A*B^4)*a*b^2 - (A^4*B - 2*A^2*B^3 + B^5)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^4 + 4*(A^6*B - A^2*B^5)*a^3*b + (A^7 + 3*A^5*B^2 + 3*A^3*B^4 + A*B^6)*a^2*b^2 + 4*(A^6*B - A^2*B^5)*a*b^3 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^4)*d*cos(d*x + c))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 105*sqrt(2)*((2*A*B*b^4 - (A^2 - B^2)*a*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c)^3 - ((A^4 + 2*A^2*B^2 + B^4)*a^2*b^3 + (A^4 + 2*A^2*B^2 + B^4)*b^5)*d*cos(d*x + c)^3)*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) - sqrt(2)*((4*A^3*B^2*a^3 + 4*(A^4*B - 2*A^2*B^3)*a^2*b + (A^5 - 6*A^3*B^2 + 5*A*B^4)*a*b^2 - (A^4*B - 2*A^2*B^3 + B^5)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^4 + 4*(A^6*B - A^2*B^5)*a^3*b + (A^7 + 3*A^5*B^2 + 3*A^3*B^4 + A*B^6)*a^2*b^2 + 4*(A^6*B - A^2*B^5)*a*b^3 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^4)*d*cos(d*x + c))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 8*(2*(4*(A^4*B + 2*A^2*B^3 + B^5)*a^5 - 7*(A^5 + 2*A^3*B^2 + A*B^4)*a^4*b - 15*(A^4*B + 2*A^2*B^3 + B^5)*a^3*b^2 - 70*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^3 - 19*(A^4*B + 2*A^2*B^3 + B^5)*a*b^4 - 63*(A^5 + 2*A^3*B^2 + A*B^4)*b^5)*cos(d*x + c)^3 + 3*((A^4*B + 2*A^2*B^3 + B^5)*a^3*b^2 + 7*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^3 + (A^4*B + 2*A^2*B^3 + B^5)*a*b^4 + 7*(A^5 + 2*A^3*B^2 + A*B^4)*b^5)*cos(d*x + c) + (15*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^3 + 15*(A^4*B + 2*A^2*B^3 + B^5)*b^5 - (4*(A^4*B + 2*A^2*B^3 + B^5)*a^4*b - 7*(A^5 + 2*A^3*B^2 + A*B^4)*a^3*b^2 + 54*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^3 - 7*(A^5 + 2*A^3*B^2 + A*B^4)*a*b^4 + 50*(A^4*B + 2*A^2*B^3 + B^5)*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 + 2*A^2*B^2 + B^4)*a^2*b^3 + (A^4 + 2*A^2*B^2 + B^4)*b^5)*d*cos(d*x + c)^3)","B",0
318,1,8926,0,13.261969," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{60 \, \sqrt{2} b^{2} d^{5} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{3} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{2} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{3}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + \sqrt{2} {\left({\left(2 \, {\left(A^{3} B^{2} + A B^{4}\right)} a + {\left(A^{4} B - B^{5}\right)} b\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{2} + {\left(3 \, A^{6} B + 5 \, A^{4} B^{3} + A^{2} B^{5} - B^{7}\right)} a b + {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{2}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(B d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left({\left(A^{2} B + B^{3}\right)} a + {\left(A^{3} + A B^{2}\right)} b\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{3} + 4 \, {\left(2 \, A^{3} B^{2} - A B^{4}\right)} a^{2} b + {\left(5 \, A^{4} B - 6 \, A^{2} B^{3} + B^{5}\right)} a b^{2} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{4} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a^{3} b + {\left(A^{6} B + 3 \, A^{4} B^{3} + 3 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a b^{3} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{4} b + 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)} a^{3} b^{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)} a^{2} b^{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)} a b^{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)} b^{5}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} b^{2} d^{5} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{3} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{2} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{3}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - \sqrt{2} {\left({\left(2 \, {\left(A^{3} B^{2} + A B^{4}\right)} a + {\left(A^{4} B - B^{5}\right)} b\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{2} + {\left(3 \, A^{6} B + 5 \, A^{4} B^{3} + A^{2} B^{5} - B^{7}\right)} a b + {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{2}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(B d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left({\left(A^{2} B + B^{3}\right)} a + {\left(A^{3} + A B^{2}\right)} b\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{3} + 4 \, {\left(2 \, A^{3} B^{2} - A B^{4}\right)} a^{2} b + {\left(5 \, A^{4} B - 6 \, A^{2} B^{3} + B^{5}\right)} a b^{2} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{4} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a^{3} b + {\left(A^{6} B + 3 \, A^{4} B^{3} + 3 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a b^{3} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{4} b + 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)} a^{3} b^{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)} a^{2} b^{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)} a b^{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)} b^{5}}\right) \cos\left(d x + c\right)^{2} - 15 \, \sqrt{2} {\left({\left(2 \, A B b^{3} - {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right)^{2} + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{3} + 4 \, {\left(2 \, A^{3} B^{2} - A B^{4}\right)} a^{2} b + {\left(5 \, A^{4} B - 6 \, A^{2} B^{3} + B^{5}\right)} a b^{2} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{4} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a^{3} b + {\left(A^{6} B + 3 \, A^{4} B^{3} + 3 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a b^{3} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{5}\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(2 \, A B b^{3} - {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right)^{2} + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{3} + 4 \, {\left(2 \, A^{3} B^{2} - A B^{4}\right)} a^{2} b + {\left(5 \, A^{4} B - 6 \, A^{2} B^{3} + B^{5}\right)} a b^{2} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{4} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a^{3} b + {\left(A^{6} B + 3 \, A^{4} B^{3} + 3 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a b^{3} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{2} + 3 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{4} - {\left(2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{4} - 5 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{3} b + 20 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{2} - 5 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a b^{3} + 18 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} b + 5 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{2} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{3} + 5 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b^{4}\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({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/60*(60*sqrt(2)*b^2*d^5*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4)*arctan(((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^2 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^3)*d^4*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4) + sqrt(2)*((2*(A^3*B^2 + A*B^4)*a + (A^4*B - B^5)*b)*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^2 + (3*A^6*B + 5*A^4*B^3 + A^2*B^5 - B^7)*a*b + (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^2)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4) + sqrt(2)*(B*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + ((A^2*B + B^3)*a + (A^3 + A*B^2)*b)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + sqrt(2)*((4*A^2*B^3*a^3 + 4*(2*A^3*B^2 - A*B^4)*a^2*b + (5*A^4*B - 6*A^2*B^3 + B^5)*a*b^2 + (A^5 - 2*A^3*B^2 + A*B^4)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^4 + 4*(A^5*B^2 - A*B^6)*a^3*b + (A^6*B + 3*A^4*B^3 + 3*A^2*B^5 + B^7)*a^2*b^2 + 4*(A^5*B^2 - A*B^6)*a*b^3 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^4)*d*cos(d*x + c))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^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)*a^4*b + 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)*a^3*b^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)*a^2*b^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)*a*b^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)*b^5))*cos(d*x + c)^2 + 60*sqrt(2)*b^2*d^5*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4)*arctan(-((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^2 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^3)*d^4*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4) - sqrt(2)*((2*(A^3*B^2 + A*B^4)*a + (A^4*B - B^5)*b)*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^2 + (3*A^6*B + 5*A^4*B^3 + A^2*B^5 - B^7)*a*b + (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^2)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4) - sqrt(2)*(B*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + ((A^2*B + B^3)*a + (A^3 + A*B^2)*b)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) - sqrt(2)*((4*A^2*B^3*a^3 + 4*(2*A^3*B^2 - A*B^4)*a^2*b + (5*A^4*B - 6*A^2*B^3 + B^5)*a*b^2 + (A^5 - 2*A^3*B^2 + A*B^4)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^4 + 4*(A^5*B^2 - A*B^6)*a^3*b + (A^6*B + 3*A^4*B^3 + 3*A^2*B^5 + B^7)*a^2*b^2 + 4*(A^5*B^2 - A*B^6)*a*b^3 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^4)*d*cos(d*x + c))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^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)*a^4*b + 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)*a^3*b^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)*a^2*b^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)*a*b^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)*b^5))*cos(d*x + c)^2 - 15*sqrt(2)*((2*A*B*b^3 - (A^2 - B^2)*a*b^2)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c)^2 + ((A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2)*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + sqrt(2)*((4*A^2*B^3*a^3 + 4*(2*A^3*B^2 - A*B^4)*a^2*b + (5*A^4*B - 6*A^2*B^3 + B^5)*a*b^2 + (A^5 - 2*A^3*B^2 + A*B^4)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^4 + 4*(A^5*B^2 - A*B^6)*a^3*b + (A^6*B + 3*A^4*B^3 + 3*A^2*B^5 + B^7)*a^2*b^2 + 4*(A^5*B^2 - A*B^6)*a*b^3 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^4)*d*cos(d*x + c))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 15*sqrt(2)*((2*A*B*b^3 - (A^2 - B^2)*a*b^2)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c)^2 + ((A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2)*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) - sqrt(2)*((4*A^2*B^3*a^3 + 4*(2*A^3*B^2 - A*B^4)*a^2*b + (5*A^4*B - 6*A^2*B^3 + B^5)*a*b^2 + (A^5 - 2*A^3*B^2 + A*B^4)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^4 + 4*(A^5*B^2 - A*B^6)*a^3*b + (A^6*B + 3*A^4*B^3 + 3*A^2*B^5 + B^7)*a^2*b^2 + 4*(A^5*B^2 - A*B^6)*a*b^3 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^4)*d*cos(d*x + c))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(3*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^2 + 3*(A^4*B + 2*A^2*B^3 + B^5)*b^4 - (2*(A^4*B + 2*A^2*B^3 + B^5)*a^4 - 5*(A^5 + 2*A^3*B^2 + A*B^4)*a^3*b + 20*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^2 - 5*(A^5 + 2*A^3*B^2 + A*B^4)*a*b^3 + 18*(A^4*B + 2*A^2*B^3 + B^5)*b^4)*cos(d*x + c)^2 + ((A^4*B + 2*A^2*B^3 + B^5)*a^3*b + 5*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^2 + (A^4*B + 2*A^2*B^3 + B^5)*a*b^3 + 5*(A^5 + 2*A^3*B^2 + A*B^4)*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^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2)","B",0
319,1,8737,0,13.614170," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} b d^{5} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{3} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{2} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{3}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + \sqrt{2} {\left({\left(2 \, {\left(A^{4} B + A^{2} B^{3}\right)} a + {\left(A^{5} - A B^{4}\right)} b\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{2} + {\left(A^{7} - A^{5} B^{2} - 5 \, A^{3} B^{4} - 3 \, A B^{6}\right)} a b - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{2}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(A d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a - {\left(A^{2} B + B^{3}\right)} b\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{3} + 4 \, {\left(A^{4} B - 2 \, A^{2} B^{3}\right)} a^{2} b + {\left(A^{5} - 6 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a b^{2} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{4} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a^{3} b + {\left(A^{7} + 3 \, A^{5} B^{2} + 3 \, A^{3} B^{4} + A B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a b^{3} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{4} b + 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)} a^{3} b^{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)} a^{2} b^{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)} a b^{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)} b^{5}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} b d^{5} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{3} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{2} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{3}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - \sqrt{2} {\left({\left(2 \, {\left(A^{4} B + A^{2} B^{3}\right)} a + {\left(A^{5} - A B^{4}\right)} b\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{2} + {\left(A^{7} - A^{5} B^{2} - 5 \, A^{3} B^{4} - 3 \, A B^{6}\right)} a b - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{2}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(A d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a - {\left(A^{2} B + B^{3}\right)} b\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{3} + 4 \, {\left(A^{4} B - 2 \, A^{2} B^{3}\right)} a^{2} b + {\left(A^{5} - 6 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a b^{2} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{4} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a^{3} b + {\left(A^{7} + 3 \, A^{5} B^{2} + 3 \, A^{3} B^{4} + A B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a b^{3} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{4} b + 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)} a^{3} b^{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)} a^{2} b^{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)} a b^{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)} b^{5}}\right) \cos\left(d x + c\right) - 3 \, \sqrt{2} {\left({\left(2 \, A B b^{2} - {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{3} + 4 \, {\left(A^{4} B - 2 \, A^{2} B^{3}\right)} a^{2} b + {\left(A^{5} - 6 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a b^{2} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{4} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a^{3} b + {\left(A^{7} + 3 \, A^{5} B^{2} + 3 \, A^{3} B^{4} + A B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a b^{3} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} 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({\left(2 \, A B b^{2} - {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{3} + 4 \, {\left(A^{4} B - 2 \, A^{2} B^{3}\right)} a^{2} b + {\left(A^{5} - 6 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a b^{2} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{4} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a^{3} b + {\left(A^{7} + 3 \, A^{5} B^{2} + 3 \, A^{3} B^{4} + A B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{6} B - A^{2} B^{5}\right)} a b^{3} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} 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({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} + 3 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{2} + 3 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b^{3}\right)} \cos\left(d x + c\right) + {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} 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({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{3}\right)} d \cos\left(d x + c\right)}"," ",0,"-1/12*(12*sqrt(2)*b*d^5*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4)*arctan(((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^2 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^3)*d^4*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4) + sqrt(2)*((2*(A^4*B + A^2*B^3)*a + (A^5 - A*B^4)*b)*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^2 + (A^7 - A^5*B^2 - 5*A^3*B^4 - 3*A*B^6)*a*b - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^2)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4) + sqrt(2)*(A*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + ((A^3 + A*B^2)*a - (A^2*B + B^3)*b)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + sqrt(2)*((4*A^3*B^2*a^3 + 4*(A^4*B - 2*A^2*B^3)*a^2*b + (A^5 - 6*A^3*B^2 + 5*A*B^4)*a*b^2 - (A^4*B - 2*A^2*B^3 + B^5)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^4 + 4*(A^6*B - A^2*B^5)*a^3*b + (A^7 + 3*A^5*B^2 + 3*A^3*B^4 + A*B^6)*a^2*b^2 + 4*(A^6*B - A^2*B^5)*a*b^3 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^4)*d*cos(d*x + c))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^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)*a^4*b + 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)*a^3*b^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)*a^2*b^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)*a*b^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)*b^5))*cos(d*x + c) + 12*sqrt(2)*b*d^5*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4)*arctan(-((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^2 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^3)*d^4*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4) - sqrt(2)*((2*(A^4*B + A^2*B^3)*a + (A^5 - A*B^4)*b)*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^2 + (A^7 - A^5*B^2 - 5*A^3*B^4 - 3*A*B^6)*a*b - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^2)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4) - sqrt(2)*(A*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + ((A^3 + A*B^2)*a - (A^2*B + B^3)*b)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) - sqrt(2)*((4*A^3*B^2*a^3 + 4*(A^4*B - 2*A^2*B^3)*a^2*b + (A^5 - 6*A^3*B^2 + 5*A*B^4)*a*b^2 - (A^4*B - 2*A^2*B^3 + B^5)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^4 + 4*(A^6*B - A^2*B^5)*a^3*b + (A^7 + 3*A^5*B^2 + 3*A^3*B^4 + A*B^6)*a^2*b^2 + 4*(A^6*B - A^2*B^5)*a*b^3 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^4)*d*cos(d*x + c))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^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)*a^4*b + 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)*a^3*b^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)*a^2*b^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)*a*b^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)*b^5))*cos(d*x + c) - 3*sqrt(2)*((2*A*B*b^2 - (A^2 - B^2)*a*b)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) - ((A^4 + 2*A^2*B^2 + B^4)*a^2*b + (A^4 + 2*A^2*B^2 + B^4)*b^3)*d*cos(d*x + c))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + sqrt(2)*((4*A^3*B^2*a^3 + 4*(A^4*B - 2*A^2*B^3)*a^2*b + (A^5 - 6*A^3*B^2 + 5*A*B^4)*a*b^2 - (A^4*B - 2*A^2*B^3 + B^5)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^4 + 4*(A^6*B - A^2*B^5)*a^3*b + (A^7 + 3*A^5*B^2 + 3*A^3*B^4 + A*B^6)*a^2*b^2 + 4*(A^6*B - A^2*B^5)*a*b^3 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^4)*d*cos(d*x + c))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 3*sqrt(2)*((2*A*B*b^2 - (A^2 - B^2)*a*b)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) - ((A^4 + 2*A^2*B^2 + B^4)*a^2*b + (A^4 + 2*A^2*B^2 + B^4)*b^3)*d*cos(d*x + c))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) - sqrt(2)*((4*A^3*B^2*a^3 + 4*(A^4*B - 2*A^2*B^3)*a^2*b + (A^5 - 6*A^3*B^2 + 5*A*B^4)*a*b^2 - (A^4*B - 2*A^2*B^3 + B^5)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^4 + 4*(A^6*B - A^2*B^5)*a^3*b + (A^7 + 3*A^5*B^2 + 3*A^3*B^4 + A*B^6)*a^2*b^2 + 4*(A^6*B - A^2*B^5)*a*b^3 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^4)*d*cos(d*x + c))*sqrt(((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(((A^4*B + 2*A^2*B^3 + B^5)*a^3 + 3*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b + (A^4*B + 2*A^2*B^3 + B^5)*a*b^2 + 3*(A^5 + 2*A^3*B^2 + A*B^4)*b^3)*cos(d*x + c) + ((A^4*B + 2*A^2*B^3 + B^5)*a^2*b + (A^4*B + 2*A^2*B^3 + B^5)*b^3)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(((A^4 + 2*A^2*B^2 + B^4)*a^2*b + (A^4 + 2*A^2*B^2 + B^4)*b^3)*d*cos(d*x + c))","B",0
320,1,8608,0,16.688600," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d^{5} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{3} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{2} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{3}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + \sqrt{2} {\left({\left(2 \, {\left(A^{3} B^{2} + A B^{4}\right)} a + {\left(A^{4} B - B^{5}\right)} b\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{2} + {\left(3 \, A^{6} B + 5 \, A^{4} B^{3} + A^{2} B^{5} - B^{7}\right)} a b + {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{2}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(B d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left({\left(A^{2} B + B^{3}\right)} a + {\left(A^{3} + A B^{2}\right)} b\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{3} + 4 \, {\left(2 \, A^{3} B^{2} - A B^{4}\right)} a^{2} b + {\left(5 \, A^{4} B - 6 \, A^{2} B^{3} + B^{5}\right)} a b^{2} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{4} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a^{3} b + {\left(A^{6} B + 3 \, A^{4} B^{3} + 3 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a b^{3} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{4} b + 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)} a^{3} b^{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)} a^{2} b^{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)} a b^{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)} b^{5}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{3} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{2} + {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{3}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - \sqrt{2} {\left({\left(2 \, {\left(A^{3} B^{2} + A B^{4}\right)} a + {\left(A^{4} B - B^{5}\right)} b\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left(2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{2} + {\left(3 \, A^{6} B + 5 \, A^{4} B^{3} + A^{2} B^{5} - B^{7}\right)} a b + {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{2}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(B d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left({\left(A^{2} B + B^{3}\right)} a + {\left(A^{3} + A B^{2}\right)} b\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{3} + 4 \, {\left(2 \, A^{3} B^{2} - A B^{4}\right)} a^{2} b + {\left(5 \, A^{4} B - 6 \, A^{2} B^{3} + B^{5}\right)} a b^{2} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{4} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a^{3} b + {\left(A^{6} B + 3 \, A^{4} B^{3} + 3 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a b^{3} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{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)} a^{4} b + 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)} a^{3} b^{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)} a^{2} b^{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)} a b^{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)} b^{5}}\right) - \sqrt{2} {\left({\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}\right)} d\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{3} + 4 \, {\left(2 \, A^{3} B^{2} - A B^{4}\right)} a^{2} b + {\left(5 \, A^{4} B - 6 \, A^{2} B^{3} + B^{5}\right)} a b^{2} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{4} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a^{3} b + {\left(A^{6} B + 3 \, A^{4} B^{3} + 3 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a b^{3} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} 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(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}\right)} d\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} + 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{3} + 4 \, {\left(2 \, A^{3} B^{2} - A B^{4}\right)} a^{2} b + {\left(5 \, A^{4} B - 6 \, A^{2} B^{3} + B^{5}\right)} a b^{2} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{3}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{4} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a^{3} b + {\left(A^{6} B + 3 \, A^{4} B^{3} + 3 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{2} + 4 \, {\left(A^{5} B^{2} - A B^{6}\right)} a b^{3} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B b - {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} + 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{5} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{4} b + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{3} b^{2} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b^{3} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{4}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{4} b + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{2} + {\left(A^{8} + 4 \, A^{6} B^{2} + 6 \, A^{4} B^{4} + 4 \, A^{2} B^{6} + B^{8}\right)} a^{2} b^{3} + 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{4} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} 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^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} 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({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}\right)} d}"," ",0,"1/4*(4*sqrt(2)*d^5*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4)*arctan(((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^2 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^3)*d^4*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4) + sqrt(2)*((2*(A^3*B^2 + A*B^4)*a + (A^4*B - B^5)*b)*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^2 + (3*A^6*B + 5*A^4*B^3 + A^2*B^5 - B^7)*a*b + (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^2)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4) + sqrt(2)*(B*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + ((A^2*B + B^3)*a + (A^3 + A*B^2)*b)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + sqrt(2)*((4*A^2*B^3*a^3 + 4*(2*A^3*B^2 - A*B^4)*a^2*b + (5*A^4*B - 6*A^2*B^3 + B^5)*a*b^2 + (A^5 - 2*A^3*B^2 + A*B^4)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^4 + 4*(A^5*B^2 - A*B^6)*a^3*b + (A^6*B + 3*A^4*B^3 + 3*A^2*B^5 + B^7)*a^2*b^2 + 4*(A^5*B^2 - A*B^6)*a*b^3 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^4)*d*cos(d*x + c))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^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)*a^4*b + 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)*a^3*b^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)*a^2*b^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)*a*b^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)*b^5)) + 4*sqrt(2)*d^5*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4)*arctan(-((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^2 + (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^3)*d^4*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4) - sqrt(2)*((2*(A^3*B^2 + A*B^4)*a + (A^4*B - B^5)*b)*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + (2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^2 + (3*A^6*B + 5*A^4*B^3 + A^2*B^5 - B^7)*a*b + (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^2)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(3/4) - sqrt(2)*(B*d^7*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + ((A^2*B + B^3)*a + (A^3 + A*B^2)*b)*d^5*sqrt((4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/d^4))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) - sqrt(2)*((4*A^2*B^3*a^3 + 4*(2*A^3*B^2 - A*B^4)*a^2*b + (5*A^4*B - 6*A^2*B^3 + B^5)*a*b^2 + (A^5 - 2*A^3*B^2 + A*B^4)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^4 + 4*(A^5*B^2 - A*B^6)*a^3*b + (A^6*B + 3*A^4*B^3 + 3*A^2*B^5 + B^7)*a^2*b^2 + 4*(A^5*B^2 - A*B^6)*a*b^3 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^4)*d*cos(d*x + c))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^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)*a^4*b + 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)*a^3*b^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)*a^2*b^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)*a*b^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)*b^5)) - sqrt(2)*((2*A*B*b - (A^2 - B^2)*a)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + ((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)*d)*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + sqrt(2)*((4*A^2*B^3*a^3 + 4*(2*A^3*B^2 - A*B^4)*a^2*b + (5*A^4*B - 6*A^2*B^3 + B^5)*a*b^2 + (A^5 - 2*A^3*B^2 + A*B^4)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^4 + 4*(A^5*B^2 - A*B^6)*a^3*b + (A^6*B + 3*A^4*B^3 + 3*A^2*B^5 + B^7)*a^2*b^2 + 4*(A^5*B^2 - A*B^6)*a*b^3 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^4)*d*cos(d*x + c))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + sqrt(2)*((2*A*B*b - (A^2 - B^2)*a)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) + ((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)*d)*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 + 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 + 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) - sqrt(2)*((4*A^2*B^3*a^3 + 4*(2*A^3*B^2 - A*B^4)*a^2*b + (5*A^4*B - 6*A^2*B^3 + B^5)*a*b^2 + (A^5 - 2*A^3*B^2 + A*B^4)*b^3)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^4 + 4*(A^5*B^2 - A*B^6)*a^3*b + (A^6*B + 3*A^4*B^3 + 3*A^2*B^5 + B^7)*a^2*b^2 + 4*(A^5*B^2 - A*B^6)*a*b^3 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^4)*d*cos(d*x + c))*sqrt(-((2*A*B*b - (A^2 - B^2)*a)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 + 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/d^4)^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^5 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^4*b + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^3*b^2 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b^3 + (A^8 - 2*A^4*B^4 + B^8)*a*b^4)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^4*b + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^2 + (A^8 + 4*A^6*B^2 + 6*A^4*B^4 + 4*A^2*B^6 + B^8)*a^2*b^3 + 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^4 + (A^8 - 2*A^4*B^4 + B^8)*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 8*((A^4*B + 2*A^2*B^3 + B^5)*a^2 + (A^4*B + 2*A^2*B^3 + B^5)*b^2)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(((A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)*d)","B",0
321,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,1,7704,0,8.100928," ","integrate((-a+b*tan(d*x+c))*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{20 \, \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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}}} \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{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{d^{4}}} \arctan\left(\frac{{\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^{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{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{d^{4}}} + {\left(3 \, a^{29} + 38 \, a^{27} b^{2} + 221 \, a^{25} b^{4} + 780 \, a^{23} b^{6} + 1859 \, a^{21} b^{8} + 3146 \, a^{19} b^{10} + 3861 \, a^{17} b^{12} + 3432 \, a^{15} b^{14} + 2145 \, a^{13} b^{16} + 858 \, a^{11} b^{18} + 143 \, a^{9} b^{20} - 52 \, a^{7} b^{22} - 39 \, a^{5} b^{24} - 10 \, a^{3} b^{26} - a b^{28}\right)} d^{2} \sqrt{\frac{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{d^{4}}} + \sqrt{2} {\left(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{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{d^{4}}} + 2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(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)} 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(2 \, {\left(9 \, a^{9} b^{3} + 12 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 4 \, a^{3} b^{9} + a b^{11}\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(9 \, a^{16} b^{3} + 48 \, a^{14} b^{5} + 100 \, a^{12} b^{7} + 96 \, a^{10} b^{9} + 30 \, a^{8} b^{11} - 16 \, a^{6} b^{13} - 12 \, a^{4} b^{15} + b^{19}\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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, 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^{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(9 \, a^{21} b^{2} + 66 \, a^{19} b^{4} + 205 \, a^{17} b^{6} + 344 \, a^{15} b^{8} + 322 \, a^{13} b^{10} + 140 \, a^{11} b^{12} - 14 \, a^{9} b^{14} - 40 \, a^{7} b^{16} - 11 \, a^{5} b^{18} + 2 \, a^{3} b^{20} + a b^{22}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{20} b^{3} + 66 \, a^{18} b^{5} + 205 \, a^{16} b^{7} + 344 \, a^{14} b^{9} + 322 \, a^{12} b^{11} + 140 \, a^{10} b^{13} - 14 \, a^{8} b^{15} - 40 \, a^{6} b^{17} - 11 \, a^{4} b^{19} + 2 \, a^{2} b^{21} + b^{23}\right)} \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^{10} b + 11 \, a^{8} b^{3} + 14 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - a^{2} b^{9} - b^{11}\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{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{d^{4}}} + 2 \, {\left(3 \, a^{17} b + 20 \, a^{15} b^{3} + 56 \, a^{13} b^{5} + 84 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 28 \, a^{7} b^{11} - 4 \, a^{3} b^{15} - a b^{17}\right)} d^{5} \sqrt{\frac{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, 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^{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}}}{9 \, a^{34} b^{2} + 129 \, a^{32} b^{4} + 856 \, a^{30} b^{6} + 3480 \, a^{28} b^{8} + 9660 \, a^{26} b^{10} + 19292 \, a^{24} b^{12} + 28392 \, a^{22} b^{14} + 30888 \, a^{20} b^{16} + 24310 \, a^{18} b^{18} + 12870 \, a^{16} b^{20} + 3432 \, a^{14} b^{22} - 728 \, a^{12} b^{24} - 1092 \, a^{10} b^{26} - 420 \, a^{8} b^{28} - 40 \, a^{6} b^{30} + 24 \, a^{4} b^{32} + 9 \, a^{2} b^{34} + b^{36}}\right) \cos\left(d x + c\right)^{2} + 20 \, \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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}}} \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{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{d^{4}}} \arctan\left(-\frac{{\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^{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{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{d^{4}}} + {\left(3 \, a^{29} + 38 \, a^{27} b^{2} + 221 \, a^{25} b^{4} + 780 \, a^{23} b^{6} + 1859 \, a^{21} b^{8} + 3146 \, a^{19} b^{10} + 3861 \, a^{17} b^{12} + 3432 \, a^{15} b^{14} + 2145 \, a^{13} b^{16} + 858 \, a^{11} b^{18} + 143 \, a^{9} b^{20} - 52 \, a^{7} b^{22} - 39 \, a^{5} b^{24} - 10 \, a^{3} b^{26} - a b^{28}\right)} d^{2} \sqrt{\frac{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{d^{4}}} - \sqrt{2} {\left(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{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{d^{4}}} + 2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(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)} 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(2 \, {\left(9 \, a^{9} b^{3} + 12 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 4 \, a^{3} b^{9} + a b^{11}\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(9 \, a^{16} b^{3} + 48 \, a^{14} b^{5} + 100 \, a^{12} b^{7} + 96 \, a^{10} b^{9} + 30 \, a^{8} b^{11} - 16 \, a^{6} b^{13} - 12 \, a^{4} b^{15} + b^{19}\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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, 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^{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(9 \, a^{21} b^{2} + 66 \, a^{19} b^{4} + 205 \, a^{17} b^{6} + 344 \, a^{15} b^{8} + 322 \, a^{13} b^{10} + 140 \, a^{11} b^{12} - 14 \, a^{9} b^{14} - 40 \, a^{7} b^{16} - 11 \, a^{5} b^{18} + 2 \, a^{3} b^{20} + a b^{22}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{20} b^{3} + 66 \, a^{18} b^{5} + 205 \, a^{16} b^{7} + 344 \, a^{14} b^{9} + 322 \, a^{12} b^{11} + 140 \, a^{10} b^{13} - 14 \, a^{8} b^{15} - 40 \, a^{6} b^{17} - 11 \, a^{4} b^{19} + 2 \, a^{2} b^{21} + b^{23}\right)} \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^{10} b + 11 \, a^{8} b^{3} + 14 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - a^{2} b^{9} - b^{11}\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{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{d^{4}}} + 2 \, {\left(3 \, a^{17} b + 20 \, a^{15} b^{3} + 56 \, a^{13} b^{5} + 84 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 28 \, a^{7} b^{11} - 4 \, a^{3} b^{15} - a b^{17}\right)} d^{5} \sqrt{\frac{9 \, a^{12} b^{2} + 30 \, a^{10} b^{4} + 31 \, a^{8} b^{6} + 4 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14}}{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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, 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^{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}}}{9 \, a^{34} b^{2} + 129 \, a^{32} b^{4} + 856 \, a^{30} b^{6} + 3480 \, a^{28} b^{8} + 9660 \, a^{26} b^{10} + 19292 \, a^{24} b^{12} + 28392 \, a^{22} b^{14} + 30888 \, a^{20} b^{16} + 24310 \, a^{18} b^{18} + 12870 \, a^{16} b^{20} + 3432 \, a^{14} b^{22} - 728 \, a^{12} b^{24} - 1092 \, a^{10} b^{26} - 420 \, a^{8} b^{28} - 40 \, a^{6} b^{30} + 24 \, a^{4} b^{32} + 9 \, a^{2} b^{34} + b^{36}}\right) \cos\left(d x + c\right)^{2} + 5 \, \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, 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^{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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}}} \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(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)} 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(2 \, {\left(9 \, a^{9} b^{3} + 12 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 4 \, a^{3} b^{9} + a b^{11}\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(9 \, a^{16} b^{3} + 48 \, a^{14} b^{5} + 100 \, a^{12} b^{7} + 96 \, a^{10} b^{9} + 30 \, a^{8} b^{11} - 16 \, a^{6} b^{13} - 12 \, a^{4} b^{15} + b^{19}\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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, 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^{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(9 \, a^{21} b^{2} + 66 \, a^{19} b^{4} + 205 \, a^{17} b^{6} + 344 \, a^{15} b^{8} + 322 \, a^{13} b^{10} + 140 \, a^{11} b^{12} - 14 \, a^{9} b^{14} - 40 \, a^{7} b^{16} - 11 \, a^{5} b^{18} + 2 \, a^{3} b^{20} + a b^{22}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{20} b^{3} + 66 \, a^{18} b^{5} + 205 \, a^{16} b^{7} + 344 \, a^{14} b^{9} + 322 \, a^{12} b^{11} + 140 \, a^{10} b^{13} - 14 \, a^{8} b^{15} - 40 \, a^{6} b^{17} - 11 \, a^{4} b^{19} + 2 \, a^{2} b^{21} + b^{23}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 5 \, \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, 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^{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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}}} \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(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)} 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(2 \, {\left(9 \, a^{9} b^{3} + 12 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 4 \, a^{3} b^{9} + a b^{11}\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(9 \, a^{16} b^{3} + 48 \, a^{14} b^{5} + 100 \, a^{12} b^{7} + 96 \, a^{10} b^{9} + 30 \, a^{8} b^{11} - 16 \, a^{6} b^{13} - 12 \, a^{4} b^{15} + b^{19}\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^{3} - 3 \, a b^{2}\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}}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, 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^{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(9 \, a^{21} b^{2} + 66 \, a^{19} b^{4} + 205 \, a^{17} b^{6} + 344 \, a^{15} b^{8} + 322 \, a^{13} b^{10} + 140 \, a^{11} b^{12} - 14 \, a^{9} b^{14} - 40 \, a^{7} b^{16} - 11 \, a^{5} b^{18} + 2 \, a^{3} b^{20} + a b^{22}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{20} b^{3} + 66 \, a^{18} b^{5} + 205 \, a^{16} b^{7} + 344 \, a^{14} b^{9} + 322 \, a^{12} b^{11} + 140 \, a^{10} b^{13} - 14 \, a^{8} b^{15} - 40 \, a^{6} b^{17} - 11 \, a^{4} b^{19} + 2 \, a^{2} b^{21} + b^{23}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(a^{14} b^{3} + 7 \, a^{12} b^{5} + 21 \, a^{10} b^{7} + 35 \, a^{8} b^{9} + 35 \, a^{6} b^{11} + 21 \, a^{4} b^{13} + 7 \, a^{2} b^{15} + b^{17} - 2 \, {\left(2 \, a^{16} b + 17 \, a^{14} b^{3} + 63 \, a^{12} b^{5} + 133 \, a^{10} b^{7} + 175 \, a^{8} b^{9} + 147 \, a^{6} b^{11} + 77 \, a^{4} b^{13} + 23 \, a^{2} b^{15} + 3 \, b^{17}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\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)}}}{20 \, {\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,"-1/20*(20*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^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*((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((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/d^4)*arctan(((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^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((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/d^4) + (3*a^29 + 38*a^27*b^2 + 221*a^25*b^4 + 780*a^23*b^6 + 1859*a^21*b^8 + 3146*a^19*b^10 + 3861*a^17*b^12 + 3432*a^15*b^14 + 2145*a^13*b^16 + 858*a^11*b^18 + 143*a^9*b^20 - 52*a^7*b^22 - 39*a^5*b^24 - 10*a^3*b^26 - a*b^28)*d^2*sqrt((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/d^4) + sqrt(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((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/d^4) + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/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^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*sqrt(((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)*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)*(2*(9*a^9*b^3 + 12*a^7*b^5 - 2*a^5*b^7 - 4*a^3*b^9 + a*b^11)*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) + (9*a^16*b^3 + 48*a^14*b^5 + 100*a^12*b^7 + 96*a^10*b^9 + 30*a^8*b^11 - 16*a^6*b^13 - 12*a^4*b^15 + b^19)*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^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*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) + (9*a^21*b^2 + 66*a^19*b^4 + 205*a^17*b^6 + 344*a^15*b^8 + 322*a^13*b^10 + 140*a^11*b^12 - 14*a^9*b^14 - 40*a^7*b^16 - 11*a^5*b^18 + 2*a^3*b^20 + a*b^22)*cos(d*x + c) + (9*a^20*b^3 + 66*a^18*b^5 + 205*a^16*b^7 + 344*a^14*b^9 + 322*a^12*b^11 + 140*a^10*b^13 - 14*a^8*b^15 - 40*a^6*b^17 - 11*a^4*b^19 + 2*a^2*b^21 + b^23)*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^10*b + 11*a^8*b^3 + 14*a^6*b^5 + 6*a^4*b^7 - a^2*b^9 - b^11)*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((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/d^4) + 2*(3*a^17*b + 20*a^15*b^3 + 56*a^13*b^5 + 84*a^11*b^7 + 70*a^9*b^9 + 28*a^7*b^11 - 4*a^3*b^15 - a*b^17)*d^5*sqrt((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/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^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*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))/(9*a^34*b^2 + 129*a^32*b^4 + 856*a^30*b^6 + 3480*a^28*b^8 + 9660*a^26*b^10 + 19292*a^24*b^12 + 28392*a^22*b^14 + 30888*a^20*b^16 + 24310*a^18*b^18 + 12870*a^16*b^20 + 3432*a^14*b^22 - 728*a^12*b^24 - 1092*a^10*b^26 - 420*a^8*b^28 - 40*a^6*b^30 + 24*a^4*b^32 + 9*a^2*b^34 + b^36))*cos(d*x + c)^2 + 20*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^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*((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((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/d^4)*arctan(-((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^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((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/d^4) + (3*a^29 + 38*a^27*b^2 + 221*a^25*b^4 + 780*a^23*b^6 + 1859*a^21*b^8 + 3146*a^19*b^10 + 3861*a^17*b^12 + 3432*a^15*b^14 + 2145*a^13*b^16 + 858*a^11*b^18 + 143*a^9*b^20 - 52*a^7*b^22 - 39*a^5*b^24 - 10*a^3*b^26 - a*b^28)*d^2*sqrt((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/d^4) - sqrt(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((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/d^4) + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/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^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*sqrt(((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)*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)*(2*(9*a^9*b^3 + 12*a^7*b^5 - 2*a^5*b^7 - 4*a^3*b^9 + a*b^11)*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) + (9*a^16*b^3 + 48*a^14*b^5 + 100*a^12*b^7 + 96*a^10*b^9 + 30*a^8*b^11 - 16*a^6*b^13 - 12*a^4*b^15 + b^19)*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^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*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) + (9*a^21*b^2 + 66*a^19*b^4 + 205*a^17*b^6 + 344*a^15*b^8 + 322*a^13*b^10 + 140*a^11*b^12 - 14*a^9*b^14 - 40*a^7*b^16 - 11*a^5*b^18 + 2*a^3*b^20 + a*b^22)*cos(d*x + c) + (9*a^20*b^3 + 66*a^18*b^5 + 205*a^16*b^7 + 344*a^14*b^9 + 322*a^12*b^11 + 140*a^10*b^13 - 14*a^8*b^15 - 40*a^6*b^17 - 11*a^4*b^19 + 2*a^2*b^21 + b^23)*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^10*b + 11*a^8*b^3 + 14*a^6*b^5 + 6*a^4*b^7 - a^2*b^9 - b^11)*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((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/d^4) + 2*(3*a^17*b + 20*a^15*b^3 + 56*a^13*b^5 + 84*a^11*b^7 + 70*a^9*b^9 + 28*a^7*b^11 - 4*a^3*b^15 - a*b^17)*d^5*sqrt((9*a^12*b^2 + 30*a^10*b^4 + 31*a^8*b^6 + 4*a^6*b^8 - 9*a^4*b^10 - 2*a^2*b^12 + b^14)/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^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*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))/(9*a^34*b^2 + 129*a^32*b^4 + 856*a^30*b^6 + 3480*a^28*b^8 + 9660*a^26*b^10 + 19292*a^24*b^12 + 28392*a^22*b^14 + 30888*a^20*b^16 + 24310*a^18*b^18 + 12870*a^16*b^20 + 3432*a^14*b^22 - 728*a^12*b^24 - 1092*a^10*b^26 - 420*a^8*b^28 - 40*a^6*b^30 + 24*a^4*b^32 + 9*a^2*b^34 + b^36))*cos(d*x + c)^2 + 5*sqrt(2)*((a^7 - a^5*b^2 - 5*a^3*b^4 - 3*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^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*((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(((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)*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)*(2*(9*a^9*b^3 + 12*a^7*b^5 - 2*a^5*b^7 - 4*a^3*b^9 + a*b^11)*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) + (9*a^16*b^3 + 48*a^14*b^5 + 100*a^12*b^7 + 96*a^10*b^9 + 30*a^8*b^11 - 16*a^6*b^13 - 12*a^4*b^15 + b^19)*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^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*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) + (9*a^21*b^2 + 66*a^19*b^4 + 205*a^17*b^6 + 344*a^15*b^8 + 322*a^13*b^10 + 140*a^11*b^12 - 14*a^9*b^14 - 40*a^7*b^16 - 11*a^5*b^18 + 2*a^3*b^20 + a*b^22)*cos(d*x + c) + (9*a^20*b^3 + 66*a^18*b^5 + 205*a^16*b^7 + 344*a^14*b^9 + 322*a^12*b^11 + 140*a^10*b^13 - 14*a^8*b^15 - 40*a^6*b^17 - 11*a^4*b^19 + 2*a^2*b^21 + b^23)*sin(d*x + c))/cos(d*x + c)) - 5*sqrt(2)*((a^7 - a^5*b^2 - 5*a^3*b^4 - 3*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^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*((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(((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)*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)*(2*(9*a^9*b^3 + 12*a^7*b^5 - 2*a^5*b^7 - 4*a^3*b^9 + a*b^11)*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) + (9*a^16*b^3 + 48*a^14*b^5 + 100*a^12*b^7 + 96*a^10*b^9 + 30*a^8*b^11 - 16*a^6*b^13 - 12*a^4*b^15 + b^19)*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^3 - 3*a*b^2)*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))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10))*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) + (9*a^21*b^2 + 66*a^19*b^4 + 205*a^17*b^6 + 344*a^15*b^8 + 322*a^13*b^10 + 140*a^11*b^12 - 14*a^9*b^14 - 40*a^7*b^16 - 11*a^5*b^18 + 2*a^3*b^20 + a*b^22)*cos(d*x + c) + (9*a^20*b^3 + 66*a^18*b^5 + 205*a^16*b^7 + 344*a^14*b^9 + 322*a^12*b^11 + 140*a^10*b^13 - 14*a^8*b^15 - 40*a^6*b^17 - 11*a^4*b^19 + 2*a^2*b^21 + b^23)*sin(d*x + c))/cos(d*x + c)) - 8*(a^14*b^3 + 7*a^12*b^5 + 21*a^10*b^7 + 35*a^8*b^9 + 35*a^6*b^11 + 21*a^4*b^13 + 7*a^2*b^15 + b^17 - 2*(2*a^16*b + 17*a^14*b^3 + 63*a^12*b^5 + 133*a^10*b^7 + 175*a^8*b^9 + 147*a^6*b^11 + 77*a^4*b^13 + 23*a^2*b^15 + 3*b^17)*cos(d*x + c)^2 + 2*(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
341,1,4304,0,2.276167," ","integrate((-a+b*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} + a 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}}}}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}} \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{a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{\sqrt{2} {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + a 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}}}}{a^{4} b^{2} + 2 \, 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^{10} + 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{a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + a 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}}}}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{\sqrt{2} {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + a 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}}}}{a^{4} b^{2} + 2 \, 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^{10} + 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}} \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)} 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) + {\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)}{\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{\frac{a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, 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^{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{a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{15} + 7 \, a^{13} b^{2} + 21 \, a^{11} b^{4} + 35 \, a^{9} b^{6} + 35 \, a^{7} b^{8} + 21 \, a^{5} b^{10} + 7 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{a^{18} b^{2} + 9 \, a^{16} b^{4} + 36 \, a^{14} b^{6} + 84 \, a^{12} b^{8} + 126 \, a^{10} b^{10} + 126 \, a^{8} b^{12} + 84 \, a^{6} b^{14} + 36 \, a^{4} b^{16} + 9 \, a^{2} b^{18} + b^{20}}\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} + a 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}}}}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}} \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{a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{\sqrt{2} {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + a 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}}}}{a^{4} b^{2} + 2 \, 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^{10} + 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{a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + a 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}}}}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}} \sqrt{-\frac{\sqrt{2} {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + a 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}}}}{a^{4} b^{2} + 2 \, 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^{10} + 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}} \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)} 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) - {\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)}{\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{\frac{a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, 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^{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{a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}}{d^{4}}} - {\left(a^{15} + 7 \, a^{13} b^{2} + 21 \, a^{11} b^{4} + 35 \, a^{9} b^{6} + 35 \, a^{7} b^{8} + 21 \, a^{5} b^{10} + 7 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{a^{18} b^{2} + 9 \, a^{16} b^{4} + 36 \, a^{14} b^{6} + 84 \, a^{12} b^{8} + 126 \, a^{10} b^{10} + 126 \, a^{8} b^{12} + 84 \, a^{6} b^{14} + 36 \, a^{4} b^{16} + 9 \, a^{2} b^{18} + b^{20}}\right) \cos\left(d x + c\right) - 3 \, \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + 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^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + a 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}}}}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}} \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{\sqrt{2} {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + a 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}}}}{a^{4} b^{2} + 2 \, 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^{10} + 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}} \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)} 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) + {\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)}{\cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + 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^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + a 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}}}}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}} \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{\sqrt{2} {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + a 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}}}}{a^{4} b^{2} + 2 \, 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^{10} + 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}} \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)} 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) - {\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)}{\cos\left(d x + c\right)}\right) + 8 \, {\left({\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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*((a^10 + 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((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)/d^4)*arctan(-(sqrt(2)*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*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((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)/d^4) - sqrt(2)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*sqrt((sqrt(2)*(a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*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)*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)*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) + (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))/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((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*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^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((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)/d^4) + (a^15 + 7*a^13*b^2 + 21*a^11*b^4 + 35*a^9*b^6 + 35*a^7*b^8 + 21*a^5*b^10 + 7*a^3*b^12 + a*b^14)*d^2*sqrt((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)/d^4))/(a^18*b^2 + 9*a^16*b^4 + 36*a^14*b^6 + 84*a^12*b^8 + 126*a^10*b^10 + 126*a^8*b^12 + 84*a^6*b^14 + 36*a^4*b^16 + 9*a^2*b^18 + b^20))*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*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*((a^10 + 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((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)/d^4)*arctan(-(sqrt(2)*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*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((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)/d^4) - sqrt(2)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*sqrt(-(sqrt(2)*(a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*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)*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)*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) - (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))/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((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*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^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((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)/d^4) - (a^15 + 7*a^13*b^2 + 21*a^11*b^4 + 35*a^9*b^6 + 35*a^7*b^8 + 21*a^5*b^10 + 7*a^3*b^12 + a*b^14)*d^2*sqrt((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)/d^4))/(a^18*b^2 + 9*a^16*b^4 + 36*a^14*b^6 + 84*a^12*b^8 + 126*a^10*b^10 + 126*a^8*b^12 + 84*a^6*b^14 + 36*a^4*b^16 + 9*a^2*b^18 + b^20))*cos(d*x + c) - 3*sqrt(2)*((a^5 + 2*a^3*b^2 + 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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*((a^10 + 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((sqrt(2)*(a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*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)*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)*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) + (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))/cos(d*x + c)) + 3*sqrt(2)*((a^5 + 2*a^3*b^2 + 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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*((a^10 + 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(-(sqrt(2)*(a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + a*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))/(a^4*b^2 + 2*a^2*b^4 + b^6))*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)*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)*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) - (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))/cos(d*x + c)) + 8*((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
342,1,3055,0,0.905791," ","integrate((-a+b*tan(d*x+c))*(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{\sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \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{5}{4}} \sqrt{\frac{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sqrt{2} {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \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}} \cos\left(d x + c\right) + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, 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) + {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\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)} \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{5}{4}} \sqrt{\frac{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}{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^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\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^{2} \sqrt{\frac{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{14} b^{2} + 7 \, a^{12} b^{4} + 21 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 35 \, a^{6} b^{10} + 21 \, a^{4} b^{12} + 7 \, a^{2} b^{14} + b^{16}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{\sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \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{5}{4}} \sqrt{\frac{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \sqrt{-\frac{\sqrt{2} {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \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}} \cos\left(d x + c\right) - {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, 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) - {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\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)} \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{5}{4}} \sqrt{\frac{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}{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^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}{d^{4}}} - {\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^{2} \sqrt{\frac{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{14} b^{2} + 7 \, a^{12} b^{4} + 21 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 35 \, a^{6} b^{10} + 21 \, a^{4} b^{12} + 7 \, a^{2} b^{14} + b^{16}}\right) + \sqrt{2} {\left({\left(a^{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^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \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{\sqrt{2} {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \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}} \cos\left(d x + c\right) + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, 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) + {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\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)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{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^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \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{\sqrt{2} {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + a d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{a^{2} b^{2} + b^{4}}} \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}} \cos\left(d x + c\right) - {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, 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) - {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\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)} \sin\left(d x + c\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^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((a^4*b^2 + 2*a^2*b^4 + b^6)/d^4)*arctan(-(sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*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)^(5/4)*sqrt((a^4*b^2 + 2*a^2*b^4 + b^6)/d^4) - sqrt(2)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*sqrt((sqrt(2)*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d*sqrt((a^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*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)*cos(d*x + c) + (a^6*b^2 + 3*a^4*b^4 + 3*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) + (a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*cos(d*x + c) + (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(5/4)*sqrt((a^4*b^2 + 2*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^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((a^4*b^2 + 2*a^2*b^4 + b^6)/d^4) + (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^2*sqrt((a^4*b^2 + 2*a^2*b^4 + b^6)/d^4))/(a^14*b^2 + 7*a^12*b^4 + 21*a^10*b^6 + 35*a^8*b^8 + 35*a^6*b^10 + 21*a^4*b^12 + 7*a^2*b^14 + b^16)) + 4*sqrt(2)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((a^4*b^2 + 2*a^2*b^4 + b^6)/d^4)*arctan(-(sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*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)^(5/4)*sqrt((a^4*b^2 + 2*a^2*b^4 + b^6)/d^4) - sqrt(2)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*sqrt(-(sqrt(2)*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d*sqrt((a^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*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)*cos(d*x + c) - (a^6*b^2 + 3*a^4*b^4 + 3*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) - (a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*cos(d*x + c) - (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(5/4)*sqrt((a^4*b^2 + 2*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^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((a^4*b^2 + 2*a^2*b^4 + b^6)/d^4) - (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^2*sqrt((a^4*b^2 + 2*a^2*b^4 + b^6)/d^4))/(a^14*b^2 + 7*a^12*b^4 + 21*a^10*b^6 + 35*a^8*b^8 + 35*a^6*b^10 + 21*a^4*b^12 + 7*a^2*b^14 + b^16)) + sqrt(2)*((a^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^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log((sqrt(2)*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d*sqrt((a^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*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)*cos(d*x + c) + (a^6*b^2 + 3*a^4*b^4 + 3*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) + (a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*cos(d*x + c) + (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^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^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(-(sqrt(2)*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d*sqrt((a^4 + 2*a^2*b^2 + b^4 + a*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(a^2*b^2 + b^4))*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)*cos(d*x + c) - (a^6*b^2 + 3*a^4*b^4 + 3*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) - (a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*cos(d*x + c) - (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*sin(d*x + c))/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
343,1,8574,0,7.076513," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(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(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{5} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{4} b + 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{2} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{3} + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{4} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{5}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(A a^{5} + B a^{4} b + 2 \, A a^{3} b^{2} + 2 \, B a^{2} b^{3} + A a b^{4} + B b^{5}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{4} + 2 \, {\left(A^{3} + A B^{2}\right)} a^{2} b^{2} + {\left(A^{3} + A B^{2}\right)} b^{4}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{4} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a^{3} b + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{2} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a b^{3} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{3} - 4 \, {\left(A^{6} B - A^{4} B^{3} - 2 \, A^{2} B^{5}\right)} a^{2} b + {\left(A^{7} - 5 \, A^{5} B^{2} - A^{3} B^{4} + 5 \, A B^{6}\right)} a b^{2} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(2 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{6} - {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a^{5} b + {\left(3 \, A^{4} B + 4 \, A^{2} B^{3} + B^{5}\right)} a^{4} b^{2} - 2 \, {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a^{3} b^{3} + 2 \, {\left(A^{2} B^{3} + B^{5}\right)} a^{2} b^{4} - {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a b^{5} - {\left(A^{4} B - B^{5}\right)} b^{6}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{5} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{4} b + 4 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{2} b^{3} + 2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a b^{4} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{5}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{2} b - 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)} a b^{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)} b^{3}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} {\left(a^{2} b^{3} + b^{5}\right)} d^{5} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{5} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{4} b + 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{2} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{3} + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{4} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{5}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(A a^{5} + B a^{4} b + 2 \, A a^{3} b^{2} + 2 \, B a^{2} b^{3} + A a b^{4} + B b^{5}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{4} + 2 \, {\left(A^{3} + A B^{2}\right)} a^{2} b^{2} + {\left(A^{3} + A B^{2}\right)} b^{4}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{4} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a^{3} b + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{2} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a b^{3} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{3} - 4 \, {\left(A^{6} B - A^{4} B^{3} - 2 \, A^{2} B^{5}\right)} a^{2} b + {\left(A^{7} - 5 \, A^{5} B^{2} - A^{3} B^{4} + 5 \, A B^{6}\right)} a b^{2} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(2 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{6} - {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a^{5} b + {\left(3 \, A^{4} B + 4 \, A^{2} B^{3} + B^{5}\right)} a^{4} b^{2} - 2 \, {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a^{3} b^{3} + 2 \, {\left(A^{2} B^{3} + B^{5}\right)} a^{2} b^{4} - {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a b^{5} - {\left(A^{4} B - B^{5}\right)} b^{6}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{5} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{4} b + 4 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{2} b^{3} + 2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a b^{4} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{5}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{2} b - 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)} a b^{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)} b^{3}}\right) \cos\left(d x + c\right)^{2} - 15 \, \sqrt{2} {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{3} d \cos\left(d x + c\right)^{2} + {\left(2 \, A B b^{4} + {\left(A^{2} - B^{2}\right)} a b^{3}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{4} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a^{3} b + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{2} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a b^{3} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{3} - 4 \, {\left(A^{6} B - A^{4} B^{3} - 2 \, A^{2} B^{5}\right)} a^{2} b + {\left(A^{7} - 5 \, A^{5} B^{2} - A^{3} B^{4} + 5 \, A B^{6}\right)} a b^{2} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\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)} b^{3} d \cos\left(d x + c\right)^{2} + {\left(2 \, A B b^{4} + {\left(A^{2} - B^{2}\right)} a b^{3}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{4} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a^{3} b + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{2} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a b^{3} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{3} - 4 \, {\left(A^{6} B - A^{4} B^{3} - 2 \, A^{2} B^{5}\right)} a^{2} b + {\left(A^{7} - 5 \, A^{5} B^{2} - A^{3} B^{4} + 5 \, A B^{6}\right)} a b^{2} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{2} + 2 \, {\left(4 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} - 5 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a b - 9 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} - {\left(4 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b - 5 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b^{2}\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^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} 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(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4)*arctan(-((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^4*b + 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^2 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^3 + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^4 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^5)*d^4*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((A*a^5 + B*a^4*b + 2*A*a^3*b^2 + 2*B*a^2*b^3 + A*a*b^4 + B*b^5)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + ((A^3 + A*B^2)*a^4 + 2*(A^3 + A*B^2)*a^2*b^2 + (A^3 + A*B^2)*b^4)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((4*A^3*B^2*a^4 - 4*(A^4*B - A^2*B^3)*a^3*b + (A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^2 - 4*(A^4*B - A^2*B^3)*a*b^3 + (A^5 - 2*A^3*B^2 + A*B^4)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^3 - 4*(A^6*B - A^4*B^3 - 2*A^2*B^5)*a^2*b + (A^7 - 5*A^5*B^2 - A^3*B^4 + 5*A*B^6)*a*b^2 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^3)*d*cos(d*x + c))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((2*(A^4*B + A^2*B^3)*a^6 - (A^5 - 2*A^3*B^2 - 3*A*B^4)*a^5*b + (3*A^4*B + 4*A^2*B^3 + B^5)*a^4*b^2 - 2*(A^5 - 2*A^3*B^2 - 3*A*B^4)*a^3*b^3 + 2*(A^2*B^3 + B^5)*a^2*b^4 - (A^5 - 2*A^3*B^2 - 3*A*B^4)*a*b^5 - (A^4*B - B^5)*b^6)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^5 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^4*b + 4*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^3*b^2 - 2*(A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^2*b^3 + 2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a*b^4 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^5)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^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)*a^2*b - 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)*a*b^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)*b^3))*cos(d*x + c)^2 + 60*sqrt(2)*(a^2*b^3 + b^5)*d^5*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4)*arctan(((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^4*b + 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^2 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^3 + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^4 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^5)*d^4*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((A*a^5 + B*a^4*b + 2*A*a^3*b^2 + 2*B*a^2*b^3 + A*a*b^4 + B*b^5)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + ((A^3 + A*B^2)*a^4 + 2*(A^3 + A*B^2)*a^2*b^2 + (A^3 + A*B^2)*b^4)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((4*A^3*B^2*a^4 - 4*(A^4*B - A^2*B^3)*a^3*b + (A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^2 - 4*(A^4*B - A^2*B^3)*a*b^3 + (A^5 - 2*A^3*B^2 + A*B^4)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^3 - 4*(A^6*B - A^4*B^3 - 2*A^2*B^5)*a^2*b + (A^7 - 5*A^5*B^2 - A^3*B^4 + 5*A*B^6)*a*b^2 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^3)*d*cos(d*x + c))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((2*(A^4*B + A^2*B^3)*a^6 - (A^5 - 2*A^3*B^2 - 3*A*B^4)*a^5*b + (3*A^4*B + 4*A^2*B^3 + B^5)*a^4*b^2 - 2*(A^5 - 2*A^3*B^2 - 3*A*B^4)*a^3*b^3 + 2*(A^2*B^3 + B^5)*a^2*b^4 - (A^5 - 2*A^3*B^2 - 3*A*B^4)*a*b^5 - (A^4*B - B^5)*b^6)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^5 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^4*b + 4*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^3*b^2 - 2*(A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^2*b^3 + 2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a*b^4 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^5)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^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)*a^2*b - 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)*a*b^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)*b^3))*cos(d*x + c)^2 - 15*sqrt(2)*((A^4 + 2*A^2*B^2 + B^4)*b^3*d*cos(d*x + c)^2 + (2*A*B*b^4 + (A^2 - B^2)*a*b^3)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c)^2)*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((4*A^3*B^2*a^4 - 4*(A^4*B - A^2*B^3)*a^3*b + (A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^2 - 4*(A^4*B - A^2*B^3)*a*b^3 + (A^5 - 2*A^3*B^2 + A*B^4)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^3 - 4*(A^6*B - A^4*B^3 - 2*A^2*B^5)*a^2*b + (A^7 - 5*A^5*B^2 - A^3*B^4 + 5*A*B^6)*a*b^2 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^3)*d*cos(d*x + c))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c)) + 15*sqrt(2)*((A^4 + 2*A^2*B^2 + B^4)*b^3*d*cos(d*x + c)^2 + (2*A*B*b^4 + (A^2 - B^2)*a*b^3)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c)^2)*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((4*A^3*B^2*a^4 - 4*(A^4*B - A^2*B^3)*a^3*b + (A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^2 - 4*(A^4*B - A^2*B^3)*a*b^3 + (A^5 - 2*A^3*B^2 + A*B^4)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^3 - 4*(A^6*B - A^4*B^3 - 2*A^2*B^5)*a^2*b + (A^7 - 5*A^5*B^2 - A^3*B^4 + 5*A*B^6)*a*b^2 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^3)*d*cos(d*x + c))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c)) - 8*(3*(A^4*B + 2*A^2*B^3 + B^5)*b^2 + 2*(4*(A^4*B + 2*A^2*B^3 + B^5)*a^2 - 5*(A^5 + 2*A^3*B^2 + A*B^4)*a*b - 9*(A^4*B + 2*A^2*B^3 + B^5)*b^2)*cos(d*x + c)^2 - (4*(A^4*B + 2*A^2*B^3 + B^5)*a*b - 5*(A^5 + 2*A^3*B^2 + A*B^4)*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 + 2*A^2*B^2 + B^4)*b^3*d*cos(d*x + c)^2)","B",0
344,1,8468,0,5.467226," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(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(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{5} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{4} b + 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{2} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{3} + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{4} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{5}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(B a^{5} - A a^{4} b + 2 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3} + B a b^{4} - A b^{5}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left({\left(A^{2} B + B^{3}\right)} a^{4} + 2 \, {\left(A^{2} B + B^{3}\right)} a^{2} b^{2} + {\left(A^{2} B + B^{3}\right)} b^{4}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a^{3} b + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a b^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} a^{2} b + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} a b^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(2 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{6} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a^{5} b + {\left(A^{5} + 4 \, A^{3} B^{2} + 3 \, A B^{4}\right)} a^{4} b^{2} - 2 \, {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a^{3} b^{3} + 2 \, {\left(A^{5} + A^{3} B^{2}\right)} a^{2} b^{4} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a b^{5} + {\left(A^{5} - A B^{4}\right)} b^{6}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{5} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{4} b + 4 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{2} - 2 \, {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{2} b^{3} + 2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a b^{4} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{5}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{2} b - 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)} a b^{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)} b^{3}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} {\left(a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{5} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{4} b + 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{2} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{3} + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{4} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{5}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(B a^{5} - A a^{4} b + 2 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3} + B a b^{4} - A b^{5}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left({\left(A^{2} B + B^{3}\right)} a^{4} + 2 \, {\left(A^{2} B + B^{3}\right)} a^{2} b^{2} + {\left(A^{2} B + B^{3}\right)} b^{4}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a^{3} b + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a b^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} a^{2} b + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} a b^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(2 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{6} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a^{5} b + {\left(A^{5} + 4 \, A^{3} B^{2} + 3 \, A B^{4}\right)} a^{4} b^{2} - 2 \, {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a^{3} b^{3} + 2 \, {\left(A^{5} + A^{3} B^{2}\right)} a^{2} b^{4} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a b^{5} + {\left(A^{5} - A B^{4}\right)} b^{6}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{5} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{4} b + 4 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{2} - 2 \, {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{2} b^{3} + 2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a b^{4} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{5}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{2} b - 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)} a b^{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)} b^{3}}\right) \cos\left(d x + c\right) + 3 \, \sqrt{2} {\left({\left(2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a^{3} b + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a b^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} a^{2} b + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} a b^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left({\left(2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a^{3} b + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a b^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} a^{2} b + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} a b^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b \sin\left(d x + c\right) - {\left(2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a - 3 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b\right)} \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)}}}{12 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2} d \cos\left(d x + c\right)}"," ",0,"-1/12*(12*sqrt(2)*(a^2*b^2 + b^4)*d^5*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4)*arctan(((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^4*b + 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^2 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^3 + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^4 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^5)*d^4*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((B*a^5 - A*a^4*b + 2*B*a^3*b^2 - 2*A*a^2*b^3 + B*a*b^4 - A*b^5)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + ((A^2*B + B^3)*a^4 + 2*(A^2*B + B^3)*a^2*b^2 + (A^2*B + B^3)*b^4)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((4*A^2*B^3*a^4 - 4*(A^3*B^2 - A*B^4)*a^3*b + (A^4*B + 2*A^2*B^3 + B^5)*a^2*b^2 - 4*(A^3*B^2 - A*B^4)*a*b^3 + (A^4*B - 2*A^2*B^3 + B^5)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*a^2*b + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*a*b^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^3)*d*cos(d*x + c))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((2*(A^3*B^2 + A*B^4)*a^6 - (3*A^4*B + 2*A^2*B^3 - B^5)*a^5*b + (A^5 + 4*A^3*B^2 + 3*A*B^4)*a^4*b^2 - 2*(3*A^4*B + 2*A^2*B^3 - B^5)*a^3*b^3 + 2*(A^5 + A^3*B^2)*a^2*b^4 - (3*A^4*B + 2*A^2*B^3 - B^5)*a*b^5 + (A^5 - A*B^4)*b^6)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^5 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^4*b + 4*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^3*b^2 - 2*(A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^2*b^3 + 2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a*b^4 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^5)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^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)*a^2*b - 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)*a*b^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)*b^3))*cos(d*x + c) + 12*sqrt(2)*(a^2*b^2 + b^4)*d^5*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4)*arctan(-((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^4*b + 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^2 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^3 + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^4 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^5)*d^4*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((B*a^5 - A*a^4*b + 2*B*a^3*b^2 - 2*A*a^2*b^3 + B*a*b^4 - A*b^5)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + ((A^2*B + B^3)*a^4 + 2*(A^2*B + B^3)*a^2*b^2 + (A^2*B + B^3)*b^4)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((4*A^2*B^3*a^4 - 4*(A^3*B^2 - A*B^4)*a^3*b + (A^4*B + 2*A^2*B^3 + B^5)*a^2*b^2 - 4*(A^3*B^2 - A*B^4)*a*b^3 + (A^4*B - 2*A^2*B^3 + B^5)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*a^2*b + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*a*b^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^3)*d*cos(d*x + c))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((2*(A^3*B^2 + A*B^4)*a^6 - (3*A^4*B + 2*A^2*B^3 - B^5)*a^5*b + (A^5 + 4*A^3*B^2 + 3*A*B^4)*a^4*b^2 - 2*(3*A^4*B + 2*A^2*B^3 - B^5)*a^3*b^3 + 2*(A^5 + A^3*B^2)*a^2*b^4 - (3*A^4*B + 2*A^2*B^3 - B^5)*a*b^5 + (A^5 - A*B^4)*b^6)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^5 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^4*b + 4*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^3*b^2 - 2*(A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^2*b^3 + 2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a*b^4 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^5)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^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)*a^2*b - 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)*a*b^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)*b^3))*cos(d*x + c) + 3*sqrt(2)*((2*A*B*b^3 + (A^2 - B^2)*a*b^2)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) - (A^4 + 2*A^2*B^2 + B^4)*b^2*d*cos(d*x + c))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((4*A^2*B^3*a^4 - 4*(A^3*B^2 - A*B^4)*a^3*b + (A^4*B + 2*A^2*B^3 + B^5)*a^2*b^2 - 4*(A^3*B^2 - A*B^4)*a*b^3 + (A^4*B - 2*A^2*B^3 + B^5)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*a^2*b + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*a*b^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^3)*d*cos(d*x + c))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*((2*A*B*b^3 + (A^2 - B^2)*a*b^2)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) - (A^4 + 2*A^2*B^2 + B^4)*b^2*d*cos(d*x + c))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((4*A^2*B^3*a^4 - 4*(A^3*B^2 - A*B^4)*a^3*b + (A^4*B + 2*A^2*B^3 + B^5)*a^2*b^2 - 4*(A^3*B^2 - A*B^4)*a*b^3 + (A^4*B - 2*A^2*B^3 + B^5)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*a^2*b + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*a*b^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^3)*d*cos(d*x + c))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c)) - 8*((A^4*B + 2*A^2*B^3 + B^5)*b*sin(d*x + c) - (2*(A^4*B + 2*A^2*B^3 + B^5)*a - 3*(A^5 + 2*A^3*B^2 + A*B^4)*b)*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((A^4 + 2*A^2*B^2 + B^4)*b^2*d*cos(d*x + c))","B",0
345,1,8365,0,6.495482," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(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(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{5} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{4} b + 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{2} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{3} + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{4} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{5}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(A a^{5} + B a^{4} b + 2 \, A a^{3} b^{2} + 2 \, B a^{2} b^{3} + A a b^{4} + B b^{5}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{4} + 2 \, {\left(A^{3} + A B^{2}\right)} a^{2} b^{2} + {\left(A^{3} + A B^{2}\right)} b^{4}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{4} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a^{3} b + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{2} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a b^{3} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{3} - 4 \, {\left(A^{6} B - A^{4} B^{3} - 2 \, A^{2} B^{5}\right)} a^{2} b + {\left(A^{7} - 5 \, A^{5} B^{2} - A^{3} B^{4} + 5 \, A B^{6}\right)} a b^{2} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(2 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{6} - {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a^{5} b + {\left(3 \, A^{4} B + 4 \, A^{2} B^{3} + B^{5}\right)} a^{4} b^{2} - 2 \, {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a^{3} b^{3} + 2 \, {\left(A^{2} B^{3} + B^{5}\right)} a^{2} b^{4} - {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a b^{5} - {\left(A^{4} B - B^{5}\right)} b^{6}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{5} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{4} b + 4 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{2} b^{3} + 2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a b^{4} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{5}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{2} b - 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)} a b^{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)} b^{3}}\right) + 4 \, \sqrt{2} {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{5} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{4} b + 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{2} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{3} + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{4} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{5}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(A a^{5} + B a^{4} b + 2 \, A a^{3} b^{2} + 2 \, B a^{2} b^{3} + A a b^{4} + B b^{5}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{4} + 2 \, {\left(A^{3} + A B^{2}\right)} a^{2} b^{2} + {\left(A^{3} + A B^{2}\right)} b^{4}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{4} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a^{3} b + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{2} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a b^{3} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{3} - 4 \, {\left(A^{6} B - A^{4} B^{3} - 2 \, A^{2} B^{5}\right)} a^{2} b + {\left(A^{7} - 5 \, A^{5} B^{2} - A^{3} B^{4} + 5 \, A B^{6}\right)} a b^{2} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(2 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{6} - {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a^{5} b + {\left(3 \, A^{4} B + 4 \, A^{2} B^{3} + B^{5}\right)} a^{4} b^{2} - 2 \, {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a^{3} b^{3} + 2 \, {\left(A^{2} B^{3} + B^{5}\right)} a^{2} b^{4} - {\left(A^{5} - 2 \, A^{3} B^{2} - 3 \, A B^{4}\right)} a b^{5} - {\left(A^{4} B - B^{5}\right)} b^{6}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{5} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{4} b + 4 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{2} b^{3} + 2 \, {\left(A^{6} B + 2 \, A^{4} B^{3} + A^{2} B^{5}\right)} a b^{4} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{5}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{2} b - 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)} a b^{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)} b^{3}}\right) - \sqrt{2} {\left({\left(2 \, A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b d\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{4} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a^{3} b + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{2} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a b^{3} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{3} - 4 \, {\left(A^{6} B - A^{4} B^{3} - 2 \, A^{2} B^{5}\right)} a^{2} b + {\left(A^{7} - 5 \, A^{5} B^{2} - A^{3} B^{4} + 5 \, A B^{6}\right)} a b^{2} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left({\left(2 \, A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b d\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{3} B^{2} a^{4} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a^{3} b + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{2} - 4 \, {\left(A^{4} B - A^{2} B^{3}\right)} a b^{3} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{5} B^{2} + A^{3} B^{4}\right)} a^{3} - 4 \, {\left(A^{6} B - A^{4} B^{3} - 2 \, A^{2} B^{5}\right)} a^{2} b + {\left(A^{7} - 5 \, A^{5} B^{2} - A^{3} B^{4} + 5 \, A B^{6}\right)} a b^{2} + {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} - {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\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{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b d}"," ",0,"1/4*(4*sqrt(2)*(a^2*b + b^3)*d^5*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4)*arctan(-((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^4*b + 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^2 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^3 + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^4 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^5)*d^4*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((A*a^5 + B*a^4*b + 2*A*a^3*b^2 + 2*B*a^2*b^3 + A*a*b^4 + B*b^5)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + ((A^3 + A*B^2)*a^4 + 2*(A^3 + A*B^2)*a^2*b^2 + (A^3 + A*B^2)*b^4)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((4*A^3*B^2*a^4 - 4*(A^4*B - A^2*B^3)*a^3*b + (A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^2 - 4*(A^4*B - A^2*B^3)*a*b^3 + (A^5 - 2*A^3*B^2 + A*B^4)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^3 - 4*(A^6*B - A^4*B^3 - 2*A^2*B^5)*a^2*b + (A^7 - 5*A^5*B^2 - A^3*B^4 + 5*A*B^6)*a*b^2 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^3)*d*cos(d*x + c))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((2*(A^4*B + A^2*B^3)*a^6 - (A^5 - 2*A^3*B^2 - 3*A*B^4)*a^5*b + (3*A^4*B + 4*A^2*B^3 + B^5)*a^4*b^2 - 2*(A^5 - 2*A^3*B^2 - 3*A*B^4)*a^3*b^3 + 2*(A^2*B^3 + B^5)*a^2*b^4 - (A^5 - 2*A^3*B^2 - 3*A*B^4)*a*b^5 - (A^4*B - B^5)*b^6)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^5 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^4*b + 4*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^3*b^2 - 2*(A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^2*b^3 + 2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a*b^4 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^5)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^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)*a^2*b - 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)*a*b^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)*b^3)) + 4*sqrt(2)*(a^2*b + b^3)*d^5*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4)*arctan(((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^4*b + 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^2 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^3 + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^4 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^5)*d^4*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((A*a^5 + B*a^4*b + 2*A*a^3*b^2 + 2*B*a^2*b^3 + A*a*b^4 + B*b^5)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + ((A^3 + A*B^2)*a^4 + 2*(A^3 + A*B^2)*a^2*b^2 + (A^3 + A*B^2)*b^4)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((4*A^3*B^2*a^4 - 4*(A^4*B - A^2*B^3)*a^3*b + (A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^2 - 4*(A^4*B - A^2*B^3)*a*b^3 + (A^5 - 2*A^3*B^2 + A*B^4)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^3 - 4*(A^6*B - A^4*B^3 - 2*A^2*B^5)*a^2*b + (A^7 - 5*A^5*B^2 - A^3*B^4 + 5*A*B^6)*a*b^2 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^3)*d*cos(d*x + c))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((2*(A^4*B + A^2*B^3)*a^6 - (A^5 - 2*A^3*B^2 - 3*A*B^4)*a^5*b + (3*A^4*B + 4*A^2*B^3 + B^5)*a^4*b^2 - 2*(A^5 - 2*A^3*B^2 - 3*A*B^4)*a^3*b^3 + 2*(A^2*B^3 + B^5)*a^2*b^4 - (A^5 - 2*A^3*B^2 - 3*A*B^4)*a*b^5 - (A^4*B - B^5)*b^6)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^5 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^4*b + 4*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a^3*b^2 - 2*(A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^2*b^3 + 2*(A^6*B + 2*A^4*B^3 + A^2*B^5)*a*b^4 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^5)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^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)*a^2*b - 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)*a*b^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)*b^3)) - sqrt(2)*((2*A*B*b^2 + (A^2 - B^2)*a*b)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*b*d)*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((4*A^3*B^2*a^4 - 4*(A^4*B - A^2*B^3)*a^3*b + (A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^2 - 4*(A^4*B - A^2*B^3)*a*b^3 + (A^5 - 2*A^3*B^2 + A*B^4)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^3 - 4*(A^6*B - A^4*B^3 - 2*A^2*B^5)*a^2*b + (A^7 - 5*A^5*B^2 - A^3*B^4 + 5*A*B^6)*a*b^2 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^3)*d*cos(d*x + c))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*((2*A*B*b^2 + (A^2 - B^2)*a*b)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*b*d)*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((4*A^3*B^2*a^4 - 4*(A^4*B - A^2*B^3)*a^3*b + (A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^2 - 4*(A^4*B - A^2*B^3)*a*b^3 + (A^5 - 2*A^3*B^2 + A*B^4)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^5*B^2 + A^3*B^4)*a^3 - 4*(A^6*B - A^4*B^3 - 2*A^2*B^5)*a^2*b + (A^7 - 5*A^5*B^2 - A^3*B^4 + 5*A*B^6)*a*b^2 + (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^3)*d*cos(d*x + c))*sqrt(-((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) - (A^4 + 2*A^2*B^2 + B^4)*a^2 - (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c)) + 8*(A^4*B + 2*A^2*B^3 + B^5)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((A^4 + 2*A^2*B^2 + B^4)*b*d)","B",0
346,1,8282,0,5.409790," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{5} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{4} b + 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{2} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{3} + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{4} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{5}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(B a^{5} - A a^{4} b + 2 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3} + B a b^{4} - A b^{5}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left({\left(A^{2} B + B^{3}\right)} a^{4} + 2 \, {\left(A^{2} B + B^{3}\right)} a^{2} b^{2} + {\left(A^{2} B + B^{3}\right)} b^{4}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a^{3} b + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a b^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} a^{2} b + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} a b^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(2 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{6} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a^{5} b + {\left(A^{5} + 4 \, A^{3} B^{2} + 3 \, A B^{4}\right)} a^{4} b^{2} - 2 \, {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a^{3} b^{3} + 2 \, {\left(A^{5} + A^{3} B^{2}\right)} a^{2} b^{4} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a b^{5} + {\left(A^{5} - A B^{4}\right)} b^{6}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{5} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{4} b + 4 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{2} - 2 \, {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{2} b^{3} + 2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a b^{4} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{5}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{2} b - 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)} a b^{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)} b^{3}}\right) + 4 \, \sqrt{2} {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{5} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{4} b + 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{2} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{3} + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{4} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{5}\right)} d^{4} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{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)} a^{3} b + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} a^{2} b^{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)} a b^{3}\right)} d^{2} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(B a^{5} - A a^{4} b + 2 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3} + B a b^{4} - A b^{5}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left({\left(A^{2} B + B^{3}\right)} a^{4} + 2 \, {\left(A^{2} B + B^{3}\right)} a^{2} b^{2} + {\left(A^{2} B + B^{3}\right)} b^{4}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \sqrt{\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a^{3} b + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a b^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} a^{2} b + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} a b^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(2 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{6} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a^{5} b + {\left(A^{5} + 4 \, A^{3} B^{2} + 3 \, A B^{4}\right)} a^{4} b^{2} - 2 \, {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a^{3} b^{3} + 2 \, {\left(A^{5} + A^{3} B^{2}\right)} a^{2} b^{4} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} a b^{5} + {\left(A^{5} - A B^{4}\right)} b^{6}\right)} d^{7} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{5} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{4} b + 4 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{2} - 2 \, {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{2} b^{3} + 2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} a b^{4} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{5}\right)} d^{5} \sqrt{\frac{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{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)} a^{2} b - 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)} a b^{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)} b^{3}}\right) - \sqrt{2} {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4} - {\left(2 \, A B b + {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a^{3} b + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a b^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} a^{2} b + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} a b^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4} - {\left(2 \, A B b + {\left(A^{2} - B^{2}\right)} a\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} a^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} a^{3} b + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} a b^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{4}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(4 \, A^{2} B^{3} a^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a^{3} b + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} a b^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{4}\right)} d^{3} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} a^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} a^{2} b + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} a b^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(2 \, A B a^{2} b + 2 \, A B b^{3} + {\left(A^{2} - B^{2}\right)} a^{3} + {\left(A^{2} - B^{2}\right)} a b^{2}\right)} d^{2} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}{4 \, A^{2} B^{2} a^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} a b + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{2}}} \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^{4} + 2 \, A^{2} B^{2} + B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{2} b + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a b^{2}\right)} \cos\left(d x + c\right) + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{3}\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)*(a^2 + b^2)*d^4*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4)*arctan(((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^4*b + 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^2 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^3 + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^4 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^5)*d^4*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((B*a^5 - A*a^4*b + 2*B*a^3*b^2 - 2*A*a^2*b^3 + B*a*b^4 - A*b^5)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + ((A^2*B + B^3)*a^4 + 2*(A^2*B + B^3)*a^2*b^2 + (A^2*B + B^3)*b^4)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((4*A^2*B^3*a^4 - 4*(A^3*B^2 - A*B^4)*a^3*b + (A^4*B + 2*A^2*B^3 + B^5)*a^2*b^2 - 4*(A^3*B^2 - A*B^4)*a*b^3 + (A^4*B - 2*A^2*B^3 + B^5)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*a^2*b + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*a*b^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^3)*d*cos(d*x + c))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((2*(A^3*B^2 + A*B^4)*a^6 - (3*A^4*B + 2*A^2*B^3 - B^5)*a^5*b + (A^5 + 4*A^3*B^2 + 3*A*B^4)*a^4*b^2 - 2*(3*A^4*B + 2*A^2*B^3 - B^5)*a^3*b^3 + 2*(A^5 + A^3*B^2)*a^2*b^4 - (3*A^4*B + 2*A^2*B^3 - B^5)*a*b^5 + (A^5 - A*B^4)*b^6)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^5 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^4*b + 4*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^3*b^2 - 2*(A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^2*b^3 + 2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a*b^4 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^5)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^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)*a^2*b - 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)*a*b^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)*b^3)) + 4*sqrt(2)*(a^2 + b^2)*d^4*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4)*arctan(-((2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^4*b + 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^2 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^3 + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^4 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^5)*d^4*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^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)*a^3*b + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*a^2*b^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)*a*b^3)*d^2*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((B*a^5 - A*a^4*b + 2*B*a^3*b^2 - 2*A*a^2*b^3 + B*a*b^4 - A*b^5)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + ((A^2*B + B^3)*a^4 + 2*(A^2*B + B^3)*a^2*b^2 + (A^2*B + B^3)*b^4)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((4*A^2*B^3*a^4 - 4*(A^3*B^2 - A*B^4)*a^3*b + (A^4*B + 2*A^2*B^3 + B^5)*a^2*b^2 - 4*(A^3*B^2 - A*B^4)*a*b^3 + (A^4*B - 2*A^2*B^3 + B^5)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*a^2*b + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*a*b^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^3)*d*cos(d*x + c))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((2*(A^3*B^2 + A*B^4)*a^6 - (3*A^4*B + 2*A^2*B^3 - B^5)*a^5*b + (A^5 + 4*A^3*B^2 + 3*A*B^4)*a^4*b^2 - 2*(3*A^4*B + 2*A^2*B^3 - B^5)*a^3*b^3 + 2*(A^5 + A^3*B^2)*a^2*b^4 - (3*A^4*B + 2*A^2*B^3 - B^5)*a*b^5 + (A^5 - A*B^4)*b^6)*d^7*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^5 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^4*b + 4*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a^3*b^2 - 2*(A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^2*b^3 + 2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*a*b^4 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^5)*d^5*sqrt((4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^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)*a^2*b - 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)*a*b^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)*b^3)) - sqrt(2)*(A^4 + 2*A^2*B^2 + B^4 - (2*A*B*b + (A^2 - B^2)*a)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((4*A^2*B^3*a^4 - 4*(A^3*B^2 - A*B^4)*a^3*b + (A^4*B + 2*A^2*B^3 + B^5)*a^2*b^2 - 4*(A^3*B^2 - A*B^4)*a*b^3 + (A^4*B - 2*A^2*B^3 + B^5)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*a^2*b + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*a*b^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^3)*d*cos(d*x + c))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(A^4 + 2*A^2*B^2 + B^4 - (2*A*B*b + (A^2 - B^2)*a)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4)*log(((4*(A^4*B^2 + A^2*B^4)*a^4 - 4*(A^5*B - A*B^5)*a^3*b + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*a^2*b^2 - 4*(A^5*B - A*B^5)*a*b^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^4)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((4*A^2*B^3*a^4 - 4*(A^3*B^2 - A*B^4)*a^3*b + (A^4*B + 2*A^2*B^3 + B^5)*a^2*b^2 - 4*(A^3*B^2 - A*B^4)*a*b^3 + (A^4*B - 2*A^2*B^3 + B^5)*b^4)*d^3*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))*cos(d*x + c) + (4*(A^4*B^3 + A^2*B^5)*a^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*a^2*b + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*a*b^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^3)*d*cos(d*x + c))*sqrt(((2*A*B*a^2*b + 2*A*B*b^3 + (A^2 - B^2)*a^3 + (A^2 - B^2)*a*b^2)*d^2*sqrt((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4)) + (A^4 + 2*A^2*B^2 + B^4)*a^2 + (A^4 + 2*A^2*B^2 + B^4)*b^2)/(4*A^2*B^2*a^2 - 4*(A^3*B - A*B^3)*a*b + (A^4 - 2*A^2*B^2 + B^4)*b^2))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((A^4 + 2*A^2*B^2 + B^4)/((a^2 + b^2)*d^4))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^2*b + (A^8 - 2*A^4*B^4 + B^8)*a*b^2)*cos(d*x + c) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^2 + (A^8 - 2*A^4*B^4 + B^8)*b^3)*sin(d*x + c))/cos(d*x + c)))/(A^4 + 2*A^2*B^2 + B^4)","B",0
347,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,1,2049,0,0.923305," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} \sqrt{\frac{B^{4} b^{2}}{d^{4}}} d^{4} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} \sqrt{\frac{B^{4} b^{2}}{d^{4}}} B^{3} 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{B^{2} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} \sqrt{\frac{B^{4} b^{2}}{d^{4}}} d^{5} \sqrt{\frac{\sqrt{2} B^{3} 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{B^{2} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(B^{4} a^{2} b^{2} + B^{4} b^{4}\right)} d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) + {\left(B^{6} a^{2} b^{3} + B^{6} 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} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{3}{4}} + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{d^{4}}} d^{4} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}} + {\left(B^{6} a^{3} + B^{6} a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{d^{4}}} d^{2}}{B^{8} a^{2} b^{2} + B^{8} b^{4}}\right) + 4 \, \sqrt{2} \sqrt{\frac{B^{4} b^{2}}{d^{4}}} d^{4} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} \sqrt{\frac{B^{4} b^{2}}{d^{4}}} B^{3} 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{B^{2} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} \sqrt{\frac{B^{4} b^{2}}{d^{4}}} d^{5} \sqrt{-\frac{\sqrt{2} B^{3} 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{B^{2} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(B^{4} a^{2} b^{2} + B^{4} b^{4}\right)} d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) - {\left(B^{6} a^{2} b^{3} + B^{6} 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} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{3}{4}} - {\left(B^{4} a^{2} + B^{4} b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{d^{4}}} d^{4} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}} - {\left(B^{6} a^{3} + B^{6} a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{d^{4}}} d^{2}}{B^{8} a^{2} b^{2} + B^{8} b^{4}}\right) + \sqrt{2} {\left(B^{4} a^{2} + B^{4} b^{2} - B^{2} a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}\right)} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} B^{3} 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{B^{2} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(B^{4} a^{2} b^{2} + B^{4} b^{4}\right)} d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) + {\left(B^{6} a^{2} b^{3} + B^{6} 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(B^{4} a^{2} + B^{4} b^{2} - B^{2} a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}\right)} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} B^{3} 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{B^{2} a^{2} + B^{2} b^{2} + a d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}}}{B^{2} b^{2}}} \left(\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(B^{4} a^{2} b^{2} + B^{4} b^{4}\right)} d^{2} \sqrt{\frac{B^{4} a^{2} + B^{4} b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) - {\left(B^{6} a^{2} b^{3} + B^{6} b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right)}{4 \, {\left(B^{4} a^{2} + B^{4} b^{2}\right)}}"," ",0,"-1/4*(4*sqrt(2)*sqrt(B^4*b^2/d^4)*d^4*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*sqrt(B^4*b^2/d^4)*B^3*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(3/4) - sqrt(2)*sqrt(B^4*b^2/d^4)*d^5*sqrt((sqrt(2)*B^3*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(3/4)*cos(d*x + c) + (B^4*a^2*b^2 + B^4*b^4)*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4)*cos(d*x + c) + (B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) + (B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(3/4) + (B^4*a^2 + B^4*b^2)*sqrt(B^4*b^2/d^4)*d^4*sqrt((B^4*a^2 + B^4*b^2)/d^4) + (B^6*a^3 + B^6*a*b^2)*sqrt(B^4*b^2/d^4)*d^2)/(B^8*a^2*b^2 + B^8*b^4)) + 4*sqrt(2)*sqrt(B^4*b^2/d^4)*d^4*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*sqrt(B^4*b^2/d^4)*B^3*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(3/4) - sqrt(2)*sqrt(B^4*b^2/d^4)*d^5*sqrt(-(sqrt(2)*B^3*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(3/4)*cos(d*x + c) - (B^4*a^2*b^2 + B^4*b^4)*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4)*cos(d*x + c) - (B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) - (B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(3/4) - (B^4*a^2 + B^4*b^2)*sqrt(B^4*b^2/d^4)*d^4*sqrt((B^4*a^2 + B^4*b^2)/d^4) - (B^6*a^3 + B^6*a*b^2)*sqrt(B^4*b^2/d^4)*d^2)/(B^8*a^2*b^2 + B^8*b^4)) + sqrt(2)*(B^4*a^2 + B^4*b^2 - B^2*a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(1/4)*log((sqrt(2)*B^3*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(3/4)*cos(d*x + c) + (B^4*a^2*b^2 + B^4*b^4)*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4)*cos(d*x + c) + (B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) + (B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*(B^4*a^2 + B^4*b^2 - B^2*a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(1/4)*log(-(sqrt(2)*B^3*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((B^2*a^2 + B^2*b^2 + a*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4))/(B^2*b^2))*((B^4*a^2 + B^4*b^2)/d^4)^(3/4)*cos(d*x + c) - (B^4*a^2*b^2 + B^4*b^4)*d^2*sqrt((B^4*a^2 + B^4*b^2)/d^4)*cos(d*x + c) - (B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) - (B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))))/(B^4*a^2 + B^4*b^2)","B",0
366,1,2127,0,1.333697," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(a^{2} + b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{4} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{\sqrt{2} B^{5} 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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \cos\left(d x + c\right) + B^{6} a b^{2} \cos\left(d x + c\right) + B^{6} b^{3} \sin\left(d x + c\right) + {\left(B^{4} a^{2} b^{2} + B^{4} b^{4}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} - \sqrt{2} {\left(B^{3} a^{4} b + 2 \, B^{3} a^{2} b^{3} + B^{3} b^{5}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} - {\left(B^{6} a^{4} + 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(B^{8} a^{3} + B^{8} a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{2}}{B^{10} b^{2}}\right) + 4 \, \sqrt{2} {\left(a^{2} + b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{4} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{-\frac{\sqrt{2} B^{5} 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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \cos\left(d x + c\right) - B^{6} a b^{2} \cos\left(d x + c\right) - B^{6} b^{3} \sin\left(d x + c\right) - {\left(B^{4} a^{2} b^{2} + B^{4} b^{4}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} - \sqrt{2} {\left(B^{3} a^{4} b + 2 \, B^{3} a^{2} b^{3} + B^{3} b^{5}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} + {\left(B^{6} a^{4} + 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{8} a^{3} + B^{8} a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{2}}{B^{10} b^{2}}\right) + \sqrt{2} {\left(B^{2} a d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - B^{4}\right)} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \log\left(\frac{\sqrt{2} B^{5} 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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \cos\left(d x + c\right) + B^{6} a b^{2} \cos\left(d x + c\right) + B^{6} b^{3} \sin\left(d x + c\right) + {\left(B^{4} a^{2} b^{2} + B^{4} b^{4}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(B^{2} a d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} - B^{4}\right)} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \log\left(-\frac{\sqrt{2} B^{5} 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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \cos\left(d x + c\right) - B^{6} a b^{2} \cos\left(d x + c\right) - B^{6} b^{3} \sin\left(d x + c\right) - {\left(B^{4} a^{2} b^{2} + B^{4} b^{4}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, B^{4}}"," ",0,"-1/4*(4*sqrt(2)*(a^2 + b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^4*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt((sqrt(2)*B^5*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*cos(d*x + c) + B^6*a*b^2*cos(d*x + c) + B^6*b^3*sin(d*x + c) + (B^4*a^2*b^2 + B^4*b^4)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(5/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)) - sqrt(2)*(B^3*a^4*b + 2*B^3*a^2*b^3 + B^3*b^5)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(5/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)) - (B^6*a^4 + 2*B^6*a^2*b^2 + B^6*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^4*sqrt(B^4/((a^2 + b^2)*d^4)) - (B^8*a^3 + B^8*a*b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^2)/(B^10*b^2)) + 4*sqrt(2)*(a^2 + b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^4*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt(-(sqrt(2)*B^5*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*cos(d*x + c) - B^6*a*b^2*cos(d*x + c) - B^6*b^3*sin(d*x + c) - (B^4*a^2*b^2 + B^4*b^4)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(5/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)) - sqrt(2)*(B^3*a^4*b + 2*B^3*a^2*b^3 + B^3*b^5)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(5/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)) + (B^6*a^4 + 2*B^6*a^2*b^2 + B^6*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^4*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^8*a^3 + B^8*a*b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^2)/(B^10*b^2)) + sqrt(2)*(B^2*a*d^2*sqrt(B^4/((a^2 + b^2)*d^4)) - B^4)*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*log((sqrt(2)*B^5*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*cos(d*x + c) + B^6*a*b^2*cos(d*x + c) + B^6*b^3*sin(d*x + c) + (B^4*a^2*b^2 + B^4*b^4)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))/cos(d*x + c)) - sqrt(2)*(B^2*a*d^2*sqrt(B^4/((a^2 + b^2)*d^4)) - B^4)*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*log(-(sqrt(2)*B^5*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 + (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*cos(d*x + c) - B^6*a*b^2*cos(d*x + c) - B^6*b^3*sin(d*x + c) - (B^4*a^2*b^2 + B^4*b^4)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))/cos(d*x + c)))/B^4","B",0
367,1,5387,0,2.701571," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(a^{3} + a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \arctan\left(-\frac{{\left(B^{6} a^{4} + 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{8} a^{3} + B^{8} a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{2} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5}\right)} \sqrt{\frac{B^{6} a \cos\left(d x + c\right) + B^{6} b \sin\left(d x + c\right) + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(B^{5} a d \cos\left(d x + c\right) + {\left(B^{3} a^{2} + B^{3} b^{2}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} + \sqrt{2} {\left({\left(B^{3} a^{5} + 2 \, B^{3} a^{3} b^{2} + B^{3} a b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{5} a^{4} + 2 \, B^{5} a^{2} b^{2} + B^{5} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{B^{10} b^{2}}\right) + 4 \, \sqrt{2} {\left(a^{3} + a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \arctan\left(\frac{{\left(B^{6} a^{4} + 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{8} a^{3} + B^{8} a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{2} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5}\right)} \sqrt{\frac{B^{6} a \cos\left(d x + c\right) + B^{6} b \sin\left(d x + c\right) + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(B^{5} a d \cos\left(d x + c\right) + {\left(B^{3} a^{2} + B^{3} b^{2}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} - \sqrt{2} {\left({\left(B^{3} a^{5} + 2 \, B^{3} a^{3} b^{2} + B^{3} a b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{5} a^{4} + 2 \, B^{5} a^{2} b^{2} + B^{5} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{B^{10} b^{2}}\right) + 2 \, B^{5} \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) + \sqrt{2} {\left(B^{2} a^{2} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + B^{4} a d\right)} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \log\left(\frac{B^{6} a \cos\left(d x + c\right) + B^{6} b \sin\left(d x + c\right) + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(B^{5} a d \cos\left(d x + c\right) + {\left(B^{3} a^{2} + B^{3} b^{2}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(B^{2} a^{2} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + B^{4} a d\right)} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \log\left(\frac{B^{6} a \cos\left(d x + c\right) + B^{6} b \sin\left(d x + c\right) + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(B^{5} a d \cos\left(d x + c\right) + {\left(B^{3} a^{2} + B^{3} b^{2}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{\cos\left(d x + c\right)}\right)}{4 \, B^{4} a d}, \frac{4 \, \sqrt{2} {\left(a^{3} + a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \arctan\left(-\frac{{\left(B^{6} a^{4} + 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{8} a^{3} + B^{8} a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{2} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5}\right)} \sqrt{\frac{B^{6} a \cos\left(d x + c\right) + B^{6} b \sin\left(d x + c\right) + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(B^{5} a d \cos\left(d x + c\right) + {\left(B^{3} a^{2} + B^{3} b^{2}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} + \sqrt{2} {\left({\left(B^{3} a^{5} + 2 \, B^{3} a^{3} b^{2} + B^{3} a b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{5} a^{4} + 2 \, B^{5} a^{2} b^{2} + B^{5} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{B^{10} b^{2}}\right) + 4 \, \sqrt{2} {\left(a^{3} + a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \arctan\left(\frac{{\left(B^{6} a^{4} + 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{8} a^{3} + B^{8} a b^{2}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{2} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5}\right)} \sqrt{\frac{B^{6} a \cos\left(d x + c\right) + B^{6} b \sin\left(d x + c\right) + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(B^{5} a d \cos\left(d x + c\right) + {\left(B^{3} a^{2} + B^{3} b^{2}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} - \sqrt{2} {\left({\left(B^{3} a^{5} + 2 \, B^{3} a^{3} b^{2} + B^{3} a b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(B^{5} a^{4} + 2 \, B^{5} a^{2} b^{2} + B^{5} b^{4}\right)} \sqrt{\frac{B^{4} b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} d^{5}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{B^{10} b^{2}}\right) + 8 \, B^{5} \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) + \sqrt{2} {\left(B^{2} a^{2} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + B^{4} a d\right)} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \log\left(\frac{B^{6} a \cos\left(d x + c\right) + B^{6} b \sin\left(d x + c\right) + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(B^{5} a d \cos\left(d x + c\right) + {\left(B^{3} a^{2} + B^{3} b^{2}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(B^{2} a^{2} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} + B^{4} a d\right)} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}} \log\left(\frac{B^{6} a \cos\left(d x + c\right) + B^{6} b \sin\left(d x + c\right) + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(B^{5} a d \cos\left(d x + c\right) + {\left(B^{3} a^{2} + B^{3} b^{2}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}} \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)}} \left(\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{B^{2} a^{2} + B^{2} b^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{2} + b^{2}\right)} d^{4}}}}{B^{2} b^{2}}}}{\cos\left(d x + c\right)}\right)}{4 \, B^{4} a d}\right]"," ",0,"[1/4*(4*sqrt(2)*(a^3 + a*b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*arctan(-((B^6*a^4 + 2*B^6*a^2*b^2 + B^6*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^4*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^8*a^3 + B^8*a*b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^2 - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5)*sqrt((B^6*a*cos(d*x + c) + B^6*b*sin(d*x + c) + (B^4*a^2 + B^4*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*(B^5*a*d*cos(d*x + c) + (B^3*a^2 + B^3*b^2)*d^3*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)) + sqrt(2)*((B^3*a^5 + 2*B^3*a^3*b^2 + B^3*a*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^5*a^4 + 2*B^5*a^2*b^2 + B^5*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/(B^10*b^2)) + 4*sqrt(2)*(a^3 + a*b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*arctan(((B^6*a^4 + 2*B^6*a^2*b^2 + B^6*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^4*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^8*a^3 + B^8*a*b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^2 + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5)*sqrt((B^6*a*cos(d*x + c) + B^6*b*sin(d*x + c) + (B^4*a^2 + B^4*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*(B^5*a*d*cos(d*x + c) + (B^3*a^2 + B^3*b^2)*d^3*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)) - sqrt(2)*((B^3*a^5 + 2*B^3*a^3*b^2 + B^3*a*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^5*a^4 + 2*B^5*a^2*b^2 + B^5*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/(B^10*b^2)) + 2*B^5*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)) + sqrt(2)*(B^2*a^2*d^3*sqrt(B^4/((a^2 + b^2)*d^4)) + B^4*a*d)*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*log((B^6*a*cos(d*x + c) + B^6*b*sin(d*x + c) + (B^4*a^2 + B^4*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*(B^5*a*d*cos(d*x + c) + (B^3*a^2 + B^3*b^2)*d^3*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/cos(d*x + c)) - sqrt(2)*(B^2*a^2*d^3*sqrt(B^4/((a^2 + b^2)*d^4)) + B^4*a*d)*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*log((B^6*a*cos(d*x + c) + B^6*b*sin(d*x + c) + (B^4*a^2 + B^4*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*(B^5*a*d*cos(d*x + c) + (B^3*a^2 + B^3*b^2)*d^3*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/cos(d*x + c)))/(B^4*a*d), 1/4*(4*sqrt(2)*(a^3 + a*b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*arctan(-((B^6*a^4 + 2*B^6*a^2*b^2 + B^6*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^4*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^8*a^3 + B^8*a*b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^2 - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5)*sqrt((B^6*a*cos(d*x + c) + B^6*b*sin(d*x + c) + (B^4*a^2 + B^4*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*(B^5*a*d*cos(d*x + c) + (B^3*a^2 + B^3*b^2)*d^3*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)) + sqrt(2)*((B^3*a^5 + 2*B^3*a^3*b^2 + B^3*a*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^5*a^4 + 2*B^5*a^2*b^2 + B^5*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/(B^10*b^2)) + 4*sqrt(2)*(a^3 + a*b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*arctan(((B^6*a^4 + 2*B^6*a^2*b^2 + B^6*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^4*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^8*a^3 + B^8*a*b^2)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^2 + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5)*sqrt((B^6*a*cos(d*x + c) + B^6*b*sin(d*x + c) + (B^4*a^2 + B^4*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*(B^5*a*d*cos(d*x + c) + (B^3*a^2 + B^3*b^2)*d^3*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)) - sqrt(2)*((B^3*a^5 + 2*B^3*a^3*b^2 + B^3*a*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^7*sqrt(B^4/((a^2 + b^2)*d^4)) + (B^5*a^4 + 2*B^5*a^2*b^2 + B^5*b^4)*sqrt(B^4*b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*d^5)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(3/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/(B^10*b^2)) + 8*B^5*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a) + sqrt(2)*(B^2*a^2*d^3*sqrt(B^4/((a^2 + b^2)*d^4)) + B^4*a*d)*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*log((B^6*a*cos(d*x + c) + B^6*b*sin(d*x + c) + (B^4*a^2 + B^4*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*(B^5*a*d*cos(d*x + c) + (B^3*a^2 + B^3*b^2)*d^3*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/cos(d*x + c)) - sqrt(2)*(B^2*a^2*d^3*sqrt(B^4/((a^2 + b^2)*d^4)) + B^4*a*d)*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2))*log((B^6*a*cos(d*x + c) + B^6*b*sin(d*x + c) + (B^4*a^2 + B^4*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*(B^5*a*d*cos(d*x + c) + (B^3*a^2 + B^3*b^2)*d^3*sqrt(B^4/((a^2 + b^2)*d^4))*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^2 + b^2)*d^4))^(1/4)*sqrt((B^2*a^2 + B^2*b^2 - (a^3 + a*b^2)*d^2*sqrt(B^4/((a^2 + b^2)*d^4)))/(B^2*b^2)))/cos(d*x + c)))/(B^4*a*d)]","B",0
368,1,6756,0,1.189937," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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}}} \arctan\left(\frac{{\left(3 \, B^{6} a^{12} + 14 \, B^{6} a^{10} b^{2} + 25 \, B^{6} a^{8} b^{4} + 20 \, B^{6} a^{6} b^{6} + 5 \, B^{6} a^{4} b^{8} - 2 \, B^{6} a^{2} b^{10} - B^{6} b^{12}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{8} a^{9} + 8 \, B^{8} a^{7} b^{2} + 6 \, B^{8} a^{5} b^{4} - B^{8} a b^{8}\right)} d^{2} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(B^{2} a^{10} + 5 \, B^{2} a^{8} b^{2} + 10 \, B^{2} a^{6} b^{4} + 10 \, B^{2} a^{4} b^{6} + 5 \, B^{2} a^{2} b^{8} + B^{2} b^{10}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \sqrt{\frac{{\left(9 \, B^{4} a^{8} b^{2} + 12 \, B^{4} a^{6} b^{4} - 2 \, B^{4} a^{4} b^{6} - 4 \, B^{4} a^{2} b^{8} + B^{4} b^{10}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{8} b^{3} + 12 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 4 \, B^{3} a^{2} b^{9} + B^{3} b^{11}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{5} b^{3} - 6 \, B^{5} a^{3} b^{5} + B^{5} a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} b^{2} - 6 \, B^{6} a^{3} b^{4} + B^{6} a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b^{3} - 6 \, B^{6} a^{2} b^{5} + B^{6} b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\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 \, B^{3} a^{15} b + 17 \, B^{3} a^{13} b^{3} + 39 \, B^{3} a^{11} b^{5} + 45 \, B^{3} a^{9} b^{7} + 25 \, B^{3} a^{7} b^{9} + 3 \, B^{3} a^{5} b^{11} - 3 \, B^{3} a^{3} b^{13} - B^{3} a b^{15}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{5} a^{12} b + 14 \, B^{5} a^{10} b^{3} + 25 \, B^{5} a^{8} b^{5} + 20 \, B^{5} a^{6} b^{7} + 5 \, B^{5} a^{4} b^{9} - 2 \, B^{5} a^{2} b^{11} - B^{5} b^{13}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, B^{10} a^{4} b^{2} - 6 \, B^{10} a^{2} b^{4} + B^{10} 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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}}} \arctan\left(-\frac{{\left(3 \, B^{6} a^{12} + 14 \, B^{6} a^{10} b^{2} + 25 \, B^{6} a^{8} b^{4} + 20 \, B^{6} a^{6} b^{6} + 5 \, B^{6} a^{4} b^{8} - 2 \, B^{6} a^{2} b^{10} - B^{6} b^{12}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{8} a^{9} + 8 \, B^{8} a^{7} b^{2} + 6 \, B^{8} a^{5} b^{4} - B^{8} a b^{8}\right)} d^{2} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(B^{2} a^{10} + 5 \, B^{2} a^{8} b^{2} + 10 \, B^{2} a^{6} b^{4} + 10 \, B^{2} a^{4} b^{6} + 5 \, B^{2} a^{2} b^{8} + B^{2} b^{10}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \sqrt{\frac{{\left(9 \, B^{4} a^{8} b^{2} + 12 \, B^{4} a^{6} b^{4} - 2 \, B^{4} a^{4} b^{6} - 4 \, B^{4} a^{2} b^{8} + B^{4} b^{10}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{8} b^{3} + 12 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 4 \, B^{3} a^{2} b^{9} + B^{3} b^{11}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{5} b^{3} - 6 \, B^{5} a^{3} b^{5} + B^{5} a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} b^{2} - 6 \, B^{6} a^{3} b^{4} + B^{6} a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b^{3} - 6 \, B^{6} a^{2} b^{5} + B^{6} b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\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 \, B^{3} a^{15} b + 17 \, B^{3} a^{13} b^{3} + 39 \, B^{3} a^{11} b^{5} + 45 \, B^{3} a^{9} b^{7} + 25 \, B^{3} a^{7} b^{9} + 3 \, B^{3} a^{5} b^{11} - 3 \, B^{3} a^{3} b^{13} - B^{3} a b^{15}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{5} a^{12} b + 14 \, B^{5} a^{10} b^{3} + 25 \, B^{5} a^{8} b^{5} + 20 \, B^{5} a^{6} b^{7} + 5 \, B^{5} a^{4} b^{9} - 2 \, B^{5} a^{2} b^{11} - B^{5} b^{13}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, B^{10} a^{4} b^{2} - 6 \, B^{10} a^{2} b^{4} + B^{10} b^{6}}\right) + \sqrt{2} {\left({\left(B^{4} a^{4} - B^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{4} a^{3} b + B^{4} a b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{4} a^{2} b^{2} + B^{4} b^{4}\right)} d - {\left({\left(B^{2} a^{7} - 3 \, B^{2} a^{5} b^{2} - B^{2} a^{3} b^{4} + 3 \, B^{2} a b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{2} a^{6} b - 2 \, B^{2} a^{4} b^{3} - 3 \, B^{2} a^{2} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{2} a^{5} b^{2} - 2 \, B^{2} a^{3} b^{4} - 3 \, B^{2} a b^{6}\right)} d^{3}\right)} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\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 \, B^{4} a^{8} b^{2} + 12 \, B^{4} a^{6} b^{4} - 2 \, B^{4} a^{4} b^{6} - 4 \, B^{4} a^{2} b^{8} + B^{4} b^{10}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{8} b^{3} + 12 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 4 \, B^{3} a^{2} b^{9} + B^{3} b^{11}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{5} b^{3} - 6 \, B^{5} a^{3} b^{5} + B^{5} a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} b^{2} - 6 \, B^{6} a^{3} b^{4} + B^{6} a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b^{3} - 6 \, B^{6} a^{2} b^{5} + B^{6} b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(B^{4} a^{4} - B^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{4} a^{3} b + B^{4} a b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{4} a^{2} b^{2} + B^{4} b^{4}\right)} d - {\left({\left(B^{2} a^{7} - 3 \, B^{2} a^{5} b^{2} - B^{2} a^{3} b^{4} + 3 \, B^{2} a b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{2} a^{6} b - 2 \, B^{2} a^{4} b^{3} - 3 \, B^{2} a^{2} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{2} a^{5} b^{2} - 2 \, B^{2} a^{3} b^{4} - 3 \, B^{2} a b^{6}\right)} d^{3}\right)} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\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 \, B^{4} a^{8} b^{2} + 12 \, B^{4} a^{6} b^{4} - 2 \, B^{4} a^{4} b^{6} - 4 \, B^{4} a^{2} b^{8} + B^{4} b^{10}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{8} b^{3} + 12 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 4 \, B^{3} a^{2} b^{9} + B^{3} b^{11}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{5} b^{3} - 6 \, B^{5} a^{3} b^{5} + B^{5} a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} b^{2} - 6 \, B^{6} a^{3} b^{4} + B^{6} a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b^{3} - 6 \, B^{6} a^{2} b^{5} + B^{6} b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(B^{5} a b \cos\left(d x + c\right)^{2} + B^{5} 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(B^{4} a^{4} - B^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{4} a^{3} b + B^{4} a b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{4} a^{2} b^{2} + B^{4} 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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))*arctan(((3*B^6*a^12 + 14*B^6*a^10*b^2 + 25*B^6*a^8*b^4 + 20*B^6*a^6*b^6 + 5*B^6*a^4*b^8 - 2*B^6*a^2*b^10 - B^6*b^12)*d^4*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^8*a^9 + 8*B^8*a^7*b^2 + 6*B^8*a^5*b^4 - B^8*a*b^8)*d^2*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (B^2*a^10 + 5*B^2*a^8*b^2 + 10*B^2*a^6*b^4 + 10*B^2*a^4*b^6 + 5*B^2*a^2*b^8 + B^2*b^10)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt(((9*B^4*a^8*b^2 + 12*B^4*a^6*b^4 - 2*B^4*a^4*b^6 - 4*B^4*a^2*b^8 + B^4*b^10)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*B^3*a^8*b^3 + 12*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 4*B^3*a^2*b^9 + B^3*b^11)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*B^5*a^5*b^3 - 6*B^5*a^3*b^5 + B^5*a*b^7)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5*b^2 - 6*B^6*a^3*b^4 + B^6*a*b^6)*cos(d*x + c) + (9*B^6*a^4*b^3 - 6*B^6*a^2*b^5 + B^6*b^7)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*(2*(3*B^3*a^15*b + 17*B^3*a^13*b^3 + 39*B^3*a^11*b^5 + 45*B^3*a^9*b^7 + 25*B^3*a^7*b^9 + 3*B^3*a^5*b^11 - 3*B^3*a^3*b^13 - B^3*a*b^15)*d^7*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^5*a^12*b + 14*B^5*a^10*b^3 + 25*B^5*a^8*b^5 + 20*B^5*a^6*b^7 + 5*B^5*a^4*b^9 - 2*B^5*a^2*b^11 - B^5*b^13)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*B^10*a^4*b^2 - 6*B^10*a^2*b^4 + B^10*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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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))*arctan(-((3*B^6*a^12 + 14*B^6*a^10*b^2 + 25*B^6*a^8*b^4 + 20*B^6*a^6*b^6 + 5*B^6*a^4*b^8 - 2*B^6*a^2*b^10 - B^6*b^12)*d^4*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^8*a^9 + 8*B^8*a^7*b^2 + 6*B^8*a^5*b^4 - B^8*a*b^8)*d^2*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (B^2*a^10 + 5*B^2*a^8*b^2 + 10*B^2*a^6*b^4 + 10*B^2*a^4*b^6 + 5*B^2*a^2*b^8 + B^2*b^10)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt(((9*B^4*a^8*b^2 + 12*B^4*a^6*b^4 - 2*B^4*a^4*b^6 - 4*B^4*a^2*b^8 + B^4*b^10)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*B^3*a^8*b^3 + 12*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 4*B^3*a^2*b^9 + B^3*b^11)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*B^5*a^5*b^3 - 6*B^5*a^3*b^5 + B^5*a*b^7)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5*b^2 - 6*B^6*a^3*b^4 + B^6*a*b^6)*cos(d*x + c) + (9*B^6*a^4*b^3 - 6*B^6*a^2*b^5 + B^6*b^7)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*(2*(3*B^3*a^15*b + 17*B^3*a^13*b^3 + 39*B^3*a^11*b^5 + 45*B^3*a^9*b^7 + 25*B^3*a^7*b^9 + 3*B^3*a^5*b^11 - 3*B^3*a^3*b^13 - B^3*a*b^15)*d^7*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^5*a^12*b + 14*B^5*a^10*b^3 + 25*B^5*a^8*b^5 + 20*B^5*a^6*b^7 + 5*B^5*a^4*b^9 - 2*B^5*a^2*b^11 - B^5*b^13)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*B^10*a^4*b^2 - 6*B^10*a^2*b^4 + B^10*b^6)) + sqrt(2)*((B^4*a^4 - B^4*b^4)*d*cos(d*x + c)^2 + 2*(B^4*a^3*b + B^4*a*b^3)*d*cos(d*x + c)*sin(d*x + c) + (B^4*a^2*b^2 + B^4*b^4)*d - ((B^2*a^7 - 3*B^2*a^5*b^2 - B^2*a^3*b^4 + 3*B^2*a*b^6)*d^3*cos(d*x + c)^2 + 2*(B^2*a^6*b - 2*B^2*a^4*b^3 - 3*B^2*a^2*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (B^2*a^5*b^2 - 2*B^2*a^3*b^4 - 3*B^2*a*b^6)*d^3)*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*B^4*a^8*b^2 + 12*B^4*a^6*b^4 - 2*B^4*a^4*b^6 - 4*B^4*a^2*b^8 + B^4*b^10)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*B^3*a^8*b^3 + 12*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 4*B^3*a^2*b^9 + B^3*b^11)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*B^5*a^5*b^3 - 6*B^5*a^3*b^5 + B^5*a*b^7)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5*b^2 - 6*B^6*a^3*b^4 + B^6*a*b^6)*cos(d*x + c) + (9*B^6*a^4*b^3 - 6*B^6*a^2*b^5 + B^6*b^7)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((B^4*a^4 - B^4*b^4)*d*cos(d*x + c)^2 + 2*(B^4*a^3*b + B^4*a*b^3)*d*cos(d*x + c)*sin(d*x + c) + (B^4*a^2*b^2 + B^4*b^4)*d - ((B^2*a^7 - 3*B^2*a^5*b^2 - B^2*a^3*b^4 + 3*B^2*a*b^6)*d^3*cos(d*x + c)^2 + 2*(B^2*a^6*b - 2*B^2*a^4*b^3 - 3*B^2*a^2*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (B^2*a^5*b^2 - 2*B^2*a^3*b^4 - 3*B^2*a*b^6)*d^3)*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*B^4*a^8*b^2 + 12*B^4*a^6*b^4 - 2*B^4*a^4*b^6 - 4*B^4*a^2*b^8 + B^4*b^10)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*B^3*a^8*b^3 + 12*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 4*B^3*a^2*b^9 + B^3*b^11)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*B^5*a^5*b^3 - 6*B^5*a^3*b^5 + B^5*a*b^7)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5*b^2 - 6*B^6*a^3*b^4 + B^6*a*b^6)*cos(d*x + c) + (9*B^6*a^4*b^3 - 6*B^6*a^2*b^5 + B^6*b^7)*sin(d*x + c))/cos(d*x + c)) - 8*(B^5*a*b*cos(d*x + c)^2 + B^5*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)))/((B^4*a^4 - B^4*b^4)*d*cos(d*x + c)^2 + 2*(B^4*a^3*b + B^4*a*b^3)*d*cos(d*x + c)*sin(d*x + c) + (B^4*a^2*b^2 + B^4*b^4)*d)","B",0
369,1,13991,0,2.562426," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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}}} \arctan\left(-\frac{{\left(3 \, B^{6} a^{12} + 14 \, B^{6} a^{10} b^{2} + 25 \, B^{6} a^{8} b^{4} + 20 \, B^{6} a^{6} b^{6} + 5 \, B^{6} a^{4} b^{8} - 2 \, B^{6} a^{2} b^{10} - B^{6} b^{12}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{8} a^{9} + 8 \, B^{8} a^{7} b^{2} + 6 \, B^{8} a^{5} b^{4} - B^{8} a b^{8}\right)} d^{2} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(B^{2} a^{11} + 5 \, B^{2} a^{9} b^{2} + 10 \, B^{2} a^{7} b^{4} + 10 \, B^{2} a^{5} b^{6} + 5 \, B^{2} a^{3} b^{8} + B^{2} a b^{10}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \sqrt{\frac{{\left(9 \, B^{4} a^{8} + 12 \, B^{4} a^{6} b^{2} - 2 \, B^{4} a^{4} b^{4} - 4 \, B^{4} a^{2} b^{6} + B^{4} b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{9} + 12 \, B^{3} a^{7} b^{2} - 2 \, B^{3} a^{5} b^{4} - 4 \, B^{3} a^{3} b^{6} + B^{3} a b^{8}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{6} - 15 \, B^{5} a^{4} b^{2} + 7 \, B^{5} a^{2} b^{4} - B^{5} b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} - 6 \, B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b - 6 \, B^{6} a^{2} b^{3} + B^{6} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\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 \, B^{3} a^{16} + 14 \, B^{3} a^{14} b^{2} + 22 \, B^{3} a^{12} b^{4} + 6 \, B^{3} a^{10} b^{6} - 20 \, B^{3} a^{8} b^{8} - 22 \, B^{3} a^{6} b^{10} - 6 \, B^{3} a^{4} b^{12} + 2 \, B^{3} a^{2} b^{14} + B^{3} b^{16}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{5} a^{13} + 14 \, B^{5} a^{11} b^{2} + 25 \, B^{5} a^{9} b^{4} + 20 \, B^{5} a^{7} b^{6} + 5 \, B^{5} a^{5} b^{8} - 2 \, B^{5} a^{3} b^{10} - B^{5} a b^{12}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, B^{10} a^{4} b^{2} - 6 \, B^{10} a^{2} b^{4} + B^{10} 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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}}} \arctan\left(\frac{{\left(3 \, B^{6} a^{12} + 14 \, B^{6} a^{10} b^{2} + 25 \, B^{6} a^{8} b^{4} + 20 \, B^{6} a^{6} b^{6} + 5 \, B^{6} a^{4} b^{8} - 2 \, B^{6} a^{2} b^{10} - B^{6} b^{12}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{8} a^{9} + 8 \, B^{8} a^{7} b^{2} + 6 \, B^{8} a^{5} b^{4} - B^{8} a b^{8}\right)} d^{2} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(B^{2} a^{11} + 5 \, B^{2} a^{9} b^{2} + 10 \, B^{2} a^{7} b^{4} + 10 \, B^{2} a^{5} b^{6} + 5 \, B^{2} a^{3} b^{8} + B^{2} a b^{10}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \sqrt{\frac{{\left(9 \, B^{4} a^{8} + 12 \, B^{4} a^{6} b^{2} - 2 \, B^{4} a^{4} b^{4} - 4 \, B^{4} a^{2} b^{6} + B^{4} b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{9} + 12 \, B^{3} a^{7} b^{2} - 2 \, B^{3} a^{5} b^{4} - 4 \, B^{3} a^{3} b^{6} + B^{3} a b^{8}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{6} - 15 \, B^{5} a^{4} b^{2} + 7 \, B^{5} a^{2} b^{4} - B^{5} b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} - 6 \, B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b - 6 \, B^{6} a^{2} b^{3} + B^{6} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\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 \, B^{3} a^{16} + 14 \, B^{3} a^{14} b^{2} + 22 \, B^{3} a^{12} b^{4} + 6 \, B^{3} a^{10} b^{6} - 20 \, B^{3} a^{8} b^{8} - 22 \, B^{3} a^{6} b^{10} - 6 \, B^{3} a^{4} b^{12} + 2 \, B^{3} a^{2} b^{14} + B^{3} b^{16}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{5} a^{13} + 14 \, B^{5} a^{11} b^{2} + 25 \, B^{5} a^{9} b^{4} + 20 \, B^{5} a^{7} b^{6} + 5 \, B^{5} a^{5} b^{8} - 2 \, B^{5} a^{3} b^{10} - B^{5} a b^{12}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, B^{10} a^{4} b^{2} - 6 \, B^{10} a^{2} b^{4} + B^{10} b^{6}}\right) + \sqrt{2} {\left({\left(B^{4} a^{6} - B^{4} a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{4} a^{5} b + B^{4} a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{4} a^{4} b^{2} + B^{4} a^{2} b^{4}\right)} d + {\left({\left(B^{2} a^{9} - 3 \, B^{2} a^{7} b^{2} - B^{2} a^{5} b^{4} + 3 \, B^{2} a^{3} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{2} a^{8} b - 2 \, B^{2} a^{6} b^{3} - 3 \, B^{2} a^{4} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{2} a^{7} b^{2} - 2 \, B^{2} a^{5} b^{4} - 3 \, B^{2} a^{3} b^{6}\right)} d^{3}\right)} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\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 \, B^{4} a^{8} + 12 \, B^{4} a^{6} b^{2} - 2 \, B^{4} a^{4} b^{4} - 4 \, B^{4} a^{2} b^{6} + B^{4} b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{9} + 12 \, B^{3} a^{7} b^{2} - 2 \, B^{3} a^{5} b^{4} - 4 \, B^{3} a^{3} b^{6} + B^{3} a b^{8}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{6} - 15 \, B^{5} a^{4} b^{2} + 7 \, B^{5} a^{2} b^{4} - B^{5} b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} - 6 \, B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b - 6 \, B^{6} a^{2} b^{3} + B^{6} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(B^{4} a^{6} - B^{4} a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{4} a^{5} b + B^{4} a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{4} a^{4} b^{2} + B^{4} a^{2} b^{4}\right)} d + {\left({\left(B^{2} a^{9} - 3 \, B^{2} a^{7} b^{2} - B^{2} a^{5} b^{4} + 3 \, B^{2} a^{3} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{2} a^{8} b - 2 \, B^{2} a^{6} b^{3} - 3 \, B^{2} a^{4} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{2} a^{7} b^{2} - 2 \, B^{2} a^{5} b^{4} - 3 \, B^{2} a^{3} b^{6}\right)} d^{3}\right)} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\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 \, B^{4} a^{8} + 12 \, B^{4} a^{6} b^{2} - 2 \, B^{4} a^{4} b^{4} - 4 \, B^{4} a^{2} b^{6} + B^{4} b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{9} + 12 \, B^{3} a^{7} b^{2} - 2 \, B^{3} a^{5} b^{4} - 4 \, B^{3} a^{3} b^{6} + B^{3} a b^{8}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{6} - 15 \, B^{5} a^{4} b^{2} + 7 \, B^{5} a^{2} b^{4} - B^{5} b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} - 6 \, B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b - 6 \, B^{6} a^{2} b^{3} + B^{6} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 2 \, {\left(B^{5} a^{2} b^{2} + B^{5} b^{4} + {\left(B^{5} a^{4} - B^{5} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{5} a^{3} b + B^{5} 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(B^{5} a^{2} b^{2} \cos\left(d x + c\right)^{2} + B^{5} 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(B^{4} a^{6} - B^{4} a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{4} a^{5} b + B^{4} a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{4} a^{4} b^{2} + B^{4} 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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}}} \arctan\left(-\frac{{\left(3 \, B^{6} a^{12} + 14 \, B^{6} a^{10} b^{2} + 25 \, B^{6} a^{8} b^{4} + 20 \, B^{6} a^{6} b^{6} + 5 \, B^{6} a^{4} b^{8} - 2 \, B^{6} a^{2} b^{10} - B^{6} b^{12}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{8} a^{9} + 8 \, B^{8} a^{7} b^{2} + 6 \, B^{8} a^{5} b^{4} - B^{8} a b^{8}\right)} d^{2} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(B^{2} a^{11} + 5 \, B^{2} a^{9} b^{2} + 10 \, B^{2} a^{7} b^{4} + 10 \, B^{2} a^{5} b^{6} + 5 \, B^{2} a^{3} b^{8} + B^{2} a b^{10}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \sqrt{\frac{{\left(9 \, B^{4} a^{8} + 12 \, B^{4} a^{6} b^{2} - 2 \, B^{4} a^{4} b^{4} - 4 \, B^{4} a^{2} b^{6} + B^{4} b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{9} + 12 \, B^{3} a^{7} b^{2} - 2 \, B^{3} a^{5} b^{4} - 4 \, B^{3} a^{3} b^{6} + B^{3} a b^{8}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{6} - 15 \, B^{5} a^{4} b^{2} + 7 \, B^{5} a^{2} b^{4} - B^{5} b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} - 6 \, B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b - 6 \, B^{6} a^{2} b^{3} + B^{6} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\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 \, B^{3} a^{16} + 14 \, B^{3} a^{14} b^{2} + 22 \, B^{3} a^{12} b^{4} + 6 \, B^{3} a^{10} b^{6} - 20 \, B^{3} a^{8} b^{8} - 22 \, B^{3} a^{6} b^{10} - 6 \, B^{3} a^{4} b^{12} + 2 \, B^{3} a^{2} b^{14} + B^{3} b^{16}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{5} a^{13} + 14 \, B^{5} a^{11} b^{2} + 25 \, B^{5} a^{9} b^{4} + 20 \, B^{5} a^{7} b^{6} + 5 \, B^{5} a^{5} b^{8} - 2 \, B^{5} a^{3} b^{10} - B^{5} a b^{12}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, B^{10} a^{4} b^{2} - 6 \, B^{10} a^{2} b^{4} + B^{10} 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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}}} \arctan\left(\frac{{\left(3 \, B^{6} a^{12} + 14 \, B^{6} a^{10} b^{2} + 25 \, B^{6} a^{8} b^{4} + 20 \, B^{6} a^{6} b^{6} + 5 \, B^{6} a^{4} b^{8} - 2 \, B^{6} a^{2} b^{10} - B^{6} b^{12}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{8} a^{9} + 8 \, B^{8} a^{7} b^{2} + 6 \, B^{8} a^{5} b^{4} - B^{8} a b^{8}\right)} d^{2} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(B^{2} a^{11} + 5 \, B^{2} a^{9} b^{2} + 10 \, B^{2} a^{7} b^{4} + 10 \, B^{2} a^{5} b^{6} + 5 \, B^{2} a^{3} b^{8} + B^{2} a b^{10}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \sqrt{\frac{{\left(9 \, B^{4} a^{8} + 12 \, B^{4} a^{6} b^{2} - 2 \, B^{4} a^{4} b^{4} - 4 \, B^{4} a^{2} b^{6} + B^{4} b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{9} + 12 \, B^{3} a^{7} b^{2} - 2 \, B^{3} a^{5} b^{4} - 4 \, B^{3} a^{3} b^{6} + B^{3} a b^{8}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{6} - 15 \, B^{5} a^{4} b^{2} + 7 \, B^{5} a^{2} b^{4} - B^{5} b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} - 6 \, B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b - 6 \, B^{6} a^{2} b^{3} + B^{6} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\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 \, B^{3} a^{16} + 14 \, B^{3} a^{14} b^{2} + 22 \, B^{3} a^{12} b^{4} + 6 \, B^{3} a^{10} b^{6} - 20 \, B^{3} a^{8} b^{8} - 22 \, B^{3} a^{6} b^{10} - 6 \, B^{3} a^{4} b^{12} + 2 \, B^{3} a^{2} b^{14} + B^{3} b^{16}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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(3 \, B^{5} a^{13} + 14 \, B^{5} a^{11} b^{2} + 25 \, B^{5} a^{9} b^{4} + 20 \, B^{5} a^{7} b^{6} + 5 \, B^{5} a^{5} b^{8} - 2 \, B^{5} a^{3} b^{10} - B^{5} a b^{12}\right)} d^{5} \sqrt{\frac{9 \, B^{4} a^{4} b^{2} - 6 \, B^{4} a^{2} b^{4} + 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{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, B^{10} a^{4} b^{2} - 6 \, B^{10} a^{2} b^{4} + B^{10} b^{6}}\right) + \sqrt{2} {\left({\left(B^{4} a^{6} - B^{4} a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{4} a^{5} b + B^{4} a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{4} a^{4} b^{2} + B^{4} a^{2} b^{4}\right)} d + {\left({\left(B^{2} a^{9} - 3 \, B^{2} a^{7} b^{2} - B^{2} a^{5} b^{4} + 3 \, B^{2} a^{3} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{2} a^{8} b - 2 \, B^{2} a^{6} b^{3} - 3 \, B^{2} a^{4} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{2} a^{7} b^{2} - 2 \, B^{2} a^{5} b^{4} - 3 \, B^{2} a^{3} b^{6}\right)} d^{3}\right)} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\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 \, B^{4} a^{8} + 12 \, B^{4} a^{6} b^{2} - 2 \, B^{4} a^{4} b^{4} - 4 \, B^{4} a^{2} b^{6} + B^{4} b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{9} + 12 \, B^{3} a^{7} b^{2} - 2 \, B^{3} a^{5} b^{4} - 4 \, B^{3} a^{3} b^{6} + B^{3} a b^{8}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{6} - 15 \, B^{5} a^{4} b^{2} + 7 \, B^{5} a^{2} b^{4} - B^{5} b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} - 6 \, B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b - 6 \, B^{6} a^{2} b^{3} + B^{6} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(B^{4} a^{6} - B^{4} a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{4} a^{5} b + B^{4} a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{4} a^{4} b^{2} + B^{4} a^{2} b^{4}\right)} d + {\left({\left(B^{2} a^{9} - 3 \, B^{2} a^{7} b^{2} - B^{2} a^{5} b^{4} + 3 \, B^{2} a^{3} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{2} a^{8} b - 2 \, B^{2} a^{6} b^{3} - 3 \, B^{2} a^{4} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{2} a^{7} b^{2} - 2 \, B^{2} a^{5} b^{4} - 3 \, B^{2} a^{3} b^{6}\right)} d^{3}\right)} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} b^{6}}} \left(\frac{B^{4}}{{\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 \, B^{4} a^{8} + 12 \, B^{4} a^{6} b^{2} - 2 \, B^{4} a^{4} b^{4} - 4 \, B^{4} a^{2} b^{6} + B^{4} b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\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 \, B^{3} a^{9} + 12 \, B^{3} a^{7} b^{2} - 2 \, B^{3} a^{5} b^{4} - 4 \, B^{3} a^{3} b^{6} + B^{3} a b^{8}\right)} d^{3} \sqrt{\frac{B^{4}}{{\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 \, B^{5} a^{6} - 15 \, B^{5} a^{4} b^{2} + 7 \, B^{5} a^{2} b^{4} - B^{5} b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{6} + 3 \, B^{2} a^{4} b^{2} + 3 \, B^{2} a^{2} b^{4} + B^{2} b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, B^{2} a^{4} b^{2} - 6 \, B^{2} a^{2} b^{4} + B^{2} 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{B^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, B^{6} a^{5} - 6 \, B^{6} a^{3} b^{2} + B^{6} a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, B^{6} a^{4} b - 6 \, B^{6} a^{2} b^{3} + B^{6} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(B^{5} a^{2} b^{2} + B^{5} b^{4} + {\left(B^{5} a^{4} - B^{5} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{5} a^{3} b + B^{5} 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(B^{5} a^{2} b^{2} \cos\left(d x + c\right)^{2} + B^{5} 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(B^{4} a^{6} - B^{4} a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(B^{4} a^{5} b + B^{4} a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(B^{4} a^{4} b^{2} + B^{4} 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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))*arctan(-((3*B^6*a^12 + 14*B^6*a^10*b^2 + 25*B^6*a^8*b^4 + 20*B^6*a^6*b^6 + 5*B^6*a^4*b^8 - 2*B^6*a^2*b^10 - B^6*b^12)*d^4*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^8*a^9 + 8*B^8*a^7*b^2 + 6*B^8*a^5*b^4 - B^8*a*b^8)*d^2*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (B^2*a^11 + 5*B^2*a^9*b^2 + 10*B^2*a^7*b^4 + 10*B^2*a^5*b^6 + 5*B^2*a^3*b^8 + B^2*a*b^10)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt(((9*B^4*a^8 + 12*B^4*a^6*b^2 - 2*B^4*a^4*b^4 - 4*B^4*a^2*b^6 + B^4*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*B^3*a^9 + 12*B^3*a^7*b^2 - 2*B^3*a^5*b^4 - 4*B^3*a^3*b^6 + B^3*a*b^8)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*B^5*a^6 - 15*B^5*a^4*b^2 + 7*B^5*a^2*b^4 - B^5*b^6)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5 - 6*B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) + (9*B^6*a^4*b - 6*B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*((3*B^3*a^16 + 14*B^3*a^14*b^2 + 22*B^3*a^12*b^4 + 6*B^3*a^10*b^6 - 20*B^3*a^8*b^8 - 22*B^3*a^6*b^10 - 6*B^3*a^4*b^12 + 2*B^3*a^2*b^14 + B^3*b^16)*d^7*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^5*a^13 + 14*B^5*a^11*b^2 + 25*B^5*a^9*b^4 + 20*B^5*a^7*b^6 + 5*B^5*a^5*b^8 - 2*B^5*a^3*b^10 - B^5*a*b^12)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*B^10*a^4*b^2 - 6*B^10*a^2*b^4 + B^10*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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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))*arctan(((3*B^6*a^12 + 14*B^6*a^10*b^2 + 25*B^6*a^8*b^4 + 20*B^6*a^6*b^6 + 5*B^6*a^4*b^8 - 2*B^6*a^2*b^10 - B^6*b^12)*d^4*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^8*a^9 + 8*B^8*a^7*b^2 + 6*B^8*a^5*b^4 - B^8*a*b^8)*d^2*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (B^2*a^11 + 5*B^2*a^9*b^2 + 10*B^2*a^7*b^4 + 10*B^2*a^5*b^6 + 5*B^2*a^3*b^8 + B^2*a*b^10)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt(((9*B^4*a^8 + 12*B^4*a^6*b^2 - 2*B^4*a^4*b^4 - 4*B^4*a^2*b^6 + B^4*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*B^3*a^9 + 12*B^3*a^7*b^2 - 2*B^3*a^5*b^4 - 4*B^3*a^3*b^6 + B^3*a*b^8)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*B^5*a^6 - 15*B^5*a^4*b^2 + 7*B^5*a^2*b^4 - B^5*b^6)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5 - 6*B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) + (9*B^6*a^4*b - 6*B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*((3*B^3*a^16 + 14*B^3*a^14*b^2 + 22*B^3*a^12*b^4 + 6*B^3*a^10*b^6 - 20*B^3*a^8*b^8 - 22*B^3*a^6*b^10 - 6*B^3*a^4*b^12 + 2*B^3*a^2*b^14 + B^3*b^16)*d^7*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^5*a^13 + 14*B^5*a^11*b^2 + 25*B^5*a^9*b^4 + 20*B^5*a^7*b^6 + 5*B^5*a^5*b^8 - 2*B^5*a^3*b^10 - B^5*a*b^12)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*B^10*a^4*b^2 - 6*B^10*a^2*b^4 + B^10*b^6)) + sqrt(2)*((B^4*a^6 - B^4*a^2*b^4)*d*cos(d*x + c)^2 + 2*(B^4*a^5*b + B^4*a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (B^4*a^4*b^2 + B^4*a^2*b^4)*d + ((B^2*a^9 - 3*B^2*a^7*b^2 - B^2*a^5*b^4 + 3*B^2*a^3*b^6)*d^3*cos(d*x + c)^2 + 2*(B^2*a^8*b - 2*B^2*a^6*b^3 - 3*B^2*a^4*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (B^2*a^7*b^2 - 2*B^2*a^5*b^4 - 3*B^2*a^3*b^6)*d^3)*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*B^4*a^8 + 12*B^4*a^6*b^2 - 2*B^4*a^4*b^4 - 4*B^4*a^2*b^6 + B^4*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*B^3*a^9 + 12*B^3*a^7*b^2 - 2*B^3*a^5*b^4 - 4*B^3*a^3*b^6 + B^3*a*b^8)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*B^5*a^6 - 15*B^5*a^4*b^2 + 7*B^5*a^2*b^4 - B^5*b^6)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5 - 6*B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) + (9*B^6*a^4*b - 6*B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((B^4*a^6 - B^4*a^2*b^4)*d*cos(d*x + c)^2 + 2*(B^4*a^5*b + B^4*a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (B^4*a^4*b^2 + B^4*a^2*b^4)*d + ((B^2*a^9 - 3*B^2*a^7*b^2 - B^2*a^5*b^4 + 3*B^2*a^3*b^6)*d^3*cos(d*x + c)^2 + 2*(B^2*a^8*b - 2*B^2*a^6*b^3 - 3*B^2*a^4*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (B^2*a^7*b^2 - 2*B^2*a^5*b^4 - 3*B^2*a^3*b^6)*d^3)*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*B^4*a^8 + 12*B^4*a^6*b^2 - 2*B^4*a^4*b^4 - 4*B^4*a^2*b^6 + B^4*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*B^3*a^9 + 12*B^3*a^7*b^2 - 2*B^3*a^5*b^4 - 4*B^3*a^3*b^6 + B^3*a*b^8)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*B^5*a^6 - 15*B^5*a^4*b^2 + 7*B^5*a^2*b^4 - B^5*b^6)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5 - 6*B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) + (9*B^6*a^4*b - 6*B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/cos(d*x + c)) + 2*(B^5*a^2*b^2 + B^5*b^4 + (B^5*a^4 - B^5*b^4)*cos(d*x + c)^2 + 2*(B^5*a^3*b + B^5*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*(B^5*a^2*b^2*cos(d*x + c)^2 + B^5*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)))/((B^4*a^6 - B^4*a^2*b^4)*d*cos(d*x + c)^2 + 2*(B^4*a^5*b + B^4*a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (B^4*a^4*b^2 + B^4*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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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))*arctan(-((3*B^6*a^12 + 14*B^6*a^10*b^2 + 25*B^6*a^8*b^4 + 20*B^6*a^6*b^6 + 5*B^6*a^4*b^8 - 2*B^6*a^2*b^10 - B^6*b^12)*d^4*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^8*a^9 + 8*B^8*a^7*b^2 + 6*B^8*a^5*b^4 - B^8*a*b^8)*d^2*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (B^2*a^11 + 5*B^2*a^9*b^2 + 10*B^2*a^7*b^4 + 10*B^2*a^5*b^6 + 5*B^2*a^3*b^8 + B^2*a*b^10)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt(((9*B^4*a^8 + 12*B^4*a^6*b^2 - 2*B^4*a^4*b^4 - 4*B^4*a^2*b^6 + B^4*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*B^3*a^9 + 12*B^3*a^7*b^2 - 2*B^3*a^5*b^4 - 4*B^3*a^3*b^6 + B^3*a*b^8)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*B^5*a^6 - 15*B^5*a^4*b^2 + 7*B^5*a^2*b^4 - B^5*b^6)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5 - 6*B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) + (9*B^6*a^4*b - 6*B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*((3*B^3*a^16 + 14*B^3*a^14*b^2 + 22*B^3*a^12*b^4 + 6*B^3*a^10*b^6 - 20*B^3*a^8*b^8 - 22*B^3*a^6*b^10 - 6*B^3*a^4*b^12 + 2*B^3*a^2*b^14 + B^3*b^16)*d^7*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^5*a^13 + 14*B^5*a^11*b^2 + 25*B^5*a^9*b^4 + 20*B^5*a^7*b^6 + 5*B^5*a^5*b^8 - 2*B^5*a^3*b^10 - B^5*a*b^12)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*B^10*a^4*b^2 - 6*B^10*a^2*b^4 + B^10*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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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))*arctan(((3*B^6*a^12 + 14*B^6*a^10*b^2 + 25*B^6*a^8*b^4 + 20*B^6*a^6*b^6 + 5*B^6*a^4*b^8 - 2*B^6*a^2*b^10 - B^6*b^12)*d^4*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^8*a^9 + 8*B^8*a^7*b^2 + 6*B^8*a^5*b^4 - B^8*a*b^8)*d^2*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (B^2*a^11 + 5*B^2*a^9*b^2 + 10*B^2*a^7*b^4 + 10*B^2*a^5*b^6 + 5*B^2*a^3*b^8 + B^2*a*b^10)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt(((9*B^4*a^8 + 12*B^4*a^6*b^2 - 2*B^4*a^4*b^4 - 4*B^4*a^2*b^6 + B^4*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*B^3*a^9 + 12*B^3*a^7*b^2 - 2*B^3*a^5*b^4 - 4*B^3*a^3*b^6 + B^3*a*b^8)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*B^5*a^6 - 15*B^5*a^4*b^2 + 7*B^5*a^2*b^4 - B^5*b^6)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5 - 6*B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) + (9*B^6*a^4*b - 6*B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*((3*B^3*a^16 + 14*B^3*a^14*b^2 + 22*B^3*a^12*b^4 + 6*B^3*a^10*b^6 - 20*B^3*a^8*b^8 - 22*B^3*a^6*b^10 - 6*B^3*a^4*b^12 + 2*B^3*a^2*b^14 + B^3*b^16)*d^7*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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)) + (3*B^5*a^13 + 14*B^5*a^11*b^2 + 25*B^5*a^9*b^4 + 20*B^5*a^7*b^6 + 5*B^5*a^5*b^8 - 2*B^5*a^3*b^10 - B^5*a*b^12)*d^5*sqrt((9*B^4*a^4*b^2 - 6*B^4*a^2*b^4 + 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((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*B^10*a^4*b^2 - 6*B^10*a^2*b^4 + B^10*b^6)) + sqrt(2)*((B^4*a^6 - B^4*a^2*b^4)*d*cos(d*x + c)^2 + 2*(B^4*a^5*b + B^4*a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (B^4*a^4*b^2 + B^4*a^2*b^4)*d + ((B^2*a^9 - 3*B^2*a^7*b^2 - B^2*a^5*b^4 + 3*B^2*a^3*b^6)*d^3*cos(d*x + c)^2 + 2*(B^2*a^8*b - 2*B^2*a^6*b^3 - 3*B^2*a^4*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (B^2*a^7*b^2 - 2*B^2*a^5*b^4 - 3*B^2*a^3*b^6)*d^3)*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*B^4*a^8 + 12*B^4*a^6*b^2 - 2*B^4*a^4*b^4 - 4*B^4*a^2*b^6 + B^4*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*B^3*a^9 + 12*B^3*a^7*b^2 - 2*B^3*a^5*b^4 - 4*B^3*a^3*b^6 + B^3*a*b^8)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*B^5*a^6 - 15*B^5*a^4*b^2 + 7*B^5*a^2*b^4 - B^5*b^6)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5 - 6*B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) + (9*B^6*a^4*b - 6*B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((B^4*a^6 - B^4*a^2*b^4)*d*cos(d*x + c)^2 + 2*(B^4*a^5*b + B^4*a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (B^4*a^4*b^2 + B^4*a^2*b^4)*d + ((B^2*a^9 - 3*B^2*a^7*b^2 - B^2*a^5*b^4 + 3*B^2*a^3*b^6)*d^3*cos(d*x + c)^2 + 2*(B^2*a^8*b - 2*B^2*a^6*b^3 - 3*B^2*a^4*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (B^2*a^7*b^2 - 2*B^2*a^5*b^4 - 3*B^2*a^3*b^6)*d^3)*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*B^4*a^8 + 12*B^4*a^6*b^2 - 2*B^4*a^4*b^4 - 4*B^4*a^2*b^6 + B^4*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*B^3*a^9 + 12*B^3*a^7*b^2 - 2*B^3*a^5*b^4 - 4*B^3*a^3*b^6 + B^3*a*b^8)*d^3*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*B^5*a^6 - 15*B^5*a^4*b^2 + 7*B^5*a^2*b^4 - B^5*b^6)*d*cos(d*x + c))*sqrt((B^2*a^6 + 3*B^2*a^4*b^2 + 3*B^2*a^2*b^4 + B^2*b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*B^2*a^4*b^2 - 6*B^2*a^2*b^4 + B^2*b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(B^4/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*B^6*a^5 - 6*B^6*a^3*b^2 + B^6*a*b^4)*cos(d*x + c) + (9*B^6*a^4*b - 6*B^6*a^2*b^3 + B^6*b^5)*sin(d*x + c))/cos(d*x + c)) + 8*(B^5*a^2*b^2 + B^5*b^4 + (B^5*a^4 - B^5*b^4)*cos(d*x + c)^2 + 2*(B^5*a^3*b + B^5*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*(B^5*a^2*b^2*cos(d*x + c)^2 + B^5*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)))/((B^4*a^6 - B^4*a^2*b^4)*d*cos(d*x + c)^2 + 2*(B^4*a^5*b + B^4*a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (B^4*a^4*b^2 + B^4*a^2*b^4)*d)]","B",0
370,1,3540,0,0.777701," ","integrate((-a+b*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \arctan\left(\frac{{\left(3 \, a^{8} + 8 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - b^{8}\right)} d^{4} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\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^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left(2 \, a d^{7} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{2} + b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{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^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - 5 \, a^{2} b^{7} + b^{9}\right)} d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - 5 \, a^{3} b^{7} + a b^{9}\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^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{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^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{9} b^{2} + 12 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \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)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(3 \, a^{5} b + 2 \, a^{3} b^{3} - a b^{5}\right)} d^{7} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(3 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{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^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}}\right) + 4 \, \sqrt{2} {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{8} + 8 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - b^{8}\right)} d^{4} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\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^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left(2 \, a d^{7} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{2} + b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{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^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - 5 \, a^{2} b^{7} + b^{9}\right)} d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - 5 \, a^{3} b^{7} + a b^{9}\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^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{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^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{9} b^{2} + 12 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \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)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(3 \, a^{5} b + 2 \, a^{3} b^{3} - a b^{5}\right)} d^{7} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(3 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{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^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}}\right) + \sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{2} + b^{2}}{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^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - 5 \, a^{2} b^{7} + b^{9}\right)} d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - 5 \, a^{3} b^{7} + a b^{9}\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^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{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^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{9} b^{2} + 12 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \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)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{2} + b^{2}}{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^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - 5 \, a^{2} b^{7} + b^{9}\right)} d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - 5 \, a^{3} b^{7} + a b^{9}\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^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{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^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{9} b^{2} + 12 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \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)} \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)*(a^2 + b^2)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^2 + b^2)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*arctan(((3*a^8 + 8*a^6*b^2 + 6*a^4*b^4 - b^8)*d^4*sqrt((a^2 + b^2)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*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^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*(2*a*d^7*sqrt((a^2 + b^2)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^2 + b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/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^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6*b^3 + 3*a^4*b^5 - 5*a^2*b^7 + b^9)*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + 2*(9*a^7*b^3 + 3*a^5*b^5 - 5*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/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^2 + b^2)/d^4)^(1/4) + (9*a^9*b^2 + 12*a^7*b^4 - 2*a^5*b^6 - 4*a^3*b^8 + a*b^10)*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)*sin(d*x + c))/cos(d*x + c))*((a^2 + b^2)/d^4)^(3/4) + sqrt(2)*(2*(3*a^5*b + 2*a^3*b^3 - a*b^5)*d^7*sqrt((a^2 + b^2)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (3*a^6*b + 5*a^4*b^3 + a^2*b^5 - b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/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^2 + b^2)/d^4)^(3/4))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)) + 4*sqrt(2)*(a^2 + b^2)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^2 + b^2)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*d^4))*arctan(-((3*a^8 + 8*a^6*b^2 + 6*a^4*b^4 - b^8)*d^4*sqrt((a^2 + b^2)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*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^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*(2*a*d^7*sqrt((a^2 + b^2)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^2 + b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/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^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6*b^3 + 3*a^4*b^5 - 5*a^2*b^7 + b^9)*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + 2*(9*a^7*b^3 + 3*a^5*b^5 - 5*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/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^2 + b^2)/d^4)^(1/4) + (9*a^9*b^2 + 12*a^7*b^4 - 2*a^5*b^6 - 4*a^3*b^8 + a*b^10)*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)*sin(d*x + c))/cos(d*x + c))*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*(2*(3*a^5*b + 2*a^3*b^3 - a*b^5)*d^7*sqrt((a^2 + b^2)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (3*a^6*b + 5*a^4*b^3 + a^2*b^5 - b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/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^2 + b^2)/d^4)^(3/4))/(9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)) + sqrt(2)*(a^4 + 2*a^2*b^2 + b^4 - (a^3 - 3*a*b^2)*d^2*sqrt((a^2 + b^2)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^2 + b^2)/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^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6*b^3 + 3*a^4*b^5 - 5*a^2*b^7 + b^9)*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + 2*(9*a^7*b^3 + 3*a^5*b^5 - 5*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/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^2 + b^2)/d^4)^(1/4) + (9*a^9*b^2 + 12*a^7*b^4 - 2*a^5*b^6 - 4*a^3*b^8 + a*b^10)*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)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(a^4 + 2*a^2*b^2 + b^4 - (a^3 - 3*a*b^2)*d^2*sqrt((a^2 + b^2)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^2 + b^2)/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^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6*b^3 + 3*a^4*b^5 - 5*a^2*b^7 + b^9)*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + 2*(9*a^7*b^3 + 3*a^5*b^5 - 5*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^5 - 2*a^3*b^2 - 3*a*b^4)*d^2*sqrt((a^2 + b^2)/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^2 + b^2)/d^4)^(1/4) + (9*a^9*b^2 + 12*a^7*b^4 - 2*a^5*b^6 - 4*a^3*b^8 + a*b^10)*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)*sin(d*x + c))/cos(d*x + c)))/(a^4 + 2*a^2*b^2 + b^4)","B",0
371,1,6318,0,1.583803," ","integrate((-a+b*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left({\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{5} \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)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} 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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{12} + 6 \, a^{10} 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^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(5 \, a^{12} + 10 \, a^{10} b^{2} - 9 \, a^{8} b^{4} - 36 \, a^{6} b^{6} - 29 \, a^{4} b^{8} - 6 \, a^{2} b^{10} + b^{12}\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^{12} + 6 \, a^{10} 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^{2} + b^{2}\right)} d^{4}}} + {\left(5 \, a^{11} + 5 \, a^{9} b^{2} - 14 \, a^{7} b^{4} - 22 \, a^{5} b^{6} - 7 \, a^{3} b^{8} + a b^{10}\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^{12} + 6 \, a^{10} 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(3 \, a^{6} + 5 \, a^{4} b^{2} + a^{2} b^{4} - b^{6}\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^{12} + 6 \, a^{10} 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^{2} + b^{2}\right)} d^{4}}} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\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^{12} + 6 \, a^{10} 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^{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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(25 \, a^{13} b^{3} - 50 \, a^{11} b^{5} - 65 \, a^{9} b^{7} + 100 \, a^{7} b^{9} + 71 \, a^{5} b^{11} - 18 \, a^{3} b^{13} + a b^{15}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{12} b^{3} - 250 \, a^{10} b^{5} + 105 \, a^{8} b^{7} + 260 \, a^{6} b^{9} - 147 \, a^{4} b^{11} + 22 \, a^{2} b^{13} - b^{15}\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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{13} b^{2} - 50 \, a^{11} b^{4} - 65 \, a^{9} b^{6} + 100 \, a^{7} b^{8} + 71 \, a^{5} b^{10} - 18 \, a^{3} b^{12} + a b^{14}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{12} b^{3} - 50 \, a^{10} b^{5} - 65 \, a^{8} b^{7} + 100 \, a^{6} b^{9} + 71 \, a^{4} b^{11} - 18 \, a^{2} b^{13} + b^{15}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(15 \, a^{12} b + 10 \, a^{10} b^{3} - 47 \, a^{8} b^{5} - 52 \, a^{6} b^{7} + a^{4} b^{9} + 10 \, a^{2} b^{11} - b^{13}\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^{12} + 6 \, a^{10} 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^{2} + b^{2}\right)} d^{4}}} + 2 \, {\left(5 \, a^{11} b + 5 \, a^{9} b^{3} - 14 \, a^{7} b^{5} - 22 \, a^{5} b^{7} - 7 \, a^{3} b^{9} + a b^{11}\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^{12} + 6 \, a^{10} 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^{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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{2} + b^{2}\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) + 4 \, \sqrt{2} {\left({\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{5} \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)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} 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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{12} + 6 \, a^{10} 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^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(5 \, a^{12} + 10 \, a^{10} b^{2} - 9 \, a^{8} b^{4} - 36 \, a^{6} b^{6} - 29 \, a^{4} b^{8} - 6 \, a^{2} b^{10} + b^{12}\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^{12} + 6 \, a^{10} 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^{2} + b^{2}\right)} d^{4}}} + {\left(5 \, a^{11} + 5 \, a^{9} b^{2} - 14 \, a^{7} b^{4} - 22 \, a^{5} b^{6} - 7 \, a^{3} b^{8} + a b^{10}\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^{12} + 6 \, a^{10} 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(3 \, a^{6} + 5 \, a^{4} b^{2} + a^{2} b^{4} - b^{6}\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^{12} + 6 \, a^{10} 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^{2} + b^{2}\right)} d^{4}}} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\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^{12} + 6 \, a^{10} 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^{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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(25 \, a^{13} b^{3} - 50 \, a^{11} b^{5} - 65 \, a^{9} b^{7} + 100 \, a^{7} b^{9} + 71 \, a^{5} b^{11} - 18 \, a^{3} b^{13} + a b^{15}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{12} b^{3} - 250 \, a^{10} b^{5} + 105 \, a^{8} b^{7} + 260 \, a^{6} b^{9} - 147 \, a^{4} b^{11} + 22 \, a^{2} b^{13} - b^{15}\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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{13} b^{2} - 50 \, a^{11} b^{4} - 65 \, a^{9} b^{6} + 100 \, a^{7} b^{8} + 71 \, a^{5} b^{10} - 18 \, a^{3} b^{12} + a b^{14}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{12} b^{3} - 50 \, a^{10} b^{5} - 65 \, a^{8} b^{7} + 100 \, a^{6} b^{9} + 71 \, a^{4} b^{11} - 18 \, a^{2} b^{13} + b^{15}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(15 \, a^{12} b + 10 \, a^{10} b^{3} - 47 \, a^{8} b^{5} - 52 \, a^{6} b^{7} + a^{4} b^{9} + 10 \, a^{2} b^{11} - b^{13}\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^{12} + 6 \, a^{10} 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^{2} + b^{2}\right)} d^{4}}} + 2 \, {\left(5 \, a^{11} b + 5 \, a^{9} b^{3} - 14 \, a^{7} b^{5} - 22 \, a^{5} b^{7} - 7 \, a^{3} b^{9} + a b^{11}\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^{12} + 6 \, a^{10} 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^{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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{2} + b^{2}\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) + \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 - {\left({\left(a^{7} - 11 \, a^{5} b^{2} + 15 \, a^{3} b^{4} - 5 \, a b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 10 \, a^{4} b^{3} + 5 \, a^{2} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} - 10 \, a^{3} b^{4} + 5 \, a b^{6}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{2} + b^{2}\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^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(25 \, a^{13} b^{3} - 50 \, a^{11} b^{5} - 65 \, a^{9} b^{7} + 100 \, a^{7} b^{9} + 71 \, a^{5} b^{11} - 18 \, a^{3} b^{13} + a b^{15}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{12} b^{3} - 250 \, a^{10} b^{5} + 105 \, a^{8} b^{7} + 260 \, a^{6} b^{9} - 147 \, a^{4} b^{11} + 22 \, a^{2} b^{13} - b^{15}\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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{13} b^{2} - 50 \, a^{11} b^{4} - 65 \, a^{9} b^{6} + 100 \, a^{7} b^{8} + 71 \, a^{5} b^{10} - 18 \, a^{3} b^{12} + a b^{14}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{12} b^{3} - 50 \, a^{10} b^{5} - 65 \, a^{8} b^{7} + 100 \, a^{6} b^{9} + 71 \, a^{4} b^{11} - 18 \, a^{2} b^{13} + b^{15}\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 - {\left({\left(a^{7} - 11 \, a^{5} b^{2} + 15 \, a^{3} b^{4} - 5 \, a b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 10 \, a^{4} b^{3} + 5 \, a^{2} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} - 10 \, a^{3} b^{4} + 5 \, a b^{6}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{2} + b^{2}\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^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(25 \, a^{13} b^{3} - 50 \, a^{11} b^{5} - 65 \, a^{9} b^{7} + 100 \, a^{7} b^{9} + 71 \, a^{5} b^{11} - 18 \, a^{3} b^{13} + a b^{15}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{12} b^{3} - 250 \, a^{10} b^{5} + 105 \, a^{8} b^{7} + 260 \, a^{6} b^{9} - 147 \, a^{4} b^{11} + 22 \, a^{2} b^{13} - b^{15}\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^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\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^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{13} b^{2} - 50 \, a^{11} b^{4} - 65 \, a^{9} b^{6} + 100 \, a^{7} b^{8} + 71 \, a^{5} b^{10} - 18 \, a^{3} b^{12} + a b^{14}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{12} b^{3} - 50 \, a^{10} b^{5} - 65 \, a^{8} b^{7} + 100 \, a^{6} b^{9} + 71 \, a^{4} b^{11} - 18 \, a^{2} b^{13} + b^{15}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 16 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b^{2} + a b^{4}\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^{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)}}"," ",0,"-1/4*(4*sqrt(2)*((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^5*cos(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d^5*cos(d*x + c)*sin(d*x + c) + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*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^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*d^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^12 + 6*a^10*b^2 + 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^2 + b^2)*d^4))^(3/4)*arctan(((5*a^12 + 10*a^10*b^2 - 9*a^8*b^4 - 36*a^6*b^6 - 29*a^4*b^8 - 6*a^2*b^10 + b^12)*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^12 + 6*a^10*b^2 + 15*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^2 + b^2)*d^4)) + (5*a^11 + 5*a^9*b^2 - 14*a^7*b^4 - 22*a^5*b^6 - 7*a^3*b^8 + a*b^10)*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^12 + 6*a^10*b^2 + 15*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)*((3*a^6 + 5*a^4*b^2 + a^2*b^4 - b^6)*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^12 + 6*a^10*b^2 + 15*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^2 + b^2)*d^4)) + 2*(a^5 + 2*a^3*b^2 + a*b^4)*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^12 + 6*a^10*b^2 + 15*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^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*d^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^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*(2*(25*a^13*b^3 - 50*a^11*b^5 - 65*a^9*b^7 + 100*a^7*b^9 + 71*a^5*b^11 - 18*a^3*b^13 + a*b^15)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + (75*a^12*b^3 - 250*a^10*b^5 + 105*a^8*b^7 + 260*a^6*b^9 - 147*a^4*b^11 + 22*a^2*b^13 - b^15)*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^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*d^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^2 + b^2)*d^4))^(1/4) + (25*a^13*b^2 - 50*a^11*b^4 - 65*a^9*b^6 + 100*a^7*b^8 + 71*a^5*b^10 - 18*a^3*b^12 + a*b^14)*cos(d*x + c) + (25*a^12*b^3 - 50*a^10*b^5 - 65*a^8*b^7 + 100*a^6*b^9 + 71*a^4*b^11 - 18*a^2*b^13 + b^15)*sin(d*x + c))/cos(d*x + c))*(1/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((15*a^12*b + 10*a^10*b^3 - 47*a^8*b^5 - 52*a^6*b^7 + a^4*b^9 + 10*a^2*b^11 - b^13)*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^12 + 6*a^10*b^2 + 15*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^2 + b^2)*d^4)) + 2*(5*a^11*b + 5*a^9*b^3 - 14*a^7*b^5 - 22*a^5*b^7 - 7*a^3*b^9 + a*b^11)*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^12 + 6*a^10*b^2 + 15*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^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*d^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^2 + b^2)*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)) + 4*sqrt(2)*((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^5*cos(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d^5*cos(d*x + c)*sin(d*x + c) + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*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^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*d^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^12 + 6*a^10*b^2 + 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^2 + b^2)*d^4))^(3/4)*arctan(-((5*a^12 + 10*a^10*b^2 - 9*a^8*b^4 - 36*a^6*b^6 - 29*a^4*b^8 - 6*a^2*b^10 + b^12)*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^12 + 6*a^10*b^2 + 15*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^2 + b^2)*d^4)) + (5*a^11 + 5*a^9*b^2 - 14*a^7*b^4 - 22*a^5*b^6 - 7*a^3*b^8 + a*b^10)*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^12 + 6*a^10*b^2 + 15*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)*((3*a^6 + 5*a^4*b^2 + a^2*b^4 - b^6)*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^12 + 6*a^10*b^2 + 15*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^2 + b^2)*d^4)) + 2*(a^5 + 2*a^3*b^2 + a*b^4)*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^12 + 6*a^10*b^2 + 15*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^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*d^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^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*(2*(25*a^13*b^3 - 50*a^11*b^5 - 65*a^9*b^7 + 100*a^7*b^9 + 71*a^5*b^11 - 18*a^3*b^13 + a*b^15)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + (75*a^12*b^3 - 250*a^10*b^5 + 105*a^8*b^7 + 260*a^6*b^9 - 147*a^4*b^11 + 22*a^2*b^13 - b^15)*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^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*d^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^2 + b^2)*d^4))^(1/4) + (25*a^13*b^2 - 50*a^11*b^4 - 65*a^9*b^6 + 100*a^7*b^8 + 71*a^5*b^10 - 18*a^3*b^12 + a*b^14)*cos(d*x + c) + (25*a^12*b^3 - 50*a^10*b^5 - 65*a^8*b^7 + 100*a^6*b^9 + 71*a^4*b^11 - 18*a^2*b^13 + b^15)*sin(d*x + c))/cos(d*x + c))*(1/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((15*a^12*b + 10*a^10*b^3 - 47*a^8*b^5 - 52*a^6*b^7 + a^4*b^9 + 10*a^2*b^11 - b^13)*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^12 + 6*a^10*b^2 + 15*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^2 + b^2)*d^4)) + 2*(5*a^11*b + 5*a^9*b^3 - 14*a^7*b^5 - 22*a^5*b^7 - 7*a^3*b^9 + a*b^11)*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^12 + 6*a^10*b^2 + 15*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^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*d^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^2 + b^2)*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)) + 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 - ((a^7 - 11*a^5*b^2 + 15*a^3*b^4 - 5*a*b^6)*d^3*cos(d*x + c)^2 + 2*(a^6*b - 10*a^4*b^3 + 5*a^2*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 - 10*a^3*b^4 + 5*a*b^6)*d^3)*sqrt(1/((a^2 + b^2)*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^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*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^2 + b^2)*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^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*(2*(25*a^13*b^3 - 50*a^11*b^5 - 65*a^9*b^7 + 100*a^7*b^9 + 71*a^5*b^11 - 18*a^3*b^13 + a*b^15)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + (75*a^12*b^3 - 250*a^10*b^5 + 105*a^8*b^7 + 260*a^6*b^9 - 147*a^4*b^11 + 22*a^2*b^13 - b^15)*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^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*d^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^2 + b^2)*d^4))^(1/4) + (25*a^13*b^2 - 50*a^11*b^4 - 65*a^9*b^6 + 100*a^7*b^8 + 71*a^5*b^10 - 18*a^3*b^12 + a*b^14)*cos(d*x + c) + (25*a^12*b^3 - 50*a^10*b^5 - 65*a^8*b^7 + 100*a^6*b^9 + 71*a^4*b^11 - 18*a^2*b^13 + b^15)*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 - ((a^7 - 11*a^5*b^2 + 15*a^3*b^4 - 5*a*b^6)*d^3*cos(d*x + c)^2 + 2*(a^6*b - 10*a^4*b^3 + 5*a^2*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 - 10*a^3*b^4 + 5*a*b^6)*d^3)*sqrt(1/((a^2 + b^2)*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^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*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^2 + b^2)*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^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*(2*(25*a^13*b^3 - 50*a^11*b^5 - 65*a^9*b^7 + 100*a^7*b^9 + 71*a^5*b^11 - 18*a^3*b^13 + a*b^15)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + (75*a^12*b^3 - 250*a^10*b^5 + 105*a^8*b^7 + 260*a^6*b^9 - 147*a^4*b^11 + 22*a^2*b^13 - b^15)*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^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d^2*sqrt(1/((a^2 + b^2)*d^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^2 + b^2)*d^4))^(1/4) + (25*a^13*b^2 - 50*a^11*b^4 - 65*a^9*b^6 + 100*a^7*b^8 + 71*a^5*b^10 - 18*a^3*b^12 + a*b^14)*cos(d*x + c) + (25*a^12*b^3 - 50*a^10*b^5 - 65*a^8*b^7 + 100*a^6*b^9 + 71*a^4*b^11 - 18*a^2*b^13 + b^15)*sin(d*x + c))/cos(d*x + c)) - 16*((a^4*b + a^2*b^3)*cos(d*x + c)^2 + (a^3*b^2 + 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^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
372,1,10036,0,1.768270," ","integrate((-a+b*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left({\left(a^{14} - a^{12} b^{2} - 19 \, a^{10} b^{4} - 45 \, a^{8} b^{6} - 45 \, a^{6} b^{8} - 19 \, a^{4} b^{10} - a^{2} b^{12} + b^{14}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{12} b^{2} + 14 \, a^{10} b^{4} + 25 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 5 \, a^{4} b^{10} - 2 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{10} b^{4} + 5 \, a^{8} b^{6} + 10 \, a^{6} b^{8} + 10 \, a^{4} b^{10} + 5 \, a^{2} b^{12} + b^{14}\right)} d^{5} + 4 \, {\left({\left(a^{13} b + 4 \, a^{11} b^{3} + 5 \, a^{9} b^{5} - 5 \, a^{5} b^{9} - 4 \, a^{3} b^{11} - a b^{13}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\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)} d^{5} \cos\left(d x + c\right)\right)} \sin\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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{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(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^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(7 \, a^{20} + 14 \, a^{18} b^{2} - 77 \, a^{16} b^{4} - 344 \, a^{14} b^{6} - 546 \, a^{12} b^{8} - 364 \, a^{10} b^{10} + 14 \, a^{8} b^{12} + 168 \, a^{6} b^{14} + 91 \, a^{4} b^{16} + 14 \, a^{2} b^{18} - b^{20}\right)} 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}}{{\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^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(7 \, a^{17} - 84 \, a^{13} b^{4} - 176 \, a^{11} b^{6} - 110 \, a^{9} b^{8} + 32 \, a^{7} b^{10} + 60 \, a^{5} b^{12} + 16 \, a^{3} b^{14} - a b^{16}\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}}{{\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(4 \, {\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^{7} \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}}{{\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^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\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^{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}}{{\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^{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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{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(147 \, a^{20} b^{3} - 1078 \, a^{18} b^{5} + 931 \, a^{16} b^{7} + 4760 \, a^{14} b^{9} - 1274 \, a^{12} b^{11} - 4452 \, a^{10} b^{13} + 1214 \, a^{8} b^{15} + 1240 \, a^{6} b^{17} - 505 \, a^{4} b^{19} + 42 \, a^{2} b^{21} - b^{23}\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) + 4 \, {\left(49 \, a^{17} b^{3} - 490 \, a^{15} b^{5} + 1470 \, a^{13} b^{7} - 994 \, a^{11} b^{9} - 1008 \, a^{9} b^{11} + 1442 \, a^{7} b^{13} - 510 \, a^{5} b^{15} + 42 \, a^{3} b^{17} - a b^{19}\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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(49 \, a^{17} b^{2} - 392 \, a^{15} b^{4} + 588 \, a^{13} b^{6} + 1064 \, a^{11} b^{8} - 938 \, a^{9} b^{10} - 504 \, a^{7} b^{12} + 428 \, a^{5} b^{14} - 40 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(49 \, a^{16} b^{3} - 392 \, a^{14} b^{5} + 588 \, a^{12} b^{7} + 1064 \, a^{10} b^{9} - 938 \, a^{8} b^{11} - 504 \, a^{6} b^{13} + 428 \, a^{4} b^{15} - 40 \, a^{2} b^{17} + b^{19}\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(4 \, {\left(7 \, a^{23} b + 7 \, a^{21} b^{3} - 91 \, a^{19} b^{5} - 267 \, a^{17} b^{7} - 202 \, a^{15} b^{9} + 182 \, a^{13} b^{11} + 378 \, a^{11} b^{13} + 154 \, a^{9} b^{15} - 77 \, a^{7} b^{17} - 77 \, a^{5} b^{19} - 15 \, a^{3} b^{21} + a b^{23}\right)} d^{7} \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}}{{\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^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(21 \, a^{20} b + 14 \, a^{18} b^{3} - 259 \, a^{16} b^{5} - 696 \, a^{14} b^{7} - 598 \, a^{12} b^{9} + 52 \, a^{10} b^{11} + 354 \, a^{8} b^{13} + 136 \, a^{6} b^{15} - 31 \, a^{4} b^{17} - 18 \, a^{2} b^{19} + 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}}{{\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^{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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{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}}\right) + 12 \, \sqrt{2} {\left({\left(a^{14} - a^{12} b^{2} - 19 \, a^{10} b^{4} - 45 \, a^{8} b^{6} - 45 \, a^{6} b^{8} - 19 \, a^{4} b^{10} - a^{2} b^{12} + b^{14}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{12} b^{2} + 14 \, a^{10} b^{4} + 25 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 5 \, a^{4} b^{10} - 2 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{10} b^{4} + 5 \, a^{8} b^{6} + 10 \, a^{6} b^{8} + 10 \, a^{4} b^{10} + 5 \, a^{2} b^{12} + b^{14}\right)} d^{5} + 4 \, {\left({\left(a^{13} b + 4 \, a^{11} b^{3} + 5 \, a^{9} b^{5} - 5 \, a^{5} b^{9} - 4 \, a^{3} b^{11} - a b^{13}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\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)} d^{5} \cos\left(d x + c\right)\right)} \sin\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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{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(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^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(7 \, a^{20} + 14 \, a^{18} b^{2} - 77 \, a^{16} b^{4} - 344 \, a^{14} b^{6} - 546 \, a^{12} b^{8} - 364 \, a^{10} b^{10} + 14 \, a^{8} b^{12} + 168 \, a^{6} b^{14} + 91 \, a^{4} b^{16} + 14 \, a^{2} b^{18} - b^{20}\right)} 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}}{{\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^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(7 \, a^{17} - 84 \, a^{13} b^{4} - 176 \, a^{11} b^{6} - 110 \, a^{9} b^{8} + 32 \, a^{7} b^{10} + 60 \, a^{5} b^{12} + 16 \, a^{3} b^{14} - a b^{16}\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}}{{\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(4 \, {\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^{7} \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}}{{\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^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\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^{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}}{{\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^{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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{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(147 \, a^{20} b^{3} - 1078 \, a^{18} b^{5} + 931 \, a^{16} b^{7} + 4760 \, a^{14} b^{9} - 1274 \, a^{12} b^{11} - 4452 \, a^{10} b^{13} + 1214 \, a^{8} b^{15} + 1240 \, a^{6} b^{17} - 505 \, a^{4} b^{19} + 42 \, a^{2} b^{21} - b^{23}\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) + 4 \, {\left(49 \, a^{17} b^{3} - 490 \, a^{15} b^{5} + 1470 \, a^{13} b^{7} - 994 \, a^{11} b^{9} - 1008 \, a^{9} b^{11} + 1442 \, a^{7} b^{13} - 510 \, a^{5} b^{15} + 42 \, a^{3} b^{17} - a b^{19}\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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(49 \, a^{17} b^{2} - 392 \, a^{15} b^{4} + 588 \, a^{13} b^{6} + 1064 \, a^{11} b^{8} - 938 \, a^{9} b^{10} - 504 \, a^{7} b^{12} + 428 \, a^{5} b^{14} - 40 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(49 \, a^{16} b^{3} - 392 \, a^{14} b^{5} + 588 \, a^{12} b^{7} + 1064 \, a^{10} b^{9} - 938 \, a^{8} b^{11} - 504 \, a^{6} b^{13} + 428 \, a^{4} b^{15} - 40 \, a^{2} b^{17} + b^{19}\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(4 \, {\left(7 \, a^{23} b + 7 \, a^{21} b^{3} - 91 \, a^{19} b^{5} - 267 \, a^{17} b^{7} - 202 \, a^{15} b^{9} + 182 \, a^{13} b^{11} + 378 \, a^{11} b^{13} + 154 \, a^{9} b^{15} - 77 \, a^{7} b^{17} - 77 \, a^{5} b^{19} - 15 \, a^{3} b^{21} + a b^{23}\right)} d^{7} \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}}{{\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^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(21 \, a^{20} b + 14 \, a^{18} b^{3} - 259 \, a^{16} b^{5} - 696 \, a^{14} b^{7} - 598 \, a^{12} b^{9} + 52 \, a^{10} b^{11} + 354 \, a^{8} b^{13} + 136 \, a^{6} b^{15} - 31 \, a^{4} b^{17} - 18 \, a^{2} b^{19} + 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}}{{\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^{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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{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}}\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^{11} - 27 \, a^{9} b^{2} + 162 \, a^{7} b^{4} - 238 \, a^{5} b^{6} + 77 \, a^{3} b^{8} - 7 \, a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{9} b^{2} - 64 \, a^{7} b^{4} + 126 \, a^{5} b^{6} - 56 \, a^{3} b^{8} + 7 \, a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{7} b^{4} - 21 \, a^{5} b^{6} + 35 \, a^{3} b^{8} - 7 \, a b^{10}\right)} d^{3} + 4 \, {\left({\left(a^{10} b - 22 \, a^{8} b^{3} + 56 \, a^{6} b^{5} - 42 \, a^{4} b^{7} + 7 \, a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{8} b^{3} - 21 \, a^{6} b^{5} + 35 \, a^{4} b^{7} - 7 \, a^{2} b^{9}\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^{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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{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(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{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(147 \, a^{20} b^{3} - 1078 \, a^{18} b^{5} + 931 \, a^{16} b^{7} + 4760 \, a^{14} b^{9} - 1274 \, a^{12} b^{11} - 4452 \, a^{10} b^{13} + 1214 \, a^{8} b^{15} + 1240 \, a^{6} b^{17} - 505 \, a^{4} b^{19} + 42 \, a^{2} b^{21} - b^{23}\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) + 4 \, {\left(49 \, a^{17} b^{3} - 490 \, a^{15} b^{5} + 1470 \, a^{13} b^{7} - 994 \, a^{11} b^{9} - 1008 \, a^{9} b^{11} + 1442 \, a^{7} b^{13} - 510 \, a^{5} b^{15} + 42 \, a^{3} b^{17} - a b^{19}\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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(49 \, a^{17} b^{2} - 392 \, a^{15} b^{4} + 588 \, a^{13} b^{6} + 1064 \, a^{11} b^{8} - 938 \, a^{9} b^{10} - 504 \, a^{7} b^{12} + 428 \, a^{5} b^{14} - 40 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(49 \, a^{16} b^{3} - 392 \, a^{14} b^{5} + 588 \, a^{12} b^{7} + 1064 \, a^{10} b^{9} - 938 \, a^{8} b^{11} - 504 \, a^{6} b^{13} + 428 \, a^{4} b^{15} - 40 \, a^{2} b^{17} + b^{19}\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^{11} - 27 \, a^{9} b^{2} + 162 \, a^{7} b^{4} - 238 \, a^{5} b^{6} + 77 \, a^{3} b^{8} - 7 \, a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{9} b^{2} - 64 \, a^{7} b^{4} + 126 \, a^{5} b^{6} - 56 \, a^{3} b^{8} + 7 \, a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{7} b^{4} - 21 \, a^{5} b^{6} + 35 \, a^{3} b^{8} - 7 \, a b^{10}\right)} d^{3} + 4 \, {\left({\left(a^{10} b - 22 \, a^{8} b^{3} + 56 \, a^{6} b^{5} - 42 \, a^{4} b^{7} + 7 \, a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{8} b^{3} - 21 \, a^{6} b^{5} + 35 \, a^{4} b^{7} - 7 \, a^{2} b^{9}\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^{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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{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(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{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(147 \, a^{20} b^{3} - 1078 \, a^{18} b^{5} + 931 \, a^{16} b^{7} + 4760 \, a^{14} b^{9} - 1274 \, a^{12} b^{11} - 4452 \, a^{10} b^{13} + 1214 \, a^{8} b^{15} + 1240 \, a^{6} b^{17} - 505 \, a^{4} b^{19} + 42 \, a^{2} b^{21} - b^{23}\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) + 4 \, {\left(49 \, a^{17} b^{3} - 490 \, a^{15} b^{5} + 1470 \, a^{13} b^{7} - 994 \, a^{11} b^{9} - 1008 \, a^{9} b^{11} + 1442 \, a^{7} b^{13} - 510 \, a^{5} b^{15} + 42 \, a^{3} b^{17} - a b^{19}\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^{17} - 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} - 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} + 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} 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{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(49 \, a^{17} b^{2} - 392 \, a^{15} b^{4} + 588 \, a^{13} b^{6} + 1064 \, a^{11} b^{8} - 938 \, a^{9} b^{10} - 504 \, a^{7} b^{12} + 428 \, a^{5} b^{14} - 40 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(49 \, a^{16} b^{3} - 392 \, a^{14} b^{5} + 588 \, a^{12} b^{7} + 1064 \, a^{10} b^{9} - 938 \, a^{8} b^{11} - 504 \, a^{6} b^{13} + 428 \, a^{4} b^{15} - 40 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left({\left(11 \, a^{5} b - 30 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(29 \, a^{3} b^{3} - 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(31 \, a^{4} b^{2} - 14 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} b^{4} - b^{6}\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^14 - a^12*b^2 - 19*a^10*b^4 - 45*a^8*b^6 - 45*a^6*b^8 - 19*a^4*b^10 - a^2*b^12 + b^14)*d^5*cos(d*x + c)^4 + 2*(3*a^12*b^2 + 14*a^10*b^4 + 25*a^8*b^6 + 20*a^6*b^8 + 5*a^4*b^10 - 2*a^2*b^12 - b^14)*d^5*cos(d*x + c)^2 + (a^10*b^4 + 5*a^8*b^6 + 10*a^6*b^8 + 10*a^4*b^10 + 5*a^2*b^12 + b^14)*d^5 + 4*((a^13*b + 4*a^11*b^3 + 5*a^9*b^5 - 5*a^5*b^9 - 4*a^3*b^11 - a*b^13)*d^5*cos(d*x + c)^3 + (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)*d^5*cos(d*x + c))*sin(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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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^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^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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((7*a^20 + 14*a^18*b^2 - 77*a^16*b^4 - 344*a^14*b^6 - 546*a^12*b^8 - 364*a^10*b^10 + 14*a^8*b^12 + 168*a^6*b^14 + 91*a^4*b^16 + 14*a^2*b^18 - b^20)*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)/((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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (7*a^17 - 84*a^13*b^4 - 176*a^11*b^6 - 110*a^9*b^8 + 32*a^7*b^10 + 60*a^5*b^12 + 16*a^3*b^14 - a*b^16)*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)/((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)*(4*(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^7*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)/((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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (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^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)/((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^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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((147*a^20*b^3 - 1078*a^18*b^5 + 931*a^16*b^7 + 4760*a^14*b^9 - 1274*a^12*b^11 - 4452*a^10*b^13 + 1214*a^8*b^15 + 1240*a^6*b^17 - 505*a^4*b^19 + 42*a^2*b^21 - b^23)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 4*(49*a^17*b^3 - 490*a^15*b^5 + 1470*a^13*b^7 - 994*a^11*b^9 - 1008*a^9*b^11 + 1442*a^7*b^13 - 510*a^5*b^15 + 42*a^3*b^17 - a*b^19)*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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (49*a^17*b^2 - 392*a^15*b^4 + 588*a^13*b^6 + 1064*a^11*b^8 - 938*a^9*b^10 - 504*a^7*b^12 + 428*a^5*b^14 - 40*a^3*b^16 + a*b^18)*cos(d*x + c) + (49*a^16*b^3 - 392*a^14*b^5 + 588*a^12*b^7 + 1064*a^10*b^9 - 938*a^8*b^11 - 504*a^6*b^13 + 428*a^4*b^15 - 40*a^2*b^17 + b^19)*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)*(4*(7*a^23*b + 7*a^21*b^3 - 91*a^19*b^5 - 267*a^17*b^7 - 202*a^15*b^9 + 182*a^13*b^11 + 378*a^11*b^13 + 154*a^9*b^15 - 77*a^7*b^17 - 77*a^5*b^19 - 15*a^3*b^21 + a*b^23)*d^7*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)/((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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (21*a^20*b + 14*a^18*b^3 - 259*a^16*b^5 - 696*a^14*b^7 - 598*a^12*b^9 + 52*a^10*b^11 + 354*a^8*b^13 + 136*a^6*b^15 - 31*a^4*b^17 - 18*a^2*b^19 + 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)/((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^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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(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)) + 12*sqrt(2)*((a^14 - a^12*b^2 - 19*a^10*b^4 - 45*a^8*b^6 - 45*a^6*b^8 - 19*a^4*b^10 - a^2*b^12 + b^14)*d^5*cos(d*x + c)^4 + 2*(3*a^12*b^2 + 14*a^10*b^4 + 25*a^8*b^6 + 20*a^6*b^8 + 5*a^4*b^10 - 2*a^2*b^12 - b^14)*d^5*cos(d*x + c)^2 + (a^10*b^4 + 5*a^8*b^6 + 10*a^6*b^8 + 10*a^4*b^10 + 5*a^2*b^12 + b^14)*d^5 + 4*((a^13*b + 4*a^11*b^3 + 5*a^9*b^5 - 5*a^5*b^9 - 4*a^3*b^11 - a*b^13)*d^5*cos(d*x + c)^3 + (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)*d^5*cos(d*x + c))*sin(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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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^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^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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((7*a^20 + 14*a^18*b^2 - 77*a^16*b^4 - 344*a^14*b^6 - 546*a^12*b^8 - 364*a^10*b^10 + 14*a^8*b^12 + 168*a^6*b^14 + 91*a^4*b^16 + 14*a^2*b^18 - b^20)*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)/((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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (7*a^17 - 84*a^13*b^4 - 176*a^11*b^6 - 110*a^9*b^8 + 32*a^7*b^10 + 60*a^5*b^12 + 16*a^3*b^14 - a*b^16)*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)/((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)*(4*(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^7*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)/((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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (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^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)/((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^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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((147*a^20*b^3 - 1078*a^18*b^5 + 931*a^16*b^7 + 4760*a^14*b^9 - 1274*a^12*b^11 - 4452*a^10*b^13 + 1214*a^8*b^15 + 1240*a^6*b^17 - 505*a^4*b^19 + 42*a^2*b^21 - b^23)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 4*(49*a^17*b^3 - 490*a^15*b^5 + 1470*a^13*b^7 - 994*a^11*b^9 - 1008*a^9*b^11 + 1442*a^7*b^13 - 510*a^5*b^15 + 42*a^3*b^17 - a*b^19)*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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (49*a^17*b^2 - 392*a^15*b^4 + 588*a^13*b^6 + 1064*a^11*b^8 - 938*a^9*b^10 - 504*a^7*b^12 + 428*a^5*b^14 - 40*a^3*b^16 + a*b^18)*cos(d*x + c) + (49*a^16*b^3 - 392*a^14*b^5 + 588*a^12*b^7 + 1064*a^10*b^9 - 938*a^8*b^11 - 504*a^6*b^13 + 428*a^4*b^15 - 40*a^2*b^17 + b^19)*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)*(4*(7*a^23*b + 7*a^21*b^3 - 91*a^19*b^5 - 267*a^17*b^7 - 202*a^15*b^9 + 182*a^13*b^11 + 378*a^11*b^13 + 154*a^9*b^15 - 77*a^7*b^17 - 77*a^5*b^19 - 15*a^3*b^21 + a*b^23)*d^7*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)/((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^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (21*a^20*b + 14*a^18*b^3 - 259*a^16*b^5 - 696*a^14*b^7 - 598*a^12*b^9 + 52*a^10*b^11 + 354*a^8*b^13 + 136*a^6*b^15 - 31*a^4*b^17 - 18*a^2*b^19 + 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)/((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^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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(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)) - 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^11 - 27*a^9*b^2 + 162*a^7*b^4 - 238*a^5*b^6 + 77*a^3*b^8 - 7*a*b^10)*d^3*cos(d*x + c)^4 + 2*(3*a^9*b^2 - 64*a^7*b^4 + 126*a^5*b^6 - 56*a^3*b^8 + 7*a*b^10)*d^3*cos(d*x + c)^2 + (a^7*b^4 - 21*a^5*b^6 + 35*a^3*b^8 - 7*a*b^10)*d^3 + 4*((a^10*b - 22*a^8*b^3 + 56*a^6*b^5 - 42*a^4*b^7 + 7*a^2*b^9)*d^3*cos(d*x + c)^3 + (a^8*b^3 - 21*a^6*b^5 + 35*a^4*b^7 - 7*a^2*b^9)*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^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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((147*a^20*b^3 - 1078*a^18*b^5 + 931*a^16*b^7 + 4760*a^14*b^9 - 1274*a^12*b^11 - 4452*a^10*b^13 + 1214*a^8*b^15 + 1240*a^6*b^17 - 505*a^4*b^19 + 42*a^2*b^21 - b^23)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 4*(49*a^17*b^3 - 490*a^15*b^5 + 1470*a^13*b^7 - 994*a^11*b^9 - 1008*a^9*b^11 + 1442*a^7*b^13 - 510*a^5*b^15 + 42*a^3*b^17 - a*b^19)*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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (49*a^17*b^2 - 392*a^15*b^4 + 588*a^13*b^6 + 1064*a^11*b^8 - 938*a^9*b^10 - 504*a^7*b^12 + 428*a^5*b^14 - 40*a^3*b^16 + a*b^18)*cos(d*x + c) + (49*a^16*b^3 - 392*a^14*b^5 + 588*a^12*b^7 + 1064*a^10*b^9 - 938*a^8*b^11 - 504*a^6*b^13 + 428*a^4*b^15 - 40*a^2*b^17 + b^19)*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^11 - 27*a^9*b^2 + 162*a^7*b^4 - 238*a^5*b^6 + 77*a^3*b^8 - 7*a*b^10)*d^3*cos(d*x + c)^4 + 2*(3*a^9*b^2 - 64*a^7*b^4 + 126*a^5*b^6 - 56*a^3*b^8 + 7*a*b^10)*d^3*cos(d*x + c)^2 + (a^7*b^4 - 21*a^5*b^6 + 35*a^3*b^8 - 7*a*b^10)*d^3 + 4*((a^10*b - 22*a^8*b^3 + 56*a^6*b^5 - 42*a^4*b^7 + 7*a^2*b^9)*d^3*cos(d*x + c)^3 + (a^8*b^3 - 21*a^6*b^5 + 35*a^4*b^7 - 7*a^2*b^9)*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^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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((147*a^20*b^3 - 1078*a^18*b^5 + 931*a^16*b^7 + 4760*a^14*b^9 - 1274*a^12*b^11 - 4452*a^10*b^13 + 1214*a^8*b^15 + 1240*a^6*b^17 - 505*a^4*b^19 + 42*a^2*b^21 - b^23)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 4*(49*a^17*b^3 - 490*a^15*b^5 + 1470*a^13*b^7 - 994*a^11*b^9 - 1008*a^9*b^11 + 1442*a^7*b^13 - 510*a^5*b^15 + 42*a^3*b^17 - a*b^19)*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^17 - 16*a^15*b^2 - 60*a^13*b^4 - 32*a^11*b^6 + 110*a^9*b^8 + 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*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))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (49*a^17*b^2 - 392*a^15*b^4 + 588*a^13*b^6 + 1064*a^11*b^8 - 938*a^9*b^10 - 504*a^7*b^12 + 428*a^5*b^14 - 40*a^3*b^16 + a*b^18)*cos(d*x + c) + (49*a^16*b^3 - 392*a^14*b^5 + 588*a^12*b^7 + 1064*a^10*b^9 - 938*a^8*b^11 - 504*a^6*b^13 + 428*a^4*b^15 - 40*a^2*b^17 + b^19)*sin(d*x + c))/cos(d*x + c)) + 8*((11*a^5*b - 30*a^3*b^3 + 7*a*b^5)*cos(d*x + c)^4 + (29*a^3*b^3 - 7*a*b^5)*cos(d*x + c)^2 + ((31*a^4*b^2 - 14*a^2*b^4 + 3*b^6)*cos(d*x + c)^3 + 3*(3*a^2*b^4 - b^6)*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
373,1,249,0,0.476746," ","integrate((1+I*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-\frac{4 i}{{\left(i \, a + b\right)} d^{2}}} \log\left({\left({\left({\left(i \, a + b\right)} d e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(i \, a + b\right)} d\right)} \sqrt{\frac{{\left(a - i \, b\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + a + i \, b}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{4 i}{{\left(i \, a + b\right)} d^{2}}} + 2 \, {\left(a - i \, b\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, a\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - \frac{1}{4} \, \sqrt{-\frac{4 i}{{\left(i \, a + b\right)} d^{2}}} \log\left({\left({\left({\left(-i \, a - b\right)} d e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-i \, a - b\right)} d\right)} \sqrt{\frac{{\left(a - i \, b\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + a + i \, b}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{4 i}{{\left(i \, a + b\right)} d^{2}}} + 2 \, {\left(a - i \, b\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, a\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right)"," ",0,"1/4*sqrt(-4*I/((I*a + b)*d^2))*log((((I*a + b)*d*e^(2*I*d*x + 2*I*c) + (I*a + b)*d)*sqrt(((a - I*b)*e^(2*I*d*x + 2*I*c) + a + I*b)/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-4*I/((I*a + b)*d^2)) + 2*(a - I*b)*e^(2*I*d*x + 2*I*c) + 2*a)*e^(-2*I*d*x - 2*I*c)) - 1/4*sqrt(-4*I/((I*a + b)*d^2))*log((((-I*a - b)*d*e^(2*I*d*x + 2*I*c) + (-I*a - b)*d)*sqrt(((a - I*b)*e^(2*I*d*x + 2*I*c) + a + I*b)/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-4*I/((I*a + b)*d^2)) + 2*(a - I*b)*e^(2*I*d*x + 2*I*c) + 2*a)*e^(-2*I*d*x - 2*I*c))","B",0
374,1,267,0,0.481240," ","integrate((1-I*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\frac{4 i}{{\left(-i \, a + b\right)} d^{2}}} \log\left(\frac{{\left({\left({\left(i \, a - b\right)} d e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(i \, a - b\right)} d\right)} \sqrt{\frac{{\left(a - i \, b\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + a + i \, b}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{4 i}{{\left(-i \, a + b\right)} d^{2}}} + 2 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, a + 2 i \, b\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(-i \, a + b\right)} d}\right) + \frac{1}{4} \, \sqrt{\frac{4 i}{{\left(-i \, a + b\right)} d^{2}}} \log\left(\frac{{\left({\left({\left(-i \, a + b\right)} d e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-i \, a + b\right)} d\right)} \sqrt{\frac{{\left(a - i \, b\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + a + i \, b}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{4 i}{{\left(-i \, a + b\right)} d^{2}}} + 2 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, a + 2 i \, b\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(-i \, a + b\right)} d}\right)"," ",0,"-1/4*sqrt(4*I/((-I*a + b)*d^2))*log((((I*a - b)*d*e^(2*I*d*x + 2*I*c) + (I*a - b)*d)*sqrt(((a - I*b)*e^(2*I*d*x + 2*I*c) + a + I*b)/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(4*I/((-I*a + b)*d^2)) + 2*a*e^(2*I*d*x + 2*I*c) + 2*a + 2*I*b)*e^(-2*I*d*x - 2*I*c)/((-I*a + b)*d)) + 1/4*sqrt(4*I/((-I*a + b)*d^2))*log((((-I*a + b)*d*e^(2*I*d*x + 2*I*c) + (-I*a + b)*d)*sqrt(((a - I*b)*e^(2*I*d*x + 2*I*c) + a + I*b)/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(4*I/((-I*a + b)*d^2)) + 2*a*e^(2*I*d*x + 2*I*c) + 2*a + 2*I*b)*e^(-2*I*d*x - 2*I*c)/((-I*a + b)*d))","B",0
375,1,28,0,0.475895," ","integrate((3+tan(x))/(4+3*tan(x))^(1/2),x, algorithm=""fricas"")","\sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \tan\left(x\right) - \sqrt{2}}{2 \, \sqrt{3 \, \tan\left(x\right) + 4}}\right)"," ",0,"sqrt(2)*arctan(1/2*(3*sqrt(2)*tan(x) - sqrt(2))/sqrt(3*tan(x) + 4))","A",0
376,1,47,0,0.564936," ","integrate((1-3*tan(x))/(4+3*tan(x))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(\frac{\tan\left(x\right)^{2} + 2 \, {\left(\sqrt{2} \tan\left(x\right) + 3 \, \sqrt{2}\right)} \sqrt{3 \, \tan\left(x\right) + 4} + 12 \, \tan\left(x\right) + 17}{\tan\left(x\right)^{2} + 1}\right)"," ",0,"1/2*sqrt(2)*log((tan(x)^2 + 2*(sqrt(2)*tan(x) + 3*sqrt(2))*sqrt(3*tan(x) + 4) + 12*tan(x) + 17)/(tan(x)^2 + 1))","B",0
377,1,855,0,0.489878," ","integrate((4-3*tan(b*x+a))/(4+3*tan(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{1}{58500} \cdot 25^{\frac{1}{4}} {\left(44 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 125\right)} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(\frac{25 \, {\left(4875 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) + 25^{\frac{1}{4}} {\left(5 \, b^{3} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) + 8 \, b \cos\left(b x + a\right)\right)} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \sqrt{\frac{4 \, \cos\left(b x + a\right) + 3 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \frac{1}{b^{4}}^{\frac{1}{4}} + 3900 \, \cos\left(b x + a\right) + 2925 \, \sin\left(b x + a\right)\right)}}{39 \, \cos\left(b x + a\right)}\right) - \frac{1}{58500} \cdot 25^{\frac{1}{4}} {\left(44 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 125\right)} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \frac{1}{b^{4}}^{\frac{1}{4}} \log\left(\frac{25 \, {\left(4875 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) - 25^{\frac{1}{4}} {\left(5 \, b^{3} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) + 8 \, b \cos\left(b x + a\right)\right)} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \sqrt{\frac{4 \, \cos\left(b x + a\right) + 3 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \frac{1}{b^{4}}^{\frac{1}{4}} + 3900 \, \cos\left(b x + a\right) + 2925 \, \sin\left(b x + a\right)\right)}}{39 \, \cos\left(b x + a\right)}\right) - \frac{1}{125} \cdot 25^{\frac{1}{4}} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{73125} \cdot 25^{\frac{3}{4}} \sqrt{\frac{1}{39}} {\left(5 \, b^{5} \sqrt{\frac{1}{b^{4}}} + 8 \, b^{3}\right)} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \sqrt{\frac{4875 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) + 25^{\frac{1}{4}} {\left(5 \, b^{3} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) + 8 \, b \cos\left(b x + a\right)\right)} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \sqrt{\frac{4 \, \cos\left(b x + a\right) + 3 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \frac{1}{b^{4}}^{\frac{1}{4}} + 3900 \, \cos\left(b x + a\right) + 2925 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \frac{1}{b^{4}}^{\frac{3}{4}} - \frac{1}{14625} \cdot 25^{\frac{3}{4}} {\left(5 \, b^{5} \sqrt{\frac{1}{b^{4}}} + 8 \, b^{3}\right)} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \sqrt{\frac{4 \, \cos\left(b x + a\right) + 3 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \frac{1}{b^{4}}^{\frac{3}{4}} - \frac{4}{3} \, b^{2} \sqrt{\frac{1}{b^{4}}} - \frac{5}{3}\right) - \frac{1}{125} \cdot 25^{\frac{1}{4}} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \frac{1}{b^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{73125} \cdot 25^{\frac{3}{4}} \sqrt{\frac{1}{39}} {\left(5 \, b^{5} \sqrt{\frac{1}{b^{4}}} + 8 \, b^{3}\right)} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \sqrt{\frac{4875 \, b^{2} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) - 25^{\frac{1}{4}} {\left(5 \, b^{3} \sqrt{\frac{1}{b^{4}}} \cos\left(b x + a\right) + 8 \, b \cos\left(b x + a\right)\right)} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \sqrt{\frac{4 \, \cos\left(b x + a\right) + 3 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \frac{1}{b^{4}}^{\frac{1}{4}} + 3900 \, \cos\left(b x + a\right) + 2925 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \frac{1}{b^{4}}^{\frac{3}{4}} - \frac{1}{14625} \cdot 25^{\frac{3}{4}} {\left(5 \, b^{5} \sqrt{\frac{1}{b^{4}}} + 8 \, b^{3}\right)} \sqrt{-11000 \, b^{2} \sqrt{\frac{1}{b^{4}}} + 31250} \sqrt{\frac{4 \, \cos\left(b x + a\right) + 3 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \frac{1}{b^{4}}^{\frac{3}{4}} + \frac{4}{3} \, b^{2} \sqrt{\frac{1}{b^{4}}} + \frac{5}{3}\right)"," ",0,"1/58500*25^(1/4)*(44*b^2*sqrt(b^(-4)) + 125)*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*(b^(-4))^(1/4)*log(25/39*(4875*b^2*sqrt(b^(-4))*cos(b*x + a) + 25^(1/4)*(5*b^3*sqrt(b^(-4))*cos(b*x + a) + 8*b*cos(b*x + a))*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*sqrt((4*cos(b*x + a) + 3*sin(b*x + a))/cos(b*x + a))*(b^(-4))^(1/4) + 3900*cos(b*x + a) + 2925*sin(b*x + a))/cos(b*x + a)) - 1/58500*25^(1/4)*(44*b^2*sqrt(b^(-4)) + 125)*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*(b^(-4))^(1/4)*log(25/39*(4875*b^2*sqrt(b^(-4))*cos(b*x + a) - 25^(1/4)*(5*b^3*sqrt(b^(-4))*cos(b*x + a) + 8*b*cos(b*x + a))*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*sqrt((4*cos(b*x + a) + 3*sin(b*x + a))/cos(b*x + a))*(b^(-4))^(1/4) + 3900*cos(b*x + a) + 2925*sin(b*x + a))/cos(b*x + a)) - 1/125*25^(1/4)*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*(b^(-4))^(1/4)*arctan(1/73125*25^(3/4)*sqrt(1/39)*(5*b^5*sqrt(b^(-4)) + 8*b^3)*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*sqrt((4875*b^2*sqrt(b^(-4))*cos(b*x + a) + 25^(1/4)*(5*b^3*sqrt(b^(-4))*cos(b*x + a) + 8*b*cos(b*x + a))*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*sqrt((4*cos(b*x + a) + 3*sin(b*x + a))/cos(b*x + a))*(b^(-4))^(1/4) + 3900*cos(b*x + a) + 2925*sin(b*x + a))/cos(b*x + a))*(b^(-4))^(3/4) - 1/14625*25^(3/4)*(5*b^5*sqrt(b^(-4)) + 8*b^3)*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*sqrt((4*cos(b*x + a) + 3*sin(b*x + a))/cos(b*x + a))*(b^(-4))^(3/4) - 4/3*b^2*sqrt(b^(-4)) - 5/3) - 1/125*25^(1/4)*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*(b^(-4))^(1/4)*arctan(1/73125*25^(3/4)*sqrt(1/39)*(5*b^5*sqrt(b^(-4)) + 8*b^3)*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*sqrt((4875*b^2*sqrt(b^(-4))*cos(b*x + a) - 25^(1/4)*(5*b^3*sqrt(b^(-4))*cos(b*x + a) + 8*b*cos(b*x + a))*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*sqrt((4*cos(b*x + a) + 3*sin(b*x + a))/cos(b*x + a))*(b^(-4))^(1/4) + 3900*cos(b*x + a) + 2925*sin(b*x + a))/cos(b*x + a))*(b^(-4))^(3/4) - 1/14625*25^(3/4)*(5*b^5*sqrt(b^(-4)) + 8*b^3)*sqrt(-11000*b^2*sqrt(b^(-4)) + 31250)*sqrt((4*cos(b*x + a) + 3*sin(b*x + a))/cos(b*x + a))*(b^(-4))^(3/4) + 4/3*b^2*sqrt(b^(-4)) + 5/3)","B",0
378,1,13690,0,21.693390," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{420 \, \sqrt{2} d^{5} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(-\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - \sqrt{2} {\left({\left(B a + A b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{3} - {\left(A^{2} B + B^{3}\right)} a^{2} b + {\left(A^{3} + A B^{2}\right)} a b^{2} - {\left(A^{2} B + B^{3}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left({\left(A^{4} B - B^{5}\right)} a^{5} + {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a^{4} b - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{3} b^{2} - 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a b^{4} - {\left(A^{5} - A B^{4}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{7} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a^{6} b + {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{5} b^{2} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{3} b^{4} - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} - {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a b^{6} + {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) \cos\left(d x + c\right)^{3} + 420 \, \sqrt{2} d^{5} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + \sqrt{2} {\left({\left(B a + A b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{3} - {\left(A^{2} B + B^{3}\right)} a^{2} b + {\left(A^{3} + A B^{2}\right)} a b^{2} - {\left(A^{2} B + B^{3}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left({\left(A^{4} B - B^{5}\right)} a^{5} + {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a^{4} b - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{3} b^{2} - 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a b^{4} - {\left(A^{5} - A B^{4}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{7} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a^{6} b + {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{5} b^{2} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{3} b^{4} - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} - {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a b^{6} + {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) \cos\left(d x + c\right)^{3} + 105 \, \sqrt{2} {\left(2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right)^{3} + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 105 \, \sqrt{2} {\left(2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right)^{3} + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(126 \, {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{4} b + 2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} + 2 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} \cos\left(d x + c\right)^{3} - 21 \, {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{4} b + 2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} + 2 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} \cos\left(d x + c\right) - 5 \, {\left(3 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{4} b + 6 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + 3 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{5} + {\left(7 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - 10 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{4} b + 14 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} - 20 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + 7 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a b^{4} - 10 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\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({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{3}}"," ",0,"1/420*(420*sqrt(2)*d^5*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan(-(((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - sqrt(2)*((B*a + A*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^3 + A*B^2)*a^3 - (A^2*B + B^3)*a^2*b + (A^3 + A*B^2)*a*b^2 - (A^2*B + B^3)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) + sqrt(2)*(((A^4*B - B^5)*a^5 + (A^5 - 4*A^3*B^2 - 5*A*B^4)*a^4*b - 4*(A^4*B + A^2*B^3)*a^3*b^2 - 4*(A^3*B^2 + A*B^4)*a^2*b^3 - (5*A^4*B + 4*A^2*B^3 - B^5)*a*b^4 - (A^5 - A*B^4)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^7 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a^6*b + (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^5*b^2 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^4*b^3 - (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^3*b^4 - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^2*b^5 - (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a*b^6 + (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12))*cos(d*x + c)^3 + 420*sqrt(2)*d^5*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan((((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + sqrt(2)*((B*a + A*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^3 + A*B^2)*a^3 - (A^2*B + B^3)*a^2*b + (A^3 + A*B^2)*a*b^2 - (A^2*B + B^3)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) - sqrt(2)*(((A^4*B - B^5)*a^5 + (A^5 - 4*A^3*B^2 - 5*A*B^4)*a^4*b - 4*(A^4*B + A^2*B^3)*a^3*b^2 - 4*(A^3*B^2 + A*B^4)*a^2*b^3 - (5*A^4*B + 4*A^2*B^3 - B^5)*a*b^4 - (A^5 - A*B^4)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^7 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a^6*b + (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^5*b^2 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^4*b^3 - (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^3*b^4 - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^2*b^5 - (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a*b^6 + (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12))*cos(d*x + c)^3 + 105*sqrt(2)*(2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c)^3 + ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^3)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - 105*sqrt(2)*(2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c)^3 + ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^3)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - 8*(126*((A^4*B + 2*A^2*B^3 + B^5)*a^5 + (A^5 + 2*A^3*B^2 + A*B^4)*a^4*b + 2*(A^4*B + 2*A^2*B^3 + B^5)*a^3*b^2 + 2*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^3 + (A^4*B + 2*A^2*B^3 + B^5)*a*b^4 + (A^5 + 2*A^3*B^2 + A*B^4)*b^5)*cos(d*x + c)^3 - 21*((A^4*B + 2*A^2*B^3 + B^5)*a^5 + (A^5 + 2*A^3*B^2 + A*B^4)*a^4*b + 2*(A^4*B + 2*A^2*B^3 + B^5)*a^3*b^2 + 2*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^3 + (A^4*B + 2*A^2*B^3 + B^5)*a*b^4 + (A^5 + 2*A^3*B^2 + A*B^4)*b^5)*cos(d*x + c) - 5*(3*(A^4*B + 2*A^2*B^3 + B^5)*a^4*b + 6*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^3 + 3*(A^4*B + 2*A^2*B^3 + B^5)*b^5 + (7*(A^5 + 2*A^3*B^2 + A*B^4)*a^5 - 10*(A^4*B + 2*A^2*B^3 + B^5)*a^4*b + 14*(A^5 + 2*A^3*B^2 + A*B^4)*a^3*b^2 - 20*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^3 + 7*(A^5 + 2*A^3*B^2 + A*B^4)*a*b^4 - 10*(A^4*B + 2*A^2*B^3 + B^5)*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^3)","B",0
379,1,13541,0,22.448838," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{60 \, \sqrt{2} d^{5} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(-\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + \sqrt{2} {\left({\left(A a - B b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{2} B + B^{3}\right)} a^{3} + {\left(A^{3} + A B^{2}\right)} a^{2} b + {\left(A^{2} B + B^{3}\right)} a b^{2} + {\left(A^{3} + A B^{2}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left({\left(A^{5} - A B^{4}\right)} a^{5} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a^{4} b + 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{2} b^{3} - {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a b^{4} + {\left(A^{4} B - B^{5}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{7} + {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a^{6} b - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} + {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{4} b^{3} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{3} b^{4} - {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{2} b^{5} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a b^{6} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} d^{5} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - \sqrt{2} {\left({\left(A a - B b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{2} B + B^{3}\right)} a^{3} + {\left(A^{3} + A B^{2}\right)} a^{2} b + {\left(A^{2} B + B^{3}\right)} a b^{2} + {\left(A^{3} + A B^{2}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left({\left(A^{5} - A B^{4}\right)} a^{5} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a^{4} b + 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{2} b^{3} - {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a b^{4} + {\left(A^{4} B - B^{5}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{7} + {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a^{6} b - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} + {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{4} b^{3} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{3} b^{4} - {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{2} b^{5} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a b^{6} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) \cos\left(d x + c\right)^{2} + 15 \, \sqrt{2} {\left(2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right)^{2} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 15 \, \sqrt{2} {\left(2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right)^{2} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{4} b + 6 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + 3 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{5} + 3 \, {\left(5 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - 6 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{4} b + 10 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} - 12 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + 5 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a b^{4} - 6 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{4} b + 2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} + 2 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} 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)}}}{60 \, {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/60*(60*sqrt(2)*d^5*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan(-(((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + sqrt(2)*((A*a - B*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^2*B + B^3)*a^3 + (A^3 + A*B^2)*a^2*b + (A^2*B + B^3)*a*b^2 + (A^3 + A*B^2)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) - sqrt(2)*(((A^5 - A*B^4)*a^5 - (5*A^4*B + 4*A^2*B^3 - B^5)*a^4*b + 4*(A^3*B^2 + A*B^4)*a^3*b^2 - 4*(A^4*B + A^2*B^3)*a^2*b^3 - (A^5 - 4*A^3*B^2 - 5*A*B^4)*a*b^4 + (A^4*B - B^5)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^7 + (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a^6*b - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^5*b^2 + (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^4*b^3 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^3*b^4 - (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^2*b^5 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a*b^6 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12))*cos(d*x + c)^2 + 60*sqrt(2)*d^5*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan((((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - sqrt(2)*((A*a - B*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^2*B + B^3)*a^3 + (A^3 + A*B^2)*a^2*b + (A^2*B + B^3)*a*b^2 + (A^3 + A*B^2)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) + sqrt(2)*(((A^5 - A*B^4)*a^5 - (5*A^4*B + 4*A^2*B^3 - B^5)*a^4*b + 4*(A^3*B^2 + A*B^4)*a^3*b^2 - 4*(A^4*B + A^2*B^3)*a^2*b^3 - (A^5 - 4*A^3*B^2 - 5*A*B^4)*a*b^4 + (A^4*B - B^5)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^7 + (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a^6*b - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^5*b^2 + (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^4*b^3 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^3*b^4 - (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^2*b^5 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a*b^6 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12))*cos(d*x + c)^2 + 15*sqrt(2)*(2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c)^2 - ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - 15*sqrt(2)*(2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c)^2 - ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - 8*(3*(A^4*B + 2*A^2*B^3 + B^5)*a^4*b + 6*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^3 + 3*(A^4*B + 2*A^2*B^3 + B^5)*b^5 + 3*(5*(A^5 + 2*A^3*B^2 + A*B^4)*a^5 - 6*(A^4*B + 2*A^2*B^3 + B^5)*a^4*b + 10*(A^5 + 2*A^3*B^2 + A*B^4)*a^3*b^2 - 12*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^3 + 5*(A^5 + 2*A^3*B^2 + A*B^4)*a*b^4 - 6*(A^4*B + 2*A^2*B^3 + B^5)*b^5)*cos(d*x + c)^2 + 5*((A^4*B + 2*A^2*B^3 + B^5)*a^5 + (A^5 + 2*A^3*B^2 + A*B^4)*a^4*b + 2*(A^4*B + 2*A^2*B^3 + B^5)*a^3*b^2 + 2*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^3 + (A^4*B + 2*A^2*B^3 + B^5)*a*b^4 + (A^5 + 2*A^3*B^2 + A*B^4)*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)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2)","B",0
380,1,13378,0,22.160486," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} d^{5} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(-\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - \sqrt{2} {\left({\left(B a + A b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{3} - {\left(A^{2} B + B^{3}\right)} a^{2} b + {\left(A^{3} + A B^{2}\right)} a b^{2} - {\left(A^{2} B + B^{3}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left({\left(A^{4} B - B^{5}\right)} a^{5} + {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a^{4} b - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{3} b^{2} - 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a b^{4} - {\left(A^{5} - A B^{4}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{7} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a^{6} b + {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{5} b^{2} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{3} b^{4} - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} - {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a b^{6} + {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} d^{5} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + \sqrt{2} {\left({\left(B a + A b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{3} - {\left(A^{2} B + B^{3}\right)} a^{2} b + {\left(A^{3} + A B^{2}\right)} a b^{2} - {\left(A^{2} B + B^{3}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left({\left(A^{4} B - B^{5}\right)} a^{5} + {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a^{4} b - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{3} b^{2} - 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a b^{4} - {\left(A^{5} - A B^{4}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{7} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a^{6} b + {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{5} b^{2} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{3} b^{4} - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} - {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a b^{6} + {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) \cos\left(d x + c\right) + 3 \, \sqrt{2} {\left(2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left(2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{4} b + 2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} + 2 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} \cos\left(d x + c\right) + {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{4} b + 2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} 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({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)}"," ",0,"-1/12*(12*sqrt(2)*d^5*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan(-(((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - sqrt(2)*((B*a + A*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^3 + A*B^2)*a^3 - (A^2*B + B^3)*a^2*b + (A^3 + A*B^2)*a*b^2 - (A^2*B + B^3)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) + sqrt(2)*(((A^4*B - B^5)*a^5 + (A^5 - 4*A^3*B^2 - 5*A*B^4)*a^4*b - 4*(A^4*B + A^2*B^3)*a^3*b^2 - 4*(A^3*B^2 + A*B^4)*a^2*b^3 - (5*A^4*B + 4*A^2*B^3 - B^5)*a*b^4 - (A^5 - A*B^4)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^7 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a^6*b + (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^5*b^2 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^4*b^3 - (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^3*b^4 - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^2*b^5 - (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a*b^6 + (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12))*cos(d*x + c) + 12*sqrt(2)*d^5*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan((((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + sqrt(2)*((B*a + A*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^3 + A*B^2)*a^3 - (A^2*B + B^3)*a^2*b + (A^3 + A*B^2)*a*b^2 - (A^2*B + B^3)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) - sqrt(2)*(((A^4*B - B^5)*a^5 + (A^5 - 4*A^3*B^2 - 5*A*B^4)*a^4*b - 4*(A^4*B + A^2*B^3)*a^3*b^2 - 4*(A^3*B^2 + A*B^4)*a^2*b^3 - (5*A^4*B + 4*A^2*B^3 - B^5)*a*b^4 - (A^5 - A*B^4)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^7 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a^6*b + (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^5*b^2 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^4*b^3 - (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^3*b^4 - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^2*b^5 - (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a*b^6 + (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12))*cos(d*x + c) + 3*sqrt(2)*(2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*(2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - 8*(3*((A^4*B + 2*A^2*B^3 + B^5)*a^5 + (A^5 + 2*A^3*B^2 + A*B^4)*a^4*b + 2*(A^4*B + 2*A^2*B^3 + B^5)*a^3*b^2 + 2*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^3 + (A^4*B + 2*A^2*B^3 + B^5)*a*b^4 + (A^5 + 2*A^3*B^2 + A*B^4)*b^5)*cos(d*x + c) + ((A^4*B + 2*A^2*B^3 + B^5)*a^4*b + 2*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^3 + (A^4*B + 2*A^2*B^3 + B^5)*b^5)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c))","B",0
381,1,13180,0,21.414250," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d^{5} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(-\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + \sqrt{2} {\left({\left(A a - B b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{2} B + B^{3}\right)} a^{3} + {\left(A^{3} + A B^{2}\right)} a^{2} b + {\left(A^{2} B + B^{3}\right)} a b^{2} + {\left(A^{3} + A B^{2}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left({\left(A^{5} - A B^{4}\right)} a^{5} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a^{4} b + 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{2} b^{3} - {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a b^{4} + {\left(A^{4} B - B^{5}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{7} + {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a^{6} b - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} + {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{4} b^{3} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{3} b^{4} - {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{2} b^{5} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a b^{6} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - \sqrt{2} {\left({\left(A a - B b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{2} B + B^{3}\right)} a^{3} + {\left(A^{3} + A B^{2}\right)} a^{2} b + {\left(A^{2} B + B^{3}\right)} a b^{2} + {\left(A^{3} + A B^{2}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left({\left(A^{5} - A B^{4}\right)} a^{5} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a^{4} b + 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{2} b^{3} - {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a b^{4} + {\left(A^{4} B - B^{5}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{7} + {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a^{6} b - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} + {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{4} b^{3} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{3} b^{4} - {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{2} b^{5} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a b^{6} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) + \sqrt{2} {\left(2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{4} b + 2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d}"," ",0,"1/4*(4*sqrt(2)*d^5*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan(-(((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + sqrt(2)*((A*a - B*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^2*B + B^3)*a^3 + (A^3 + A*B^2)*a^2*b + (A^2*B + B^3)*a*b^2 + (A^3 + A*B^2)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) - sqrt(2)*(((A^5 - A*B^4)*a^5 - (5*A^4*B + 4*A^2*B^3 - B^5)*a^4*b + 4*(A^3*B^2 + A*B^4)*a^3*b^2 - 4*(A^4*B + A^2*B^3)*a^2*b^3 - (A^5 - 4*A^3*B^2 - 5*A*B^4)*a*b^4 + (A^4*B - B^5)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^7 + (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a^6*b - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^5*b^2 + (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^4*b^3 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^3*b^4 - (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^2*b^5 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a*b^6 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12)) + 4*sqrt(2)*d^5*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan((((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - sqrt(2)*((A*a - B*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^2*B + B^3)*a^3 + (A^3 + A*B^2)*a^2*b + (A^2*B + B^3)*a*b^2 + (A^3 + A*B^2)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) + sqrt(2)*(((A^5 - A*B^4)*a^5 - (5*A^4*B + 4*A^2*B^3 - B^5)*a^4*b + 4*(A^3*B^2 + A*B^4)*a^3*b^2 - 4*(A^4*B + A^2*B^3)*a^2*b^3 - (A^5 - 4*A^3*B^2 - 5*A*B^4)*a*b^4 + (A^4*B - B^5)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^7 + (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a^6*b - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^5*b^2 + (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^4*b^3 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^3*b^4 - (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^2*b^5 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a*b^6 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12)) + sqrt(2)*(2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) + 8*((A^4*B + 2*A^2*B^3 + B^5)*a^4*b + 2*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^3 + (A^4*B + 2*A^2*B^3 + B^5)*b^5)*sqrt(sin(d*x + c)/cos(d*x + c)))/(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d)","B",0
382,1,13523,0,21.845664," ","integrate((a+b*tan(d*x+c))*(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{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(-\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - \sqrt{2} {\left({\left(B a + A b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{3} - {\left(A^{2} B + B^{3}\right)} a^{2} b + {\left(A^{3} + A B^{2}\right)} a b^{2} - {\left(A^{2} B + B^{3}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left({\left(A^{4} B - B^{5}\right)} a^{5} + {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a^{4} b - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{3} b^{2} - 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a b^{4} - {\left(A^{5} - A B^{4}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{7} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a^{6} b + {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{5} b^{2} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{3} b^{4} - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} - {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a b^{6} + {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) + 4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + \sqrt{2} {\left({\left(B a + A b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{3} - {\left(A^{2} B + B^{3}\right)} a^{2} b + {\left(A^{3} + A B^{2}\right)} a b^{2} - {\left(A^{2} B + B^{3}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left({\left(A^{4} B - B^{5}\right)} a^{5} + {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a^{4} b - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{3} b^{2} - 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a b^{4} - {\left(A^{5} - A B^{4}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{7} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a^{6} b + {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{5} b^{2} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{3} b^{4} - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} - {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a b^{6} + {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) + 8 \, {\left({\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} + 2 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} 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({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d + 2 \, {\left({\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d + 2 \, {\left({\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left({\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d\right)}}"," ",0,"1/4*(4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan(-(((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - sqrt(2)*((B*a + A*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^3 + A*B^2)*a^3 - (A^2*B + B^3)*a^2*b + (A^3 + A*B^2)*a*b^2 - (A^2*B + B^3)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) + sqrt(2)*(((A^4*B - B^5)*a^5 + (A^5 - 4*A^3*B^2 - 5*A*B^4)*a^4*b - 4*(A^4*B + A^2*B^3)*a^3*b^2 - 4*(A^3*B^2 + A*B^4)*a^2*b^3 - (5*A^4*B + 4*A^2*B^3 - B^5)*a*b^4 - (A^5 - A*B^4)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^7 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a^6*b + (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^5*b^2 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^4*b^3 - (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^3*b^4 - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^2*b^5 - (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a*b^6 + (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12)) + 4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan((((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + sqrt(2)*((B*a + A*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^3 + A*B^2)*a^3 - (A^2*B + B^3)*a^2*b + (A^3 + A*B^2)*a*b^2 - (A^2*B + B^3)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) - sqrt(2)*(((A^4*B - B^5)*a^5 + (A^5 - 4*A^3*B^2 - 5*A*B^4)*a^4*b - 4*(A^4*B + A^2*B^3)*a^3*b^2 - 4*(A^3*B^2 + A*B^4)*a^2*b^3 - (5*A^4*B + 4*A^2*B^3 - B^5)*a*b^4 - (A^5 - A*B^4)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^7 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a^6*b + (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^5*b^2 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^4*b^3 - (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^3*b^4 - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^2*b^5 - (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a*b^6 + (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12)) + 8*((A^5 + 2*A^3*B^2 + A*B^4)*a^5 + 2*(A^5 + 2*A^3*B^2 + A*B^4)*a^3*b^2 + (A^5 + 2*A^3*B^2 + A*B^4)*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)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2 - ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d + 2*((A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*cos(d*x + c)^2 - (A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2 - ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d + 2*((A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*cos(d*x + c)^2 - (A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)))/(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2 - ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d)","B",0
383,1,13671,0,21.362432," ","integrate((a+b*tan(d*x+c))*(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{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(-\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + \sqrt{2} {\left({\left(A a - B b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{2} B + B^{3}\right)} a^{3} + {\left(A^{3} + A B^{2}\right)} a^{2} b + {\left(A^{2} B + B^{3}\right)} a b^{2} + {\left(A^{3} + A B^{2}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left({\left(A^{5} - A B^{4}\right)} a^{5} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a^{4} b + 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{2} b^{3} - {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a b^{4} + {\left(A^{4} B - B^{5}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{7} + {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a^{6} b - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} + {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{4} b^{3} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{3} b^{4} - {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{2} b^{5} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a b^{6} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) + 12 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - \sqrt{2} {\left({\left(A a - B b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{2} B + B^{3}\right)} a^{3} + {\left(A^{3} + A B^{2}\right)} a^{2} b + {\left(A^{2} B + B^{3}\right)} a b^{2} + {\left(A^{3} + A B^{2}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left({\left(A^{5} - A B^{4}\right)} a^{5} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a^{4} b + 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{2} b^{3} - {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a b^{4} + {\left(A^{4} B - B^{5}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - {\left({\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} a^{7} + {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a^{6} b - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} + {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{4} b^{3} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{3} b^{4} - {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{2} b^{5} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a b^{6} - {\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) - 3 \, \sqrt{2} {\left({\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d - 2 \, {\left({\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left({\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d - 2 \, {\left({\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a^{4} b - 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{2} b^{3} + {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left({\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} a^{7} - {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a^{6} b - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{5} b^{2} + {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{3} b^{4} + {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a b^{6} - {\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} + 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left({\left({\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} + 2 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{4} b + 2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} + 2 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} 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({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d\right)}}"," ",0,"-1/12*(12*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan(-(((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + sqrt(2)*((A*a - B*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^2*B + B^3)*a^3 + (A^3 + A*B^2)*a^2*b + (A^2*B + B^3)*a*b^2 + (A^3 + A*B^2)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) - sqrt(2)*(((A^5 - A*B^4)*a^5 - (5*A^4*B + 4*A^2*B^3 - B^5)*a^4*b + 4*(A^3*B^2 + A*B^4)*a^3*b^2 - 4*(A^4*B + A^2*B^3)*a^2*b^3 - (A^5 - 4*A^3*B^2 - 5*A*B^4)*a*b^4 + (A^4*B - B^5)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^7 + (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a^6*b - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^5*b^2 + (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^4*b^3 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^3*b^4 - (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^2*b^5 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a*b^6 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12)) + 12*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan((((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - sqrt(2)*((A*a - B*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^2*B + B^3)*a^3 + (A^3 + A*B^2)*a^2*b + (A^2*B + B^3)*a*b^2 + (A^3 + A*B^2)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) + sqrt(2)*(((A^5 - A*B^4)*a^5 - (5*A^4*B + 4*A^2*B^3 - B^5)*a^4*b + 4*(A^3*B^2 + A*B^4)*a^3*b^2 - 4*(A^4*B + A^2*B^3)*a^2*b^3 - (A^5 - 4*A^3*B^2 - 5*A*B^4)*a*b^4 + (A^4*B - B^5)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - ((A^6*B + A^4*B^3 - A^2*B^5 - B^7)*a^7 + (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a^6*b - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^5*b^2 + (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^4*b^3 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^3*b^4 - (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^2*b^5 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a*b^6 - (A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12)) - 3*sqrt(2)*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2 - ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d - 2*((A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*cos(d*x + c)^2 - (A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) + 3*sqrt(2)*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2 - ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d - 2*((A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*cos(d*x + c)^2 - (A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^4*B - 2*A^2*B^3 + B^5)*a^5 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a^4*b - 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^3*b^2 - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^2*b^3 + (9*A^4*B - 10*A^2*B^3 + B^5)*a*b^4 + (A^5 - 2*A^3*B^2 + A*B^4)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - ((A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*a^7 - (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a^6*b - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^5*b^2 + (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^4*b^3 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^3*b^4 + (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^2*b^5 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a*b^6 - (A^6*B - A^4*B^3 - A^2*B^5 + B^7)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 + 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - 8*(((A^5 + 2*A^3*B^2 + A*B^4)*a^5 + 2*(A^5 + 2*A^3*B^2 + A*B^4)*a^3*b^2 + (A^5 + 2*A^3*B^2 + A*B^4)*a*b^4)*cos(d*x + c)^2 + 3*((A^4*B + 2*A^2*B^3 + B^5)*a^5 + (A^5 + 2*A^3*B^2 + A*B^4)*a^4*b + 2*(A^4*B + 2*A^2*B^3 + B^5)*a^3*b^2 + 2*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^3 + (A^4*B + 2*A^2*B^3 + B^5)*a*b^4 + (A^5 + 2*A^3*B^2 + A*B^4)*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)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2 - ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d)","B",0
384,1,14358,0,20.000236," ","integrate((a+b*tan(d*x+c))*(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{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(-\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} - \sqrt{2} {\left({\left(B a + A b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{3} - {\left(A^{2} B + B^{3}\right)} a^{2} b + {\left(A^{3} + A B^{2}\right)} a b^{2} - {\left(A^{2} B + B^{3}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left({\left(A^{4} B - B^{5}\right)} a^{5} + {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a^{4} b - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{3} b^{2} - 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a b^{4} - {\left(A^{5} - A B^{4}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{7} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a^{6} b + {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{5} b^{2} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{3} b^{4} - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} - {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a b^{6} + {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} 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{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \arctan\left(\frac{{\left({\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{8} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{7} b + 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{6} b^{2} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{5} b^{3} - 12 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a^{3} b^{5} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} a^{2} b^{6} - 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} a b^{7} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} b^{8}\right)} d^{4} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + \sqrt{2} {\left({\left(B a + A b\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{3} + A B^{2}\right)} a^{3} - {\left(A^{2} B + B^{3}\right)} a^{2} b + {\left(A^{3} + A B^{2}\right)} a b^{2} - {\left(A^{2} B + B^{3}\right)} b^{3}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left({\left(A^{4} B - B^{5}\right)} a^{5} + {\left(A^{5} - 4 \, A^{3} B^{2} - 5 \, A B^{4}\right)} a^{4} b - 4 \, {\left(A^{4} B + A^{2} B^{3}\right)} a^{3} b^{2} - 4 \, {\left(A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} - {\left(5 \, A^{4} B + 4 \, A^{2} B^{3} - B^{5}\right)} a b^{4} - {\left(A^{5} - A B^{4}\right)} b^{5}\right)} d^{7} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} + {\left({\left(A^{7} + A^{5} B^{2} - A^{3} B^{4} - A B^{6}\right)} a^{7} - {\left(5 \, A^{6} B + 9 \, A^{4} B^{3} + 3 \, A^{2} B^{5} - B^{7}\right)} a^{6} b + {\left(A^{7} + 5 \, A^{5} B^{2} + 7 \, A^{3} B^{4} + 3 \, A B^{6}\right)} a^{5} b^{2} - {\left(9 \, A^{6} B + 17 \, A^{4} B^{3} + 7 \, A^{2} B^{5} - B^{7}\right)} a^{4} b^{3} - {\left(A^{7} - 7 \, A^{5} B^{2} - 17 \, A^{3} B^{4} - 9 \, A B^{6}\right)} a^{3} b^{4} - {\left(3 \, A^{6} B + 7 \, A^{4} B^{3} + 5 \, A^{2} B^{5} + B^{7}\right)} a^{2} b^{5} - {\left(A^{7} - 3 \, A^{5} B^{2} - 9 \, A^{3} B^{4} - 5 \, A B^{6}\right)} a b^{6} + {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} b^{7}\right)} d^{5} \sqrt{\frac{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{3}{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)} a^{12} - 8 \, {\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)} a^{11} b + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{10} b^{2} - 24 \, {\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)} a^{9} b^{3} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{8} b^{4} - 16 \, {\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)} a^{7} b^{5} - 4 \, {\left(A^{12} - 22 \, A^{10} B^{2} - 97 \, A^{8} B^{4} - 148 \, A^{6} B^{6} - 97 \, A^{4} B^{8} - 22 \, A^{2} B^{10} + B^{12}\right)} a^{6} b^{6} + 16 \, {\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)} a^{5} b^{7} - {\left(A^{12} - 62 \, A^{10} B^{2} - 257 \, A^{8} B^{4} - 388 \, A^{6} B^{6} - 257 \, A^{4} B^{8} - 62 \, A^{2} B^{10} + B^{12}\right)} a^{4} b^{8} + 24 \, {\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)} a^{3} b^{9} + 2 \, {\left(A^{12} + 10 \, A^{10} B^{2} + 31 \, A^{8} B^{4} + 44 \, A^{6} B^{6} + 31 \, A^{4} B^{8} + 10 \, A^{2} B^{10} + B^{12}\right)} a^{2} b^{10} + 8 \, {\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)} a b^{11} + {\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)} b^{12}}\right) + 15 \, \sqrt{2} {\left({\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2} + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d + 2 \, {\left({\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 15 \, \sqrt{2} {\left({\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2} + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d + 2 \, {\left({\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{3}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left({\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} a^{6} - 8 \, {\left(A^{5} B - A B^{5}\right)} a^{5} b - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{4} b^{2} - {\left(A^{6} - 17 \, A^{4} B^{2} - 17 \, A^{2} B^{4} + B^{6}\right)} a^{2} b^{4} + 8 \, {\left(A^{5} B - A B^{5}\right)} a b^{5} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} b^{6}\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left({\left(A^{5} - 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(9 \, A^{4} B - 10 \, A^{2} B^{3} + B^{5}\right)} a^{4} b - 2 \, {\left(A^{5} - 14 \, A^{3} B^{2} + 5 \, A B^{4}\right)} a^{3} b^{2} + 2 \, {\left(5 \, A^{4} B - 14 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} - 10 \, A^{3} B^{2} + 9 \, A B^{4}\right)} a b^{4} - {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} d^{3} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left({\left(A^{6} B - A^{4} B^{3} - A^{2} B^{5} + B^{7}\right)} a^{7} + {\left(A^{7} - 9 \, A^{5} B^{2} - A^{3} B^{4} + 9 \, A B^{6}\right)} a^{6} b - {\left(9 \, A^{6} B - 17 \, A^{4} B^{3} - 25 \, A^{2} B^{5} + B^{7}\right)} a^{5} b^{2} - {\left(A^{7} - 17 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + A B^{6}\right)} a^{4} b^{3} - {\left(A^{6} B - 17 \, A^{4} B^{3} - 17 \, A^{2} B^{5} + B^{7}\right)} a^{3} b^{4} - {\left(A^{7} - 25 \, A^{5} B^{2} - 17 \, A^{3} B^{4} + 9 \, A B^{6}\right)} a^{2} b^{5} + {\left(9 \, A^{6} B - A^{4} B^{3} - 9 \, A^{2} B^{5} + B^{7}\right)} a b^{6} + {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4} - 2 \, {\left(A B a^{2} - A B b^{2} + {\left(A^{2} - B^{2}\right)} a b\right)} d^{2} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}}}{{\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} - 8 \, {\left(A^{3} B - A B^{3}\right)} a^{3} b - 2 \, {\left(A^{4} - 10 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + 8 \, {\left(A^{3} B - A B^{3}\right)} a b^{3} + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left({\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} a^{8} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{7} b + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{6} b^{2} - 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{5} b^{3} - 2 \, {\left(A^{8} - 16 \, A^{6} B^{2} - 34 \, A^{4} B^{4} - 16 \, A^{2} B^{6} + B^{8}\right)} a^{4} b^{4} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a^{3} b^{5} + 16 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} a^{2} b^{6} + 8 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} a b^{7} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(5 \, {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{4} b + 2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} + 2 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left({\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{5} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{4} b + 2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{3} b^{2} + 2 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{2} b^{3} + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a b^{4} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left({\left(6 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - 5 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{4} b + 12 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} - 10 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + 6 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a b^{4} - 5 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\right)} \cos\left(d x + c\right)^{3} - 5 \, {\left({\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{5} - {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{4} b + 2 \, {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a^{3} b^{2} - 2 \, {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} a^{2} b^{3} + {\left(A^{5} + 2 \, A^{3} B^{2} + A B^{4}\right)} a b^{4} - {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} b^{5}\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({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} b^{4}\right)} d \cos\left(d x + c\right)^{2} + {\left({\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{4} + 2 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} a^{2} b^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} 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(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan(-(((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) - sqrt(2)*((B*a + A*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^3 + A*B^2)*a^3 - (A^2*B + B^3)*a^2*b + (A^3 + A*B^2)*a*b^2 - (A^2*B + B^3)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) + sqrt(2)*(((A^4*B - B^5)*a^5 + (A^5 - 4*A^3*B^2 - 5*A*B^4)*a^4*b - 4*(A^4*B + A^2*B^3)*a^3*b^2 - 4*(A^3*B^2 + A*B^4)*a^2*b^3 - (5*A^4*B + 4*A^2*B^3 - B^5)*a*b^4 - (A^5 - A*B^4)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^7 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a^6*b + (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^5*b^2 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^4*b^3 - (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^3*b^4 - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^2*b^5 - (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a*b^6 + (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12)) + 60*sqrt(2)*(d^5*cos(d*x + c)^4 - 2*d^5*cos(d*x + c)^2 + d^5)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4)*arctan((((A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^8 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^7*b + 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^6*b^2 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^5*b^3 - 12*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a^3*b^5 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*a^2*b^6 - 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*a*b^7 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*b^8)*d^4*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + sqrt(2)*((B*a + A*b)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^3 + A*B^2)*a^3 - (A^2*B + B^3)*a^2*b + (A^3 + A*B^2)*a*b^2 - (A^2*B + B^3)*b^3)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(3/4) - sqrt(2)*(((A^4*B - B^5)*a^5 + (A^5 - 4*A^3*B^2 - 5*A*B^4)*a^4*b - 4*(A^4*B + A^2*B^3)*a^3*b^2 - 4*(A^3*B^2 + A*B^4)*a^2*b^3 - (5*A^4*B + 4*A^2*B^3 - B^5)*a*b^4 - (A^5 - A*B^4)*b^5)*d^7*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4) + ((A^7 + A^5*B^2 - A^3*B^4 - A*B^6)*a^7 - (5*A^6*B + 9*A^4*B^3 + 3*A^2*B^5 - B^7)*a^6*b + (A^7 + 5*A^5*B^2 + 7*A^3*B^4 + 3*A*B^6)*a^5*b^2 - (9*A^6*B + 17*A^4*B^3 + 7*A^2*B^5 - B^7)*a^4*b^3 - (A^7 - 7*A^5*B^2 - 17*A^3*B^4 - 9*A*B^6)*a^3*b^4 - (3*A^6*B + 7*A^4*B^3 + 5*A^2*B^5 + B^7)*a^2*b^5 - (A^7 - 3*A^5*B^2 - 9*A^3*B^4 - 5*A*B^6)*a*b^6 + (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*b^7)*d^5*sqrt(((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*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)*a^12 - 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^11*b + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^10*b^2 - 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^9*b^3 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^8*b^4 - 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^7*b^5 - 4*(A^12 - 22*A^10*B^2 - 97*A^8*B^4 - 148*A^6*B^6 - 97*A^4*B^8 - 22*A^2*B^10 + B^12)*a^6*b^6 + 16*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^5*b^7 - (A^12 - 62*A^10*B^2 - 257*A^8*B^4 - 388*A^6*B^6 - 257*A^4*B^8 - 62*A^2*B^10 + B^12)*a^4*b^8 + 24*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a^3*b^9 + 2*(A^12 + 10*A^10*B^2 + 31*A^8*B^4 + 44*A^6*B^6 + 31*A^4*B^8 + 10*A^2*B^10 + B^12)*a^2*b^10 + 8*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*a*b^11 + (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)*b^12)) + 15*sqrt(2)*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^4 - 2*((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2 + ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d + 2*((A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*cos(d*x + c)^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*cos(d*x + c)^2 + (A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - 15*sqrt(2)*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^4 - 2*((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2 + ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d + 2*((A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*cos(d*x + c)^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3*cos(d*x + c)^2 + (A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^3)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4)*log((((A^6 - A^4*B^2 - A^2*B^4 + B^6)*a^6 - 8*(A^5*B - A*B^5)*a^5*b - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^4*b^2 - (A^6 - 17*A^4*B^2 - 17*A^2*B^4 + B^6)*a^2*b^4 + 8*(A^5*B - A*B^5)*a*b^5 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*b^6)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) - sqrt(2)*(((A^5 - 2*A^3*B^2 + A*B^4)*a^5 - (9*A^4*B - 10*A^2*B^3 + B^5)*a^4*b - 2*(A^5 - 14*A^3*B^2 + 5*A*B^4)*a^3*b^2 + 2*(5*A^4*B - 14*A^2*B^3 + B^5)*a^2*b^3 + (A^5 - 10*A^3*B^2 + 9*A*B^4)*a*b^4 - (A^4*B - 2*A^2*B^3 + B^5)*b^5)*d^3*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)*cos(d*x + c) + ((A^6*B - A^4*B^3 - A^2*B^5 + B^7)*a^7 + (A^7 - 9*A^5*B^2 - A^3*B^4 + 9*A*B^6)*a^6*b - (9*A^6*B - 17*A^4*B^3 - 25*A^2*B^5 + B^7)*a^5*b^2 - (A^7 - 17*A^5*B^2 - 17*A^3*B^4 + A*B^6)*a^4*b^3 - (A^6*B - 17*A^4*B^3 - 17*A^2*B^5 + B^7)*a^3*b^4 - (A^7 - 25*A^5*B^2 - 17*A^3*B^4 + 9*A*B^6)*a^2*b^5 + (9*A^6*B - A^4*B^3 - 9*A^2*B^5 + B^7)*a*b^6 + (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*b^7)*d*cos(d*x + c))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4 - 2*(A*B*a^2 - A*B*b^2 + (A^2 - B^2)*a*b)*d^2*sqrt(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4))/((A^4 - 2*A^2*B^2 + B^4)*a^4 - 8*(A^3*B - A*B^3)*a^3*b - 2*(A^4 - 10*A^2*B^2 + B^4)*a^2*b^2 + 8*(A^3*B - A*B^3)*a*b^3 + (A^4 - 2*A^2*B^2 + B^4)*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)/d^4)^(1/4) + ((A^8 - 2*A^4*B^4 + B^8)*a^8 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^7*b + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^6*b^2 - 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^5*b^3 - 2*(A^8 - 16*A^6*B^2 - 34*A^4*B^4 - 16*A^2*B^6 + B^8)*a^4*b^4 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a^3*b^5 + 16*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*a^2*b^6 + 8*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*a*b^7 + (A^8 - 2*A^4*B^4 + B^8)*b^8)*sin(d*x + c))/cos(d*x + c)) - 8*(5*((A^4*B + 2*A^2*B^3 + B^5)*a^5 + (A^5 + 2*A^3*B^2 + A*B^4)*a^4*b + 2*(A^4*B + 2*A^2*B^3 + B^5)*a^3*b^2 + 2*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^3 + (A^4*B + 2*A^2*B^3 + B^5)*a*b^4 + (A^5 + 2*A^3*B^2 + A*B^4)*b^5)*cos(d*x + c)^4 - 5*((A^4*B + 2*A^2*B^3 + B^5)*a^5 + (A^5 + 2*A^3*B^2 + A*B^4)*a^4*b + 2*(A^4*B + 2*A^2*B^3 + B^5)*a^3*b^2 + 2*(A^5 + 2*A^3*B^2 + A*B^4)*a^2*b^3 + (A^4*B + 2*A^2*B^3 + B^5)*a*b^4 + (A^5 + 2*A^3*B^2 + A*B^4)*b^5)*cos(d*x + c)^2 - 3*((6*(A^5 + 2*A^3*B^2 + A*B^4)*a^5 - 5*(A^4*B + 2*A^2*B^3 + B^5)*a^4*b + 12*(A^5 + 2*A^3*B^2 + A*B^4)*a^3*b^2 - 10*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^3 + 6*(A^5 + 2*A^3*B^2 + A*B^4)*a*b^4 - 5*(A^4*B + 2*A^2*B^3 + B^5)*b^5)*cos(d*x + c)^3 - 5*((A^5 + 2*A^3*B^2 + A*B^4)*a^5 - (A^4*B + 2*A^2*B^3 + B^5)*a^4*b + 2*(A^5 + 2*A^3*B^2 + A*B^4)*a^3*b^2 - 2*(A^4*B + 2*A^2*B^3 + B^5)*a^2*b^3 + (A^5 + 2*A^3*B^2 + A*B^4)*a*b^4 - (A^4*B + 2*A^2*B^3 + B^5)*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)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^4 - 2*((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d*cos(d*x + c)^2 + ((A^4 + 2*A^2*B^2 + B^4)*a^4 + 2*(A^4 + 2*A^2*B^2 + B^4)*a^2*b^2 + (A^4 + 2*A^2*B^2 + B^4)*b^4)*d)","B",0
385,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
405,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
406,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
407,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
408,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
414,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,1,592,0,1.024016," ","integrate(tan(d*x+c)^(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B^{3} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} + B^{4} - \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{B^{4}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B^{3} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - B^{4} - \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{-\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{B^{4}}\right) \cos\left(d x + c\right) + 3 \, \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) \log\left(\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) \log\left(-\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, B \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)}"," ",0,"1/12*(12*sqrt(2)*d*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B^3*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c)) + B^4 - sqrt(2)*d*(B^4/d^4)^(1/4)*sqrt((sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^6*sin(d*x + c))/cos(d*x + c)))/B^4)*cos(d*x + c) + 12*sqrt(2)*d*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B^3*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c)) - B^4 - sqrt(2)*d*(B^4/d^4)^(1/4)*sqrt(-(sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^6*sin(d*x + c))/cos(d*x + c)))/B^4)*cos(d*x + c) + 3*sqrt(2)*d*(B^4/d^4)^(1/4)*cos(d*x + c)*log((sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^6*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*d*(B^4/d^4)^(1/4)*cos(d*x + c)*log(-(sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^6*sin(d*x + c))/cos(d*x + c)) + 8*B*sqrt(sin(d*x + c)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","B",0
417,1,529,0,0.523222," ","integrate(tan(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - \sqrt{2} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} + B^{4}}{B^{4}}\right) + 4 \, \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - \sqrt{2} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{-\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - B^{4}}{B^{4}}\right) - \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, B \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(4*sqrt(2)*d*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c)) - sqrt(2)*d^3*(B^4/d^4)^(3/4)*sqrt((sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^2*sin(d*x + c))/cos(d*x + c)) + B^4)/B^4) + 4*sqrt(2)*d*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c)) - sqrt(2)*d^3*(B^4/d^4)^(3/4)*sqrt(-(sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^2*sin(d*x + c))/cos(d*x + c)) - B^4)/B^4) - sqrt(2)*d*(B^4/d^4)^(1/4)*log((sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^2*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*d*(B^4/d^4)^(1/4)*log(-(sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^2*sin(d*x + c))/cos(d*x + c)) + 8*B*sqrt(sin(d*x + c)/cos(d*x + c)))/d","B",0
418,1,525,0,0.668396," ","integrate(tan(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\sqrt{2} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B^{3} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} + B^{4} - \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{B^{4}}\right) - \sqrt{2} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B^{3} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - B^{4} - \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{-\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{B^{4}}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)"," ",0,"-sqrt(2)*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B^3*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c)) + B^4 - sqrt(2)*d*(B^4/d^4)^(1/4)*sqrt((sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^6*sin(d*x + c))/cos(d*x + c)))/B^4) - sqrt(2)*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B^3*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c)) - B^4 - sqrt(2)*d*(B^4/d^4)^(1/4)*sqrt(-(sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^6*sin(d*x + c))/cos(d*x + c)))/B^4) - 1/4*sqrt(2)*(B^4/d^4)^(1/4)*log((sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^6*sin(d*x + c))/cos(d*x + c)) + 1/4*sqrt(2)*(B^4/d^4)^(1/4)*log(-(sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^6*sin(d*x + c))/cos(d*x + c))","B",0
419,1,501,0,0.663304," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\sqrt{2} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - \sqrt{2} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} + B^{4}}{B^{4}}\right) - \sqrt{2} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - \sqrt{2} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{-\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - B^{4}}{B^{4}}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)"," ",0,"-sqrt(2)*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c)) - sqrt(2)*d^3*(B^4/d^4)^(3/4)*sqrt((sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^2*sin(d*x + c))/cos(d*x + c)) + B^4)/B^4) - sqrt(2)*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c)) - sqrt(2)*d^3*(B^4/d^4)^(3/4)*sqrt(-(sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^2*sin(d*x + c))/cos(d*x + c)) - B^4)/B^4) + 1/4*sqrt(2)*(B^4/d^4)^(1/4)*log((sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^2*sin(d*x + c))/cos(d*x + c)) - 1/4*sqrt(2)*(B^4/d^4)^(1/4)*log(-(sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^2*sin(d*x + c))/cos(d*x + c))","B",0
420,1,642,0,0.810686," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, B \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) + 4 \, {\left(\sqrt{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} d\right)} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B^{3} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} + B^{4} - \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{B^{4}}\right) + 4 \, {\left(\sqrt{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} d\right)} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B^{3} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - B^{4} - \sqrt{2} d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{-\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{B^{4}}\right) + {\left(\sqrt{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} d\right)} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - {\left(\sqrt{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} d\right)} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} B^{3} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - B^{4} d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/4*(8*B*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 4*(sqrt(2)*d*cos(d*x + c)^2 - sqrt(2)*d)*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B^3*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c)) + B^4 - sqrt(2)*d*(B^4/d^4)^(1/4)*sqrt((sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^6*sin(d*x + c))/cos(d*x + c)))/B^4) + 4*(sqrt(2)*d*cos(d*x + c)^2 - sqrt(2)*d)*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B^3*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c)) - B^4 - sqrt(2)*d*(B^4/d^4)^(1/4)*sqrt(-(sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^6*sin(d*x + c))/cos(d*x + c)))/B^4) + (sqrt(2)*d*cos(d*x + c)^2 - sqrt(2)*d)*(B^4/d^4)^(1/4)*log((sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^6*sin(d*x + c))/cos(d*x + c)) - (sqrt(2)*d*cos(d*x + c)^2 - sqrt(2)*d)*(B^4/d^4)^(1/4)*log(-(sqrt(2)*B^3*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - B^4*d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^6*sin(d*x + c))/cos(d*x + c)))/(d*cos(d*x + c)^2 - d)","B",0
421,1,615,0,0.839571," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, B \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)^{2} + 12 \, {\left(\sqrt{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} d\right)} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - \sqrt{2} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} + B^{4}}{B^{4}}\right) + 12 \, {\left(\sqrt{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} d\right)} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} B d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - \sqrt{2} d^{3} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{-\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - B^{4}}{B^{4}}\right) - 3 \, {\left(\sqrt{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} d\right)} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) + B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, {\left(\sqrt{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} d\right)} \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} B d \left(\frac{B^{4}}{d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - d^{2} \sqrt{\frac{B^{4}}{d^{4}}} \cos\left(d x + c\right) - B^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/12*(8*B*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c)^2 + 12*(sqrt(2)*d*cos(d*x + c)^2 - sqrt(2)*d)*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c)) - sqrt(2)*d^3*(B^4/d^4)^(3/4)*sqrt((sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^2*sin(d*x + c))/cos(d*x + c)) + B^4)/B^4) + 12*(sqrt(2)*d*cos(d*x + c)^2 - sqrt(2)*d)*(B^4/d^4)^(1/4)*arctan(-(sqrt(2)*B*d^3*(B^4/d^4)^(3/4)*sqrt(sin(d*x + c)/cos(d*x + c)) - sqrt(2)*d^3*(B^4/d^4)^(3/4)*sqrt(-(sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^2*sin(d*x + c))/cos(d*x + c)) - B^4)/B^4) - 3*(sqrt(2)*d*cos(d*x + c)^2 - sqrt(2)*d)*(B^4/d^4)^(1/4)*log((sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + d^2*sqrt(B^4/d^4)*cos(d*x + c) + B^2*sin(d*x + c))/cos(d*x + c)) + 3*(sqrt(2)*d*cos(d*x + c)^2 - sqrt(2)*d)*(B^4/d^4)^(1/4)*log(-(sqrt(2)*B*d*(B^4/d^4)^(1/4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - d^2*sqrt(B^4/d^4)*cos(d*x + c) - B^2*sin(d*x + c))/cos(d*x + c)))/(d*cos(d*x + c)^2 - d)","B",0
422,1,8974,0,15.499021," ","integrate(tan(d*x+c)^(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(-\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} b^{4}}\right) + 2 \, B^{5} 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(B^{2} a^{3} b^{2} + B^{2} a b^{4}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(B^{4} a^{2} b + B^{4} b^{3}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b^{2} + B^{2} a b^{4}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(B^{4} a^{2} b + B^{4} b^{3}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(B^{5} a^{2} + B^{5} b^{2}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(B^{4} a^{2} b + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(-\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} b^{4}}\right) - 8 \, B^{5} 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(B^{2} a^{3} b^{2} + B^{2} a b^{4}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(B^{4} a^{2} b + B^{4} b^{3}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b^{2} + B^{2} a b^{4}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(B^{4} a^{2} b + B^{4} b^{3}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(B^{5} a^{2} + B^{5} b^{2}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(B^{4} a^{2} b + B^{4} 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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(-((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 4*sqrt(2)*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 2*B^5*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*(B^2*a^3*b^2 + B^2*a*b^4)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (B^4*a^2*b + B^4*b^3)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(2*(B^2*a^3*b^2 + B^2*a*b^4)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (B^4*a^2*b + B^4*b^3)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) + 8*(B^5*a^2 + B^5*b^2)*sqrt(sin(d*x + c)/cos(d*x + c)))/((B^4*a^2*b + B^4*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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(-((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 4*sqrt(2)*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) - 8*B^5*a^2*sqrt(a/b)*arctan(b*sqrt(a/b)*sqrt(sin(d*x + c)/cos(d*x + c))/a) - sqrt(2)*(2*(B^2*a^3*b^2 + B^2*a*b^4)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (B^4*a^2*b + B^4*b^3)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(2*(B^2*a^3*b^2 + B^2*a*b^4)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (B^4*a^2*b + B^4*b^3)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) + 8*(B^5*a^2 + B^5*b^2)*sqrt(sin(d*x + c)/cos(d*x + c)))/((B^4*a^2*b + B^4*b^3)*d)]","B",0
423,1,8860,0,14.149447," ","integrate(tan(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{6} b + 3 \, B^{2} a^{4} b^{3} + 3 \, B^{2} a^{2} b^{5} + B^{2} b^{7}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(B^{3} a^{11} + 3 \, B^{3} a^{9} b^{2} + 2 \, B^{3} a^{7} b^{4} - 2 \, B^{3} a^{5} b^{6} - 3 \, B^{3} a^{3} b^{8} - B^{3} a b^{10}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{8} b + 2 \, B^{5} a^{6} b^{3} - 2 \, B^{5} a^{2} b^{7} - B^{5} b^{9}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(-\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{6} b + 3 \, B^{2} a^{4} b^{3} + 3 \, B^{2} a^{2} b^{5} + B^{2} b^{7}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(B^{3} a^{11} + 3 \, B^{3} a^{9} b^{2} + 2 \, B^{3} a^{7} b^{4} - 2 \, B^{3} a^{5} b^{6} - 3 \, B^{3} a^{3} b^{8} - B^{3} a b^{10}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{8} b + 2 \, B^{5} a^{6} b^{3} - 2 \, B^{5} a^{2} b^{7} - B^{5} b^{9}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} b^{4}}\right) - 2 \, B^{5} 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) + \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(B^{4} a^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{6} b + 3 \, B^{2} a^{4} b^{3} + 3 \, B^{2} a^{2} b^{5} + B^{2} b^{7}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(B^{3} a^{11} + 3 \, B^{3} a^{9} b^{2} + 2 \, B^{3} a^{7} b^{4} - 2 \, B^{3} a^{5} b^{6} - 3 \, B^{3} a^{3} b^{8} - B^{3} a b^{10}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{8} b + 2 \, B^{5} a^{6} b^{3} - 2 \, B^{5} a^{2} b^{7} - B^{5} b^{9}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(-\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{6} b + 3 \, B^{2} a^{4} b^{3} + 3 \, B^{2} a^{2} b^{5} + B^{2} b^{7}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(B^{3} a^{11} + 3 \, B^{3} a^{9} b^{2} + 2 \, B^{3} a^{7} b^{4} - 2 \, B^{3} a^{5} b^{6} - 3 \, B^{3} a^{3} b^{8} - B^{3} a b^{10}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{8} b + 2 \, B^{5} a^{6} b^{3} - 2 \, B^{5} a^{2} b^{7} - B^{5} b^{9}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} b^{4}}\right) - 8 \, B^{5} 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) + \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(B^{4} a^{2} + B^{4} 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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^2*a^6*b + 3*B^2*a^4*b^3 + 3*B^2*a^2*b^5 + B^2*b^7)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((B^3*a^11 + 3*B^3*a^9*b^2 + 2*B^3*a^7*b^4 - 2*B^3*a^5*b^6 - 3*B^3*a^3*b^8 - B^3*a*b^10)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^5*a^8*b + 2*B^5*a^6*b^3 - 2*B^5*a^2*b^7 - B^5*b^9)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(-((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^2*a^6*b + 3*B^2*a^4*b^3 + 3*B^2*a^2*b^5 + B^2*b^7)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((B^3*a^11 + 3*B^3*a^9*b^2 + 2*B^3*a^7*b^4 - 2*B^3*a^5*b^6 - 3*B^3*a^3*b^8 - B^3*a*b^10)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^5*a^8*b + 2*B^5*a^6*b^3 - 2*B^5*a^2*b^7 - B^5*b^9)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) - 2*B^5*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)) + sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)))/((B^4*a^2 + B^4*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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^2*a^6*b + 3*B^2*a^4*b^3 + 3*B^2*a^2*b^5 + B^2*b^7)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((B^3*a^11 + 3*B^3*a^9*b^2 + 2*B^3*a^7*b^4 - 2*B^3*a^5*b^6 - 3*B^3*a^3*b^8 - B^3*a*b^10)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^5*a^8*b + 2*B^5*a^6*b^3 - 2*B^5*a^2*b^7 - B^5*b^9)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(-((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^2*a^6*b + 3*B^2*a^4*b^3 + 3*B^2*a^2*b^5 + B^2*b^7)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((B^3*a^11 + 3*B^3*a^9*b^2 + 2*B^3*a^7*b^4 - 2*B^3*a^5*b^6 - 3*B^3*a^3*b^8 - B^3*a*b^10)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^5*a^8*b + 2*B^5*a^6*b^3 - 2*B^5*a^2*b^7 - B^5*b^9)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) - 8*B^5*a*sqrt(a/b)*arctan(b*sqrt(a/b)*sqrt(sin(d*x + c)/cos(d*x + c))/a) + sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)))/((B^4*a^2 + B^4*b^2)*d)]","B",0
424,1,8971,0,15.103432," ","integrate(tan(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(-\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} b^{4}}\right) - 2 \, \sqrt{-a b} B^{5} \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) - \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(B^{4} a^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(-\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} b^{4}}\right) + 8 \, \sqrt{a b} B^{5} \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) - \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(B^{4} a^{2} + B^{4} 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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(-((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) - 2*sqrt(-a*b)*B^5*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)) - sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)))/((B^4*a^2 + B^4*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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(-((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 8*sqrt(a*b)*B^5*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))) - sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)))/((B^4*a^2 + B^4*b^2)*d)]","B",0
425,1,8968,0,17.417217," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{6} b + 3 \, B^{2} a^{4} b^{3} + 3 \, B^{2} a^{2} b^{5} + B^{2} b^{7}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(B^{3} a^{11} + 3 \, B^{3} a^{9} b^{2} + 2 \, B^{3} a^{7} b^{4} - 2 \, B^{3} a^{5} b^{6} - 3 \, B^{3} a^{3} b^{8} - B^{3} a b^{10}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{8} b + 2 \, B^{5} a^{6} b^{3} - 2 \, B^{5} a^{2} b^{7} - B^{5} b^{9}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(-\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{6} b + 3 \, B^{2} a^{4} b^{3} + 3 \, B^{2} a^{2} b^{5} + B^{2} b^{7}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(B^{3} a^{11} + 3 \, B^{3} a^{9} b^{2} + 2 \, B^{3} a^{7} b^{4} - 2 \, B^{3} a^{5} b^{6} - 3 \, B^{3} a^{3} b^{8} - B^{3} a b^{10}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{8} b + 2 \, B^{5} a^{6} b^{3} - 2 \, B^{5} a^{2} b^{7} - B^{5} b^{9}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} b^{4}}\right) + 2 \, B^{5} 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) + \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(B^{4} a^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{6} b + 3 \, B^{2} a^{4} b^{3} + 3 \, B^{2} a^{2} b^{5} + B^{2} b^{7}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(B^{3} a^{11} + 3 \, B^{3} a^{9} b^{2} + 2 \, B^{3} a^{7} b^{4} - 2 \, B^{3} a^{5} b^{6} - 3 \, B^{3} a^{3} b^{8} - B^{3} a b^{10}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{8} b + 2 \, B^{5} a^{6} b^{3} - 2 \, B^{5} a^{2} b^{7} - B^{5} b^{9}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(-\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{6} b + 3 \, B^{2} a^{4} b^{3} + 3 \, B^{2} a^{2} b^{5} + B^{2} b^{7}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(B^{3} a^{11} + 3 \, B^{3} a^{9} b^{2} + 2 \, B^{3} a^{7} b^{4} - 2 \, B^{3} a^{5} b^{6} - 3 \, B^{3} a^{3} b^{8} - B^{3} a b^{10}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{8} b + 2 \, B^{5} a^{6} b^{3} - 2 \, B^{5} a^{2} b^{7} - B^{5} b^{9}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} b^{4}}\right) + 8 \, B^{5} 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) + \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, {\left(B^{2} a^{3} b + B^{2} a b^{3}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(B^{4} a^{2} + B^{4} b^{2}\right)} d\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{6} b - B^{3} a^{4} b^{3} - B^{3} a^{2} b^{5} + B^{3} b^{7}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(B^{5} a^{5} - 2 \, B^{5} a^{3} b^{2} + B^{5} a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(B^{4} a^{2} + B^{4} 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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^2*a^6*b + 3*B^2*a^4*b^3 + 3*B^2*a^2*b^5 + B^2*b^7)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((B^3*a^11 + 3*B^3*a^9*b^2 + 2*B^3*a^7*b^4 - 2*B^3*a^5*b^6 - 3*B^3*a^3*b^8 - B^3*a*b^10)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^5*a^8*b + 2*B^5*a^6*b^3 - 2*B^5*a^2*b^7 - B^5*b^9)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(-((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^2*a^6*b + 3*B^2*a^4*b^3 + 3*B^2*a^2*b^5 + B^2*b^7)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((B^3*a^11 + 3*B^3*a^9*b^2 + 2*B^3*a^7*b^4 - 2*B^3*a^5*b^6 - 3*B^3*a^3*b^8 - B^3*a*b^10)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^5*a^8*b + 2*B^5*a^6*b^3 - 2*B^5*a^2*b^7 - B^5*b^9)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 2*B^5*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)) + sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)))/((B^4*a^2 + B^4*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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^2*a^6*b + 3*B^2*a^4*b^3 + 3*B^2*a^2*b^5 + B^2*b^7)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((B^3*a^11 + 3*B^3*a^9*b^2 + 2*B^3*a^7*b^4 - 2*B^3*a^5*b^6 - 3*B^3*a^3*b^8 - B^3*a*b^10)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^5*a^8*b + 2*B^5*a^6*b^3 - 2*B^5*a^2*b^7 - B^5*b^9)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(-((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^2*a^6*b + 3*B^2*a^4*b^3 + 3*B^2*a^2*b^5 + B^2*b^7)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((B^3*a^11 + 3*B^3*a^9*b^2 + 2*B^3*a^7*b^4 - 2*B^3*a^5*b^6 - 3*B^3*a^3*b^8 - B^3*a*b^10)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + (B^5*a^8*b + 2*B^5*a^6*b^3 - 2*B^5*a^2*b^7 - B^5*b^9)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 8*B^5*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))) + sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*(B^2*a^3*b + B^2*a*b^3)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (B^4*a^2 + B^4*b^2)*d)*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^6*b - B^3*a^4*b^3 - B^3*a^2*b^5 + B^3*b^7)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (B^5*a^5 - 2*B^5*a^3*b^2 + B^5*a*b^4)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)))/((B^4*a^2 + B^4*b^2)*d)]","B",0
426,1,9596,0,24.853764," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(-\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} b^{4}}\right) + 8 \, {\left(B^{5} a^{2} + B^{5} 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(B^{4} a^{3} + B^{4} a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(B^{4} a^{3} + B^{4} a b^{2}\right)} d - 2 \, {\left({\left(B^{2} a^{4} b + B^{2} a^{2} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(B^{2} a^{4} b + B^{2} a^{2} b^{3}\right)} d^{3}\right)} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(B^{4} a^{3} + B^{4} a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(B^{4} a^{3} + B^{4} a b^{2}\right)} d - 2 \, {\left({\left(B^{2} a^{4} b + B^{2} a^{2} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(B^{2} a^{4} b + B^{2} a^{2} b^{3}\right)} d^{3}\right)} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 2 \, {\left(B^{5} b^{2} \cos\left(d x + c\right)^{2} - B^{5} 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(B^{4} a^{3} + B^{4} a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(B^{4} a^{3} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(-\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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}}} \arctan\left(\frac{{\left(B^{6} a^{8} + 2 \, B^{6} a^{6} b^{2} - 2 \, B^{6} a^{2} b^{6} - B^{6} b^{8}\right)} d^{4} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{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{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{2} a^{7} + 3 \, B^{2} a^{5} b^{2} + 3 \, B^{2} a^{3} b^{4} + B^{2} a b^{6}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(B^{3} a^{10} b + 3 \, B^{3} a^{8} b^{3} + 2 \, B^{3} a^{6} b^{5} - 2 \, B^{3} a^{4} b^{7} - 3 \, B^{3} a^{2} b^{9} - B^{3} b^{11}\right)} d^{7} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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(B^{5} a^{9} + 2 \, B^{5} a^{7} b^{2} - 2 \, B^{5} a^{3} b^{6} - B^{5} a b^{8}\right)} d^{5} \sqrt{\frac{B^{4} a^{4} - 2 \, B^{4} a^{2} b^{2} + B^{4} 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{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{B^{10} a^{4} - 2 \, B^{10} a^{2} b^{2} + B^{10} b^{4}}\right) + 8 \, {\left(B^{5} a^{2} + B^{5} 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(B^{4} a^{3} + B^{4} a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(B^{4} a^{3} + B^{4} a b^{2}\right)} d - 2 \, {\left({\left(B^{2} a^{4} b + B^{2} a^{2} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(B^{2} a^{4} b + B^{2} a^{2} b^{3}\right)} d^{3}\right)} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(B^{4} a^{3} + B^{4} a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(B^{4} a^{3} + B^{4} a b^{2}\right)} d - 2 \, {\left({\left(B^{2} a^{4} b + B^{2} a^{2} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(B^{2} a^{4} b + B^{2} a^{2} b^{3}\right)} d^{3}\right)} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(B^{4} a^{6} - B^{4} a^{4} b^{2} - B^{4} a^{2} b^{4} + B^{4} b^{6}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(B^{3} a^{7} - B^{3} a^{5} b^{2} - B^{3} a^{3} b^{4} + B^{3} a b^{6}\right)} d^{3} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(B^{5} a^{4} b - 2 \, B^{5} a^{2} b^{3} + B^{5} b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{B^{2} a^{4} + 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{B^{2} a^{4} - 2 \, B^{2} a^{2} b^{2} + B^{2} b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{B^{4}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(B^{6} a^{4} - 2 \, B^{6} a^{2} b^{2} + B^{6} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(B^{5} b^{2} \cos\left(d x + c\right)^{2} - B^{5} 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(B^{4} a^{3} + B^{4} a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(B^{4} a^{3} + B^{4} 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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(-((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 8*(B^5*a^2 + B^5*b^2)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + sqrt(2)*((B^4*a^3 + B^4*a*b^2)*d*cos(d*x + c)^2 - (B^4*a^3 + B^4*a*b^2)*d - 2*((B^2*a^4*b + B^2*a^2*b^3)*d^3*cos(d*x + c)^2 - (B^2*a^4*b + B^2*a^2*b^3)*d^3)*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((B^4*a^3 + B^4*a*b^2)*d*cos(d*x + c)^2 - (B^4*a^3 + B^4*a*b^2)*d - 2*((B^2*a^4*b + B^2*a^2*b^3)*d^3*cos(d*x + c)^2 - (B^2*a^4*b + B^2*a^2*b^3)*d^3)*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) + 2*(B^5*b^2*cos(d*x + c)^2 - B^5*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)))/((B^4*a^3 + B^4*a*b^2)*d*cos(d*x + c)^2 - (B^4*a^3 + B^4*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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(-((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*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((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*arctan(((B^6*a^8 + 2*B^6*a^6*b^2 - 2*B^6*a^2*b^6 - B^6*b^8)*d^4*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*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(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^2*a^7 + 3*B^2*a^5*b^2 + 3*B^2*a^3*b^4 + B^2*a*b^6)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((B^3*a^10*b + 3*B^3*a^8*b^3 + 2*B^3*a^6*b^5 - 2*B^3*a^4*b^7 - 3*B^3*a^2*b^9 - B^3*b^11)*d^7*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (B^5*a^9 + 2*B^5*a^7*b^2 - 2*B^5*a^3*b^6 - B^5*a*b^8)*d^5*sqrt((B^4*a^4 - 2*B^4*a^2*b^2 + B^4*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(B^10*a^4 - 2*B^10*a^2*b^2 + B^10*b^4)) + 8*(B^5*a^2 + B^5*b^2)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + sqrt(2)*((B^4*a^3 + B^4*a*b^2)*d*cos(d*x + c)^2 - (B^4*a^3 + B^4*a*b^2)*d - 2*((B^2*a^4*b + B^2*a^2*b^3)*d^3*cos(d*x + c)^2 - (B^2*a^4*b + B^2*a^2*b^3)*d^3)*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((B^4*a^3 + B^4*a*b^2)*d*cos(d*x + c)^2 - (B^4*a^3 + B^4*a*b^2)*d - 2*((B^2*a^4*b + B^2*a^2*b^3)*d^3*cos(d*x + c)^2 - (B^2*a^4*b + B^2*a^2*b^3)*d^3)*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((B^4*a^6 - B^4*a^4*b^2 - B^4*a^2*b^4 + B^4*b^6)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((B^3*a^7 - B^3*a^5*b^2 - B^3*a^3*b^4 + B^3*a*b^6)*d^3*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (B^5*a^4*b - 2*B^5*a^2*b^3 + B^5*b^5)*d*cos(d*x + c))*sqrt((B^2*a^4 + 2*B^2*a^2*b^2 + B^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(B^2*a^4 - 2*B^2*a^2*b^2 + B^2*b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(B^4/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (B^6*a^4 - 2*B^6*a^2*b^2 + B^6*b^4)*sin(d*x + c))/cos(d*x + c)) - 8*(B^5*b^2*cos(d*x + c)^2 - B^5*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))))/((B^4*a^3 + B^4*a*b^2)*d*cos(d*x + c)^2 - (B^4*a^3 + B^4*a*b^2)*d)]","B",0
427,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
443,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
444,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
445,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
447,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(13/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(3/2*b*B/a+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
454,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
455,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
461,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
462,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
463,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
465,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
467,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
468,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
469,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,-1,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(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
472,-1,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(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
473,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/3)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,1,278,0,1.025009," ","integrate((-tan(f*x+e)+I)/(c+d*tan(f*x+e))^(1/3),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \left(-\frac{i}{{\left(i \, c + d\right)} f^{3}}\right)^{\frac{1}{3}} \log\left(\frac{1}{2} \, {\left(\sqrt{3} {\left(i \, c + d\right)} f^{2} + {\left(c - i \, d\right)} f^{2}\right)} \left(-\frac{i}{{\left(i \, c + d\right)} f^{3}}\right)^{\frac{2}{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)^{\frac{1}{3}}\right) + \frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \left(-\frac{i}{{\left(i \, c + d\right)} f^{3}}\right)^{\frac{1}{3}} \log\left(\frac{1}{2} \, {\left(\sqrt{3} {\left(-i \, c - d\right)} f^{2} + {\left(c - i \, d\right)} f^{2}\right)} \left(-\frac{i}{{\left(i \, c + d\right)} f^{3}}\right)^{\frac{2}{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)^{\frac{1}{3}}\right) + \left(-\frac{i}{{\left(i \, c + d\right)} f^{3}}\right)^{\frac{1}{3}} \log\left(-{\left(c - i \, d\right)} f^{2} \left(-\frac{i}{{\left(i \, c + d\right)} f^{3}}\right)^{\frac{2}{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)^{\frac{1}{3}}\right)"," ",0,"1/2*(I*sqrt(3) - 1)*(-I/((I*c + d)*f^3))^(1/3)*log(1/2*(sqrt(3)*(I*c + d)*f^2 + (c - I*d)*f^2)*(-I/((I*c + d)*f^3))^(2/3) + (((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)) + 1/2*(-I*sqrt(3) - 1)*(-I/((I*c + d)*f^3))^(1/3)*log(1/2*(sqrt(3)*(-I*c - d)*f^2 + (c - I*d)*f^2)*(-I/((I*c + d)*f^3))^(2/3) + (((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)) + (-I/((I*c + d)*f^3))^(1/3)*log(-(c - I*d)*f^2*(-I/((I*c + d)*f^3))^(2/3) + (((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^(1/3))","B",0
478,1,2721,0,1.204707," ","integrate((d-c*tan(f*x+e))/(c+d*tan(f*x+e))^(2/3),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{{\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) - 2 \, \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) - {\left(\sqrt{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) - \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} \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) + \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) + \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{{\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(\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) - \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{{\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(\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)"," ",0,"1/2*((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)) - 2*((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)) - (sqrt(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)) - ((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)*((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)) + ((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)) + 1/4*(sqrt(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)) - ((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)) - 1/4*(sqrt(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)) + ((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))","B",0
479,0,0,0,1.058306," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{4} \tan\left(d x + c\right)^{5} + A a^{4} + {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)\right)} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b^4*tan(d*x + c)^5 + A*a^4 + (4*B*a*b^3 + A*b^4)*tan(d*x + c)^4 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*tan(d*x + c)^3 + 2*(2*B*a^3*b + 3*A*a^2*b^2)*tan(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*tan(d*x + c))*tan(d*x + c)^m, x)","F",0
480,0,0,0,0.731986," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \tan\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)\right)} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b^3*tan(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*tan(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*tan(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*tan(d*x + c))*tan(d*x + c)^m, x)","F",0
481,0,0,0,1.061911," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \tan\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \tan\left(d x + c\right)\right)} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b^2*tan(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*tan(d*x + c)^2 + (B*a^2 + 2*A*a*b)*tan(d*x + c))*tan(d*x + c)^m, x)","F",0
482,0,0,0,0.532769," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \tan\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \tan\left(d x + c\right)\right)} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b*tan(d*x + c)^2 + A*a + (B*a + A*b)*tan(d*x + c))*tan(d*x + c)^m, x)","F",0
483,0,0,0,0.479988," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{b \tan\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*tan(d*x + c) + A)*tan(d*x + c)^m/(b*tan(d*x + c) + a), x)","F",0
484,0,0,0,0.583584," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} \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((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
485,0,0,0,0.629583," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{b^{3} \tan\left(d x + c\right)^{3} + 3 \, a b^{2} \tan\left(d x + c\right)^{2} + 3 \, a^{2} b \tan\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*tan(d*x + c) + A)*tan(d*x + c)^m/(b^3*tan(d*x + c)^3 + 3*a*b^2*tan(d*x + c)^2 + 3*a^2*b*tan(d*x + c) + a^3), x)","F",0
486,0,0,0,0.726775," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{b^{4} \tan\left(d x + c\right)^{4} + 4 \, a b^{3} \tan\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \tan\left(d x + c\right)^{2} + 4 \, a^{3} b \tan\left(d x + c\right) + a^{4}}, x\right)"," ",0,"integral((B*tan(d*x + c) + A)*tan(d*x + c)^m/(b^4*tan(d*x + c)^4 + 4*a*b^3*tan(d*x + c)^3 + 6*a^2*b^2*tan(d*x + c)^2 + 4*a^3*b*tan(d*x + c) + a^4), x)","F",0
487,0,0,0,0.595341," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \tan\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \tan\left(d x + c\right)\right)} \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b^2*tan(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*tan(d*x + c)^2 + (B*a^2 + 2*A*a*b)*tan(d*x + c))*sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^m, x)","F",0
488,0,0,0,0.621763," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \tan\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \tan\left(d x + c\right)\right)} \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b*tan(d*x + c)^2 + A*a + (B*a + A*b)*tan(d*x + c))*sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^m, x)","F",0
489,0,0,0,0.486663," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^m, x)","F",0
490,0,0,0,0.516069," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{\sqrt{b \tan\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*tan(d*x + c) + A)*tan(d*x + c)^m/sqrt(b*tan(d*x + c) + a), x)","F",0
491,0,0,0,0.611190," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} \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((B*tan(d*x + c) + A)*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
492,0,0,0,0.610985," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{m}}{b^{3} \tan\left(d x + c\right)^{3} + 3 \, a b^{2} \tan\left(d x + c\right)^{2} + 3 \, a^{2} b \tan\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^m/(b^3*tan(d*x + c)^3 + 3*a*b^2*tan(d*x + c)^2 + 3*a^2*b*tan(d*x + c) + a^3), x)","F",0
493,0,0,0,0.870208," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^n*tan(d*x + c)^m, x)","F",0
494,0,0,0,0.531157," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right)^{5} + A \tan\left(d x + c\right)^{4}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((B*tan(d*x + c)^5 + A*tan(d*x + c)^4)*(b*tan(d*x + c) + a)^n, x)","F",0
495,0,0,0,0.505011," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right)^{4} + A \tan\left(d x + c\right)^{3}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((B*tan(d*x + c)^4 + A*tan(d*x + c)^3)*(b*tan(d*x + c) + a)^n, x)","F",0
496,0,0,0,0.529202," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right)^{3} + A \tan\left(d x + c\right)^{2}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((B*tan(d*x + c)^3 + A*tan(d*x + c)^2)*(b*tan(d*x + c) + a)^n, x)","F",0
497,0,0,0,0.599368," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right)^{2} + A \tan\left(d x + c\right)\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((B*tan(d*x + c)^2 + A*tan(d*x + c))*(b*tan(d*x + c) + a)^n, x)","F",0
498,0,0,0,0.509758," ","integrate((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^n, x)","F",0
499,0,0,0,0.683566," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cot\left(d x + c\right) \tan\left(d x + c\right) + A \cot\left(d x + c\right)\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((B*cot(d*x + c)*tan(d*x + c) + A*cot(d*x + c))*(b*tan(d*x + c) + a)^n, x)","F",0
500,0,0,0,0.523137," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cot\left(d x + c\right)^{2} \tan\left(d x + c\right) + A \cot\left(d x + c\right)^{2}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((B*cot(d*x + c)^2*tan(d*x + c) + A*cot(d*x + c)^2)*(b*tan(d*x + c) + a)^n, x)","F",0
501,0,0,0,0.503759," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cot\left(d x + c\right)^{3} \tan\left(d x + c\right) + A \cot\left(d x + c\right)^{3}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((B*cot(d*x + c)^3*tan(d*x + c) + A*cot(d*x + c)^3)*(b*tan(d*x + c) + a)^n, x)","F",0
502,1,432,0,0.537913," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{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{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\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{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - 8 \, {\left({\left(23 \, A - 20 i \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} - 6 \, {\left(4 \, A - 5 i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(13 \, A - 10 i \, B\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}}}{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*(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 + 8*A*B - 4*I*B^2)*a^2/d^2)*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - 15*(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 + 8*A*B - 4*I*B^2)*a^2/d^2)*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - 8*((23*A - 20*I*B)*a*e^(4*I*d*x + 4*I*c) - 6*(4*A - 5*I*B)*a*e^(2*I*d*x + 2*I*c) + (13*A - 10*I*B)*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
503,1,380,0,0.507178," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))*(A+B*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{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - {\left({\left(-32 i \, A - 24 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(16 i \, A + 24 \, B\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}}}{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 - 8*A*B + 4*I*B^2)*a^2/d^2)*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - 3*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - ((-32*I*A - 24*B)*a*e^(2*I*d*x + 2*I*c) + (16*I*A + 24*B)*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
504,1,314,0,0.504157," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, A 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}} - \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} d \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) + \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} d \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right)}{4 \, d}"," ",0,"-1/4*(8*A*a*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 + 8*A*B - 4*I*B^2)*a^2/d^2)*d*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) + sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*d*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)))/d","B",0
505,1,362,0,0.531434," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) + 8 \, {\left(B a e^{\left(2 i \, d x + 2 i \, c\right)} - B 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 - 8*A*B + 4*I*B^2)*a^2/d^2)*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) + 8*(B*a*e^(2*I*d*x + 2*I*c) - B*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
506,1,428,0,0.496872," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),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{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\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{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 8 \, A B - 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - {\left(8 \, {\left(3 \, A - 4 i \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, B a e^{\left(2 i \, d x + 2 i \, c\right)} - 8 \, {\left(3 \, A - 2 i \, B\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}}}{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 + 8*A*B - 4*I*B^2)*a^2/d^2)*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*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 + 8*A*B - 4*I*B^2)*a^2/d^2)*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((4*I*A^2 + 8*A*B - 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - (8*(3*A - 4*I*B)*a*e^(4*I*d*x + 4*I*c) + 16*I*B*a*e^(2*I*d*x + 2*I*c) - 8*(3*A - 2*I*B)*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
507,1,482,0,0.551017," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{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{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\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{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} a^{2}}{d^{2}}} \log\left(-\frac{{\left(2 \, {\left(A - i \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-4 i \, A^{2} - 8 \, A B + 4 i \, B^{2}\right)} 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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{{\left(i \, A + B\right)} a}\right) - {\left({\left(-160 i \, A - 184 \, B\right)} a e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-80 i \, A - 8 \, B\right)} a e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(160 i \, A + 88 \, B\right)} a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(80 i \, A + 104 \, B\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}}}{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*(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((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) + (d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - 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((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*log(-(2*(A - I*B)*a*e^(2*I*d*x + 2*I*c) - (d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-4*I*A^2 - 8*A*B + 4*I*B^2)*a^2/d^2)*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)/((I*A + B)*a)) - ((-160*I*A - 184*B)*a*e^(6*I*d*x + 6*I*c) + (-80*I*A - 8*B)*a*e^(4*I*d*x + 4*I*c) + (160*I*A + 88*B)*a*e^(2*I*d*x + 2*I*c) + (80*I*A + 104*B)*a)*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
508,1,446,0,0.593469," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 15 \, \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 8 \, {\left({\left(43 \, A - 35 i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 6 \, {\left(9 \, A - 10 i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(23 \, A - 25 i \, B\right)} 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^2 + 32*A*B - 16*I*B^2)*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(-(4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 15*sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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(-(4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 8*((43*A - 35*I*B)*a^2*e^(4*I*d*x + 4*I*c) - 6*(9*A - 10*I*B)*a^2*e^(2*I*d*x + 2*I*c) + (23*A - 25*I*B)*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
509,1,392,0,0.511274," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(-\frac{{\left(4 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 3 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(-\frac{{\left(4 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - {\left({\left(-56 i \, A - 24 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(40 i \, A + 24 \, B\right)} 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^2 - 32*A*B + 16*I*B^2)*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(-(4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 3*sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(-(4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - ((-56*I*A - 24*B)*a^2*e^(2*I*d*x + 2*I*c) + (40*I*A + 24*B)*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
510,1,384,0,0.554492," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(-\frac{{\left(4 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(-\frac{{\left(4 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 8 \, {\left({\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(A + i \, B\right)} 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^2 + 32*A*B - 16*I*B^2)*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(-(4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(-(4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 8*((A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + (A + I*B)*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
511,1,436,0,0.522739," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 3 \, \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(-16 i \, A^{2} - 32 \, A B + 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) + {\left({\left(24 i \, A + 56 \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 16 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-24 i \, A - 40 \, B\right)} 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^2 - 32*A*B + 16*I*B^2)*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(-(4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) + sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 3*sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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(-(4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((-16*I*A^2 - 32*A*B + 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) + ((24*I*A + 56*B)*a^2*e^(4*I*d*x + 4*I*c) - 16*B*a^2*e^(2*I*d*x + 2*I*c) + (-24*I*A - 40*B)*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
512,1,503,0,0.552597," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 15 \, \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(16 i \, A^{2} + 32 \, A B - 16 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 2 \, B\right)} a^{2}}\right) - 8 \, {\left({\left(35 \, A - 43 i \, B\right)} a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(25 \, A - 11 i \, B\right)} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(35 \, A - 31 i \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(25 \, A - 23 i \, B\right)} 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^2 + 32*A*B - 16*I*B^2)*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(-(4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 15*sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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(-(4*(A - I*B)*a^2*e^(2*I*d*x + 2*I*c) - sqrt((16*I*A^2 + 32*A*B - 16*I*B^2)*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)/((2*I*A + 2*B)*a^2)) - 8*((35*A - 43*I*B)*a^2*e^(6*I*d*x + 6*I*c) + (25*A - 11*I*B)*a^2*e^(4*I*d*x + 4*I*c) - (35*A - 31*I*B)*a^2*e^(2*I*d*x + 2*I*c) - (25*A - 23*I*B)*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
513,1,503,0,0.552866," ","integrate(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 105 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) + {\left({\left(5104 i \, A + 4368 \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-10336 i \, A - 10752 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(8816 i \, A + 9072 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-2624 i \, A - 2688 \, B\right)} 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}}}{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*(105*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 105*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) + ((5104*I*A + 4368*B)*a^3*e^(6*I*d*x + 6*I*c) + (-10336*I*A - 10752*B)*a^3*e^(4*I*d*x + 4*I*c) + (8816*I*A + 9072*B)*a^3*e^(2*I*d*x + 2*I*c) + (-2624*I*A - 2688*B)*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
514,1,447,0,0.523170," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 15 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 16 \, {\left({\left(39 \, A - 25 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 3 \, {\left(19 \, A - 15 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(6 \, A - 5 i \, B\right)} 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}}}{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((64*I*A^2 + 128*A*B - 64*I*B^2)*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(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 15*sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 16*((39*A - 25*I*B)*a^3*e^(4*I*d*x + 4*I*c) - 3*(19*A - 15*I*B)*a^3*e^(2*I*d*x + 2*I*c) + 4*(6*A - 5*I*B)*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
515,1,407,0,0.571005," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} a^{6}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - d\right)} \log\left(-\frac{{\left(8 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 3 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} a^{6}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - d\right)} \log\left(-\frac{{\left(8 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - {\left({\left(-80 i \, A - 48 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-16 i \, A + 48 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 64 i \, A 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)} - d\right)}}"," ",0,"-1/12*(3*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*a^6/d^2)*(d*e^(4*I*d*x + 4*I*c) - d)*log(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 3*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*a^6/d^2)*(d*e^(4*I*d*x + 4*I*c) - d)*log(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - ((-80*I*A - 48*B)*a^3*e^(4*I*d*x + 4*I*c) + (-16*I*A + 48*B)*a^3*e^(2*I*d*x + 2*I*c) + 64*I*A*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) - d)","B",0
516,1,442,0,0.552505," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 3 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - {\left(16 \, {\left(3 \, A - 5 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 16 \, {\left(3 \, A + i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 64 i \, B 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^2 + 128*A*B - 64*I*B^2)*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(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 3*sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - (16*(3*A - 5*I*B)*a^3*e^(4*I*d*x + 4*I*c) + 16*(3*A + I*B)*a^3*e^(2*I*d*x + 2*I*c) + 64*I*B*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
517,1,497,0,0.664270," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 15 \, \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(-64 i \, A^{2} - 128 \, A B + 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) + {\left({\left(400 i \, A + 624 \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(320 i \, A + 288 \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-400 i \, A - 528 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-320 i \, A - 384 \, B\right)} 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}}}{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((-64*I*A^2 - 128*A*B + 64*I*B^2)*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(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) + sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 15*sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((-64*I*A^2 - 128*A*B + 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) + ((400*I*A + 624*B)*a^3*e^(6*I*d*x + 6*I*c) + (320*I*A + 288*B)*a^3*e^(4*I*d*x + 4*I*c) + (-400*I*A - 528*B)*a^3*e^(2*I*d*x + 2*I*c) + (-320*I*A - 384*B)*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
518,1,561,0,0.651058," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} a^{6}}{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(8 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 105 \, \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} a^{6}}{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(8 \, {\left(A - i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{{\left(64 i \, A^{2} + 128 \, A B - 64 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{3}}\right) - 16 \, {\left({\left(273 \, A - 319 i \, B\right)} a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 3 \, {\left(133 \, A - 109 i \, B\right)} a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 5 \, {\left(21 \, A - 19 i \, B\right)} a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 3 \, {\left(133 \, A - 129 i \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 \, {\left(42 \, A - 41 i \, B\right)} 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}}}{420 \, {\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,"-1/420*(105*sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*a^6/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(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 105*sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*a^6/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(-(8*(A - I*B)*a^3*e^(2*I*d*x + 2*I*c) - sqrt((64*I*A^2 + 128*A*B - 64*I*B^2)*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)/((4*I*A + 4*B)*a^3)) - 16*((273*A - 319*I*B)*a^3*e^(8*I*d*x + 8*I*c) + 3*(133*A - 109*I*B)*a^3*e^(6*I*d*x + 6*I*c) - 5*(21*A - 19*I*B)*a^3*e^(4*I*d*x + 4*I*c) - 3*(133*A - 129*I*B)*a^3*e^(2*I*d*x + 2*I*c) - 4*(42*A - 41*I*B)*a^3)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(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
519,1,715,0,0.569597," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{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{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} \log\left(-\frac{2 \, {\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} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 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{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} \log\left(\frac{2 \, {\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} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 6 \, {\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{9 i \, A^{2} - 12 \, A B - 4 i \, B^{2}}{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{9 i \, A^{2} - 12 \, A B - 4 i \, B^{2}}{a^{2} d^{2}}} + 3 \, A + 2 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 6 \, {\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{9 i \, A^{2} - 12 \, A B - 4 i \, B^{2}}{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{9 i \, A^{2} - 12 \, A B - 4 i \, B^{2}}{a^{2} d^{2}}} - 3 \, A - 2 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, {\left({\left(19 i \, A - 27 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-38 i \, A + 30 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\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}}}{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*(a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*log(-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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*(a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*log(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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 6*(a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))*sqrt((9*I*A^2 - 12*A*B - 4*I*B^2)/(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((9*I*A^2 - 12*A*B - 4*I*B^2)/(a^2*d^2)) + 3*A + 2*I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 6*(a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))*sqrt((9*I*A^2 - 12*A*B - 4*I*B^2)/(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((9*I*A^2 - 12*A*B - 4*I*B^2)/(a^2*d^2)) - 3*A - 2*I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*((19*I*A - 27*B)*e^(4*I*d*x + 4*I*c) + (-38*I*A + 30*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(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
520,1,625,0,0.621324," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} - 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - a d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} - 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) + 2 \, a d \sqrt{\frac{-4 i \, A^{2} + 4 \, A B + i \, B^{2}}{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} + 4 \, A B + i \, B^{2}}{a^{2} d^{2}}} + 2 i \, A - B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, a d \sqrt{\frac{-4 i \, A^{2} + 4 \, A B + i \, B^{2}}{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} + 4 \, A B + i \, B^{2}}{a^{2} d^{2}}} - 2 i \, A + B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, {\left({\left(9 \, A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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)}}{8 \, a d}"," ",0,"1/8*(a*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(1/2*((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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) - 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - a*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(1/2*((-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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) - 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 2*a*d*sqrt((-4*I*A^2 + 4*A*B + I*B^2)/(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 + 4*A*B + I*B^2)/(a^2*d^2)) + 2*I*A - B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*a*d*sqrt((-4*I*A^2 + 4*A*B + I*B^2)/(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 + 4*A*B + I*B^2)/(a^2*d^2)) - 2*I*A + B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*((9*A + I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*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*d)","B",0
521,1,570,0,0.501808," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{2 \, {\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} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - a d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{2 \, {\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} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 2 \, a d \sqrt{\frac{i \, A^{2}}{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}}{a^{2} d^{2}}} + A\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 2 \, a d \sqrt{\frac{i \, A^{2}}{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}}{a^{2} d^{2}}} - A\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 2 \, {\left({\left(-i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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)}}{8 \, a d}"," ",0,"1/8*(a*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(-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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - a*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a*d*sqrt(I*A^2/(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/(a^2*d^2)) + A)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 2*a*d*sqrt(I*A^2/(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/(a^2*d^2)) - A)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 2*((-I*A + B)*e^(2*I*d*x + 2*I*c) + I*A - B)*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*d)","B",0
522,1,573,0,0.546346," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} - 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - a d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} - 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) + 2 \, a d \sqrt{\frac{i \, B^{2}}{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 \, B^{2}}{a^{2} d^{2}}} + B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, a d \sqrt{\frac{i \, B^{2}}{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 \, B^{2}}{a^{2} d^{2}}} - B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, {\left({\left(A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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)}}{8 \, a d}"," ",0,"-1/8*(a*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(1/2*((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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) - 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - a*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(1/2*((-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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) - 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 2*a*d*sqrt(I*B^2/(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*B^2/(a^2*d^2)) + B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*a*d*sqrt(I*B^2/(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*B^2/(a^2*d^2)) - B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*((A + I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*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*d)","B",0
523,1,700,0,1.088359," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} \log\left(-\frac{2 \, {\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} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} \log\left(\frac{2 \, {\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} - 2 \, A B + i \, B^{2}}{a^{2} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) + 2 \, {\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 \, A^{2} - 4 \, A B - 4 i \, B^{2}}{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{i \, A^{2} - 4 \, A B - 4 i \, B^{2}}{a^{2} d^{2}}} + A + 2 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, {\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 \, A^{2} - 4 \, A B - 4 i \, B^{2}}{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{i \, A^{2} - 4 \, A B - 4 i \, B^{2}}{a^{2} d^{2}}} - A - 2 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, {\left({\left(i \, A - 9 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, B e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\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}}}{8 \, {\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,"-1/8*((a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*log(-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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - (a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2))*log(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((-I*A^2 - 2*A*B + I*B^2)/(a^2*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 2*(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt((I*A^2 - 4*A*B - 4*I*B^2)/(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((I*A^2 - 4*A*B - 4*I*B^2)/(a^2*d^2)) + A + 2*I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt((I*A^2 - 4*A*B - 4*I*B^2)/(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((I*A^2 - 4*A*B - 4*I*B^2)/(a^2*d^2)) - A - 2*I*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*((I*A - 9*B)*e^(4*I*d*x + 4*I*c) + 8*B*e^(2*I*d*x + 2*I*c) - I*A + B)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(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
524,1,796,0,0.658631," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\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)} \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} - 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 3 \, {\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)} \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{2} d^{2}}} - 4 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 6 \, {\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)} \sqrt{\frac{-4 i \, A^{2} + 12 \, A B + 9 i \, B^{2}}{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} + 12 \, A B + 9 i \, B^{2}}{a^{2} d^{2}}} + 2 i \, A - 3 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + 6 \, {\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)} \sqrt{\frac{-4 i \, A^{2} + 12 \, A B + 9 i \, B^{2}}{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} + 12 \, A B + 9 i \, B^{2}}{a^{2} d^{2}}} - 2 i \, A + 3 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - 2 \, {\left({\left(27 \, A + 19 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(3 \, A + 19 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(27 \, A + 35 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, A - 3 i \, B\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}}}{24 \, {\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,"1/24*(3*(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))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*log(1/2*((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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) - 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*(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))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2))*log(1/2*((-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((I*A^2 + 2*A*B - I*B^2)/(a^2*d^2)) - 4*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 6*(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))*sqrt((-4*I*A^2 + 12*A*B + 9*I*B^2)/(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 + 12*A*B + 9*I*B^2)/(a^2*d^2)) + 2*I*A - 3*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) + 6*(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))*sqrt((-4*I*A^2 + 12*A*B + 9*I*B^2)/(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 + 12*A*B + 9*I*B^2)/(a^2*d^2)) - 2*I*A + 3*B)*e^(-2*I*d*x - 2*I*c)/(a*d)) - 2*((27*A + 19*I*B)*e^(6*I*d*x + 6*I*c) + (3*A + 19*I*B)*e^(4*I*d*x + 4*I*c) - (27*A + 35*I*B)*e^(2*I*d*x + 2*I*c) - 3*A - 3*I*B)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(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
525,1,671,0,0.581858," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} - 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) - 2 \, a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} - 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) + a^{2} d \sqrt{\frac{-529 i \, A^{2} + 322 \, A B + 49 i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left({\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 \, A^{2} + 322 \, A B + 49 i \, B^{2}}{a^{4} d^{2}}} + 23 i \, A - 7 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - a^{2} d \sqrt{\frac{-529 i \, A^{2} + 322 \, A B + 49 i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left({\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 \, A^{2} + 322 \, A B + 49 i \, B^{2}}{a^{4} d^{2}}} - 23 i \, A + 7 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - 2 \, {\left(6 \, {\left(7 \, A + i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(9 \, A + 5 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"1/32*(2*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/4*((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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) - 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/4*((-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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) - 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + a^2*d*sqrt((-529*I*A^2 + 322*A*B + 49*I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*((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*I*A^2 + 322*A*B + 49*I*B^2)/(a^4*d^2)) + 23*I*A - 7*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - a^2*d*sqrt((-529*I*A^2 + 322*A*B + 49*I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*((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*I*A^2 + 322*A*B + 49*I*B^2)/(a^4*d^2)) - 23*I*A + 7*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - 2*(6*(7*A + I*B)*e^(4*I*d*x + 4*I*c) - (9*A + 5*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*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)/(a^2*d)","B",0
526,1,666,0,1.084752," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{2 \, {\left({\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 2 \, a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{2 \, {\left({\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - a^{2} d \sqrt{\frac{49 i \, A^{2} + 14 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left({\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 \, A^{2} + 14 \, A B - i \, B^{2}}{a^{4} d^{2}}} + 7 \, A - i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + a^{2} d \sqrt{\frac{49 i \, A^{2} + 14 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left({\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 \, A^{2} + 14 \, A B - i \, B^{2}}{a^{4} d^{2}}} - 7 \, A + i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + 2 \, {\left({\left(-6 i \, A + 2 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(5 i \, A - B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"1/32*(2*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - a^2*d*sqrt((49*I*A^2 + 14*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*((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*I*A^2 + 14*A*B - I*B^2)/(a^4*d^2)) + 7*A - I*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + a^2*d*sqrt((49*I*A^2 + 14*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*((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*I*A^2 + 14*A*B - I*B^2)/(a^4*d^2)) - 7*A + I*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + 2*((-6*I*A + 2*B)*e^(4*I*d*x + 4*I*c) + (5*I*A - B)*e^(2*I*d*x + 2*I*c) + I*A - B)*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)/(a^2*d)","B",0
527,1,665,0,0.627154," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} - 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) - 2 \, a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} - 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) - a^{2} d \sqrt{\frac{-i \, A^{2} + 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left({\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 \, A^{2} + 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} + i \, A - B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + a^{2} d \sqrt{\frac{-i \, A^{2} + 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left({\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 \, A^{2} + 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} - i \, A + B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - 2 \, {\left(2 \, {\left(A - i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(A - 3 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"-1/32*(2*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/4*((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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) - 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/4*((-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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) - 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - a^2*d*sqrt((-I*A^2 + 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*((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((-I*A^2 + 2*A*B + I*B^2)/(a^4*d^2)) + I*A - B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + a^2*d*sqrt((-I*A^2 + 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*((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((-I*A^2 + 2*A*B + I*B^2)/(a^4*d^2)) - I*A + B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - 2*(2*(A - I*B)*e^(4*I*d*x + 4*I*c) - (A - 3*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*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)/(a^2*d)","B",0
528,1,662,0,1.608832," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{2 \, {\left({\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 2 \, a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{2 \, {\left({\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{4} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) + a^{2} d \sqrt{\frac{i \, A^{2} + 14 \, A B - 49 i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left({\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 \, A^{2} + 14 \, A B - 49 i \, B^{2}}{a^{4} d^{2}}} + A - 7 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - a^{2} d \sqrt{\frac{i \, A^{2} + 14 \, A B - 49 i \, B^{2}}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left({\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 \, A^{2} + 14 \, A B - 49 i \, B^{2}}{a^{4} d^{2}}} - A + 7 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - 2 \, {\left({\left(-2 i \, A + 6 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(3 i \, A - 7 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\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(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"-1/32*(2*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^4*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + a^2*d*sqrt((I*A^2 + 14*A*B - 49*I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*((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((I*A^2 + 14*A*B - 49*I*B^2)/(a^4*d^2)) + A - 7*I*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - a^2*d*sqrt((I*A^2 + 14*A*B - 49*I*B^2)/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*((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((I*A^2 + 14*A*B - 49*I*B^2)/(a^4*d^2)) - A + 7*I*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - 2*((-2*I*A + 6*B)*e^(4*I*d*x + 4*I*c) + (3*I*A - 7*B)*e^(2*I*d*x + 2*I*c) - I*A + B)*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)/(a^2*d)","B",0
529,1,763,0,1.008346," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} - 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) - 2 \, {\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{4} d^{2}}} - 8 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, {\left(i \, A + B\right)}}\right) + {\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{-49 i \, A^{2} + 322 \, A B + 529 i \, B^{2}}{a^{4} d^{2}}} \log\left(\frac{{\left({\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 \, A^{2} + 322 \, A B + 529 i \, B^{2}}{a^{4} d^{2}}} + 7 i \, A - 23 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - {\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{-49 i \, A^{2} + 322 \, A B + 529 i \, B^{2}}{a^{4} d^{2}}} \log\left(-\frac{{\left({\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 \, A^{2} + 322 \, A B + 529 i \, B^{2}}{a^{4} d^{2}}} - 7 i \, A + 23 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + 2 \, {\left(6 \, {\left(A + 7 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(A + 33 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(3 \, A + 5 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\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}}}{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*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*log(1/4*((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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) - 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 2*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2))*log(1/4*((-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((I*A^2 + 2*A*B - I*B^2)/(a^4*d^2)) - 8*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + (a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt((-49*I*A^2 + 322*A*B + 529*I*B^2)/(a^4*d^2))*log(1/8*((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*I*A^2 + 322*A*B + 529*I*B^2)/(a^4*d^2)) + 7*I*A - 23*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - (a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt((-49*I*A^2 + 322*A*B + 529*I*B^2)/(a^4*d^2))*log(-1/8*((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*I*A^2 + 322*A*B + 529*I*B^2)/(a^4*d^2)) - 7*I*A + 23*B)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + 2*(6*(A + 7*I*B)*e^(6*I*d*x + 6*I*c) - (A + 33*I*B)*e^(4*I*d*x + 4*I*c) - 2*(3*A + 5*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))","B",0
530,1,690,0,0.642769," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} - 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) - 3 \, a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} - 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) + 3 \, a^{3} d \sqrt{\frac{-841 i \, A^{2} + 348 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left({\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{-841 i \, A^{2} + 348 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} + 29 i \, A - 6 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 3 \, a^{3} d \sqrt{\frac{-841 i \, A^{2} + 348 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{{\left({\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{-841 i \, A^{2} + 348 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} - 29 i \, A + 6 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 2 \, {\left(2 \, {\left(73 \, A + 10 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(41 \, A + 14 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(8 \, A + 5 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(3*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) - 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((-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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) - 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 3*a^3*d*sqrt((-841*I*A^2 + 348*A*B + 36*I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((-841*I*A^2 + 348*A*B + 36*I*B^2)/(a^6*d^2)) + 29*I*A - 6*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 3*a^3*d*sqrt((-841*I*A^2 + 348*A*B + 36*I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-1/8*((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((-841*I*A^2 + 348*A*B + 36*I*B^2)/(a^6*d^2)) - 29*I*A + 6*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 2*(2*(73*A + 10*I*B)*e^(6*I*d*x + 6*I*c) - (41*A + 14*I*B)*e^(4*I*d*x + 4*I*c) - (8*A + 5*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*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)/(a^3*d)","B",0
531,1,682,0,0.519601," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{2 \, {\left({\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{2 \, {\left({\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 3 \, a^{3} d \sqrt{\frac{36 i \, A^{2} + 12 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{{\left({\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{36 i \, A^{2} + 12 \, A B - i \, B^{2}}{a^{6} d^{2}}} + 6 \, A - i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 3 \, a^{3} d \sqrt{\frac{36 i \, A^{2} + 12 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left({\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{36 i \, A^{2} + 12 \, A B - i \, B^{2}}{a^{6} d^{2}}} - 6 \, A + i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 2 \, {\left({\left(-20 i \, A + 2 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(14 i \, A + B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(5 i \, A - 2 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(3*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((36*I*A^2 + 12*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-1/8*((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((36*I*A^2 + 12*A*B - I*B^2)/(a^6*d^2)) + 6*A - I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 3*a^3*d*sqrt((36*I*A^2 + 12*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((36*I*A^2 + 12*A*B - I*B^2)/(a^6*d^2)) - 6*A + I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 2*((-20*I*A + 2*B)*e^(6*I*d*x + 6*I*c) + (14*I*A + B)*e^(4*I*d*x + 4*I*c) + (5*I*A - 2*B)*e^(2*I*d*x + 2*I*c) + I*A - B)*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)/(a^3*d)","B",0
532,1,637,0,0.542656," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} - 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) - 3 \, a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} - 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) - 24 \, a^{3} d \sqrt{-\frac{i \, A^{2}}{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 \, A^{2}}{64 \, a^{6} d^{2}}} + i \, A\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 24 \, a^{3} d \sqrt{-\frac{i \, A^{2}}{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 \, A^{2}}{64 \, a^{6} d^{2}}} - i \, A\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 2 \, {\left(2 \, {\left(A - 2 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(A + 4 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(2 \, A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"-1/96*(3*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) - 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((-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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) - 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 24*a^3*d*sqrt(-1/64*I*A^2/(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^2/(a^6*d^2)) + I*A)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 24*a^3*d*sqrt(-1/64*I*A^2/(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^2/(a^6*d^2)) - I*A)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 2*(2*(A - 2*I*B)*e^(6*I*d*x + 6*I*c) + (A + 4*I*B)*e^(4*I*d*x + 4*I*c) - (2*A - I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*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)/(a^3*d)","B",0
533,1,634,0,0.536239," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{2 \, {\left({\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{2 \, {\left({\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 24 \, a^{3} d \sqrt{-\frac{i \, B^{2}}{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 \, B^{2}}{64 \, a^{6} d^{2}}} + i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 24 \, a^{3} d \sqrt{-\frac{i \, B^{2}}{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 \, B^{2}}{64 \, a^{6} d^{2}}} - i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 2 \, {\left({\left(-4 i \, A - 2 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(4 i \, A + 5 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(i \, A - 4 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\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(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"-1/96*(3*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 24*a^3*d*sqrt(-1/64*I*B^2/(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*B^2/(a^6*d^2)) + I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 24*a^3*d*sqrt(-1/64*I*B^2/(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*B^2/(a^6*d^2)) - I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 2*((-4*I*A - 2*B)*e^(6*I*d*x + 6*I*c) + (4*I*A + 5*B)*e^(4*I*d*x + 4*I*c) + (I*A - 4*B)*e^(2*I*d*x + 2*I*c) - I*A + B)*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)/(a^3*d)","B",0
534,1,687,0,0.549259," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} - 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) - 3 \, a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{6} d^{2}}} - 16 \, {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, {\left(i \, A + B\right)}}\right) + 3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 12 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left({\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 \, A^{2} - 12 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} + i \, A + 6 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 3 \, a^{3} d \sqrt{\frac{-i \, A^{2} - 12 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{{\left({\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 \, A^{2} - 12 \, A B + 36 i \, B^{2}}{a^{6} d^{2}}} - i \, A - 6 \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 2 \, {\left(2 \, {\left(A + 10 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(5 \, A + 26 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(4 \, A + 7 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(3*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) - 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((-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((I*A^2 + 2*A*B - I*B^2)/(a^6*d^2)) - 16*(A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 3*a^3*d*sqrt((-I*A^2 - 12*A*B + 36*I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*((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((-I*A^2 - 12*A*B + 36*I*B^2)/(a^6*d^2)) + I*A + 6*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 3*a^3*d*sqrt((-I*A^2 - 12*A*B + 36*I*B^2)/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-1/8*((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((-I*A^2 - 12*A*B + 36*I*B^2)/(a^6*d^2)) - I*A - 6*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 2*(2*(A + 10*I*B)*e^(6*I*d*x + 6*I*c) - (5*A + 26*I*B)*e^(4*I*d*x + 4*I*c) + (4*A + 7*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*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)/(a^3*d)","B",0
535,1,781,0,0.517587," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\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)} \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} \log\left(-\frac{2 \, {\left({\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} + {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) - 3 \, {\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)} \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} \log\left(\frac{2 \, {\left({\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 \, A^{2} - 2 \, A B + i \, B^{2}}{a^{6} d^{2}}} - {\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{i \, A + B}\right) + 3 \, {\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)} \sqrt{\frac{36 i \, A^{2} - 348 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} \log\left(\frac{{\left({\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{36 i \, A^{2} - 348 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} + 6 \, A + 29 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 3 \, {\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)} \sqrt{\frac{36 i \, A^{2} - 348 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} \log\left(-\frac{{\left({\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{36 i \, A^{2} - 348 \, A B - 841 i \, B^{2}}{a^{6} d^{2}}} - 6 \, A - 29 i \, B\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 2 \, {\left({\left(-20 i \, A + 146 \, B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(6 i \, A - 105 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(19 i \, A - 49 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-6 i \, A + 9 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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}}}{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*(3*(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*log(-2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) + (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) - 3*(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2))*log(2*((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((-I*A^2 - 2*A*B + I*B^2)/(a^6*d^2)) - (A - I*B)*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/(I*A + B)) + 3*(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((36*I*A^2 - 348*A*B - 841*I*B^2)/(a^6*d^2))*log(1/8*((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((36*I*A^2 - 348*A*B - 841*I*B^2)/(a^6*d^2)) + 6*A + 29*I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 3*(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))*sqrt((36*I*A^2 - 348*A*B - 841*I*B^2)/(a^6*d^2))*log(-1/8*((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((36*I*A^2 - 348*A*B - 841*I*B^2)/(a^6*d^2)) - 6*A - 29*I*B)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 2*((-20*I*A + 146*B)*e^(8*I*d*x + 8*I*c) + (6*I*A - 105*B)*e^(6*I*d*x + 6*I*c) + (19*I*A - 49*B)*e^(4*I*d*x + 4*I*c) + (-6*I*A + 9*B)*e^(2*I*d*x + 2*I*c) + I*A - B)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))","B",0
536,1,475,0,0.518819," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} {\left({\left(17 \, A - 10 i \, B\right)} e^{\left(5 i \, d x + 5 i \, c\right)} - 10 \, {\left(2 \, A - i \, B\right)} e^{\left(3 i \, d x + 3 i \, c\right)} + 15 \, 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}} - 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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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)*((17*A - 10*I*B)*e^(5*I*d*x + 5*I*c) - 10*(2*A - I*B)*e^(3*I*d*x + 3*I*c) + 15*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)) - 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^2 + 16*A*B - 8*I*B^2)*a/d^2)*log((sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a/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)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 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^2 + 16*A*B - 8*I*B^2)*a/d^2)*log((sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a/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)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
537,1,425,0,0.476107," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-16 i \, A - 24 \, B\right)} e^{\left(3 i \, d x + 3 i \, c\right)} + 24 \, B 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{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a}{d^{2}}} \log\left(-\frac{{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a}{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}} + 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a}{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}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right)}{12 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/12*(sqrt(2)*((-16*I*A - 24*B)*e^(3*I*d*x + 3*I*c) + 24*B*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((-8*I*A^2 - 16*A*B + 8*I*B^2)*a/d^2)*log(-(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a/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)) + 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 3*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a/d^2)*log((sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a/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)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
538,1,364,0,0.507082," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),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)} - d \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + d \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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) - d*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a/d^2)*log((sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a/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)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + d*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a/d^2)*log((sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a/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)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)))/d","B",0
539,1,574,0,0.570799," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a}{d^{2}}} \log\left(-\frac{{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a}{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}} + 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \frac{1}{4} \, \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{{\left(-8 i \, A^{2} - 16 \, A B + 8 i \, B^{2}\right)} a}{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}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + \frac{1}{4} \, \sqrt{\frac{4 i \, B^{2} a}{d^{2}}} \log\left(-\frac{{\left(48 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 16 \, B a^{2} - \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{4 i \, B^{2} a}{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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{B}\right) - \frac{1}{4} \, \sqrt{\frac{4 i \, B^{2} a}{d^{2}}} \log\left(-\frac{{\left(48 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 16 \, B a^{2} - \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{4 i \, B^{2} a}{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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{B}\right)"," ",0,"1/4*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a/d^2)*log(-(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a/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)) + 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 1/4*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a/d^2)*log((sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((-8*I*A^2 - 16*A*B + 8*I*B^2)*a/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)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 1/4*sqrt(4*I*B^2*a/d^2)*log(-(48*B*a^2*e^(2*I*d*x + 2*I*c) - 16*B*a^2 - 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(4*I*B^2*a/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)))*e^(-2*I*d*x - 2*I*c)/B) - 1/4*sqrt(4*I*B^2*a/d^2)*log(-(48*B*a^2*e^(2*I*d*x + 2*I*c) - 16*B*a^2 - 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(4*I*B^2*a/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)))*e^(-2*I*d*x - 2*I*c)/B)","B",0
540,1,785,0,0.555126," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-4 i \, B e^{\left(3 i \, d x + 3 i \, c\right)} + 4 i \, B 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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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{{\left(8 i \, A^{2} + 16 \, A B - 8 i \, B^{2}\right)} a}{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}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 4 \, A B - i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(-96 i \, A - 48 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(32 i \, A + 16 \, B\right)} a^{2} + 32 \, \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{{\left(4 i \, A^{2} + 4 \, A B - i \, B^{2}\right)} a}{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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 i \, A + B}\right) + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{{\left(4 i \, A^{2} + 4 \, A B - i \, B^{2}\right)} a}{d^{2}}} \log\left(\frac{{\left({\left(-96 i \, A - 48 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(32 i \, A + 16 \, B\right)} a^{2} - 32 \, \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{{\left(4 i \, A^{2} + 4 \, A B - i \, B^{2}\right)} a}{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}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 i \, A + B}\right)}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/4*(sqrt(2)*(-4*I*B*e^(3*I*d*x + 3*I*c) + 4*I*B*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^2 + 16*A*B - 8*I*B^2)*a/d^2)*log((sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a/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)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a/d^2)*log((sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((8*I*A^2 + 16*A*B - 8*I*B^2)*a/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)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 4*A*B - I*B^2)*a/d^2)*log(((-96*I*A - 48*B)*a^2*e^(2*I*d*x + 2*I*c) + (32*I*A + 16*B)*a^2 + 32*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt((4*I*A^2 + 4*A*B - I*B^2)*a/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)))*e^(-2*I*d*x - 2*I*c)/(2*I*A + B)) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt((4*I*A^2 + 4*A*B - I*B^2)*a/d^2)*log(((-96*I*A - 48*B)*a^2*e^(2*I*d*x + 2*I*c) + (32*I*A + 16*B)*a^2 - 32*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt((4*I*A^2 + 4*A*B - I*B^2)*a/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)))*e^(-2*I*d*x - 2*I*c)/(2*I*A + B)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
541,1,564,0,0.531231," ","integrate(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(1688 i \, A + 1512 \, B\right)} a e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(-2968 i \, A - 3192 \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(3080 i \, A + 2520 \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-840 i \, A - 840 \, B\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}} + 105 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{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 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - 105 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{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 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\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*(sqrt(2)*((1688*I*A + 1512*B)*a*e^(7*I*d*x + 7*I*c) + (-2968*I*A - 3192*B)*a*e^(5*I*d*x + 5*I*c) + (3080*I*A + 2520*B)*a*e^(3*I*d*x + 3*I*c) + (-840*I*A - 840*B)*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*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/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(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)) - 105*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/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(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*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
542,1,508,0,0.598087," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} {\left({\left(27 \, A - 25 i \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} - 10 \, {\left(3 \, A - 4 i \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + 15 \, {\left(A - i \, B\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}} - 15 \, \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{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 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 15 \, \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{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 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\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)*((27*A - 25*I*B)*a*e^(5*I*d*x + 5*I*c) - 10*(3*A - 4*I*B)*a*e^(3*I*d*x + 3*I*c) + 15*(A - I*B)*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)) - 15*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)) + 15*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
543,1,456,0,0.575762," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-40 i \, A - 24 \, B\right)} a e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(24 i \, A + 24 \, B\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}} - 3 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(-\frac{{\left(8 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 3 \, \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(-\frac{{\left(8 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} 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 - 24*B)*a*e^(3*I*d*x + 3*I*c) + (24*I*A + 24*B)*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*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)) + 3*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
544,1,671,0,0.562056," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} A 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{4 i \, B^{2} a^{3}}{d^{2}}} d \log\left(-\frac{16 \, {\left(3 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - B a^{2} + \sqrt{2} \sqrt{-\frac{4 i \, B^{2} a^{3}}{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)}}{B}\right) - \sqrt{-\frac{4 i \, B^{2} a^{3}}{d^{2}}} d \log\left(-\frac{16 \, {\left(3 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - B a^{2} - \sqrt{2} \sqrt{-\frac{4 i \, B^{2} a^{3}}{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)}}{B}\right) - \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{d^{2}}} d \log\left(-\frac{{\left(8 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{d^{2}}} d \log\left(-\frac{{\left(8 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right)}{4 \, d}"," ",0,"-1/4*(8*sqrt(2)*A*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(-4*I*B^2*a^3/d^2)*d*log(-16*(3*B*a^2*e^(2*I*d*x + 2*I*c) - B*a^2 + sqrt(2)*sqrt(-4*I*B^2*a^3/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)/B) - sqrt(-4*I*B^2*a^3/d^2)*d*log(-16*(3*B*a^2*e^(2*I*d*x + 2*I*c) - B*a^2 - sqrt(2)*sqrt(-4*I*B^2*a^3/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)/B) - sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/d^2)*d*log(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)) + sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/d^2)*d*log(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)))/d","B",0
545,1,818,0,0.558704," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(B a e^{\left(3 i \, d x + 3 i \, c\right)} - B 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}} + \sqrt{\frac{{\left(-4 i \, A^{2} - 12 \, A B + 9 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left({\left(-96 i \, A - 144 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(32 i \, A + 48 \, B\right)} a^{2} + \sqrt{2} \sqrt{\frac{{\left(-4 i \, A^{2} - 12 \, A B + 9 i \, B^{2}\right)} a^{3}}{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}} \sqrt{\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 i \, A + 3 \, B}\right) - \sqrt{\frac{{\left(-4 i \, A^{2} - 12 \, A B + 9 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left({\left(-96 i \, A - 144 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(32 i \, A + 48 \, B\right)} a^{2} + \sqrt{2} \sqrt{\frac{{\left(-4 i \, A^{2} - 12 \, A B + 9 i \, B^{2}\right)} a^{3}}{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}} \sqrt{\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 i \, A + 3 \, B}\right) + \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(-\frac{{\left(8 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) - \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(-\frac{{\left(8 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(-32 i \, A^{2} - 64 \, A B + 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right)}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/4*(4*sqrt(2)*(B*a*e^(3*I*d*x + 3*I*c) - B*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)) + sqrt((-4*I*A^2 - 12*A*B + 9*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(((-96*I*A - 144*B)*a^2*e^(2*I*d*x + 2*I*c) + (32*I*A + 48*B)*a^2 + sqrt(2)*sqrt((-4*I*A^2 - 12*A*B + 9*I*B^2)*a^3/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))*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)/(2*I*A + 3*B)) - sqrt((-4*I*A^2 - 12*A*B + 9*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(((-96*I*A - 144*B)*a^2*e^(2*I*d*x + 2*I*c) + (32*I*A + 48*B)*a^2 + sqrt(2)*sqrt((-4*I*A^2 - 12*A*B + 9*I*B^2)*a^3/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))*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)/(2*I*A + 3*B)) + sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) + sqrt(2)*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)) - sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt((-32*I*A^2 - 64*A*B + 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
546,1,907,0,0.630302," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left({\left(4 \, A - 7 i \, B\right)} a e^{\left(5 i \, d x + 5 i \, c\right)} + 4 i \, B a e^{\left(3 i \, d x + 3 i \, c\right)} - {\left(4 \, A - 3 i \, B\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}} - \sqrt{\frac{{\left(144 i \, A^{2} + 264 \, A B - 121 i \, B^{2}\right)} a^{3}}{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({\left(-576 i \, A - 528 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(192 i \, A + 176 \, B\right)} a^{2} + 32 \, \sqrt{2} \sqrt{\frac{{\left(144 i \, A^{2} + 264 \, A B - 121 i \, B^{2}\right)} a^{3}}{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)}}{12 i \, A + 11 \, B}\right) + \sqrt{\frac{{\left(144 i \, A^{2} + 264 \, A B - 121 i \, B^{2}\right)} a^{3}}{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({\left(-576 i \, A - 528 \, B\right)} a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(192 i \, A + 176 \, B\right)} a^{2} - 32 \, \sqrt{2} \sqrt{\frac{{\left(144 i \, A^{2} + 264 \, A B - 121 i \, B^{2}\right)} a^{3}}{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)}}{12 i \, A + 11 \, B}\right) - 4 \, \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{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 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\right) + 4 \, \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{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 \, {\left(A - i \, B\right)} a^{2} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(32 i \, A^{2} + 64 \, A B - 32 i \, B^{2}\right)} a^{3}}{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)}}{{\left(2 i \, A + 2 \, B\right)} a}\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*(4*sqrt(2)*((4*A - 7*I*B)*a*e^(5*I*d*x + 5*I*c) + 4*I*B*a*e^(3*I*d*x + 3*I*c) - (4*A - 3*I*B)*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)) - sqrt((144*I*A^2 + 264*A*B - 121*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(((-576*I*A - 528*B)*a^2*e^(2*I*d*x + 2*I*c) + (192*I*A + 176*B)*a^2 + 32*sqrt(2)*sqrt((144*I*A^2 + 264*A*B - 121*I*B^2)*a^3/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)/(12*I*A + 11*B)) + sqrt((144*I*A^2 + 264*A*B - 121*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(((-576*I*A - 528*B)*a^2*e^(2*I*d*x + 2*I*c) + (192*I*A + 176*B)*a^2 - 32*sqrt(2)*sqrt((144*I*A^2 + 264*A*B - 121*I*B^2)*a^3/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)/(12*I*A + 11*B)) - 4*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)) + 4*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(-(8*(A - I*B)*a^2*e^(I*d*x + I*c) - sqrt(2)*sqrt((32*I*A^2 + 64*A*B - 32*I*B^2)*a^3/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)/((2*I*A + 2*B)*a)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
547,1,627,0,0.721843," ","integrate(cot(d*x+c)^(11/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, \sqrt{2} {\left(2 \, {\left(323 \, A - 300 i \, B\right)} a^{2} e^{\left(9 i \, d x + 9 i \, c\right)} - 27 \, {\left(61 \, A - 65 i \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + 63 \, {\left(37 \, A - 35 i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 1365 \, {\left(A - i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 315 \, {\left(A - i \, B\right)} 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{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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(16 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 315 \, \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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(16 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right)}{1260 \, {\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,"-1/1260*(16*sqrt(2)*(2*(323*A - 300*I*B)*a^2*e^(9*I*d*x + 9*I*c) - 27*(61*A - 65*I*B)*a^2*e^(7*I*d*x + 7*I*c) + 63*(37*A - 35*I*B)*a^2*e^(5*I*d*x + 5*I*c) - 1365*(A - I*B)*a^2*e^(3*I*d*x + 3*I*c) + 315*(A - I*B)*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((128*I*A^2 + 256*A*B - 128*I*B^2)*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(-(16*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)) + 315*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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(-(16*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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)/((4*I*A + 4*B)*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
548,1,572,0,0.515173," ","integrate(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(3200 i \, A + 2912 \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + {\left(-6160 i \, A - 6832 \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + {\left(5600 i \, A + 5600 \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-1680 i \, A - 1680 \, B\right)} 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}} + 105 \, \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - 105 \, \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\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*(sqrt(2)*((3200*I*A + 2912*B)*a^2*e^(7*I*d*x + 7*I*c) + (-6160*I*A - 6832*B)*a^2*e^(5*I*d*x + 5*I*c) + (5600*I*A + 5600*B)*a^2*e^(3*I*d*x + 3*I*c) + (-1680*I*A - 1680*B)*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)) + 105*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*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(-(16*(A - I*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)) - 105*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*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(-(16*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*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)/((4*I*A + 4*B)*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
549,1,513,0,0.539300," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, \sqrt{2} {\left(2 \, {\left(13 \, A - 10 i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 35 \, {\left(A - i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 15 \, {\left(A - i \, B\right)} 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{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 15 \, \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} 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)*(2*(13*A - 10*I*B)*a^2*e^(5*I*d*x + 5*I*c) - 35*(A - I*B)*a^2*e^(3*I*d*x + 3*I*c) + 15*(A - I*B)*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^2 + 256*A*B - 128*I*B^2)*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*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)) + 15*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
550,1,778,0,0.587610," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-64 i \, A - 24 \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(48 i \, A + 24 \, B\right)} 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{4 i \, B^{2} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(-\frac{{\left(48 \, B a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 16 \, B a^{3} - \sqrt{2} \sqrt{\frac{4 i \, B^{2} 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)}}{B a}\right) + 3 \, \sqrt{\frac{4 i \, B^{2} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(-\frac{{\left(48 \, B a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 16 \, B a^{3} - \sqrt{2} \sqrt{\frac{4 i \, B^{2} 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)}}{B a}\right) - 3 \, \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(-\frac{{\left(16 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 3 \, \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(-\frac{{\left(16 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} 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 - 24*B)*a^2*e^(3*I*d*x + 3*I*c) + (48*I*A + 24*B)*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(4*I*B^2*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(-(48*B*a^3*e^(2*I*d*x + 2*I*c) - 16*B*a^3 - sqrt(2)*sqrt(4*I*B^2*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)/(B*a)) + 3*sqrt(4*I*B^2*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(-(48*B*a^3*e^(2*I*d*x + 2*I*c) - 16*B*a^3 - sqrt(2)*sqrt(4*I*B^2*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)/(B*a)) - 3*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(-(16*(A - I*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)) + 3*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(-(16*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
551,1,842,0,0.535750," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left({\left(2 \, A - i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(2 \, A + i \, B\right)} 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{{\left(4 i \, A^{2} + 20 \, A B - 25 i \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left({\left(-96 i \, A - 240 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(32 i \, A + 80 \, B\right)} a^{3} + 32 \, \sqrt{2} \sqrt{\frac{{\left(4 i \, A^{2} + 20 \, A B - 25 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 5 \, B\right)} a}\right) + \sqrt{\frac{{\left(4 i \, A^{2} + 20 \, A B - 25 i \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left({\left(-96 i \, A - 240 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(32 i \, A + 80 \, B\right)} a^{3} - 32 \, \sqrt{2} \sqrt{\frac{{\left(4 i \, A^{2} + 20 \, A B - 25 i \, B^{2}\right)} 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)}}{{\left(2 i \, A + 5 \, B\right)} a}\right) - \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(-\frac{{\left(16 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(-\frac{{\left(16 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right)}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/4*(4*sqrt(2)*((2*A - I*B)*a^2*e^(3*I*d*x + 3*I*c) + (2*A + I*B)*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((4*I*A^2 + 20*A*B - 25*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(((-96*I*A - 240*B)*a^3*e^(2*I*d*x + 2*I*c) + (32*I*A + 80*B)*a^3 + 32*sqrt(2)*sqrt((4*I*A^2 + 20*A*B - 25*I*B^2)*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)/((2*I*A + 5*B)*a)) + sqrt((4*I*A^2 + 20*A*B - 25*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(((-96*I*A - 240*B)*a^3*e^(2*I*d*x + 2*I*c) + (32*I*A + 80*B)*a^3 - 32*sqrt(2)*sqrt((4*I*A^2 + 20*A*B - 25*I*B^2)*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)/((2*I*A + 5*B)*a)) - sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(-(16*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)) + sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(-(16*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
552,1,921,0,0.562886," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left({\left(4 i \, A + 11 \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 4 \, B a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + {\left(-4 i \, A - 7 \, B\right)} 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{{\left(-400 i \, A^{2} - 920 \, A B + 529 i \, B^{2}\right)} 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 \, {\left(-960 i \, A - 1104 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(320 i \, A + 368 \, B\right)} a^{3} + \sqrt{2} \sqrt{\frac{{\left(-400 i \, A^{2} - 920 \, A B + 529 i \, B^{2}\right)} a^{5}}{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)}}{4 \, {\left(20 i \, A + 23 \, B\right)} a}\right) - \sqrt{\frac{{\left(-400 i \, A^{2} - 920 \, A B + 529 i \, B^{2}\right)} 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 \, {\left(-960 i \, A - 1104 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, {\left(320 i \, A + 368 \, B\right)} a^{3} + \sqrt{2} \sqrt{\frac{{\left(-400 i \, A^{2} - 920 \, A B + 529 i \, B^{2}\right)} a^{5}}{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)}}{4 \, {\left(20 i \, A + 23 \, B\right)} a}\right) + 4 \, \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) - 4 \, \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(-128 i \, A^{2} - 256 \, A B + 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\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*(4*sqrt(2)*((4*I*A + 11*B)*a^2*e^(5*I*d*x + 5*I*c) - 4*B*a^2*e^(3*I*d*x + 3*I*c) + (-4*I*A - 7*B)*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((-400*I*A^2 - 920*A*B + 529*I*B^2)*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*(-960*I*A - 1104*B)*a^3*e^(2*I*d*x + 2*I*c) + 4*(320*I*A + 368*B)*a^3 + sqrt(2)*sqrt((-400*I*A^2 - 920*A*B + 529*I*B^2)*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)/((20*I*A + 23*B)*a)) - sqrt((-400*I*A^2 - 920*A*B + 529*I*B^2)*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*(-960*I*A - 1104*B)*a^3*e^(2*I*d*x + 2*I*c) + 4*(320*I*A + 368*B)*a^3 + sqrt(2)*sqrt((-400*I*A^2 - 920*A*B + 529*I*B^2)*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)/((20*I*A + 23*B)*a)) + 4*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*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*(A - I*B)*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)) - 4*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*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*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((-128*I*A^2 - 256*A*B + 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
553,1,1007,0,0.644525," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left({\left(66 \, A - 91 i \, B\right)} a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + 7 \, {\left(6 \, A - i \, B\right)} a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - {\left(66 \, A - 59 i \, B\right)} a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 3 \, {\left(14 \, A - 13 i \, B\right)} 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{{\left(2116 i \, A^{2} + 4140 \, A B - 2025 i \, B^{2}\right)} 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({\left(-2208 i \, A - 2160 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(736 i \, A + 720 \, B\right)} a^{3} + 32 \, \sqrt{2} \sqrt{\frac{{\left(2116 i \, A^{2} + 4140 \, A B - 2025 i \, B^{2}\right)} 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)}}{{\left(46 i \, A + 45 \, B\right)} a}\right) + 3 \, \sqrt{\frac{{\left(2116 i \, A^{2} + 4140 \, A B - 2025 i \, B^{2}\right)} 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({\left(-2208 i \, A - 2160 \, B\right)} a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(736 i \, A + 720 \, B\right)} a^{3} - 32 \, \sqrt{2} \sqrt{\frac{{\left(2116 i \, A^{2} + 4140 \, A B - 2025 i \, B^{2}\right)} 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)}}{{\left(46 i \, A + 45 \, B\right)} a}\right) - 24 \, \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right) + 24 \, \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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 \, {\left(A - i \, B\right)} a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{{\left(128 i \, A^{2} + 256 \, A B - 128 i \, B^{2}\right)} 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)}}{{\left(4 i \, A + 4 \, B\right)} a^{2}}\right)}{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*(4*sqrt(2)*((66*A - 91*I*B)*a^2*e^(7*I*d*x + 7*I*c) + 7*(6*A - I*B)*a^2*e^(5*I*d*x + 5*I*c) - (66*A - 59*I*B)*a^2*e^(3*I*d*x + 3*I*c) - 3*(14*A - 13*I*B)*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((2116*I*A^2 + 4140*A*B - 2025*I*B^2)*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(((-2208*I*A - 2160*B)*a^3*e^(2*I*d*x + 2*I*c) + (736*I*A + 720*B)*a^3 + 32*sqrt(2)*sqrt((2116*I*A^2 + 4140*A*B - 2025*I*B^2)*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)/((46*I*A + 45*B)*a)) + 3*sqrt((2116*I*A^2 + 4140*A*B - 2025*I*B^2)*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(((-2208*I*A - 2160*B)*a^3*e^(2*I*d*x + 2*I*c) + (736*I*A + 720*B)*a^3 - 32*sqrt(2)*sqrt((2116*I*A^2 + 4140*A*B - 2025*I*B^2)*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)/((46*I*A + 45*B)*a)) - 24*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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(-(16*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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)/((4*I*A + 4*B)*a^2)) + 24*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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(-(16*(A - I*B)*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt((128*I*A^2 + 256*A*B - 128*I*B^2)*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)/((4*I*A + 4*B)*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
554,1,482,0,0.578475," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(14 i \, A - 30 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-36 i \, A + 36 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i \, A - 6 \, B\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(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^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} \log\left(-\frac{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^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} + 2 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} \log\left(\frac{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^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} - 2 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\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)*((14*I*A - 30*B)*e^(4*I*d*x + 4*I*c) + (-36*I*A + 36*B)*e^(2*I*d*x + 2*I*c) + 6*I*A - 6*B)*sqrt(a/(e^(2*I*d*x + 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*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(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^2 - 4*A*B + 2*I*B^2)/(a*d^2)) + 2*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 3*(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(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^2 - 4*A*B + 2*I*B^2)/(a*d^2)) - 2*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)))/(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))","B",0
555,1,422,0,0.482167," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\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^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\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^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 2 \, \sqrt{2} {\left({\left(5 \, A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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 d}"," ",0,"1/4*(a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(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^2 + 4*A*B - 2*I*B^2)/(a*d^2)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(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^2 + 4*A*B - 2*I*B^2)/(a*d^2)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 2*sqrt(2)*((5*A + I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*sqrt(a/(e^(2*I*d*x + 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*d)","B",0
556,1,421,0,0.539828," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{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^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} + 2 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - a d \sqrt{\frac{-2 i \, A^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{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^{2} - 4 \, A B + 2 i \, B^{2}}{a d^{2}}} - 2 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + \sqrt{2} {\left({\left(-2 i \, A + 2 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, A - 2 \, B\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 d}"," ",0,"1/4*(a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(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^2 - 4*A*B + 2*I*B^2)/(a*d^2)) + 2*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - a*d*sqrt((-2*I*A^2 - 4*A*B + 2*I*B^2)/(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^2 - 4*A*B + 2*I*B^2)/(a*d^2)) - 2*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + sqrt(2)*((-2*I*A + 2*B)*e^(2*I*d*x + 2*I*c) + 2*I*A - 2*B)*sqrt(a/(e^(2*I*d*x + 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*d)","B",0
557,1,732,0,0.683163," ","integrate((A+B*tan(d*x+c))/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^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\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^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - a d \sqrt{\frac{2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\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^{2} + 4 \, A B - 2 i \, B^{2}}{a d^{2}}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - a d \sqrt{-\frac{4 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{16 \, {\left(3 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - B a^{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{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 \, B^{2}}{a d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{B}\right) + a d \sqrt{-\frac{4 i \, B^{2}}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{16 \, {\left(3 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - B a^{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{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 \, B^{2}}{a d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{B}\right) - 2 \, \sqrt{2} {\left({\left(A + i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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 d}"," ",0,"-1/4*(a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(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^2 + 4*A*B - 2*I*B^2)/(a*d^2)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - a*d*sqrt((2*I*A^2 + 4*A*B - 2*I*B^2)/(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^2 + 4*A*B - 2*I*B^2)/(a*d^2)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - a*d*sqrt(-4*I*B^2/(a*d^2))*e^(I*d*x + I*c)*log(-16*(3*B*a^2*e^(2*I*d*x + 2*I*c) - B*a^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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I*B^2/(a*d^2)))*e^(-2*I*d*x - 2*I*c)/B) + a*d*sqrt(-4*I*B^2/(a*d^2))*e^(I*d*x + I*c)*log(-16*(3*B*a^2*e^(2*I*d*x + 2*I*c) - B*a^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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I*B^2/(a*d^2)))*e^(-2*I*d*x - 2*I*c)/B) - 2*sqrt(2)*((A + I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*sqrt(a/(e^(2*I*d*x + 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*d)","B",0
558,1,466,0,0.784154," ","integrate(cot(d*x+c)^(3/2)*(A+B*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{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \sqrt{2} {\left(2 \, {\left(19 \, A + 4 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(13 \, A + 7 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*sqrt(1/2)*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*sqrt(1/2)*(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((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 3*sqrt(1/2)*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*sqrt(1/2)*(-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((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*(2*(19*A + 4*I*B)*e^(4*I*d*x + 4*I*c) - (13*A + 7*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^2*d)","B",0
559,1,462,0,0.478223," ","integrate(cot(d*x+c)^(1/2)*(A+B*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{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{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{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} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} + {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{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{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} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} - {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + \sqrt{2} {\left({\left(-8 i \, A + 2 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(7 i \, A - B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\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(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2)) + (A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 3*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2)) - (A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + sqrt(2)*((-8*I*A + 2*B)*e^(4*I*d*x + 4*I*c) + (7*I*A - B)*e^(2*I*d*x + 2*I*c) + I*A - B)*sqrt(a/(e^(2*I*d*x + 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)/(a^2*d)","B",0
560,1,462,0,0.527916," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{3} d^{2}}} - 4 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \sqrt{2} {\left(2 \, {\left(A - 2 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(A - 5 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - A - i \, B\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(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"-1/12*(3*sqrt(1/2)*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*sqrt(1/2)*(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((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 3*sqrt(1/2)*a^2*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*sqrt(1/2)*(-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((I*A^2 + 2*A*B - I*B^2)/(a^3*d^2)) - 4*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*(2*(A - 2*I*B)*e^(4*I*d*x + 4*I*c) - (A - 5*I*B)*e^(2*I*d*x + 2*I*c) - A - I*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^2*d)","B",0
561,1,781,0,0.517185," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{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{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} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} + {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{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{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} - 2 \, A B + i \, B^{2}}{a^{3} d^{2}}} - {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + 3 \, a^{2} d \sqrt{\frac{4 i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{{\left(48 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 16 \, B a^{2} - \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 \, B^{2}}{a^{3} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{B}\right) - 3 \, a^{2} d \sqrt{\frac{4 i \, B^{2}}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{{\left(48 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 16 \, B a^{2} - \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 \, B^{2}}{a^{3} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{B}\right) - \sqrt{2} {\left({\left(-4 i \, A + 10 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(5 i \, A - 11 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\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(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"-1/12*(3*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2)) + (A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 3*sqrt(1/2)*a^2*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^3*d^2)) - (A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + 3*a^2*d*sqrt(4*I*B^2/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-(48*B*a^2*e^(2*I*d*x + 2*I*c) - 16*B*a^2 - 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*B^2/(a^3*d^2)))*e^(-2*I*d*x - 2*I*c)/B) - 3*a^2*d*sqrt(4*I*B^2/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-(48*B*a^2*e^(2*I*d*x + 2*I*c) - 16*B*a^2 - 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*B^2/(a^3*d^2)))*e^(-2*I*d*x - 2*I*c)/B) - sqrt(2)*((-4*I*A + 10*B)*e^(4*I*d*x + 4*I*c) + (5*I*A - 11*B)*e^(2*I*d*x + 2*I*c) - I*A + B)*sqrt(a/(e^(2*I*d*x + 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)/(a^2*d)","B",0
562,1,485,0,0.519784," ","integrate(cot(d*x+c)^(3/2)*(A+B*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{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} - 8 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} - 8 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - \sqrt{2} {\left({\left(463 \, A + 83 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, {\left(97 \, A + 32 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(13 \, A + 8 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, A - 3 i \, B\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(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(15*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(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((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2)) - 8*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 15*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(-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((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2)) - 8*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*((463*A + 83*I*B)*e^(6*I*d*x + 6*I*c) - 2*(97*A + 32*I*B)*e^(4*I*d*x + 4*I*c) - 2*(13*A + 8*I*B)*e^(2*I*d*x + 2*I*c) - 3*A - 3*I*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^3*d)","B",0
563,1,479,0,0.496134," ","integrate(cot(d*x+c)^(1/2)*(A+B*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{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-\frac{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{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} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} + {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{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{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} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} - {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) + \sqrt{2} {\left({\left(-83 i \, A + 3 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(64 i \, A + 6 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(16 i \, A - 6 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, A - 3 \, B\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(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(15*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2)) + (A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 15*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2)) - (A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) + sqrt(2)*((-83*I*A + 3*B)*e^(6*I*d*x + 6*I*c) + (64*I*A + 6*B)*e^(4*I*d*x + 4*I*c) + (16*I*A - 6*B)*e^(2*I*d*x + 2*I*c) + 3*I*A - 3*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^3*d)","B",0
564,1,485,0,0.467554," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} - 8 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} - 8 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - \sqrt{2} {\left({\left(3 \, A - 17 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, {\left(3 \, A + 8 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(3 \, A - 2 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, A - 3 i \, B\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(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"-1/120*(15*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(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((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2)) - 8*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 15*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(-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((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2)) - 8*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*((3*A - 17*I*B)*e^(6*I*d*x + 6*I*c) + 2*(3*A + 8*I*B)*e^(4*I*d*x + 4*I*c) - 2*(3*A - 2*I*B)*e^(2*I*d*x + 2*I*c) - 3*A - 3*I*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^3*d)","B",0
565,1,480,0,0.607317," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-\frac{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{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} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} + {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{-i \, A^{2} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{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{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} - 2 \, A B + i \, B^{2}}{a^{5} d^{2}}} - {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{i \, A + B}\right) - \sqrt{2} {\left({\left(-17 i \, A - 23 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(16 i \, A + 34 \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(4 i \, A - 14 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, A + 3 \, B\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(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"-1/120*(15*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2)) + (A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 15*sqrt(1/2)*a^3*d*sqrt((-I*A^2 - 2*A*B + I*B^2)/(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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt((-I*A^2 - 2*A*B + I*B^2)/(a^5*d^2)) - (A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - sqrt(2)*((-17*I*A - 23*B)*e^(6*I*d*x + 6*I*c) + (16*I*A + 34*B)*e^(4*I*d*x + 4*I*c) + (4*I*A - 14*B)*e^(2*I*d*x + 2*I*c) - 3*I*A + 3*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^3*d)","B",0
566,1,802,0,0.540720," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} - 8 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{i \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{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 \, A^{2} + 2 \, A B - i \, B^{2}}{a^{5} d^{2}}} - 8 \, {\left(A - i \, B\right)} a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, {\left(i \, A + B\right)}}\right) - 30 \, a^{3} d \sqrt{-\frac{4 i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-\frac{16 \, {\left(3 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - B a^{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{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 \, B^{2}}{a^{5} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{B}\right) + 30 \, a^{3} d \sqrt{-\frac{4 i \, B^{2}}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-\frac{16 \, {\left(3 \, B a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - B a^{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{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 \, B^{2}}{a^{5} d^{2}}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{B}\right) - \sqrt{2} {\left({\left(23 \, A + 123 i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, {\left(17 \, A + 72 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(7 \, A + 12 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, A - 3 i \, B\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(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(15*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(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((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2)) - 8*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 15*sqrt(1/2)*a^3*d*sqrt((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(-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((I*A^2 + 2*A*B - I*B^2)/(a^5*d^2)) - 8*(A - I*B)*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/(I*A + B)) - 30*a^3*d*sqrt(-4*I*B^2/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-16*(3*B*a^2*e^(2*I*d*x + 2*I*c) - B*a^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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I*B^2/(a^5*d^2)))*e^(-2*I*d*x - 2*I*c)/B) + 30*a^3*d*sqrt(-4*I*B^2/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-16*(3*B*a^2*e^(2*I*d*x + 2*I*c) - B*a^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((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I*B^2/(a^5*d^2)))*e^(-2*I*d*x - 2*I*c)/B) - sqrt(2)*((23*A + 123*I*B)*e^(6*I*d*x + 6*I*c) - 2*(17*A + 72*I*B)*e^(4*I*d*x + 4*I*c) + 2*(7*A + 12*I*B)*e^(2*I*d*x + 2*I*c) - 3*A - 3*I*B)*sqrt(a/(e^(2*I*d*x + 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)/(a^3*d)","B",0
567,0,0,0,0.508373," ","integrate(cot(d*x+c)^m*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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} \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}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(((A - I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))^m/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
568,0,0,0,0.457088," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left({\left(A - i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, A e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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}}}{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(-((A - I*B)*e^(4*I*d*x + 4*I*c) + 2*A*e^(2*I*d*x + 2*I*c) + A + I*B)*(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), x)","F",0
569,0,0,0,0.469530," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(i \, A + B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} \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}}}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}, x\right)"," ",0,"integral(((I*A + B)*e^(2*I*d*x + 2*I*c) + I*A - B)*(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^(2*I*d*x + 2*I*c) - 1), x)","F",0
570,0,0,0,0.582905," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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}}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(((A - I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*(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^(2*I*d*x + 2*I*c) + 1), x)","F",0
571,0,0,0,0.566157," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(-i \, A - B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, B e^{\left(2 i \, d x + 2 i \, c\right)} + i \, A - B\right)} \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}}}{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(((-I*A - B)*e^(4*I*d*x + 4*I*c) + 2*B*e^(2*I*d*x + 2*I*c) + I*A - B)*(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), x)","F",0
572,0,0,0,0.603870," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left({\left(A - i \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(A - 3 i \, B\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(A + 3 i \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + A + i \, B\right)} \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}}}{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(-((A - I*B)*e^(6*I*d*x + 6*I*c) - (A - 3*I*B)*e^(4*I*d*x + 4*I*c) - (A + 3*I*B)*e^(2*I*d*x + 2*I*c) + A + I*B)*(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^(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
573,0,0,0,0.503674," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(i \, A + B\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-2 i \, A - 4 \, B\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, B e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(2 i \, A - 4 \, B\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, A + B\right)} \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}}}{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(((I*A + B)*e^(8*I*d*x + 8*I*c) + (-2*I*A - 4*B)*e^(6*I*d*x + 6*I*c) + 6*B*e^(4*I*d*x + 4*I*c) + (2*I*A - 4*B)*e^(2*I*d*x + 2*I*c) - I*A + B)*(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^(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
574,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
577,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
598,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
599,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
600,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
603,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
604,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
605,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
606,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
607,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
608,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
609,-2,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
610,-2,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
611,-2,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
612,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(13/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
639,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
640,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
641,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
642,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
645,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
646,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
647,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
648,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
649,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
650,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
651,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
652,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
653,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
654,-1,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/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
655,-1,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/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
656,0,0,0,1.858460," ","integrate(cot(d*x+c)^m*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n} \cot\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^n*cot(d*x + c)^m, x)","F",0
657,0,0,0,1.788144," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cot\left(d x + c\right) \tan\left(d x + c\right) + A \cot\left(d x + c\right)\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sqrt{\cot\left(d x + c\right)}, x\right)"," ",0,"integral((B*cot(d*x + c)*tan(d*x + c) + A*cot(d*x + c))*(b*tan(d*x + c) + a)^n*sqrt(cot(d*x + c)), x)","F",0
658,0,0,0,0.945183," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*sqrt(cot(d*x + c)), x)","F",0
659,0,0,0,0.925000," ","integrate((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n/sqrt(cot(d*x + c)), x)","F",0
660,0,0,0,1.440228," ","integrate((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n/cot(d*x + c)^(3/2), x)","F",0
661,0,0,0,1.008250," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right)^{2} + A \tan\left(d x + c\right)\right)} {\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)^2 + A*tan(d*x + c))*(b*tan(d*x + c) + a)^n*sqrt(tan(d*x + c)), x)","F",0
662,0,0,0,0.672967," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*sqrt(tan(d*x + c)), x)","F",0
663,0,0,0,0.944955," ","integrate((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n/sqrt(tan(d*x + c)), x)","F",0
664,0,0,0,1.686377," ","integrate((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n/tan(d*x + c)^(3/2), x)","F",0
665,1,93,0,1.889972," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x, algorithm=""fricas"")","\frac{{\left({\left(i \, A - B\right)} a n + {\left(i \, A + B\right)} a + {\left({\left(i \, A + B\right)} a n + {\left(i \, A + B\right)} a\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,"((I*A - B)*a*n + (I*A + B)*a + ((I*A + B)*a*n + (I*A + B)*a)*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
666,1,99,0,1.163084," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(20 i \, A + 20 \, B\right)} a c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(20 i \, A - 12 \, B\right)} a 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*((20*I*A + 20*B)*a*c^4*e^(2*I*f*x + 2*I*e) + (20*I*A - 12*B)*a*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)","B",0
667,1,87,0,0.997279," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(8 i \, A + 8 \, B\right)} a c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, A - 4 \, B\right)} a 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*((8*I*A + 8*B)*a*c^3*e^(2*I*f*x + 2*I*e) + (8*I*A - 4*B)*a*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
668,1,75,0,0.559172," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(6 i \, A + 6 \, B\right)} a c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 i \, A - 2 \, B\right)} a 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*((6*I*A + 6*B)*a*c^2*e^(2*I*f*x + 2*I*e) + (6*I*A - 2*B)*a*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)","A",0
669,1,53,0,0.844020," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 i \, A + 2 \, B\right)} a c e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, A a 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,"((2*I*A + 2*B)*a*c*e^(2*I*f*x + 2*I*e) + 2*I*A*a*c)/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","C",0
670,1,64,0,1.708232," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, B a - {\left({\left(-i \, A - B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A - B\right)} a\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*B*a - ((-I*A - B)*a*e^(2*I*f*x + 2*I*e) + (-I*A - B)*a)*log(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(2*I*f*x + 2*I*e) + f)","A",0
671,1,43,0,1.204862," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(-i \, A - B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, B a \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{2 \, c f}"," ",0,"1/2*((-I*A - B)*a*e^(2*I*f*x + 2*I*e) + 2*B*a*log(e^(2*I*f*x + 2*I*e) + 1))/(c*f)","A",0
672,1,45,0,0.639737," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(-i \, A - B\right)} a e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-2 i \, A + 2 \, B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)}}{8 \, c^{2} f}"," ",0,"1/8*((-I*A - B)*a*e^(4*I*f*x + 4*I*e) + (-2*I*A + 2*B)*a*e^(2*I*f*x + 2*I*e))/(c^2*f)","A",0
673,1,58,0,0.844537," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(-i \, A - B\right)} a e^{\left(6 i \, f x + 6 i \, e\right)} - 3 i \, A a e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-3 i \, A + 3 \, B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)}}{24 \, c^{3} f}"," ",0,"1/24*((-I*A - B)*a*e^(6*I*f*x + 6*I*e) - 3*I*A*a*e^(4*I*f*x + 4*I*e) + (-3*I*A + 3*B)*a*e^(2*I*f*x + 2*I*e))/(c^3*f)","A",0
674,1,81,0,0.662767," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(-3 i \, A - 3 \, B\right)} a e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-12 i \, A - 4 \, B\right)} a e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-18 i \, A + 6 \, B\right)} a e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-12 i \, A + 12 \, B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)}}{192 \, c^{4} f}"," ",0,"1/192*((-3*I*A - 3*B)*a*e^(8*I*f*x + 8*I*e) + (-12*I*A - 4*B)*a*e^(6*I*f*x + 6*I*e) + (-18*I*A + 6*B)*a*e^(4*I*f*x + 4*I*e) + (-12*I*A + 12*B)*a*e^(2*I*f*x + 2*I*e))/(c^4*f)","A",0
675,1,94,0,1.058481," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^5,x, algorithm=""fricas"")","\frac{{\left(-2 i \, A - 2 \, B\right)} a e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-10 i \, A - 5 \, B\right)} a e^{\left(8 i \, f x + 8 i \, e\right)} - 20 i \, A a e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-20 i \, A + 10 \, B\right)} a e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-10 i \, A + 10 \, B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)}}{320 \, c^{5} f}"," ",0,"1/320*((-2*I*A - 2*B)*a*e^(10*I*f*x + 10*I*e) + (-10*I*A - 5*B)*a*e^(8*I*f*x + 8*I*e) - 20*I*A*a*e^(6*I*f*x + 6*I*e) + (-20*I*A + 10*B)*a*e^(4*I*f*x + 4*I*e) + (-10*I*A + 10*B)*a*e^(2*I*f*x + 2*I*e))/(c^5*f)","B",0
676,1,205,0,0.939865," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x, algorithm=""fricas"")","\frac{{\left({\left(2 i \, A - 2 \, B\right)} a^{2} n + {\left(4 i \, A + 4 \, B\right)} a^{2} + {\left({\left(2 i \, A + 2 \, B\right)} a^{2} n^{2} + {\left(6 i \, A + 6 \, B\right)} a^{2} n + {\left(4 i \, A + 4 \, B\right)} a^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left({\left(2 i \, A - 2 \, B\right)} a^{2} n^{2} + 8 i \, A a^{2} n + {\left(8 i \, A + 8 \, B\right)} 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^{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,"((2*I*A - 2*B)*a^2*n + (4*I*A + 4*B)*a^2 + ((2*I*A + 2*B)*a^2*n^2 + (6*I*A + 6*B)*a^2*n + (4*I*A + 4*B)*a^2)*e^(4*I*f*x + 4*I*e) + ((2*I*A - 2*B)*a^2*n^2 + 8*I*A*a^2*n + (8*I*A + 8*B)*a^2)*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))","B",0
677,1,150,0,0.852838," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5,x, algorithm=""fricas"")","\frac{{\left(1344 i \, A + 1344 \, B\right)} a^{2} c^{5} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(1568 i \, A - 672 \, B\right)} a^{2} c^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(224 i \, A - 96 \, B\right)} a^{2} c^{5}}{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*((1344*I*A + 1344*B)*a^2*c^5*e^(4*I*f*x + 4*I*e) + (1568*I*A - 672*B)*a^2*c^5*e^(2*I*f*x + 2*I*e) + (224*I*A - 96*B)*a^2*c^5)/(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)","A",0
678,1,138,0,0.867131," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(120 i \, A + 120 \, B\right)} a^{2} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(144 i \, A - 48 \, B\right)} a^{2} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(24 i \, A - 8 \, B\right)} a^{2} 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*((120*I*A + 120*B)*a^2*c^4*e^(4*I*f*x + 4*I*e) + (144*I*A - 48*B)*a^2*c^4*e^(2*I*f*x + 2*I*e) + (24*I*A - 8*B)*a^2*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
679,1,126,0,1.301589," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(80 i \, A + 80 \, B\right)} a^{2} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(100 i \, A - 20 \, B\right)} a^{2} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(20 i \, A - 4 \, B\right)} a^{2} 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*((80*I*A + 80*B)*a^2*c^3*e^(4*I*f*x + 4*I*e) + (100*I*A - 20*B)*a^2*c^3*e^(2*I*f*x + 2*I*e) + (20*I*A - 4*B)*a^2*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)","A",0
680,1,104,0,0.679197," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(12 i \, A + 12 \, B\right)} a^{2} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 16 i \, A a^{2} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, A a^{2} 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*((12*I*A + 12*B)*a^2*c^2*e^(4*I*f*x + 4*I*e) + 16*I*A*a^2*c^2*e^(2*I*f*x + 2*I*e) + 4*I*A*a^2*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)","C",0
681,1,96,0,1.087198," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(12 i \, A + 12 \, B\right)} a^{2} c e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(18 i \, A + 6 \, B\right)} a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 i \, A + 2 \, B\right)} a^{2} 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*((12*I*A + 12*B)*a^2*c*e^(4*I*f*x + 4*I*e) + (18*I*A + 6*B)*a^2*c*e^(2*I*f*x + 2*I*e) + (6*I*A + 2*B)*a^2*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)","A",0
682,1,125,0,0.657135," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(-2 i \, A - 6 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-2 i \, A - 4 \, B\right)} a^{2} + {\left({\left(-2 i \, A - 2 \, B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-4 i \, A - 4 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-2 i \, A - 2 \, B\right)} a^{2}\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,"((-2*I*A - 6*B)*a^2*e^(2*I*f*x + 2*I*e) + (-2*I*A - 4*B)*a^2 + ((-2*I*A - 2*B)*a^2*e^(4*I*f*x + 4*I*e) + (-4*I*A - 4*B)*a^2*e^(2*I*f*x + 2*I*e) + (-2*I*A - 2*B)*a^2)*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
683,1,111,0,0.641188," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(-i \, A - B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-i \, A - B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, B a^{2} + {\left({\left(i \, A + 3 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A + 3 \, B\right)} a^{2}\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,"((-I*A - B)*a^2*e^(4*I*f*x + 4*I*e) + (-I*A - B)*a^2*e^(2*I*f*x + 2*I*e) + 2*B*a^2 + ((I*A + 3*B)*a^2*e^(2*I*f*x + 2*I*e) + (I*A + 3*B)*a^2)*log(e^(2*I*f*x + 2*I*e) + 1))/(c*f*e^(2*I*f*x + 2*I*e) + c*f)","A",0
684,1,62,0,0.692977," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(-i \, A - B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, B a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 4 \, B a^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{4 \, c^{2} f}"," ",0,"1/4*((-I*A - B)*a^2*e^(4*I*f*x + 4*I*e) + 4*B*a^2*e^(2*I*f*x + 2*I*e) - 4*B*a^2*log(e^(2*I*f*x + 2*I*e) + 1))/(c^2*f)","A",0
685,1,49,0,0.581589," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(-2 i \, A - 2 \, B\right)} a^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-3 i \, A + 3 \, B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)}}{24 \, c^{3} f}"," ",0,"1/24*((-2*I*A - 2*B)*a^2*e^(6*I*f*x + 6*I*e) + (-3*I*A + 3*B)*a^2*e^(4*I*f*x + 4*I*e))/(c^3*f)","A",0
686,1,64,0,0.772683," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(-3 i \, A - 3 \, B\right)} a^{2} e^{\left(8 i \, f x + 8 i \, e\right)} - 8 i \, A a^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-6 i \, A + 6 \, B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)}}{96 \, c^{4} f}"," ",0,"1/96*((-3*I*A - 3*B)*a^2*e^(8*I*f*x + 8*I*e) - 8*I*A*a^2*e^(6*I*f*x + 6*I*e) + (-6*I*A + 6*B)*a^2*e^(4*I*f*x + 4*I*e))/(c^4*f)","A",0
687,1,89,0,1.611424," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^5,x, algorithm=""fricas"")","\frac{{\left(-12 i \, A - 12 \, B\right)} a^{2} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-45 i \, A - 15 \, B\right)} a^{2} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-60 i \, A + 20 \, B\right)} a^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-30 i \, A + 30 \, B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)}}{960 \, c^{5} f}"," ",0,"1/960*((-12*I*A - 12*B)*a^2*e^(10*I*f*x + 10*I*e) + (-45*I*A - 15*B)*a^2*e^(8*I*f*x + 8*I*e) + (-60*I*A + 20*B)*a^2*e^(6*I*f*x + 6*I*e) + (-30*I*A + 30*B)*a^2*e^(4*I*f*x + 4*I*e))/(c^5*f)","A",0
688,1,104,0,0.881007," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^6,x, algorithm=""fricas"")","\frac{{\left(-5 i \, A - 5 \, B\right)} a^{2} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-24 i \, A - 12 \, B\right)} a^{2} e^{\left(10 i \, f x + 10 i \, e\right)} - 45 i \, A a^{2} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-40 i \, A + 20 \, B\right)} a^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-15 i \, A + 15 \, B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)}}{960 \, c^{6} f}"," ",0,"1/960*((-5*I*A - 5*B)*a^2*e^(12*I*f*x + 12*I*e) + (-24*I*A - 12*B)*a^2*e^(10*I*f*x + 10*I*e) - 45*I*A*a^2*e^(8*I*f*x + 8*I*e) + (-40*I*A + 20*B)*a^2*e^(6*I*f*x + 6*I*e) + (-15*I*A + 15*B)*a^2*e^(4*I*f*x + 4*I*e))/(c^6*f)","A",0
689,1,332,0,2.986131," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x, algorithm=""fricas"")","\frac{{\left({\left(8 i \, A - 8 \, B\right)} a^{3} n + {\left(24 i \, A + 24 \, B\right)} a^{3} + {\left({\left(4 i \, A + 4 \, B\right)} a^{3} n^{3} + {\left(24 i \, A + 24 \, B\right)} a^{3} n^{2} + {\left(44 i \, A + 44 \, B\right)} a^{3} n + {\left(24 i \, A + 24 \, B\right)} a^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left({\left(4 i \, A - 4 \, B\right)} a^{3} n^{3} + {\left(32 i \, A - 8 \, B\right)} a^{3} n^{2} + {\left(84 i \, A + 36 \, B\right)} a^{3} n + {\left(72 i \, A + 72 \, B\right)} a^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left({\left(8 i \, A - 8 \, B\right)} a^{3} n^{2} + 48 i \, A a^{3} n + {\left(72 i \, A + 72 \, B\right)} 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^{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,"((8*I*A - 8*B)*a^3*n + (24*I*A + 24*B)*a^3 + ((4*I*A + 4*B)*a^3*n^3 + (24*I*A + 24*B)*a^3*n^2 + (44*I*A + 44*B)*a^3*n + (24*I*A + 24*B)*a^3)*e^(6*I*f*x + 6*I*e) + ((4*I*A - 4*B)*a^3*n^3 + (32*I*A - 8*B)*a^3*n^2 + (84*I*A + 36*B)*a^3*n + (72*I*A + 72*B)*a^3)*e^(4*I*f*x + 4*I*e) + ((8*I*A - 8*B)*a^3*n^2 + 48*I*A*a^3*n + (72*I*A + 72*B)*a^3)*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
690,1,197,0,0.867642," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^6,x, algorithm=""fricas"")","\frac{{\left(2688 i \, A + 2688 \, B\right)} a^{3} c^{6} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(3456 i \, A - 1152 \, B\right)} a^{3} c^{6} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(864 i \, A - 288 \, B\right)} a^{3} c^{6} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(96 i \, A - 32 \, B\right)} a^{3} c^{6}}{63 \, {\left(f e^{\left(18 i \, f x + 18 i \, e\right)} + 9 \, f e^{\left(16 i \, f x + 16 i \, e\right)} + 36 \, f e^{\left(14 i \, f x + 14 i \, e\right)} + 84 \, f e^{\left(12 i \, f x + 12 i \, e\right)} + 126 \, f e^{\left(10 i \, f x + 10 i \, e\right)} + 126 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 84 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 36 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 9 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/63*((2688*I*A + 2688*B)*a^3*c^6*e^(6*I*f*x + 6*I*e) + (3456*I*A - 1152*B)*a^3*c^6*e^(4*I*f*x + 4*I*e) + (864*I*A - 288*B)*a^3*c^6*e^(2*I*f*x + 2*I*e) + (96*I*A - 32*B)*a^3*c^6)/(f*e^(18*I*f*x + 18*I*e) + 9*f*e^(16*I*f*x + 16*I*e) + 36*f*e^(14*I*f*x + 14*I*e) + 84*f*e^(12*I*f*x + 12*I*e) + 126*f*e^(10*I*f*x + 10*I*e) + 126*f*e^(8*I*f*x + 8*I*e) + 84*f*e^(6*I*f*x + 6*I*e) + 36*f*e^(4*I*f*x + 4*I*e) + 9*f*e^(2*I*f*x + 2*I*e) + f)","A",0
691,1,185,0,0.815610," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5,x, algorithm=""fricas"")","\frac{{\left(2688 i \, A + 2688 \, B\right)} a^{3} c^{5} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(3584 i \, A - 896 \, B\right)} a^{3} c^{5} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(1024 i \, A - 256 \, B\right)} a^{3} c^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(128 i \, A - 32 \, B\right)} a^{3} c^{5}}{105 \, {\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,"1/105*((2688*I*A + 2688*B)*a^3*c^5*e^(6*I*f*x + 6*I*e) + (3584*I*A - 896*B)*a^3*c^5*e^(4*I*f*x + 4*I*e) + (1024*I*A - 256*B)*a^3*c^5*e^(2*I*f*x + 2*I*e) + (128*I*A - 32*B)*a^3*c^5)/(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
692,1,173,0,0.679542," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(1680 i \, A + 1680 \, B\right)} a^{3} c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(2352 i \, A - 336 \, B\right)} a^{3} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(784 i \, A - 112 \, B\right)} a^{3} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(112 i \, A - 16 \, B\right)} a^{3} c^{4}}{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*((1680*I*A + 1680*B)*a^3*c^4*e^(6*I*f*x + 6*I*e) + (2352*I*A - 336*B)*a^3*c^4*e^(4*I*f*x + 4*I*e) + (784*I*A - 112*B)*a^3*c^4*e^(2*I*f*x + 2*I*e) + (112*I*A - 16*B)*a^3*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)","A",0
693,1,146,0,0.821577," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(160 i \, A + 160 \, B\right)} a^{3} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + 240 i \, A a^{3} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 96 i \, A a^{3} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, A a^{3} 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*((160*I*A + 160*B)*a^3*c^3*e^(6*I*f*x + 6*I*e) + 240*I*A*a^3*c^3*e^(4*I*f*x + 4*I*e) + 96*I*A*a^3*c^3*e^(2*I*f*x + 2*I*e) + 16*I*A*a^3*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)","C",0
694,1,149,0,1.180175," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(120 i \, A + 120 \, B\right)} a^{3} c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(200 i \, A + 40 \, B\right)} a^{3} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(100 i \, A + 20 \, B\right)} a^{3} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(20 i \, A + 4 \, B\right)} a^{3} c^{2}}{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*((120*I*A + 120*B)*a^3*c^2*e^(6*I*f*x + 6*I*e) + (200*I*A + 40*B)*a^3*c^2*e^(4*I*f*x + 4*I*e) + (100*I*A + 20*B)*a^3*c^2*e^(2*I*f*x + 2*I*e) + (20*I*A + 4*B)*a^3*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)","A",0
695,1,129,0,0.657606," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(24 i \, A + 24 \, B\right)} a^{3} c e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(48 i \, A + 24 \, B\right)} a^{3} c e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(32 i \, A + 16 \, B\right)} a^{3} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, A + 4 \, B\right)} a^{3} c}{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 + 24*B)*a^3*c*e^(6*I*f*x + 6*I*e) + (48*I*A + 24*B)*a^3*c*e^(4*I*f*x + 4*I*e) + (32*I*A + 16*B)*a^3*c*e^(2*I*f*x + 2*I*e) + (8*I*A + 4*B)*a^3*c)/(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
696,1,178,0,0.768426," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(-24 i \, A - 48 \, B\right)} a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-42 i \, A - 66 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-18 i \, A - 26 \, B\right)} a^{3} + {\left({\left(-12 i \, A - 12 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-36 i \, A - 36 \, B\right)} a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-36 i \, A - 36 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-12 i \, A - 12 \, B\right)} a^{3}\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*((-24*I*A - 48*B)*a^3*e^(4*I*f*x + 4*I*e) + (-42*I*A - 66*B)*a^3*e^(2*I*f*x + 2*I*e) + (-18*I*A - 26*B)*a^3 + ((-12*I*A - 12*B)*a^3*e^(6*I*f*x + 6*I*e) + (-36*I*A - 36*B)*a^3*e^(4*I*f*x + 4*I*e) + (-36*I*A - 36*B)*a^3*e^(2*I*f*x + 2*I*e) + (-12*I*A - 12*B)*a^3)*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)","A",0
697,1,164,0,0.867443," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(-2 i \, A - 2 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-4 i \, A - 4 \, B\right)} a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 8 \, B a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, A + 8 \, B\right)} a^{3} + {\left({\left(4 i \, A + 8 \, B\right)} a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(8 i \, A + 16 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 i \, A + 8 \, B\right)} a^{3}\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,"((-2*I*A - 2*B)*a^3*e^(6*I*f*x + 6*I*e) + (-4*I*A - 4*B)*a^3*e^(4*I*f*x + 4*I*e) + 8*B*a^3*e^(2*I*f*x + 2*I*e) + (2*I*A + 8*B)*a^3 + ((4*I*A + 8*B)*a^3*e^(4*I*f*x + 4*I*e) + (8*I*A + 16*B)*a^3*e^(2*I*f*x + 2*I*e) + (4*I*A + 8*B)*a^3)*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
698,1,136,0,1.204927," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(-i \, A - B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(i \, A + 5 \, B\right)} a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(2 i \, A + 6 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 4 \, B a^{3} + {\left({\left(-2 i \, A - 10 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-2 i \, A - 10 \, B\right)} a^{3}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{2 \, {\left(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} f\right)}}"," ",0,"1/2*((-I*A - B)*a^3*e^(6*I*f*x + 6*I*e) + (I*A + 5*B)*a^3*e^(4*I*f*x + 4*I*e) + (2*I*A + 6*B)*a^3*e^(2*I*f*x + 2*I*e) - 4*B*a^3 + ((-2*I*A - 10*B)*a^3*e^(2*I*f*x + 2*I*e) + (-2*I*A - 10*B)*a^3)*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
699,1,77,0,0.585030," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(-i \, A - B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, B a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 6 \, B a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 6 \, B a^{3} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{6 \, c^{3} f}"," ",0,"1/6*((-I*A - B)*a^3*e^(6*I*f*x + 6*I*e) + 3*B*a^3*e^(4*I*f*x + 4*I*e) - 6*B*a^3*e^(2*I*f*x + 2*I*e) + 6*B*a^3*log(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f)","A",0
700,1,49,0,0.681076," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(-3 i \, A - 3 \, B\right)} a^{3} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-4 i \, A + 4 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)}}{48 \, c^{4} f}"," ",0,"1/48*((-3*I*A - 3*B)*a^3*e^(8*I*f*x + 8*I*e) + (-4*I*A + 4*B)*a^3*e^(6*I*f*x + 6*I*e))/(c^4*f)","A",0
701,1,64,0,0.849944," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^5,x, algorithm=""fricas"")","\frac{{\left(-6 i \, A - 6 \, B\right)} a^{3} e^{\left(10 i \, f x + 10 i \, e\right)} - 15 i \, A a^{3} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-10 i \, A + 10 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)}}{240 \, c^{5} f}"," ",0,"1/240*((-6*I*A - 6*B)*a^3*e^(10*I*f*x + 10*I*e) - 15*I*A*a^3*e^(8*I*f*x + 8*I*e) + (-10*I*A + 10*B)*a^3*e^(6*I*f*x + 6*I*e))/(c^5*f)","A",0
702,1,89,0,0.767974," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^6,x, algorithm=""fricas"")","\frac{{\left(-10 i \, A - 10 \, B\right)} a^{3} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-36 i \, A - 12 \, B\right)} a^{3} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-45 i \, A + 15 \, B\right)} a^{3} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-20 i \, A + 20 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)}}{960 \, c^{6} f}"," ",0,"1/960*((-10*I*A - 10*B)*a^3*e^(12*I*f*x + 12*I*e) + (-36*I*A - 12*B)*a^3*e^(10*I*f*x + 10*I*e) + (-45*I*A + 15*B)*a^3*e^(8*I*f*x + 8*I*e) + (-20*I*A + 20*B)*a^3*e^(6*I*f*x + 6*I*e))/(c^6*f)","A",0
703,1,104,0,0.749588," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^7,x, algorithm=""fricas"")","\frac{{\left(-30 i \, A - 30 \, B\right)} a^{3} e^{\left(14 i \, f x + 14 i \, e\right)} + {\left(-140 i \, A - 70 \, B\right)} a^{3} e^{\left(12 i \, f x + 12 i \, e\right)} - 252 i \, A a^{3} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-210 i \, A + 105 \, B\right)} a^{3} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-70 i \, A + 70 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)}}{6720 \, c^{7} f}"," ",0,"1/6720*((-30*I*A - 30*B)*a^3*e^(14*I*f*x + 14*I*e) + (-140*I*A - 70*B)*a^3*e^(12*I*f*x + 12*I*e) - 252*I*A*a^3*e^(10*I*f*x + 10*I*e) + (-210*I*A + 105*B)*a^3*e^(8*I*f*x + 8*I*e) + (-70*I*A + 70*B)*a^3*e^(6*I*f*x + 6*I*e))/(c^7*f)","A",0
704,1,129,0,1.673033," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^8,x, algorithm=""fricas"")","\frac{{\left(-105 i \, A - 105 \, B\right)} a^{3} e^{\left(16 i \, f x + 16 i \, e\right)} + {\left(-600 i \, A - 360 \, B\right)} a^{3} e^{\left(14 i \, f x + 14 i \, e\right)} + {\left(-1400 i \, A - 280 \, B\right)} a^{3} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-1680 i \, A + 336 \, B\right)} a^{3} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-1050 i \, A + 630 \, B\right)} a^{3} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-280 i \, A + 280 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)}}{53760 \, c^{8} f}"," ",0,"1/53760*((-105*I*A - 105*B)*a^3*e^(16*I*f*x + 16*I*e) + (-600*I*A - 360*B)*a^3*e^(14*I*f*x + 14*I*e) + (-1400*I*A - 280*B)*a^3*e^(12*I*f*x + 12*I*e) + (-1680*I*A + 336*B)*a^3*e^(10*I*f*x + 10*I*e) + (-1050*I*A + 630*B)*a^3*e^(8*I*f*x + 8*I*e) + (-280*I*A + 280*B)*a^3*e^(6*I*f*x + 6*I*e))/(c^8*f)","A",0
705,0,0,0,0.588747," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + A + i \, B\right)} \left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*((A - I*B)*e^(2*I*f*x + 2*I*e) + A + I*B)*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(-2*I*f*x - 2*I*e)/a, x)","F",0
706,1,297,0,0.888358," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{24 \, {\left(3 \, A + 5 i \, B\right)} c^{4} f x e^{\left(8 i \, f x + 8 i \, e\right)} - {\left(12 i \, A - 12 \, B\right)} c^{4} + {\left(72 \, {\left(3 \, A + 5 i \, B\right)} c^{4} f x - {\left(36 i \, A - 60 \, B\right)} c^{4}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(72 \, {\left(3 \, A + 5 i \, B\right)} c^{4} f x - {\left(90 i \, A - 150 \, B\right)} c^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(24 \, {\left(3 \, A + 5 i \, B\right)} c^{4} f x - {\left(66 i \, A - 110 \, B\right)} c^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left({\left(-36 i \, A + 60 \, B\right)} c^{4} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-108 i \, A + 180 \, B\right)} c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-108 i \, A + 180 \, B\right)} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-36 i \, A + 60 \, B\right)} 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)}{3 \, {\left(a f e^{\left(8 i \, f x + 8 i \, e\right)} + 3 \, a f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, 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,"-1/3*(24*(3*A + 5*I*B)*c^4*f*x*e^(8*I*f*x + 8*I*e) - (12*I*A - 12*B)*c^4 + (72*(3*A + 5*I*B)*c^4*f*x - (36*I*A - 60*B)*c^4)*e^(6*I*f*x + 6*I*e) + (72*(3*A + 5*I*B)*c^4*f*x - (90*I*A - 150*B)*c^4)*e^(4*I*f*x + 4*I*e) + (24*(3*A + 5*I*B)*c^4*f*x - (66*I*A - 110*B)*c^4)*e^(2*I*f*x + 2*I*e) - ((-36*I*A + 60*B)*c^4*e^(8*I*f*x + 8*I*e) + (-108*I*A + 180*B)*c^4*e^(6*I*f*x + 6*I*e) + (-108*I*A + 180*B)*c^4*e^(4*I*f*x + 4*I*e) + (-36*I*A + 60*B)*c^4*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(a*f*e^(8*I*f*x + 8*I*e) + 3*a*f*e^(6*I*f*x + 6*I*e) + 3*a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))","B",0
707,1,221,0,1.533101," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{8 \, {\left(A + 2 i \, B\right)} c^{3} f x e^{\left(6 i \, f x + 6 i \, e\right)} - {\left(2 i \, A - 2 \, B\right)} c^{3} + {\left(16 \, {\left(A + 2 i \, B\right)} c^{3} f x - {\left(4 i \, A - 8 \, B\right)} c^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(8 \, {\left(A + 2 i \, B\right)} c^{3} f x - {\left(6 i \, A - 12 \, B\right)} c^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left({\left(-4 i \, A + 8 \, B\right)} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-8 i \, A + 16 \, B\right)} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-4 i \, A + 8 \, B\right)} 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(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,"-(8*(A + 2*I*B)*c^3*f*x*e^(6*I*f*x + 6*I*e) - (2*I*A - 2*B)*c^3 + (16*(A + 2*I*B)*c^3*f*x - (4*I*A - 8*B)*c^3)*e^(4*I*f*x + 4*I*e) + (8*(A + 2*I*B)*c^3*f*x - (6*I*A - 12*B)*c^3)*e^(2*I*f*x + 2*I*e) - ((-4*I*A + 8*B)*c^3*e^(6*I*f*x + 6*I*e) + (-8*I*A + 16*B)*c^3*e^(4*I*f*x + 4*I*e) + (-4*I*A + 8*B)*c^3*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))","B",0
708,1,153,0,0.608005," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, {\left(A + 3 i \, B\right)} c^{2} f x e^{\left(4 i \, f x + 4 i \, e\right)} - {\left(i \, A - B\right)} c^{2} + {\left(2 \, {\left(A + 3 i \, B\right)} c^{2} f x - {\left(i \, A - 3 \, B\right)} c^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left({\left(-i \, A + 3 \, B\right)} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-i \, A + 3 \, B\right)} c^{2} 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,"-(2*(A + 3*I*B)*c^2*f*x*e^(4*I*f*x + 4*I*e) - (I*A - B)*c^2 + (2*(A + 3*I*B)*c^2*f*x - (I*A - 3*B)*c^2)*e^(2*I*f*x + 2*I*e) - ((-I*A + 3*B)*c^2*e^(4*I*f*x + 4*I*e) + (-I*A + 3*B)*c^2*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
709,1,67,0,0.735749," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(-4 i \, B c f x e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, B c e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + {\left(i \, A - B\right)} c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a f}"," ",0,"1/2*(-4*I*B*c*f*x*e^(2*I*f*x + 2*I*e) + 2*B*c*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + (I*A - B)*c)*e^(-2*I*f*x - 2*I*e)/(a*f)","A",0
710,1,42,0,0.538063," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(A - i \, B\right)} f x e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a f}"," ",0,"1/4*(2*(A - I*B)*f*x*e^(2*I*f*x + 2*I*e) + I*A - B)*e^(-2*I*f*x - 2*I*e)/(a*f)","A",0
711,1,58,0,2.128945," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(4 \, A f x e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A - B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + i \, A - B\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a c f}"," ",0,"1/8*(4*A*f*x*e^(2*I*f*x + 2*I*e) + (-I*A - B)*e^(4*I*f*x + 4*I*e) + I*A - B)*e^(-2*I*f*x - 2*I*e)/(a*c*f)","C",0
712,1,81,0,0.754447," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(3 \, A + i \, B\right)} f x e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A - B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-6 i \, A - 2 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 i \, A - 2 \, B\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{32 \, a c^{2} f}"," ",0,"1/32*(4*(3*A + I*B)*f*x*e^(2*I*f*x + 2*I*e) + (-I*A - B)*e^(6*I*f*x + 6*I*e) + (-6*I*A - 2*B)*e^(4*I*f*x + 4*I*e) + 2*I*A - 2*B)*e^(-2*I*f*x - 2*I*e)/(a*c^2*f)","A",0
713,1,93,0,1.725505," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, {\left(2 \, A + i \, B\right)} f x e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A - B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-6 i \, A - 3 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} - 18 i \, A e^{\left(4 i \, f x + 4 i \, e\right)} + 3 i \, A - 3 \, B\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{96 \, a c^{3} f}"," ",0,"1/96*(12*(2*A + I*B)*f*x*e^(2*I*f*x + 2*I*e) + (-I*A - B)*e^(8*I*f*x + 8*I*e) + (-6*I*A - 3*B)*e^(6*I*f*x + 6*I*e) - 18*I*A*e^(4*I*f*x + 4*I*e) + 3*I*A - 3*B)*e^(-2*I*f*x - 2*I*e)/(a*c^3*f)","A",0
714,1,115,0,1.088272," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(24 \, {\left(5 \, A + 3 i \, B\right)} f x e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-3 i \, A - 3 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-20 i \, A - 12 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-60 i \, A - 12 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-120 i \, A + 24 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 12 i \, A - 12 \, B\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{768 \, a c^{4} f}"," ",0,"1/768*(24*(5*A + 3*I*B)*f*x*e^(2*I*f*x + 2*I*e) + (-3*I*A - 3*B)*e^(10*I*f*x + 10*I*e) + (-20*I*A - 12*B)*e^(8*I*f*x + 8*I*e) + (-60*I*A - 12*B)*e^(6*I*f*x + 6*I*e) + (-120*I*A + 24*B)*e^(4*I*f*x + 4*I*e) + 12*I*A - 12*B)*e^(-2*I*f*x - 2*I*e)/(a*c^4*f)","A",0
715,0,0,0,0.756781," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, A e^{\left(2 i \, f x + 2 i \, e\right)} + A + i \, B\right)} \left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(-4 i \, f x - 4 i \, e\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*((A - I*B)*e^(4*I*f*x + 4*I*e) + 2*A*e^(2*I*f*x + 2*I*e) + A + I*B)*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(-4*I*f*x - 4*I*e)/a^2, x)","F",0
716,1,320,0,0.592245," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{48 \, {\left(3 \, A + 7 i \, B\right)} c^{5} f x e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-18 i \, A + 42 \, B\right)} c^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 i \, A - 6 \, B\right)} c^{5} + {\left(144 \, {\left(3 \, A + 7 i \, B\right)} c^{5} f x + {\left(-72 i \, A + 168 \, B\right)} c^{5}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(144 \, {\left(3 \, A + 7 i \, B\right)} c^{5} f x + {\left(-180 i \, A + 420 \, B\right)} c^{5}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(48 \, {\left(3 \, A + 7 i \, B\right)} c^{5} f x + {\left(-132 i \, A + 308 \, B\right)} c^{5}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left({\left(72 i \, A - 168 \, B\right)} c^{5} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(216 i \, A - 504 \, B\right)} c^{5} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(216 i \, A - 504 \, B\right)} c^{5} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(72 i \, A - 168 \, B\right)} c^{5} 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)}{3 \, {\left(a^{2} f e^{\left(10 i \, f x + 10 i \, e\right)} + 3 \, a^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} + 3 \, 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,"1/3*(48*(3*A + 7*I*B)*c^5*f*x*e^(10*I*f*x + 10*I*e) + (-18*I*A + 42*B)*c^5*e^(2*I*f*x + 2*I*e) + (6*I*A - 6*B)*c^5 + (144*(3*A + 7*I*B)*c^5*f*x + (-72*I*A + 168*B)*c^5)*e^(8*I*f*x + 8*I*e) + (144*(3*A + 7*I*B)*c^5*f*x + (-180*I*A + 420*B)*c^5)*e^(6*I*f*x + 6*I*e) + (48*(3*A + 7*I*B)*c^5*f*x + (-132*I*A + 308*B)*c^5)*e^(4*I*f*x + 4*I*e) + ((72*I*A - 168*B)*c^5*e^(10*I*f*x + 10*I*e) + (216*I*A - 504*B)*c^5*e^(8*I*f*x + 8*I*e) + (216*I*A - 504*B)*c^5*e^(6*I*f*x + 6*I*e) + (72*I*A - 168*B)*c^5*e^(4*I*f*x + 4*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(a^2*f*e^(10*I*f*x + 10*I*e) + 3*a^2*f*e^(8*I*f*x + 8*I*e) + 3*a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))","A",0
717,1,242,0,0.963110," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{12 \, {\left(A + 3 i \, B\right)} c^{4} f x e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-2 i \, A + 6 \, B\right)} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A - B\right)} c^{4} + {\left(24 \, {\left(A + 3 i \, B\right)} c^{4} f x + {\left(-6 i \, A + 18 \, B\right)} c^{4}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(12 \, {\left(A + 3 i \, B\right)} c^{4} f x + {\left(-9 i \, A + 27 \, B\right)} c^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left({\left(6 i \, A - 18 \, B\right)} c^{4} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(12 i \, A - 36 \, B\right)} c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(6 i \, A - 18 \, B\right)} 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(8 i \, f x + 8 i \, e\right)} + 2 \, 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*(A + 3*I*B)*c^4*f*x*e^(8*I*f*x + 8*I*e) + (-2*I*A + 6*B)*c^4*e^(2*I*f*x + 2*I*e) + (I*A - B)*c^4 + (24*(A + 3*I*B)*c^4*f*x + (-6*I*A + 18*B)*c^4)*e^(6*I*f*x + 6*I*e) + (12*(A + 3*I*B)*c^4*f*x + (-9*I*A + 27*B)*c^4)*e^(4*I*f*x + 4*I*e) + ((6*I*A - 18*B)*c^4*e^(8*I*f*x + 8*I*e) + (12*I*A - 36*B)*c^4*e^(6*I*f*x + 6*I*e) + (6*I*A - 18*B)*c^4*e^(4*I*f*x + 4*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(a^2*f*e^(8*I*f*x + 8*I*e) + 2*a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))","A",0
718,1,174,0,0.572883," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(A + 5 i \, B\right)} c^{3} f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-i \, A + 5 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A - B\right)} c^{3} + {\left(4 \, {\left(A + 5 i \, B\right)} c^{3} f x + {\left(-2 i \, A + 10 \, B\right)} c^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left({\left(2 i \, A - 10 \, B\right)} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(2 i \, A - 10 \, B\right)} c^{3} 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)}{2 \, {\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,"1/2*(4*(A + 5*I*B)*c^3*f*x*e^(6*I*f*x + 6*I*e) + (-I*A + 5*B)*c^3*e^(2*I*f*x + 2*I*e) + (I*A - B)*c^3 + (4*(A + 5*I*B)*c^3*f*x + (-2*I*A + 10*B)*c^3)*e^(4*I*f*x + 4*I*e) + ((2*I*A - 10*B)*c^3*e^(6*I*f*x + 6*I*e) + (2*I*A - 10*B)*c^3*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
719,1,88,0,1.002380," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(8 i \, B c^{2} f x e^{\left(4 i \, f x + 4 i \, e\right)} - 4 \, B c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 4 \, B c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A - B\right)} c^{2}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{4 \, a^{2} f}"," ",0,"1/4*(8*I*B*c^2*f*x*e^(4*I*f*x + 4*I*e) - 4*B*c^2*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 4*B*c^2*e^(2*I*f*x + 2*I*e) + (I*A - B)*c^2)*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
720,1,45,0,0.854357," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left({\left(2 i \, A + 2 \, B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A - B\right)} c\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{8 \, a^{2} f}"," ",0,"1/8*((2*I*A + 2*B)*c*e^(2*I*f*x + 2*I*e) + (I*A - B)*c)*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
721,1,54,0,1.085208," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(A - i \, B\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + 4 i \, A e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, a^{2} f}"," ",0,"1/16*(4*(A - I*B)*f*x*e^(4*I*f*x + 4*I*e) + 4*I*A*e^(2*I*f*x + 2*I*e) + I*A - B)*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
722,1,81,0,0.662432," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(3 \, A - i \, B\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-2 i \, A - 2 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(6 i \, A - 2 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{32 \, a^{2} c f}"," ",0,"1/32*(4*(3*A - I*B)*f*x*e^(4*I*f*x + 4*I*e) + (-2*I*A - 2*B)*e^(6*I*f*x + 6*I*e) + (6*I*A - 2*B)*e^(2*I*f*x + 2*I*e) + I*A - B)*e^(-4*I*f*x - 4*I*e)/(a^2*c*f)","A",0
723,1,92,0,0.858876," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(24 \, A f x e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-i \, A - B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-8 i \, A - 4 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(8 i \, A - 4 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{64 \, a^{2} c^{2} f}"," ",0,"1/64*(24*A*f*x*e^(4*I*f*x + 4*I*e) + (-I*A - B)*e^(8*I*f*x + 8*I*e) + (-8*I*A - 4*B)*e^(6*I*f*x + 6*I*e) + (8*I*A - 4*B)*e^(2*I*f*x + 2*I*e) + I*A - B)*e^(-4*I*f*x - 4*I*e)/(a^2*c^2*f)","C",0
724,1,115,0,3.242265," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(24 \, {\left(5 \, A + i \, B\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-2 i \, A - 2 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-15 i \, A - 9 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-60 i \, A - 12 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(30 i \, A - 18 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, A - 3 \, B\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{384 \, a^{2} c^{3} f}"," ",0,"1/384*(24*(5*A + I*B)*f*x*e^(4*I*f*x + 4*I*e) + (-2*I*A - 2*B)*e^(10*I*f*x + 10*I*e) + (-15*I*A - 9*B)*e^(8*I*f*x + 8*I*e) + (-60*I*A - 12*B)*e^(6*I*f*x + 6*I*e) + (30*I*A - 18*B)*e^(2*I*f*x + 2*I*e) + 3*I*A - 3*B)*e^(-4*I*f*x - 4*I*e)/(a^2*c^3*f)","A",0
725,1,127,0,1.220451," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(120 \, {\left(3 \, A + i \, B\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-3 i \, A - 3 \, B\right)} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-24 i \, A - 16 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-90 i \, A - 30 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} - 240 i \, A e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(72 i \, A - 48 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 6 i \, A - 6 \, B\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{1536 \, a^{2} c^{4} f}"," ",0,"1/1536*(120*(3*A + I*B)*f*x*e^(4*I*f*x + 4*I*e) + (-3*I*A - 3*B)*e^(12*I*f*x + 12*I*e) + (-24*I*A - 16*B)*e^(10*I*f*x + 10*I*e) + (-90*I*A - 30*B)*e^(8*I*f*x + 8*I*e) - 240*I*A*e^(6*I*f*x + 6*I*e) + (72*I*A - 48*B)*e^(2*I*f*x + 2*I*e) + 6*I*A - 6*B)*e^(-4*I*f*x - 4*I*e)/(a^2*c^4*f)","A",0
726,1,149,0,1.182036," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^5,x, algorithm=""fricas"")","\frac{{\left(120 \, {\left(7 \, A + 3 i \, B\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-4 i \, A - 4 \, B\right)} e^{\left(14 i \, f x + 14 i \, e\right)} + {\left(-35 i \, A - 25 \, B\right)} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-140 i \, A - 60 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-350 i \, A - 50 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-700 i \, A + 100 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(140 i \, A - 100 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 10 i \, A - 10 \, B\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{5120 \, a^{2} c^{5} f}"," ",0,"1/5120*(120*(7*A + 3*I*B)*f*x*e^(4*I*f*x + 4*I*e) + (-4*I*A - 4*B)*e^(14*I*f*x + 14*I*e) + (-35*I*A - 25*B)*e^(12*I*f*x + 12*I*e) + (-140*I*A - 60*B)*e^(10*I*f*x + 10*I*e) + (-350*I*A - 50*B)*e^(8*I*f*x + 8*I*e) + (-700*I*A + 100*B)*e^(6*I*f*x + 6*I*e) + (140*I*A - 100*B)*e^(2*I*f*x + 2*I*e) + 10*I*A - 10*B)*e^(-4*I*f*x - 4*I*e)/(a^2*c^5*f)","A",0
727,0,0,0,1.171080," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(3 \, A - i \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(3 \, A + i \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + A + i \, B\right)} \left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(-6 i \, f x - 6 i \, e\right)}}{8 \, a^{3}}, x\right)"," ",0,"integral(1/8*((A - I*B)*e^(6*I*f*x + 6*I*e) + (3*A - I*B)*e^(4*I*f*x + 4*I*e) + (3*A + I*B)*e^(2*I*f*x + 2*I*e) + A + I*B)*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(-6*I*f*x - 6*I*e)/a^3, x)","F",0
728,1,269,0,0.705339," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{48 \, {\left(A + 4 i \, B\right)} c^{5} f x e^{\left(10 i \, f x + 10 i \, e\right)} - {\left(8 i \, A - 32 \, B\right)} c^{5} e^{\left(4 i \, f x + 4 i \, e\right)} - {\left(-2 i \, A + 8 \, B\right)} c^{5} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(2 i \, A - 2 \, B\right)} c^{5} + {\left(96 \, {\left(A + 4 i \, B\right)} c^{5} f x - {\left(24 i \, A - 96 \, B\right)} c^{5}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(48 \, {\left(A + 4 i \, B\right)} c^{5} f x - {\left(36 i \, A - 144 \, B\right)} c^{5}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} - {\left({\left(-24 i \, A + 96 \, B\right)} c^{5} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-48 i \, A + 192 \, B\right)} c^{5} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-24 i \, A + 96 \, B\right)} c^{5} e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{3 \, {\left(a^{3} f e^{\left(10 i \, f x + 10 i \, e\right)} + 2 \, a^{3} f e^{\left(8 i \, f x + 8 i \, e\right)} + a^{3} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)}}"," ",0,"-1/3*(48*(A + 4*I*B)*c^5*f*x*e^(10*I*f*x + 10*I*e) - (8*I*A - 32*B)*c^5*e^(4*I*f*x + 4*I*e) - (-2*I*A + 8*B)*c^5*e^(2*I*f*x + 2*I*e) - (2*I*A - 2*B)*c^5 + (96*(A + 4*I*B)*c^5*f*x - (24*I*A - 96*B)*c^5)*e^(8*I*f*x + 8*I*e) + (48*(A + 4*I*B)*c^5*f*x - (36*I*A - 144*B)*c^5)*e^(6*I*f*x + 6*I*e) - ((-24*I*A + 96*B)*c^5*e^(10*I*f*x + 10*I*e) + (-48*I*A + 192*B)*c^5*e^(8*I*f*x + 8*I*e) + (-24*I*A + 96*B)*c^5*e^(6*I*f*x + 6*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(a^3*f*e^(10*I*f*x + 10*I*e) + 2*a^3*f*e^(8*I*f*x + 8*I*e) + a^3*f*e^(6*I*f*x + 6*I*e))","A",0
729,1,199,0,1.200568," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(A + 7 i \, B\right)} c^{4} f x e^{\left(8 i \, f x + 8 i \, e\right)} - {\left(3 i \, A - 21 \, B\right)} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} - {\left(-i \, A + 7 \, B\right)} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(2 i \, A - 2 \, B\right)} c^{4} + {\left(12 \, {\left(A + 7 i \, B\right)} c^{4} f x - {\left(6 i \, A - 42 \, B\right)} c^{4}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} - {\left({\left(-6 i \, A + 42 \, B\right)} c^{4} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-6 i \, A + 42 \, B\right)} c^{4} e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{6 \, {\left(a^{3} f e^{\left(8 i \, f x + 8 i \, e\right)} + a^{3} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)}}"," ",0,"-1/6*(12*(A + 7*I*B)*c^4*f*x*e^(8*I*f*x + 8*I*e) - (3*I*A - 21*B)*c^4*e^(4*I*f*x + 4*I*e) - (-I*A + 7*B)*c^4*e^(2*I*f*x + 2*I*e) - (2*I*A - 2*B)*c^4 + (12*(A + 7*I*B)*c^4*f*x - (6*I*A - 42*B)*c^4)*e^(6*I*f*x + 6*I*e) - ((-6*I*A + 42*B)*c^4*e^(8*I*f*x + 8*I*e) + (-6*I*A + 42*B)*c^4*e^(6*I*f*x + 6*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(a^3*f*e^(8*I*f*x + 8*I*e) + a^3*f*e^(6*I*f*x + 6*I*e))","A",0
730,1,103,0,0.569105," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(-12 i \, B c^{3} f x e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, B c^{3} 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 \, B c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, B c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A - B\right)} c^{3}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{6 \, a^{3} f}"," ",0,"1/6*(-12*I*B*c^3*f*x*e^(6*I*f*x + 6*I*e) + 6*B*c^3*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 6*B*c^3*e^(4*I*f*x + 4*I*e) + 3*B*c^3*e^(2*I*f*x + 2*I*e) + (I*A - B)*c^3)*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
731,1,49,0,1.822009," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left({\left(3 i \, A + 3 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, A - 2 \, B\right)} c^{2}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{24 \, a^{3} f}"," ",0,"1/24*((3*I*A + 3*B)*c^2*e^(2*I*f*x + 2*I*e) + (2*I*A - 2*B)*c^2)*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
732,1,58,0,0.583304," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left({\left(3 i \, A + 3 \, B\right)} c e^{\left(4 i \, f x + 4 i \, e\right)} + 3 i \, A c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A - B\right)} c\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{24 \, a^{3} f}"," ",0,"1/24*((3*I*A + 3*B)*c*e^(4*I*f*x + 4*I*e) + 3*I*A*c*e^(2*I*f*x + 2*I*e) + (I*A - B)*c)*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
733,1,76,0,0.824652," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, {\left(A - i \, B\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(18 i \, A + 6 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(9 i \, A - 3 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, A - 2 \, B\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{96 \, a^{3} f}"," ",0,"1/96*(12*(A - I*B)*f*x*e^(6*I*f*x + 6*I*e) + (18*I*A + 6*B)*e^(4*I*f*x + 4*I*e) + (9*I*A - 3*B)*e^(2*I*f*x + 2*I*e) + 2*I*A - 2*B)*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
734,1,93,0,1.540380," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(12 \, {\left(2 \, A - i \, B\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-3 i \, A - 3 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + 18 i \, A e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 i \, A - 3 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{96 \, a^{3} c f}"," ",0,"1/96*(12*(2*A - I*B)*f*x*e^(6*I*f*x + 6*I*e) + (-3*I*A - 3*B)*e^(8*I*f*x + 8*I*e) + 18*I*A*e^(4*I*f*x + 4*I*e) + (6*I*A - 3*B)*e^(2*I*f*x + 2*I*e) + I*A - B)*e^(-6*I*f*x - 6*I*e)/(a^3*c*f)","A",0
735,1,115,0,0.564871," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(24 \, {\left(5 \, A - i \, B\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-3 i \, A - 3 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-30 i \, A - 18 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(60 i \, A - 12 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(15 i \, A - 9 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, A - 2 \, B\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{384 \, a^{3} c^{2} f}"," ",0,"1/384*(24*(5*A - I*B)*f*x*e^(6*I*f*x + 6*I*e) + (-3*I*A - 3*B)*e^(10*I*f*x + 10*I*e) + (-30*I*A - 18*B)*e^(8*I*f*x + 8*I*e) + (60*I*A - 12*B)*e^(4*I*f*x + 4*I*e) + (15*I*A - 9*B)*e^(2*I*f*x + 2*I*e) + 2*I*A - 2*B)*e^(-6*I*f*x - 6*I*e)/(a^3*c^2*f)","A",0
736,1,126,0,1.123557," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(120 \, A f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-i \, A - B\right)} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-9 i \, A - 6 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-45 i \, A - 15 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(45 i \, A - 15 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(9 i \, A - 6 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{384 \, a^{3} c^{3} f}"," ",0,"1/384*(120*A*f*x*e^(6*I*f*x + 6*I*e) + (-I*A - B)*e^(12*I*f*x + 12*I*e) + (-9*I*A - 6*B)*e^(10*I*f*x + 10*I*e) + (-45*I*A - 15*B)*e^(8*I*f*x + 8*I*e) + (45*I*A - 15*B)*e^(4*I*f*x + 4*I*e) + (9*I*A - 6*B)*e^(2*I*f*x + 2*I*e) + I*A - B)*e^(-6*I*f*x - 6*I*e)/(a^3*c^3*f)","C",0
737,1,149,0,0.740101," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(120 \, {\left(7 \, A + i \, B\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-3 i \, A - 3 \, B\right)} e^{\left(14 i \, f x + 14 i \, e\right)} + {\left(-28 i \, A - 20 \, B\right)} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-126 i \, A - 54 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-420 i \, A - 60 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(252 i \, A - 108 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(42 i \, A - 30 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, A - 4 \, B\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{3072 \, a^{3} c^{4} f}"," ",0,"1/3072*(120*(7*A + I*B)*f*x*e^(6*I*f*x + 6*I*e) + (-3*I*A - 3*B)*e^(14*I*f*x + 14*I*e) + (-28*I*A - 20*B)*e^(12*I*f*x + 12*I*e) + (-126*I*A - 54*B)*e^(10*I*f*x + 10*I*e) + (-420*I*A - 60*B)*e^(8*I*f*x + 8*I*e) + (252*I*A - 108*B)*e^(4*I*f*x + 4*I*e) + (42*I*A - 30*B)*e^(2*I*f*x + 2*I*e) + 4*I*A - 4*B)*e^(-6*I*f*x - 6*I*e)/(a^3*c^4*f)","A",0
738,1,161,0,0.853235," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^5,x, algorithm=""fricas"")","\frac{{\left(840 \, {\left(4 \, A + i \, B\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-6 i \, A - 6 \, B\right)} e^{\left(16 i \, f x + 16 i \, e\right)} + {\left(-60 i \, A - 45 \, B\right)} e^{\left(14 i \, f x + 14 i \, e\right)} + {\left(-280 i \, A - 140 \, B\right)} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-840 i \, A - 210 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} - 2100 i \, A e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(840 i \, A - 420 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(120 i \, A - 90 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 10 i \, A - 10 \, B\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{15360 \, a^{3} c^{5} f}"," ",0,"1/15360*(840*(4*A + I*B)*f*x*e^(6*I*f*x + 6*I*e) + (-6*I*A - 6*B)*e^(16*I*f*x + 16*I*e) + (-60*I*A - 45*B)*e^(14*I*f*x + 14*I*e) + (-280*I*A - 140*B)*e^(12*I*f*x + 12*I*e) + (-840*I*A - 210*B)*e^(10*I*f*x + 10*I*e) - 2100*I*A*e^(8*I*f*x + 8*I*e) + (840*I*A - 420*B)*e^(4*I*f*x + 4*I*e) + (120*I*A - 90*B)*e^(2*I*f*x + 2*I*e) + 10*I*A - 10*B)*e^(-6*I*f*x - 6*I*e)/(a^3*c^5*f)","A",0
739,1,183,0,0.890166," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^6,x, algorithm=""fricas"")","\frac{{\left(1680 \, {\left(3 \, A + i \, B\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-5 i \, A - 5 \, B\right)} e^{\left(18 i \, f x + 18 i \, e\right)} + {\left(-54 i \, A - 42 \, B\right)} e^{\left(16 i \, f x + 16 i \, e\right)} + {\left(-270 i \, A - 150 \, B\right)} e^{\left(14 i \, f x + 14 i \, e\right)} + {\left(-840 i \, A - 280 \, B\right)} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-1890 i \, A - 210 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-3780 i \, A + 420 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(1080 i \, A - 600 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(135 i \, A - 105 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 10 i \, A - 10 \, B\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{30720 \, a^{3} c^{6} f}"," ",0,"1/30720*(1680*(3*A + I*B)*f*x*e^(6*I*f*x + 6*I*e) + (-5*I*A - 5*B)*e^(18*I*f*x + 18*I*e) + (-54*I*A - 42*B)*e^(16*I*f*x + 16*I*e) + (-270*I*A - 150*B)*e^(14*I*f*x + 14*I*e) + (-840*I*A - 280*B)*e^(12*I*f*x + 12*I*e) + (-1890*I*A - 210*B)*e^(10*I*f*x + 10*I*e) + (-3780*I*A + 420*B)*e^(8*I*f*x + 8*I*e) + (1080*I*A - 600*B)*e^(4*I*f*x + 4*I*e) + (135*I*A - 105*B)*e^(2*I*f*x + 2*I*e) + 10*I*A - 10*B)*e^(-6*I*f*x - 6*I*e)/(a^3*c^6*f)","A",0
740,1,107,0,1.534308," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(144 i \, A + 144 \, B\right)} a c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(144 i \, A - 80 \, B\right)} a c^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{63 \, {\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,"1/63*sqrt(2)*((144*I*A + 144*B)*a*c^3*e^(2*I*f*x + 2*I*e) + (144*I*A - 80*B)*a*c^3)*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)","B",0
741,1,95,0,1.114201," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(56 i \, A + 56 \, B\right)} a c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(56 i \, A - 24 \, B\right)} a 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)*((56*I*A + 56*B)*a*c^2*e^(2*I*f*x + 2*I*e) + (56*I*A - 24*B)*a*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
742,1,79,0,1.319841," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(20 i \, A + 20 \, B\right)} a c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(20 i \, A - 4 \, B\right)} a 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)*((20*I*A + 20*B)*a*c*e^(2*I*f*x + 2*I*e) + (20*I*A - 4*B)*a*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
743,1,65,0,0.747892," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))*(A+B*tan(f*x+e)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(6 i \, A + 6 \, B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 i \, A + 2 \, B\right)} a\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)*((6*I*A + 6*B)*a*e^(2*I*f*x + 2*I*e) + (6*I*A + 2*B)*a)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(2*I*f*x + 2*I*e) + f)","A",0
744,1,55,0,1.285179," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-i \, A - B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A - 3 \, B\right)} a\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{c f}"," ",0,"sqrt(2)*((-I*A - B)*a*e^(2*I*f*x + 2*I*e) + (-I*A - 3*B)*a)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c*f)","A",0
745,1,74,0,0.686398," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-i \, A - B\right)} a e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-2 i \, A + 4 \, B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A + 5 \, B\right)} 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 - B)*a*e^(4*I*f*x + 4*I*e) + (-2*I*A + 4*B)*a*e^(2*I*f*x + 2*I*e) + (-I*A + 5*B)*a)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^2*f)","A",0
746,1,90,0,1.092334," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-3 i \, A - 3 \, B\right)} a e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-9 i \, A + B\right)} a e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-9 i \, A + 11 \, B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-3 i \, A + 7 \, B\right)} a\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, c^{3} f}"," ",0,"1/60*sqrt(2)*((-3*I*A - 3*B)*a*e^(6*I*f*x + 6*I*e) + (-9*I*A + B)*a*e^(4*I*f*x + 4*I*e) + (-9*I*A + 11*B)*a*e^(2*I*f*x + 2*I*e) + (-3*I*A + 7*B)*a)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f)","A",0
747,1,110,0,1.562615," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-5 i \, A - 5 \, B\right)} a e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-20 i \, A - 6 \, B\right)} a e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-30 i \, A + 12 \, B\right)} a e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-20 i \, A + 22 \, B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-5 i \, A + 9 \, B\right)} a\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{280 \, c^{4} f}"," ",0,"1/280*sqrt(2)*((-5*I*A - 5*B)*a*e^(8*I*f*x + 8*I*e) + (-20*I*A - 6*B)*a*e^(6*I*f*x + 6*I*e) + (-30*I*A + 12*B)*a*e^(4*I*f*x + 4*I*e) + (-20*I*A + 22*B)*a*e^(2*I*f*x + 2*I*e) + (-5*I*A + 9*B)*a)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^4*f)","B",0
748,1,146,0,1.519121," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(3168 i \, A + 3168 \, B\right)} a^{2} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(3872 i \, A - 1056 \, B\right)} a^{2} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(704 i \, A - 192 \, B\right)} a^{2} c^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{693 \, {\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,"1/693*sqrt(2)*((3168*I*A + 3168*B)*a^2*c^3*e^(4*I*f*x + 4*I*e) + (3872*I*A - 1056*B)*a^2*c^3*e^(2*I*f*x + 2*I*e) + (704*I*A - 192*B)*a^2*c^3)*sqrt(c/(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)","A",0
749,1,134,0,2.690931," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(1008 i \, A + 1008 \, B\right)} a^{2} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(1296 i \, A - 144 \, B\right)} a^{2} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(288 i \, A - 32 \, B\right)} a^{2} 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)*((1008*I*A + 1008*B)*a^2*c^2*e^(4*I*f*x + 4*I*e) + (1296*I*A - 144*B)*a^2*c^2*e^(2*I*f*x + 2*I*e) + (288*I*A - 32*B)*a^2*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
750,1,116,0,1.926151," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(280 i \, A + 280 \, B\right)} a^{2} c e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(392 i \, A + 56 \, B\right)} a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(112 i \, A + 16 \, B\right)} a^{2} 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)*((280*I*A + 280*B)*a^2*c*e^(4*I*f*x + 4*I*e) + (392*I*A + 56*B)*a^2*c*e^(2*I*f*x + 2*I*e) + (112*I*A + 16*B)*a^2*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
751,1,101,0,1.492675," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(60 i \, A + 60 \, B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(100 i \, A + 60 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(40 i \, A + 24 \, B\right)} a^{2}\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)*((60*I*A + 60*B)*a^2*e^(4*I*f*x + 4*I*e) + (100*I*A + 60*B)*a^2*e^(2*I*f*x + 2*I*e) + (40*I*A + 24*B)*a^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)","A",0
752,1,92,0,1.249681," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-6 i \, A - 6 \, B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-18 i \, A - 30 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-12 i \, A - 20 \, B\right)} a^{2}\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)*((-6*I*A - 6*B)*a^2*e^(4*I*f*x + 4*I*e) + (-18*I*A - 30*B)*a^2*e^(2*I*f*x + 2*I*e) + (-12*I*A - 20*B)*a^2)*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
753,1,80,0,0.964678," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-i \, A - B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(i \, A + 7 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, A + 14 \, B\right)} 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 - B)*a^2*e^(4*I*f*x + 4*I*e) + (I*A + 7*B)*a^2*e^(2*I*f*x + 2*I*e) + (2*I*A + 14*B)*a^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^2*f)","A",0
754,1,100,0,1.569634," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-3 i \, A - 3 \, B\right)} a^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-4 i \, A + 6 \, B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(i \, A - 9 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, A - 18 \, B\right)} 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 - 3*B)*a^2*e^(6*I*f*x + 6*I*e) + (-4*I*A + 6*B)*a^2*e^(4*I*f*x + 4*I*e) + (I*A - 9*B)*a^2*e^(2*I*f*x + 2*I*e) + (2*I*A - 18*B)*a^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f)","A",0
755,1,120,0,0.614797," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-15 i \, A - 15 \, B\right)} a^{2} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-39 i \, A + 3 \, B\right)} a^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-27 i \, A + 29 \, B\right)} a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(3 i \, A - 11 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 i \, A - 22 \, B\right)} a^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{420 \, c^{4} f}"," ",0,"1/420*sqrt(2)*((-15*I*A - 15*B)*a^2*e^(8*I*f*x + 8*I*e) + (-39*I*A + 3*B)*a^2*e^(6*I*f*x + 6*I*e) + (-27*I*A + 29*B)*a^2*e^(4*I*f*x + 4*I*e) + (3*I*A - 11*B)*a^2*e^(2*I*f*x + 2*I*e) + (6*I*A - 22*B)*a^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^4*f)","A",0
756,1,181,0,2.467477," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(82368 i \, A + 82368 \, B\right)} a^{3} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(118976 i \, A - 9152 \, B\right)} a^{3} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(43264 i \, A - 3328 \, B\right)} a^{3} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6656 i \, A - 512 \, B\right)} a^{3} c^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{9009 \, {\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,"1/9009*sqrt(2)*((82368*I*A + 82368*B)*a^3*c^3*e^(6*I*f*x + 6*I*e) + (118976*I*A - 9152*B)*a^3*c^3*e^(4*I*f*x + 4*I*e) + (43264*I*A - 3328*B)*a^3*c^3*e^(2*I*f*x + 2*I*e) + (6656*I*A - 512*B)*a^3*c^3)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(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
757,1,169,0,2.045020," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(22176 i \, A + 22176 \, B\right)} a^{3} c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(34848 i \, A + 3168 \, B\right)} a^{3} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(15488 i \, A + 1408 \, B\right)} a^{3} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2816 i \, A + 256 \, B\right)} a^{3} c^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{3465 \, {\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,"1/3465*sqrt(2)*((22176*I*A + 22176*B)*a^3*c^2*e^(6*I*f*x + 6*I*e) + (34848*I*A + 3168*B)*a^3*c^2*e^(4*I*f*x + 4*I*e) + (15488*I*A + 1408*B)*a^3*c^2*e^(2*I*f*x + 2*I*e) + (2816*I*A + 256*B)*a^3*c^2)*sqrt(c/(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)","A",0
758,1,149,0,0.932268," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(1680 i \, A + 1680 \, B\right)} a^{3} c e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(3024 i \, A + 1008 \, B\right)} a^{3} c e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(1728 i \, A + 576 \, B\right)} a^{3} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(384 i \, A + 128 \, B\right)} a^{3} c\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)*((1680*I*A + 1680*B)*a^3*c*e^(6*I*f*x + 6*I*e) + (3024*I*A + 1008*B)*a^3*c*e^(4*I*f*x + 4*I*e) + (1728*I*A + 576*B)*a^3*c*e^(2*I*f*x + 2*I*e) + (384*I*A + 128*B)*a^3*c)*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
759,1,133,0,0.986666," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(840 i \, A + 840 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(1960 i \, A + 1400 \, B\right)} a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(1568 i \, A + 1120 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(448 i \, A + 320 \, B\right)} a^{3}\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)*((840*I*A + 840*B)*a^3*e^(6*I*f*x + 6*I*e) + (1960*I*A + 1400*B)*a^3*e^(4*I*f*x + 4*I*e) + (1568*I*A + 1120*B)*a^3*e^(2*I*f*x + 2*I*e) + (448*I*A + 320*B)*a^3)*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
760,1,125,0,1.402142," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-60 i \, A - 60 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-300 i \, A - 420 \, B\right)} a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-400 i \, A - 560 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-160 i \, A - 224 \, B\right)} a^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{15 \, {\left(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\right)}}"," ",0,"1/15*sqrt(2)*((-60*I*A - 60*B)*a^3*e^(6*I*f*x + 6*I*e) + (-300*I*A - 420*B)*a^3*e^(4*I*f*x + 4*I*e) + (-400*I*A - 560*B)*a^3*e^(2*I*f*x + 2*I*e) + (-160*I*A - 224*B)*a^3)*sqrt(c/(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
761,1,116,0,0.919196," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-2 i \, A - 2 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(6 i \, A + 18 \, B\right)} a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(24 i \, A + 72 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 i \, A + 48 \, B\right)} a^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{3 \, {\left(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} f\right)}}"," ",0,"1/3*sqrt(2)*((-2*I*A - 2*B)*a^3*e^(6*I*f*x + 6*I*e) + (6*I*A + 18*B)*a^3*e^(4*I*f*x + 4*I*e) + (24*I*A + 72*B)*a^3*e^(2*I*f*x + 2*I*e) + (16*I*A + 48*B)*a^3)*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)","A",0
762,1,100,0,1.054946," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-3 i \, A - 3 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(i \, A + 11 \, B\right)} a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-4 i \, A - 44 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-8 i \, A - 88 \, B\right)} 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*B)*a^3*e^(6*I*f*x + 6*I*e) + (I*A + 11*B)*a^3*e^(4*I*f*x + 4*I*e) + (-4*I*A - 44*B)*a^3*e^(2*I*f*x + 2*I*e) + (-8*I*A - 88*B)*a^3)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f)","A",0
763,1,120,0,2.293050," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(-15 i \, A - 15 \, B\right)} a^{3} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-18 i \, A + 24 \, B\right)} a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(i \, A - 13 \, B\right)} a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-4 i \, A + 52 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-8 i \, A + 104 \, B\right)} a^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{210 \, c^{4} f}"," ",0,"1/210*sqrt(2)*((-15*I*A - 15*B)*a^3*e^(8*I*f*x + 8*I*e) + (-18*I*A + 24*B)*a^3*e^(6*I*f*x + 6*I*e) + (I*A - 13*B)*a^3*e^(4*I*f*x + 4*I*e) + (-4*I*A + 52*B)*a^3*e^(2*I*f*x + 2*I*e) + (-8*I*A + 104*B)*a^3)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^4*f)","A",0
764,1,461,0,0.706722," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{15 \, \sqrt{-\frac{{\left(800 \, A^{2} + 2880 i \, A B - 2592 \, B^{2}\right)} c^{7}}{a^{2} f^{2}}} {\left(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)}\right)} \log\left(\frac{{\left({\left(-40 i \, A + 72 \, B\right)} c^{4} + \sqrt{2} \sqrt{-\frac{{\left(800 \, A^{2} + 2880 i \, A B - 2592 \, B^{2}\right)} c^{7}}{a^{2} f^{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}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}\right) - 15 \, \sqrt{-\frac{{\left(800 \, A^{2} + 2880 i \, A B - 2592 \, B^{2}\right)} c^{7}}{a^{2} f^{2}}} {\left(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)}\right)} \log\left(\frac{{\left({\left(-40 i \, A + 72 \, B\right)} c^{4} - \sqrt{2} \sqrt{-\frac{{\left(800 \, A^{2} + 2880 i \, A B - 2592 \, B^{2}\right)} c^{7}}{a^{2} f^{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}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}\right) + \sqrt{2} {\left({\left(600 i \, A - 1080 \, B\right)} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(1400 i \, A - 2520 \, B\right)} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(920 i \, A - 1656 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(120 i \, A - 120 \, B\right)} c^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(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)}\right)}}"," ",0,"1/60*(15*sqrt(-(800*A^2 + 2880*I*A*B - 2592*B^2)*c^7/(a^2*f^2))*(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))*log(((-40*I*A + 72*B)*c^4 + sqrt(2)*sqrt(-(800*A^2 + 2880*I*A*B - 2592*B^2)*c^7/(a^2*f^2))*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a*f)) - 15*sqrt(-(800*A^2 + 2880*I*A*B - 2592*B^2)*c^7/(a^2*f^2))*(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))*log(((-40*I*A + 72*B)*c^4 - sqrt(2)*sqrt(-(800*A^2 + 2880*I*A*B - 2592*B^2)*c^7/(a^2*f^2))*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a*f)) + sqrt(2)*((600*I*A - 1080*B)*c^3*e^(6*I*f*x + 6*I*e) + (1400*I*A - 2520*B)*c^3*e^(4*I*f*x + 4*I*e) + (920*I*A - 1656*B)*c^3*e^(2*I*f*x + 2*I*e) + (120*I*A - 120*B)*c^3)*sqrt(c/(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))","B",0
765,1,402,0,1.199749," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, {\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)} \sqrt{-\frac{{\left(72 \, A^{2} + 336 i \, A B - 392 \, B^{2}\right)} c^{5}}{a^{2} f^{2}}} \log\left(\frac{{\left({\left(-12 i \, A + 28 \, B\right)} c^{3} + \sqrt{2} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{-\frac{{\left(72 \, A^{2} + 336 i \, A B - 392 \, B^{2}\right)} 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) - 3 \, {\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)} \sqrt{-\frac{{\left(72 \, A^{2} + 336 i \, A B - 392 \, B^{2}\right)} c^{5}}{a^{2} f^{2}}} \log\left(\frac{{\left({\left(-12 i \, A + 28 \, B\right)} c^{3} - \sqrt{2} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{-\frac{{\left(72 \, A^{2} + 336 i \, A B - 392 \, B^{2}\right)} 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({\left(36 i \, A - 84 \, B\right)} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(48 i \, A - 112 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(12 i \, A - 12 \, B\right)} c^{2}\right)} \sqrt{\frac{c}{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*(a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))*sqrt(-(72*A^2 + 336*I*A*B - 392*B^2)*c^5/(a^2*f^2))*log(((-12*I*A + 28*B)*c^3 + sqrt(2)*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(-(72*A^2 + 336*I*A*B - 392*B^2)*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)) - 3*(a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))*sqrt(-(72*A^2 + 336*I*A*B - 392*B^2)*c^5/(a^2*f^2))*log(((-12*I*A + 28*B)*c^3 - sqrt(2)*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(-(72*A^2 + 336*I*A*B - 392*B^2)*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)*((36*I*A - 84*B)*c^2*e^(4*I*f*x + 4*I*e) + (48*I*A - 112*B)*c^2*e^(2*I*f*x + 2*I*e) + (12*I*A - 12*B)*c^2)*sqrt(c/(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
766,1,337,0,0.609166," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a f \sqrt{-\frac{{\left(2 \, A^{2} + 20 i \, A B - 50 \, B^{2}\right)} c^{3}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left({\left(-2 i \, A + 10 \, B\right)} c^{2} + \sqrt{2} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{-\frac{{\left(2 \, A^{2} + 20 i \, A B - 50 \, B^{2}\right)} c^{3}}{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) - a f \sqrt{-\frac{{\left(2 \, A^{2} + 20 i \, A B - 50 \, B^{2}\right)} c^{3}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left({\left(-2 i \, A + 10 \, B\right)} c^{2} - \sqrt{2} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{-\frac{{\left(2 \, A^{2} + 20 i \, A B - 50 \, B^{2}\right)} c^{3}}{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({\left(2 i \, A - 10 \, B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, A - 2 \, B\right)} 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*(a*f*sqrt(-(2*A^2 + 20*I*A*B - 50*B^2)*c^3/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(((-2*I*A + 10*B)*c^2 + sqrt(2)*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(-(2*A^2 + 20*I*A*B - 50*B^2)*c^3/(a^2*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a*f)) - a*f*sqrt(-(2*A^2 + 20*I*A*B - 50*B^2)*c^3/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(((-2*I*A + 10*B)*c^2 - sqrt(2)*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(-(2*A^2 + 20*I*A*B - 50*B^2)*c^3/(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)*((2*I*A - 10*B)*c*e^(2*I*f*x + 2*I*e) + (2*I*A - 2*B)*c)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
767,1,326,0,1.987294," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(\sqrt{\frac{1}{2}} a f \sqrt{-\frac{{\left(A^{2} - 6 i \, A B - 9 \, B^{2}\right)} 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{{\left(A^{2} - 6 i \, A B - 9 \, B^{2}\right)} c}{a^{2} f^{2}}} + {\left(i \, A + 3 \, B\right)} c\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}\right) - \sqrt{\frac{1}{2}} a f \sqrt{-\frac{{\left(A^{2} - 6 i \, A B - 9 \, B^{2}\right)} 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{{\left(A^{2} - 6 i \, A B - 9 \, B^{2}\right)} c}{a^{2} f^{2}}} - {\left(i \, A + 3 \, B\right)} c\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}\right) + \sqrt{2} {\left({\left(i \, A - B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\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(1/2)*a*f*sqrt(-(A^2 - 6*I*A*B - 9*B^2)*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(-(A^2 - 6*I*A*B - 9*B^2)*c/(a^2*f^2)) + (I*A + 3*B)*c)*e^(-I*f*x - I*e)/(a*f)) - sqrt(1/2)*a*f*sqrt(-(A^2 - 6*I*A*B - 9*B^2)*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(-(A^2 - 6*I*A*B - 9*B^2)*c/(a^2*f^2)) - (I*A + 3*B)*c)*e^(-I*f*x - I*e)/(a*f)) + sqrt(2)*((I*A - B)*e^(2*I*f*x + 2*I*e) + I*A - B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
768,1,356,0,0.735953," ","integrate((A+B*tan(f*x+e))/(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 c f \sqrt{-\frac{9 \, A^{2} - 6 i \, A B - B^{2}}{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(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{9 \, A^{2} - 6 i \, A B - B^{2}}{a^{2} c f^{2}}} + 3 i \, A + B\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a f}\right) - \sqrt{\frac{1}{2}} a c f \sqrt{-\frac{9 \, A^{2} - 6 i \, A B - B^{2}}{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(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{9 \, A^{2} - 6 i \, A B - B^{2}}{a^{2} c f^{2}}} - 3 i \, A - B\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a f}\right) + \sqrt{2} {\left({\left(-2 i \, A - 2 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-i \, A - 3 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\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)}}{8 \, a c f}"," ",0,"1/8*(sqrt(1/2)*a*c*f*sqrt(-(9*A^2 - 6*I*A*B - B^2)/(a^2*c*f^2))*e^(2*I*f*x + 2*I*e)*log(1/2*(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(-(9*A^2 - 6*I*A*B - B^2)/(a^2*c*f^2)) + 3*I*A + B)*e^(-I*f*x - I*e)/(a*f)) - sqrt(1/2)*a*c*f*sqrt(-(9*A^2 - 6*I*A*B - B^2)/(a^2*c*f^2))*e^(2*I*f*x + 2*I*e)*log(-1/2*(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(-(9*A^2 - 6*I*A*B - B^2)/(a^2*c*f^2)) - 3*I*A - B)*e^(-I*f*x - I*e)/(a*f)) + sqrt(2)*((-2*I*A - 2*B)*e^(4*I*f*x + 4*I*e) + (-I*A - 3*B)*e^(2*I*f*x + 2*I*e) + I*A - B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*c*f)","B",0
769,1,388,0,1.571616," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a c^{2} f \sqrt{-\frac{25 \, A^{2} + 10 i \, A B - B^{2}}{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(a c f e^{\left(2 i \, f x + 2 i \, e\right)} + a c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{25 \, A^{2} + 10 i \, A B - B^{2}}{a^{2} c^{3} f^{2}}} + 5 i \, A - B\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a c f}\right) - 3 \, \sqrt{\frac{1}{2}} a c^{2} f \sqrt{-\frac{25 \, A^{2} + 10 i \, A B - B^{2}}{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(a c f e^{\left(2 i \, f x + 2 i \, e\right)} + a c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{25 \, A^{2} + 10 i \, A B - B^{2}}{a^{2} c^{3} f^{2}}} - 5 i \, A + B\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a c f}\right) + \sqrt{2} {\left({\left(-2 i \, A - 2 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-16 i \, A - 4 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-11 i \, A - 5 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, A - 3 \, B\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)}}{48 \, a c^{2} f}"," ",0,"1/48*(3*sqrt(1/2)*a*c^2*f*sqrt(-(25*A^2 + 10*I*A*B - B^2)/(a^2*c^3*f^2))*e^(2*I*f*x + 2*I*e)*log(1/4*(sqrt(2)*sqrt(1/2)*(a*c*f*e^(2*I*f*x + 2*I*e) + a*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(25*A^2 + 10*I*A*B - B^2)/(a^2*c^3*f^2)) + 5*I*A - B)*e^(-I*f*x - I*e)/(a*c*f)) - 3*sqrt(1/2)*a*c^2*f*sqrt(-(25*A^2 + 10*I*A*B - B^2)/(a^2*c^3*f^2))*e^(2*I*f*x + 2*I*e)*log(-1/4*(sqrt(2)*sqrt(1/2)*(a*c*f*e^(2*I*f*x + 2*I*e) + a*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(25*A^2 + 10*I*A*B - B^2)/(a^2*c^3*f^2)) - 5*I*A + B)*e^(-I*f*x - I*e)/(a*c*f)) + sqrt(2)*((-2*I*A - 2*B)*e^(6*I*f*x + 6*I*e) + (-16*I*A - 4*B)*e^(4*I*f*x + 4*I*e) + (-11*I*A - 5*B)*e^(2*I*f*x + 2*I*e) + 3*I*A - 3*B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*c^2*f)","B",0
770,1,415,0,1.961123," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} a c^{3} f \sqrt{-\frac{49 \, A^{2} + 42 i \, A B - 9 \, B^{2}}{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(a c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{49 \, A^{2} + 42 i \, A B - 9 \, B^{2}}{a^{2} c^{5} f^{2}}} + 7 i \, A - 3 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{8 \, a c^{2} f}\right) - 15 \, \sqrt{\frac{1}{2}} a c^{3} f \sqrt{-\frac{49 \, A^{2} + 42 i \, A B - 9 \, B^{2}}{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(a c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{49 \, A^{2} + 42 i \, A B - 9 \, B^{2}}{a^{2} c^{5} f^{2}}} - 7 i \, A + 3 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{8 \, a c^{2} f}\right) + \sqrt{2} {\left({\left(-6 i \, A - 6 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-38 i \, A - 18 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-148 i \, A + 12 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-101 i \, A + 9 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 15 i \, A - 15 \, B\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)}}{480 \, a c^{3} f}"," ",0,"1/480*(15*sqrt(1/2)*a*c^3*f*sqrt(-(49*A^2 + 42*I*A*B - 9*B^2)/(a^2*c^5*f^2))*e^(2*I*f*x + 2*I*e)*log(1/8*(sqrt(2)*sqrt(1/2)*(a*c^2*f*e^(2*I*f*x + 2*I*e) + a*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(49*A^2 + 42*I*A*B - 9*B^2)/(a^2*c^5*f^2)) + 7*I*A - 3*B)*e^(-I*f*x - I*e)/(a*c^2*f)) - 15*sqrt(1/2)*a*c^3*f*sqrt(-(49*A^2 + 42*I*A*B - 9*B^2)/(a^2*c^5*f^2))*e^(2*I*f*x + 2*I*e)*log(-1/8*(sqrt(2)*sqrt(1/2)*(a*c^2*f*e^(2*I*f*x + 2*I*e) + a*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(49*A^2 + 42*I*A*B - 9*B^2)/(a^2*c^5*f^2)) - 7*I*A + 3*B)*e^(-I*f*x - I*e)/(a*c^2*f)) + sqrt(2)*((-6*I*A - 6*B)*e^(8*I*f*x + 8*I*e) + (-38*I*A - 18*B)*e^(6*I*f*x + 6*I*e) + (-148*I*A + 12*B)*e^(4*I*f*x + 4*I*e) + (-101*I*A + 9*B)*e^(2*I*f*x + 2*I*e) + 15*I*A - 15*B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*c^3*f)","B",0
771,1,507,0,4.078686," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{15 \, \sqrt{-\frac{{\left(2450 \, A^{2} + 12740 i \, A B - 16562 \, B^{2}\right)} c^{9}}{a^{4} f^{2}}} {\left(a^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} + 2 \, 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)} \log\left(\frac{{\left({\left(70 i \, A - 182 \, B\right)} c^{5} + \sqrt{2} \sqrt{-\frac{{\left(2450 \, A^{2} + 12740 i \, A B - 16562 \, B^{2}\right)} c^{9}}{a^{4} f^{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}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a^{2} f}\right) - 15 \, \sqrt{-\frac{{\left(2450 \, A^{2} + 12740 i \, A B - 16562 \, B^{2}\right)} c^{9}}{a^{4} f^{2}}} {\left(a^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} + 2 \, 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)} \log\left(\frac{{\left({\left(70 i \, A - 182 \, B\right)} c^{5} - \sqrt{2} \sqrt{-\frac{{\left(2450 \, A^{2} + 12740 i \, A B - 16562 \, B^{2}\right)} c^{9}}{a^{4} f^{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}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a^{2} f}\right) + \sqrt{2} {\left({\left(-1050 i \, A + 2730 \, B\right)} c^{4} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-2450 i \, A + 6370 \, B\right)} c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-1610 i \, A + 4186 \, B\right)} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-150 i \, A + 390 \, B\right)} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(60 i \, A - 60 \, B\right)} c^{4}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(a^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} + 2 \, 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,"1/60*(15*sqrt(-(2450*A^2 + 12740*I*A*B - 16562*B^2)*c^9/(a^4*f^2))*(a^2*f*e^(8*I*f*x + 8*I*e) + 2*a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))*log(((70*I*A - 182*B)*c^5 + sqrt(2)*sqrt(-(2450*A^2 + 12740*I*A*B - 16562*B^2)*c^9/(a^4*f^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)))*e^(-I*f*x - I*e)/(a^2*f)) - 15*sqrt(-(2450*A^2 + 12740*I*A*B - 16562*B^2)*c^9/(a^4*f^2))*(a^2*f*e^(8*I*f*x + 8*I*e) + 2*a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))*log(((70*I*A - 182*B)*c^5 - sqrt(2)*sqrt(-(2450*A^2 + 12740*I*A*B - 16562*B^2)*c^9/(a^4*f^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)))*e^(-I*f*x - I*e)/(a^2*f)) + sqrt(2)*((-1050*I*A + 2730*B)*c^4*e^(8*I*f*x + 8*I*e) + (-2450*I*A + 6370*B)*c^4*e^(6*I*f*x + 6*I*e) + (-1610*I*A + 4186*B)*c^4*e^(4*I*f*x + 4*I*e) + (-150*I*A + 390*B)*c^4*e^(2*I*f*x + 2*I*e) + (60*I*A - 60*B)*c^4)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(a^2*f*e^(8*I*f*x + 8*I*e) + 2*a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))","B",0
772,1,454,0,0.739653," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} {\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{{\left(225 \, A^{2} + 1650 i \, A B - 3025 \, B^{2}\right)} c^{7}}{a^{4} f^{2}}} \log\left(\frac{{\left({\left(15 i \, A - 55 \, B\right)} c^{4} + \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{{\left(225 \, A^{2} + 1650 i \, A B - 3025 \, B^{2}\right)} c^{7}}{a^{4} 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^{2} f}\right) - 3 \, \sqrt{\frac{1}{2}} {\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{{\left(225 \, A^{2} + 1650 i \, A B - 3025 \, B^{2}\right)} c^{7}}{a^{4} f^{2}}} \log\left(\frac{{\left({\left(15 i \, A - 55 \, B\right)} c^{4} - \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{{\left(225 \, A^{2} + 1650 i \, A B - 3025 \, B^{2}\right)} c^{7}}{a^{4} 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^{2} f}\right) + \sqrt{2} {\left({\left(-45 i \, A + 165 \, B\right)} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-60 i \, A + 220 \, B\right)} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-9 i \, A + 33 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 i \, A - 6 \, B\right)} c^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{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)}}"," ",0,"1/12*(3*sqrt(1/2)*(a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))*sqrt(-(225*A^2 + 1650*I*A*B - 3025*B^2)*c^7/(a^4*f^2))*log(((15*I*A - 55*B)*c^4 + sqrt(2)*sqrt(1/2)*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(-(225*A^2 + 1650*I*A*B - 3025*B^2)*c^7/(a^4*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a^2*f)) - 3*sqrt(1/2)*(a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))*sqrt(-(225*A^2 + 1650*I*A*B - 3025*B^2)*c^7/(a^4*f^2))*log(((15*I*A - 55*B)*c^4 - sqrt(2)*sqrt(1/2)*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(-(225*A^2 + 1650*I*A*B - 3025*B^2)*c^7/(a^4*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a^2*f)) + sqrt(2)*((-45*I*A + 165*B)*c^3*e^(6*I*f*x + 6*I*e) + (-60*I*A + 220*B)*c^3*e^(4*I*f*x + 4*I*e) + (-9*I*A + 33*B)*c^3*e^(2*I*f*x + 2*I*e) + (6*I*A - 6*B)*c^3)*sqrt(c/(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
773,1,387,0,0.901613," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(\sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{{\left(9 \, A^{2} + 162 i \, A B - 729 \, B^{2}\right)} c^{5}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left({\left(3 i \, A - 27 \, B\right)} 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{{\left(9 \, A^{2} + 162 i \, A B - 729 \, B^{2}\right)} c^{5}}{a^{4} 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)}}{2 \, a^{2} f}\right) - \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{{\left(9 \, A^{2} + 162 i \, A B - 729 \, B^{2}\right)} c^{5}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left({\left(3 i \, A - 27 \, B\right)} 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{{\left(9 \, A^{2} + 162 i \, A B - 729 \, B^{2}\right)} c^{5}}{a^{4} 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)}}{2 \, a^{2} f}\right) + \sqrt{2} {\left({\left(-3 i \, A + 27 \, B\right)} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-i \, A + 9 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, A - 2 \, B\right)} 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*(sqrt(1/2)*a^2*f*sqrt(-(9*A^2 + 162*I*A*B - 729*B^2)*c^5/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/2*((3*I*A - 27*B)*c^3 + sqrt(2)*sqrt(1/2)*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(-(9*A^2 + 162*I*A*B - 729*B^2)*c^5/(a^4*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a^2*f)) - sqrt(1/2)*a^2*f*sqrt(-(9*A^2 + 162*I*A*B - 729*B^2)*c^5/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/2*((3*I*A - 27*B)*c^3 - sqrt(2)*sqrt(1/2)*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(-(9*A^2 + 162*I*A*B - 729*B^2)*c^5/(a^4*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a^2*f)) + sqrt(2)*((-3*I*A + 27*B)*c^2*e^(4*I*f*x + 4*I*e) + (-I*A + 9*B)*c^2*e^(2*I*f*x + 2*I*e) + (2*I*A - 2*B)*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
774,1,373,0,0.812365," ","integrate((A+B*tan(f*x+e))*(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{{\left(A^{2} - 14 i \, A B - 49 \, B^{2}\right)} c^{3}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left({\left(-i \, A - 7 \, B\right)} c^{2} + \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{{\left(A^{2} - 14 i \, A B - 49 \, B^{2}\right)} c^{3}}{a^{4} f^{2}}}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2} f}\right) - \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{{\left(A^{2} - 14 i \, A B - 49 \, B^{2}\right)} c^{3}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left({\left(-i \, A - 7 \, B\right)} c^{2} - \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{{\left(A^{2} - 14 i \, A B - 49 \, B^{2}\right)} c^{3}}{a^{4} f^{2}}}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2} f}\right) + \sqrt{2} {\left({\left(i \, A + 7 \, B\right)} c e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(3 i \, A + 5 \, B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, A - 2 \, B\right)} 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(-(A^2 - 14*I*A*B - 49*B^2)*c^3/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/4*((-I*A - 7*B)*c^2 + 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(-(A^2 - 14*I*A*B - 49*B^2)*c^3/(a^4*f^2)))*e^(-I*f*x - I*e)/(a^2*f)) - sqrt(1/2)*a^2*f*sqrt(-(A^2 - 14*I*A*B - 49*B^2)*c^3/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/4*((-I*A - 7*B)*c^2 - 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(-(A^2 - 14*I*A*B - 49*B^2)*c^3/(a^4*f^2)))*e^(-I*f*x - I*e)/(a^2*f)) + sqrt(2)*((I*A + 7*B)*c*e^(4*I*f*x + 4*I*e) + (3*I*A + 5*B)*c*e^(2*I*f*x + 2*I*e) + (2*I*A - 2*B)*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
775,1,362,0,0.837503," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(\sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{{\left(9 \, A^{2} - 30 i \, A B - 25 \, B^{2}\right)} c}{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{{\left(9 \, A^{2} - 30 i \, A B - 25 \, B^{2}\right)} c}{a^{4} f^{2}}} + {\left(3 i \, A + 5 \, B\right)} c\right)} e^{\left(-i \, f x - i \, e\right)}}{8 \, a^{2} f}\right) - \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{{\left(9 \, A^{2} - 30 i \, A B - 25 \, B^{2}\right)} c}{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{{\left(9 \, A^{2} - 30 i \, A B - 25 \, B^{2}\right)} c}{a^{4} f^{2}}} - {\left(3 i \, A + 5 \, B\right)} c\right)} e^{\left(-i \, f x - i \, e\right)}}{8 \, a^{2} f}\right) + \sqrt{2} {\left({\left(5 i \, A + 3 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(7 i \, A + B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, A - 2 \, B\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)}}{32 \, a^{2} f}"," ",0,"1/32*(sqrt(1/2)*a^2*f*sqrt(-(9*A^2 - 30*I*A*B - 25*B^2)*c/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/8*(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(-(9*A^2 - 30*I*A*B - 25*B^2)*c/(a^4*f^2)) + (3*I*A + 5*B)*c)*e^(-I*f*x - I*e)/(a^2*f)) - sqrt(1/2)*a^2*f*sqrt(-(9*A^2 - 30*I*A*B - 25*B^2)*c/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/8*(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(-(9*A^2 - 30*I*A*B - 25*B^2)*c/(a^4*f^2)) - (3*I*A + 5*B)*c)*e^(-I*f*x - I*e)/(a^2*f)) + sqrt(2)*((5*I*A + 3*B)*e^(4*I*f*x + 4*I*e) + (7*I*A + B)*e^(2*I*f*x + 2*I*e) + 2*I*A - 2*B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","B",0
776,1,387,0,0.763510," ","integrate((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(\sqrt{\frac{1}{2}} a^{2} c f \sqrt{-\frac{225 \, A^{2} - 270 i \, A B - 81 \, B^{2}}{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(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{225 \, A^{2} - 270 i \, A B - 81 \, B^{2}}{a^{4} c f^{2}}} + 15 i \, A + 9 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{16 \, a^{2} f}\right) - \sqrt{\frac{1}{2}} a^{2} c f \sqrt{-\frac{225 \, A^{2} - 270 i \, A B - 81 \, B^{2}}{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(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{225 \, A^{2} - 270 i \, A B - 81 \, B^{2}}{a^{4} c f^{2}}} - 15 i \, A - 9 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{16 \, a^{2} f}\right) + \sqrt{2} {\left({\left(-8 i \, A - 8 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(i \, A - 9 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(11 i \, A - 3 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, A - 2 \, B\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)}}{64 \, a^{2} c f}"," ",0,"1/64*(sqrt(1/2)*a^2*c*f*sqrt(-(225*A^2 - 270*I*A*B - 81*B^2)/(a^4*c*f^2))*e^(4*I*f*x + 4*I*e)*log(1/16*(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(-(225*A^2 - 270*I*A*B - 81*B^2)/(a^4*c*f^2)) + 15*I*A + 9*B)*e^(-I*f*x - I*e)/(a^2*f)) - sqrt(1/2)*a^2*c*f*sqrt(-(225*A^2 - 270*I*A*B - 81*B^2)/(a^4*c*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/16*(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(-(225*A^2 - 270*I*A*B - 81*B^2)/(a^4*c*f^2)) - 15*I*A - 9*B)*e^(-I*f*x - I*e)/(a^2*f)) + sqrt(2)*((-8*I*A - 8*B)*e^(6*I*f*x + 6*I*e) + (I*A - 9*B)*e^(4*I*f*x + 4*I*e) + (11*I*A - 3*B)*e^(2*I*f*x + 2*I*e) + 2*I*A - 2*B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*c*f)","B",0
777,1,419,0,1.635432," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} c^{2} f \sqrt{-\frac{1225 \, A^{2} - 350 i \, A B - 25 \, B^{2}}{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(a^{2} c f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{1225 \, A^{2} - 350 i \, A B - 25 \, B^{2}}{a^{4} c^{3} f^{2}}} + 35 i \, A + 5 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{32 \, a^{2} c f}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} c^{2} f \sqrt{-\frac{1225 \, A^{2} - 350 i \, A B - 25 \, B^{2}}{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(a^{2} c f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{1225 \, A^{2} - 350 i \, A B - 25 \, B^{2}}{a^{4} c^{3} f^{2}}} - 35 i \, A - 5 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{32 \, a^{2} c f}\right) + \sqrt{2} {\left({\left(-8 i \, A - 8 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-88 i \, A - 40 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-41 i \, A - 47 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(45 i \, A - 21 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 6 i \, A - 6 \, B\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)}}{384 \, a^{2} c^{2} f}"," ",0,"1/384*(3*sqrt(1/2)*a^2*c^2*f*sqrt(-(1225*A^2 - 350*I*A*B - 25*B^2)/(a^4*c^3*f^2))*e^(4*I*f*x + 4*I*e)*log(1/32*(sqrt(2)*sqrt(1/2)*(a^2*c*f*e^(2*I*f*x + 2*I*e) + a^2*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(1225*A^2 - 350*I*A*B - 25*B^2)/(a^4*c^3*f^2)) + 35*I*A + 5*B)*e^(-I*f*x - I*e)/(a^2*c*f)) - 3*sqrt(1/2)*a^2*c^2*f*sqrt(-(1225*A^2 - 350*I*A*B - 25*B^2)/(a^4*c^3*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/32*(sqrt(2)*sqrt(1/2)*(a^2*c*f*e^(2*I*f*x + 2*I*e) + a^2*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(1225*A^2 - 350*I*A*B - 25*B^2)/(a^4*c^3*f^2)) - 35*I*A - 5*B)*e^(-I*f*x - I*e)/(a^2*c*f)) + sqrt(2)*((-8*I*A - 8*B)*e^(8*I*f*x + 8*I*e) + (-88*I*A - 40*B)*e^(6*I*f*x + 6*I*e) + (-41*I*A - 47*B)*e^(4*I*f*x + 4*I*e) + (45*I*A - 21*B)*e^(2*I*f*x + 2*I*e) + 6*I*A - 6*B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*c^2*f)","B",0
778,1,444,0,1.188223," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} a^{2} c^{3} f \sqrt{-\frac{3969 \, A^{2} + 882 i \, A B - 49 \, B^{2}}{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(a^{2} c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{3969 \, A^{2} + 882 i \, A B - 49 \, B^{2}}{a^{4} c^{5} f^{2}}} + 63 i \, A - 7 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{64 \, a^{2} c^{2} f}\right) - 15 \, \sqrt{\frac{1}{2}} a^{2} c^{3} f \sqrt{-\frac{3969 \, A^{2} + 882 i \, A B - 49 \, B^{2}}{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(a^{2} c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{3969 \, A^{2} + 882 i \, A B - 49 \, B^{2}}{a^{4} c^{5} f^{2}}} - 63 i \, A + 7 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{64 \, a^{2} c^{2} f}\right) + \sqrt{2} {\left({\left(-24 i \, A - 24 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-192 i \, A - 112 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-1032 i \, A - 152 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-609 i \, A - 199 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(285 i \, A - 165 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 30 i \, A - 30 \, B\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)}}{3840 \, a^{2} c^{3} f}"," ",0,"1/3840*(15*sqrt(1/2)*a^2*c^3*f*sqrt(-(3969*A^2 + 882*I*A*B - 49*B^2)/(a^4*c^5*f^2))*e^(4*I*f*x + 4*I*e)*log(1/64*(sqrt(2)*sqrt(1/2)*(a^2*c^2*f*e^(2*I*f*x + 2*I*e) + a^2*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(3969*A^2 + 882*I*A*B - 49*B^2)/(a^4*c^5*f^2)) + 63*I*A - 7*B)*e^(-I*f*x - I*e)/(a^2*c^2*f)) - 15*sqrt(1/2)*a^2*c^3*f*sqrt(-(3969*A^2 + 882*I*A*B - 49*B^2)/(a^4*c^5*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/64*(sqrt(2)*sqrt(1/2)*(a^2*c^2*f*e^(2*I*f*x + 2*I*e) + a^2*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(3969*A^2 + 882*I*A*B - 49*B^2)/(a^4*c^5*f^2)) - 63*I*A + 7*B)*e^(-I*f*x - I*e)/(a^2*c^2*f)) + sqrt(2)*((-24*I*A - 24*B)*e^(10*I*f*x + 10*I*e) + (-192*I*A - 112*B)*e^(8*I*f*x + 8*I*e) + (-1032*I*A - 152*B)*e^(6*I*f*x + 6*I*e) + (-609*I*A - 199*B)*e^(4*I*f*x + 4*I*e) + (285*I*A - 165*B)*e^(2*I*f*x + 2*I*e) + 30*I*A - 30*B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*c^3*f)","B",0
779,1,476,0,0.959445," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} {\left(a^{3} f e^{\left(8 i \, f x + 8 i \, e\right)} + a^{3} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{-\frac{{\left(1225 \, A^{2} + 12250 i \, A B - 30625 \, B^{2}\right)} c^{9}}{a^{6} f^{2}}} \log\left(\frac{{\left({\left(-35 i \, A + 175 \, B\right)} c^{5} + \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{{\left(1225 \, A^{2} + 12250 i \, A B - 30625 \, B^{2}\right)} c^{9}}{a^{6} 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)}}{2 \, a^{3} f}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{3} f e^{\left(8 i \, f x + 8 i \, e\right)} + a^{3} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{-\frac{{\left(1225 \, A^{2} + 12250 i \, A B - 30625 \, B^{2}\right)} c^{9}}{a^{6} f^{2}}} \log\left(\frac{{\left({\left(-35 i \, A + 175 \, B\right)} c^{5} - \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{{\left(1225 \, A^{2} + 12250 i \, A B - 30625 \, B^{2}\right)} c^{9}}{a^{6} 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)}}{2 \, a^{3} f}\right) + \sqrt{2} {\left({\left(105 i \, A - 525 \, B\right)} c^{4} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(140 i \, A - 700 \, B\right)} c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(21 i \, A - 105 \, B\right)} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-6 i \, A + 30 \, B\right)} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, A - 8 \, B\right)} c^{4}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{24 \, {\left(a^{3} f e^{\left(8 i \, f x + 8 i \, e\right)} + a^{3} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)}}"," ",0,"1/24*(3*sqrt(1/2)*(a^3*f*e^(8*I*f*x + 8*I*e) + a^3*f*e^(6*I*f*x + 6*I*e))*sqrt(-(1225*A^2 + 12250*I*A*B - 30625*B^2)*c^9/(a^6*f^2))*log(1/2*((-35*I*A + 175*B)*c^5 + sqrt(2)*sqrt(1/2)*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(-(1225*A^2 + 12250*I*A*B - 30625*B^2)*c^9/(a^6*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a^3*f)) - 3*sqrt(1/2)*(a^3*f*e^(8*I*f*x + 8*I*e) + a^3*f*e^(6*I*f*x + 6*I*e))*sqrt(-(1225*A^2 + 12250*I*A*B - 30625*B^2)*c^9/(a^6*f^2))*log(1/2*((-35*I*A + 175*B)*c^5 - sqrt(2)*sqrt(1/2)*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(-(1225*A^2 + 12250*I*A*B - 30625*B^2)*c^9/(a^6*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a^3*f)) + sqrt(2)*((105*I*A - 525*B)*c^4*e^(8*I*f*x + 8*I*e) + (140*I*A - 700*B)*c^4*e^(6*I*f*x + 6*I*e) + (21*I*A - 105*B)*c^4*e^(4*I*f*x + 4*I*e) + (-6*I*A + 30*B)*c^4*e^(2*I*f*x + 2*I*e) + (8*I*A - 8*B)*c^4)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(a^3*f*e^(8*I*f*x + 8*I*e) + a^3*f*e^(6*I*f*x + 6*I*e))","B",0
780,1,408,0,3.148198," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{{\left(25 \, A^{2} + 650 i \, A B - 4225 \, B^{2}\right)} c^{7}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left({\left(-5 i \, A + 65 \, B\right)} c^{4} + \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{{\left(25 \, A^{2} + 650 i \, A B - 4225 \, B^{2}\right)} c^{7}}{a^{6} 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)}}{4 \, a^{3} f}\right) - 3 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{{\left(25 \, A^{2} + 650 i \, A B - 4225 \, B^{2}\right)} c^{7}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left({\left(-5 i \, A + 65 \, B\right)} c^{4} - \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{{\left(25 \, A^{2} + 650 i \, A B - 4225 \, B^{2}\right)} c^{7}}{a^{6} 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)}}{4 \, a^{3} f}\right) + \sqrt{2} {\left({\left(15 i \, A - 195 \, B\right)} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(5 i \, A - 65 \, B\right)} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-2 i \, A + 26 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, A - 8 \, B\right)} c^{3}\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)}}{48 \, a^{3} f}"," ",0,"1/48*(3*sqrt(1/2)*a^3*f*sqrt(-(25*A^2 + 650*I*A*B - 4225*B^2)*c^7/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/4*((-5*I*A + 65*B)*c^4 + sqrt(2)*sqrt(1/2)*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(-(25*A^2 + 650*I*A*B - 4225*B^2)*c^7/(a^6*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a^3*f)) - 3*sqrt(1/2)*a^3*f*sqrt(-(25*A^2 + 650*I*A*B - 4225*B^2)*c^7/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/4*((-5*I*A + 65*B)*c^4 - sqrt(2)*sqrt(1/2)*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(-(25*A^2 + 650*I*A*B - 4225*B^2)*c^7/(a^6*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a^3*f)) + sqrt(2)*((15*I*A - 195*B)*c^3*e^(6*I*f*x + 6*I*e) + (5*I*A - 65*B)*c^3*e^(4*I*f*x + 4*I*e) + (-2*I*A + 26*B)*c^3*e^(2*I*f*x + 2*I*e) + (8*I*A - 8*B)*c^3)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
781,1,400,0,0.914920," ","integrate((A+B*tan(f*x+e))*(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{{\left(A^{2} - 22 i \, A B - 121 \, B^{2}\right)} c^{5}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left({\left(i \, A + 11 \, B\right)} 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{{\left(A^{2} - 22 i \, A B - 121 \, B^{2}\right)} 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{{\left(A^{2} - 22 i \, A B - 121 \, B^{2}\right)} c^{5}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left({\left(i \, A + 11 \, B\right)} 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{{\left(A^{2} - 22 i \, A B - 121 \, B^{2}\right)} c^{5}}{a^{6} f^{2}}}\right)} e^{\left(-i \, f x - i \, e\right)}}{8 \, a^{3} f}\right) + \sqrt{2} {\left({\left(-3 i \, A - 33 \, B\right)} c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-i \, A - 11 \, B\right)} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(10 i \, A + 14 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, A - 8 \, B\right)} 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(-(A^2 - 22*I*A*B - 121*B^2)*c^5/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*((I*A + 11*B)*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(-(A^2 - 22*I*A*B - 121*B^2)*c^5/(a^6*f^2)))*e^(-I*f*x - I*e)/(a^3*f)) - 3*sqrt(1/2)*a^3*f*sqrt(-(A^2 - 22*I*A*B - 121*B^2)*c^5/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*((I*A + 11*B)*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(-(A^2 - 22*I*A*B - 121*B^2)*c^5/(a^6*f^2)))*e^(-I*f*x - I*e)/(a^3*f)) + sqrt(2)*((-3*I*A - 33*B)*c^2*e^(6*I*f*x + 6*I*e) + (-I*A - 11*B)*c^2*e^(4*I*f*x + 4*I*e) + (10*I*A + 14*B)*c^2*e^(2*I*f*x + 2*I*e) + (8*I*A - 8*B)*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
782,1,392,0,0.934565," ","integrate((A+B*tan(f*x+e))*(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{{\left(A^{2} - 6 i \, A B - 9 \, B^{2}\right)} c^{3}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left({\left(-i \, A - 3 \, B\right)} c^{2} + \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{{\left(A^{2} - 6 i \, A B - 9 \, B^{2}\right)} c^{3}}{a^{6} f^{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{{\left(A^{2} - 6 i \, A B - 9 \, B^{2}\right)} c^{3}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left({\left(-i \, A - 3 \, B\right)} c^{2} - \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{{\left(A^{2} - 6 i \, A B - 9 \, B^{2}\right)} c^{3}}{a^{6} f^{2}}}\right)} e^{\left(-i \, f x - i \, e\right)}}{16 \, a^{3} f}\right) + \sqrt{2} {\left({\left(3 i \, A + 9 \, B\right)} c e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(17 i \, A + 19 \, B\right)} c e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(22 i \, A + 2 \, B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, A - 8 \, B\right)} 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(-(A^2 - 6*I*A*B - 9*B^2)*c^3/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/16*((-I*A - 3*B)*c^2 + 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(-(A^2 - 6*I*A*B - 9*B^2)*c^3/(a^6*f^2)))*e^(-I*f*x - I*e)/(a^3*f)) - 3*sqrt(1/2)*a^3*f*sqrt(-(A^2 - 6*I*A*B - 9*B^2)*c^3/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/16*((-I*A - 3*B)*c^2 - 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(-(A^2 - 6*I*A*B - 9*B^2)*c^3/(a^6*f^2)))*e^(-I*f*x - I*e)/(a^3*f)) + sqrt(2)*((3*I*A + 9*B)*c*e^(6*I*f*x + 6*I*e) + (17*I*A + 19*B)*c*e^(4*I*f*x + 4*I*e) + (22*I*A + 2*B)*c*e^(2*I*f*x + 2*I*e) + (8*I*A - 8*B)*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
783,1,382,0,0.596602," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{{\left(25 \, A^{2} - 70 i \, A B - 49 \, B^{2}\right)} c}{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{{\left(25 \, A^{2} - 70 i \, A B - 49 \, B^{2}\right)} c}{a^{6} f^{2}}} + {\left(5 i \, A + 7 \, B\right)} c\right)} e^{\left(-i \, f x - i \, e\right)}}{32 \, a^{3} f}\right) - 3 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{{\left(25 \, A^{2} - 70 i \, A B - 49 \, B^{2}\right)} c}{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{{\left(25 \, A^{2} - 70 i \, A B - 49 \, B^{2}\right)} c}{a^{6} f^{2}}} - {\left(5 i \, A + 7 \, B\right)} c\right)} e^{\left(-i \, f x - i \, e\right)}}{32 \, a^{3} f}\right) + \sqrt{2} {\left({\left(33 i \, A + 27 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(59 i \, A + 25 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(34 i \, A - 10 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, A - 8 \, B\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)}}{384 \, a^{3} f}"," ",0,"1/384*(3*sqrt(1/2)*a^3*f*sqrt(-(25*A^2 - 70*I*A*B - 49*B^2)*c/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/32*(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(-(25*A^2 - 70*I*A*B - 49*B^2)*c/(a^6*f^2)) + (5*I*A + 7*B)*c)*e^(-I*f*x - I*e)/(a^3*f)) - 3*sqrt(1/2)*a^3*f*sqrt(-(25*A^2 - 70*I*A*B - 49*B^2)*c/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/32*(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(-(25*A^2 - 70*I*A*B - 49*B^2)*c/(a^6*f^2)) - (5*I*A + 7*B)*c)*e^(-I*f*x - I*e)/(a^3*f)) + sqrt(2)*((33*I*A + 27*B)*e^(6*I*f*x + 6*I*e) + (59*I*A + 25*B)*e^(4*I*f*x + 4*I*e) + (34*I*A - 10*B)*e^(2*I*f*x + 2*I*e) + 8*I*A - 8*B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
784,1,405,0,1.199998," ","integrate((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{3} c f \sqrt{-\frac{1225 \, A^{2} - 1750 i \, A B - 625 \, B^{2}}{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(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{1225 \, A^{2} - 1750 i \, A B - 625 \, B^{2}}{a^{6} c f^{2}}} + 35 i \, A + 25 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{64 \, a^{3} f}\right) - 3 \, \sqrt{\frac{1}{2}} a^{3} c f \sqrt{-\frac{1225 \, A^{2} - 1750 i \, A B - 625 \, B^{2}}{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(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{1225 \, A^{2} - 1750 i \, A B - 625 \, B^{2}}{a^{6} c f^{2}}} - 35 i \, A - 25 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{64 \, a^{3} f}\right) + \sqrt{2} {\left({\left(-48 i \, A - 48 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(39 i \, A - 27 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(125 i \, A + 7 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(46 i \, A - 22 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, A - 8 \, B\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)}}{768 \, a^{3} c f}"," ",0,"1/768*(3*sqrt(1/2)*a^3*c*f*sqrt(-(1225*A^2 - 1750*I*A*B - 625*B^2)/(a^6*c*f^2))*e^(6*I*f*x + 6*I*e)*log(1/64*(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(-(1225*A^2 - 1750*I*A*B - 625*B^2)/(a^6*c*f^2)) + 35*I*A + 25*B)*e^(-I*f*x - I*e)/(a^3*f)) - 3*sqrt(1/2)*a^3*c*f*sqrt(-(1225*A^2 - 1750*I*A*B - 625*B^2)/(a^6*c*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/64*(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(-(1225*A^2 - 1750*I*A*B - 625*B^2)/(a^6*c*f^2)) - 35*I*A - 25*B)*e^(-I*f*x - I*e)/(a^3*f)) + sqrt(2)*((-48*I*A - 48*B)*e^(8*I*f*x + 8*I*e) + (39*I*A - 27*B)*e^(6*I*f*x + 6*I*e) + (125*I*A + 7*B)*e^(4*I*f*x + 4*I*e) + (46*I*A - 22*B)*e^(2*I*f*x + 2*I*e) + 8*I*A - 8*B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*c*f)","B",0
785,1,436,0,0.729734," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{3} c^{2} f \sqrt{-\frac{11025 \, A^{2} - 7350 i \, A B - 1225 \, B^{2}}{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(a^{3} c f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{11025 \, A^{2} - 7350 i \, A B - 1225 \, B^{2}}{a^{6} c^{3} f^{2}}} + 105 i \, A + 35 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{128 \, a^{3} c f}\right) - 3 \, \sqrt{\frac{1}{2}} a^{3} c^{2} f \sqrt{-\frac{11025 \, A^{2} - 7350 i \, A B - 1225 \, B^{2}}{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(a^{3} c f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{11025 \, A^{2} - 7350 i \, A B - 1225 \, B^{2}}{a^{6} c^{3} f^{2}}} - 105 i \, A - 35 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{128 \, a^{3} c f}\right) + \sqrt{2} {\left({\left(-16 i \, A - 16 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-224 i \, A - 128 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-43 i \, A - 121 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(215 i \, A - 35 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(58 i \, A - 34 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, A - 8 \, B\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)}}{1536 \, a^{3} c^{2} f}"," ",0,"1/1536*(3*sqrt(1/2)*a^3*c^2*f*sqrt(-(11025*A^2 - 7350*I*A*B - 1225*B^2)/(a^6*c^3*f^2))*e^(6*I*f*x + 6*I*e)*log(1/128*(sqrt(2)*sqrt(1/2)*(a^3*c*f*e^(2*I*f*x + 2*I*e) + a^3*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(11025*A^2 - 7350*I*A*B - 1225*B^2)/(a^6*c^3*f^2)) + 105*I*A + 35*B)*e^(-I*f*x - I*e)/(a^3*c*f)) - 3*sqrt(1/2)*a^3*c^2*f*sqrt(-(11025*A^2 - 7350*I*A*B - 1225*B^2)/(a^6*c^3*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/128*(sqrt(2)*sqrt(1/2)*(a^3*c*f*e^(2*I*f*x + 2*I*e) + a^3*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(11025*A^2 - 7350*I*A*B - 1225*B^2)/(a^6*c^3*f^2)) - 105*I*A - 35*B)*e^(-I*f*x - I*e)/(a^3*c*f)) + sqrt(2)*((-16*I*A - 16*B)*e^(10*I*f*x + 10*I*e) + (-224*I*A - 128*B)*e^(8*I*f*x + 8*I*e) + (-43*I*A - 121*B)*e^(6*I*f*x + 6*I*e) + (215*I*A - 35*B)*e^(4*I*f*x + 4*I*e) + (58*I*A - 34*B)*e^(2*I*f*x + 2*I*e) + 8*I*A - 8*B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*c^2*f)","A",0
786,1,461,0,3.055840," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} a^{3} c^{3} f \sqrt{-\frac{53361 \, A^{2} - 9702 i \, A B - 441 \, B^{2}}{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(a^{3} c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{53361 \, A^{2} - 9702 i \, A B - 441 \, B^{2}}{a^{6} c^{5} f^{2}}} + 231 i \, A + 21 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{256 \, a^{3} c^{2} f}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} c^{3} f \sqrt{-\frac{53361 \, A^{2} - 9702 i \, A B - 441 \, B^{2}}{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(a^{3} c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{53361 \, A^{2} - 9702 i \, A B - 441 \, B^{2}}{a^{6} c^{5} f^{2}}} - 231 i \, A - 21 \, B\right)} e^{\left(-i \, f x - i \, e\right)}}{256 \, a^{3} c^{2} f}\right) + \sqrt{2} {\left({\left(-48 i \, A - 48 \, B\right)} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-464 i \, A - 304 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-3184 i \, A - 944 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-1433 i \, A - 1003 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(1645 i \, A - 505 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(350 i \, A - 230 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 40 i \, A - 40 \, B\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)}}{15360 \, a^{3} c^{3} f}"," ",0,"1/15360*(15*sqrt(1/2)*a^3*c^3*f*sqrt(-(53361*A^2 - 9702*I*A*B - 441*B^2)/(a^6*c^5*f^2))*e^(6*I*f*x + 6*I*e)*log(1/256*(sqrt(2)*sqrt(1/2)*(a^3*c^2*f*e^(2*I*f*x + 2*I*e) + a^3*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(53361*A^2 - 9702*I*A*B - 441*B^2)/(a^6*c^5*f^2)) + 231*I*A + 21*B)*e^(-I*f*x - I*e)/(a^3*c^2*f)) - 15*sqrt(1/2)*a^3*c^3*f*sqrt(-(53361*A^2 - 9702*I*A*B - 441*B^2)/(a^6*c^5*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/256*(sqrt(2)*sqrt(1/2)*(a^3*c^2*f*e^(2*I*f*x + 2*I*e) + a^3*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(53361*A^2 - 9702*I*A*B - 441*B^2)/(a^6*c^5*f^2)) - 231*I*A - 21*B)*e^(-I*f*x - I*e)/(a^3*c^2*f)) + sqrt(2)*((-48*I*A - 48*B)*e^(12*I*f*x + 12*I*e) + (-464*I*A - 304*B)*e^(10*I*f*x + 10*I*e) + (-3184*I*A - 944*B)*e^(8*I*f*x + 8*I*e) + (-1433*I*A - 1003*B)*e^(6*I*f*x + 6*I*e) + (1645*I*A - 505*B)*e^(4*I*f*x + 4*I*e) + (350*I*A - 230*B)*e^(2*I*f*x + 2*I*e) + 40*I*A - 40*B)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*c^3*f)","A",0
787,1,599,0,0.806840," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{{\left(400 \, A^{2} + 600 i \, A B - 225 \, B^{2}\right)} a c^{7}}{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{2 \, {\left({\left({\left(-80 i \, A + 60 \, B\right)} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-80 i \, A + 60 \, B\right)} c^{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}} + 2 \, \sqrt{\frac{{\left(400 \, A^{2} + 600 i \, A B - 225 \, B^{2}\right)} a c^{7}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-20 i \, A + 15 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-20 i \, A + 15 \, B\right)} c^{3}}\right) - 3 \, \sqrt{\frac{{\left(400 \, A^{2} + 600 i \, A B - 225 \, B^{2}\right)} a c^{7}}{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{2 \, {\left({\left({\left(-80 i \, A + 60 \, B\right)} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-80 i \, A + 60 \, B\right)} c^{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}} - 2 \, \sqrt{\frac{{\left(400 \, A^{2} + 600 i \, A B - 225 \, B^{2}\right)} a c^{7}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-20 i \, A + 15 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-20 i \, A + 15 \, B\right)} c^{3}}\right) - 4 \, {\left({\left(-60 i \, A + 45 \, B\right)} c^{3} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-220 i \, A + 165 \, B\right)} c^{3} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-292 i \, A + 219 \, B\right)} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-132 i \, A + 147 \, B\right)} c^{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}}}{48 \, {\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,"-1/48*(3*sqrt((400*A^2 + 600*I*A*B - 225*B^2)*a*c^7/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(2*(((-80*I*A + 60*B)*c^3*e^(3*I*f*x + 3*I*e) + (-80*I*A + 60*B)*c^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*sqrt((400*A^2 + 600*I*A*B - 225*B^2)*a*c^7/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-20*I*A + 15*B)*c^3*e^(2*I*f*x + 2*I*e) + (-20*I*A + 15*B)*c^3)) - 3*sqrt((400*A^2 + 600*I*A*B - 225*B^2)*a*c^7/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(2*(((-80*I*A + 60*B)*c^3*e^(3*I*f*x + 3*I*e) + (-80*I*A + 60*B)*c^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*sqrt((400*A^2 + 600*I*A*B - 225*B^2)*a*c^7/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-20*I*A + 15*B)*c^3*e^(2*I*f*x + 2*I*e) + (-20*I*A + 15*B)*c^3)) - 4*((-60*I*A + 45*B)*c^3*e^(7*I*f*x + 7*I*e) + (-220*I*A + 165*B)*c^3*e^(5*I*f*x + 5*I*e) + (-292*I*A + 219*B)*c^3*e^(3*I*f*x + 3*I*e) + (-132*I*A + 147*B)*c^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)))/(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
788,1,543,0,0.734240," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{{\left(9 \, A^{2} + 12 i \, A B - 4 \, B^{2}\right)} a 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{2 \, {\left({\left({\left(-12 i \, A + 8 \, B\right)} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-12 i \, A + 8 \, B\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}} + 2 \, \sqrt{\frac{{\left(9 \, A^{2} + 12 i \, A B - 4 \, B^{2}\right)} a c^{5}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-3 i \, A + 2 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-3 i \, A + 2 \, B\right)} c^{2}}\right) - 3 \, \sqrt{\frac{{\left(9 \, A^{2} + 12 i \, A B - 4 \, B^{2}\right)} a 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{2 \, {\left({\left({\left(-12 i \, A + 8 \, B\right)} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-12 i \, A + 8 \, B\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}} - 2 \, \sqrt{\frac{{\left(9 \, A^{2} + 12 i \, A B - 4 \, B^{2}\right)} a c^{5}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-3 i \, A + 2 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-3 i \, A + 2 \, B\right)} c^{2}}\right) - 2 \, {\left({\left(-18 i \, A + 12 \, B\right)} c^{2} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-48 i \, A + 32 \, B\right)} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-30 i \, A + 36 \, B\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}}}{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((9*A^2 + 12*I*A*B - 4*B^2)*a*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(2*(((-12*I*A + 8*B)*c^2*e^(3*I*f*x + 3*I*e) + (-12*I*A + 8*B)*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*sqrt((9*A^2 + 12*I*A*B - 4*B^2)*a*c^5/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-3*I*A + 2*B)*c^2*e^(2*I*f*x + 2*I*e) + (-3*I*A + 2*B)*c^2)) - 3*sqrt((9*A^2 + 12*I*A*B - 4*B^2)*a*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(2*(((-12*I*A + 8*B)*c^2*e^(3*I*f*x + 3*I*e) + (-12*I*A + 8*B)*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*sqrt((9*A^2 + 12*I*A*B - 4*B^2)*a*c^5/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-3*I*A + 2*B)*c^2*e^(2*I*f*x + 2*I*e) + (-3*I*A + 2*B)*c^2)) - 2*((-18*I*A + 12*B)*c^2*e^(5*I*f*x + 5*I*e) + (-48*I*A + 32*B)*c^2*e^(3*I*f*x + 3*I*e) + (-30*I*A + 36*B)*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
789,1,458,0,0.987628," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{{\left(4 \, A^{2} + 4 i \, A B - B^{2}\right)} a c^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{2 \, {\left({\left({\left(-8 i \, A + 4 \, B\right)} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-8 i \, A + 4 \, B\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}} + 2 \, \sqrt{\frac{{\left(4 \, A^{2} + 4 i \, A B - B^{2}\right)} a c^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-2 i \, A + B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-2 i \, A + B\right)} c}\right) - \sqrt{\frac{{\left(4 \, A^{2} + 4 i \, A B - B^{2}\right)} a c^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{2 \, {\left({\left({\left(-8 i \, A + 4 \, B\right)} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-8 i \, A + 4 \, B\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}} - 2 \, \sqrt{\frac{{\left(4 \, A^{2} + 4 i \, A B - B^{2}\right)} a c^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-2 i \, A + B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-2 i \, A + B\right)} c}\right) - 2 \, {\left({\left(-4 i \, A + 2 \, B\right)} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-4 i \, A + 6 \, B\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}}}{4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/4*(sqrt((4*A^2 + 4*I*A*B - B^2)*a*c^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log(2*(((-8*I*A + 4*B)*c*e^(3*I*f*x + 3*I*e) + (-8*I*A + 4*B)*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*sqrt((4*A^2 + 4*I*A*B - B^2)*a*c^3/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-2*I*A + B)*c*e^(2*I*f*x + 2*I*e) + (-2*I*A + B)*c)) - sqrt((4*A^2 + 4*I*A*B - B^2)*a*c^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log(2*(((-8*I*A + 4*B)*c*e^(3*I*f*x + 3*I*e) + (-8*I*A + 4*B)*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*sqrt((4*A^2 + 4*I*A*B - B^2)*a*c^3/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-2*I*A + B)*c*e^(2*I*f*x + 2*I*e) + (-2*I*A + B)*c)) - 2*((-4*I*A + 2*B)*c*e^(3*I*f*x + 3*I*e) + (-4*I*A + 6*B)*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
790,1,291,0,0.932284," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)),x, algorithm=""fricas"")","\frac{4 \, B \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)} - \sqrt{\frac{A^{2} a 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^{2} a 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) + \sqrt{\frac{A^{2} a 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^{2} a 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 \, f}"," ",0,"1/2*(4*B*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) - sqrt(A^2*a*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^2*a*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)) + sqrt(A^2*a*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^2*a*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
791,1,336,0,1.531173," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{c f \sqrt{-\frac{B^{2} a}{c f^{2}}} \log\left(\frac{4 \, {\left(2 \, {\left(B e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(c f e^{\left(2 i \, f x + 2 i \, e\right)} - c f\right)} \sqrt{-\frac{B^{2} a}{c f^{2}}}\right)}}{B e^{\left(2 i \, f x + 2 i \, e\right)} + B}\right) - c f \sqrt{-\frac{B^{2} a}{c f^{2}}} \log\left(\frac{4 \, {\left(2 \, {\left(B e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(c f e^{\left(2 i \, f x + 2 i \, e\right)} - c f\right)} \sqrt{-\frac{B^{2} a}{c f^{2}}}\right)}}{B e^{\left(2 i \, f x + 2 i \, e\right)} + B}\right) - {\left({\left(-2 i \, A - 2 \, B\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-2 i \, A - 2 \, B\right)} 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(-B^2*a/(c*f^2))*log(4*(2*(B*e^(3*I*f*x + 3*I*e) + B*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)*sqrt(-B^2*a/(c*f^2)))/(B*e^(2*I*f*x + 2*I*e) + B)) - c*f*sqrt(-B^2*a/(c*f^2))*log(4*(2*(B*e^(3*I*f*x + 3*I*e) + B*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)*sqrt(-B^2*a/(c*f^2)))/(B*e^(2*I*f*x + 2*I*e) + B)) - ((-2*I*A - 2*B)*e^(3*I*f*x + 3*I*e) + (-2*I*A - 2*B)*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
792,1,94,0,0.626188," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(-i \, A - B\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-4 i \, A + 2 \, B\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-3 i \, A + 3 \, B\right)} 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*((-I*A - B)*e^(5*I*f*x + 5*I*e) + (-4*I*A + 2*B)*e^(3*I*f*x + 3*I*e) + (-3*I*A + 3*B)*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)","A",0
793,1,111,0,1.379695," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(-3 i \, A - 3 \, B\right)} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-13 i \, A - 3 \, B\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-25 i \, A + 15 \, B\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-15 i \, A + 15 \, B\right)} 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}}}{60 \, c^{3} f}"," ",0,"1/60*((-3*I*A - 3*B)*e^(7*I*f*x + 7*I*e) + (-13*I*A - 3*B)*e^(5*I*f*x + 5*I*e) + (-25*I*A + 15*B)*e^(3*I*f*x + 3*I*e) + (-15*I*A + 15*B)*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)","A",0
794,1,128,0,0.649944," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left({\left(-15 i \, A - 15 \, B\right)} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-78 i \, A - 36 \, B\right)} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-168 i \, A + 14 \, B\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-210 i \, A + 140 \, B\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-105 i \, A + 105 \, B\right)} 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}}}{840 \, c^{4} f}"," ",0,"1/840*((-15*I*A - 15*B)*e^(9*I*f*x + 9*I*e) + (-78*I*A - 36*B)*e^(7*I*f*x + 7*I*e) + (-168*I*A + 14*B)*e^(5*I*f*x + 5*I*e) + (-210*I*A + 140*B)*e^(3*I*f*x + 3*I*e) + (-105*I*A + 105*B)*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^4*f)","A",0
795,1,676,0,0.750182," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{{\left(25 \, A^{2} + 20 i \, A B - 4 \, B^{2}\right)} a^{3} c^{7}}{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{2 \, {\left({\left({\left(-20 i \, A + 8 \, B\right)} a c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-20 i \, A + 8 \, B\right)} a c^{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}} + 2 \, \sqrt{\frac{{\left(25 \, A^{2} + 20 i \, A B - 4 \, B^{2}\right)} a^{3} c^{7}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-5 i \, A + 2 \, B\right)} a c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-5 i \, A + 2 \, B\right)} a c^{3}}\right) - 15 \, \sqrt{\frac{{\left(25 \, A^{2} + 20 i \, A B - 4 \, B^{2}\right)} a^{3} c^{7}}{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{2 \, {\left({\left({\left(-20 i \, A + 8 \, B\right)} a c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-20 i \, A + 8 \, B\right)} a c^{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}} - 2 \, \sqrt{\frac{{\left(25 \, A^{2} + 20 i \, A B - 4 \, B^{2}\right)} a^{3} c^{7}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-5 i \, A + 2 \, B\right)} a c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-5 i \, A + 2 \, B\right)} a c^{3}}\right) - 4 \, {\left({\left(-75 i \, A + 30 \, B\right)} a c^{3} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-350 i \, A + 140 \, B\right)} a c^{3} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-640 i \, A + 256 \, B\right)} a c^{3} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-290 i \, A + 500 \, B\right)} a c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(75 i \, A - 30 \, B\right)} a c^{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}}}{240 \, {\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,"-1/240*(15*sqrt((25*A^2 + 20*I*A*B - 4*B^2)*a^3*c^7/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(2*(((-20*I*A + 8*B)*a*c^3*e^(3*I*f*x + 3*I*e) + (-20*I*A + 8*B)*a*c^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*sqrt((25*A^2 + 20*I*A*B - 4*B^2)*a^3*c^7/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-5*I*A + 2*B)*a*c^3*e^(2*I*f*x + 2*I*e) + (-5*I*A + 2*B)*a*c^3)) - 15*sqrt((25*A^2 + 20*I*A*B - 4*B^2)*a^3*c^7/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(2*(((-20*I*A + 8*B)*a*c^3*e^(3*I*f*x + 3*I*e) + (-20*I*A + 8*B)*a*c^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*sqrt((25*A^2 + 20*I*A*B - 4*B^2)*a^3*c^7/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-5*I*A + 2*B)*a*c^3*e^(2*I*f*x + 2*I*e) + (-5*I*A + 2*B)*a*c^3)) - 4*((-75*I*A + 30*B)*a*c^3*e^(9*I*f*x + 9*I*e) + (-350*I*A + 140*B)*a*c^3*e^(7*I*f*x + 7*I*e) + (-640*I*A + 256*B)*a*c^3*e^(5*I*f*x + 5*I*e) + (-290*I*A + 500*B)*a*c^3*e^(3*I*f*x + 3*I*e) + (75*I*A - 30*B)*a*c^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)))/(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
796,1,611,0,0.803473," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{{\left(16 \, A^{2} + 8 i \, A B - B^{2}\right)} a^{3} 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{2 \, {\left({\left({\left(-16 i \, A + 4 \, B\right)} a c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-16 i \, A + 4 \, B\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}} + 2 \, \sqrt{\frac{{\left(16 \, A^{2} + 8 i \, A B - B^{2}\right)} a^{3} c^{5}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-4 i \, A + B\right)} a c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-4 i \, A + B\right)} a c^{2}}\right) - 3 \, \sqrt{\frac{{\left(16 \, A^{2} + 8 i \, A B - B^{2}\right)} a^{3} 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{2 \, {\left({\left({\left(-16 i \, A + 4 \, B\right)} a c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-16 i \, A + 4 \, B\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}} - 2 \, \sqrt{\frac{{\left(16 \, A^{2} + 8 i \, A B - B^{2}\right)} a^{3} c^{5}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-4 i \, A + B\right)} a c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-4 i \, A + B\right)} a c^{2}}\right) - 4 \, {\left({\left(-12 i \, A + 3 \, B\right)} a c^{2} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-44 i \, A + 11 \, B\right)} a c^{2} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-20 i \, A + 53 \, B\right)} a c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(12 i \, A - 3 \, B\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}}}{48 \, {\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,"-1/48*(3*sqrt((16*A^2 + 8*I*A*B - B^2)*a^3*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(2*(((-16*I*A + 4*B)*a*c^2*e^(3*I*f*x + 3*I*e) + (-16*I*A + 4*B)*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)) + 2*sqrt((16*A^2 + 8*I*A*B - B^2)*a^3*c^5/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-4*I*A + B)*a*c^2*e^(2*I*f*x + 2*I*e) + (-4*I*A + B)*a*c^2)) - 3*sqrt((16*A^2 + 8*I*A*B - B^2)*a^3*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(2*(((-16*I*A + 4*B)*a*c^2*e^(3*I*f*x + 3*I*e) + (-16*I*A + 4*B)*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)) - 2*sqrt((16*A^2 + 8*I*A*B - B^2)*a^3*c^5/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-4*I*A + B)*a*c^2*e^(2*I*f*x + 2*I*e) + (-4*I*A + B)*a*c^2)) - 4*((-12*I*A + 3*B)*a*c^2*e^(7*I*f*x + 7*I*e) + (-44*I*A + 11*B)*a*c^2*e^(5*I*f*x + 5*I*e) + (-20*I*A + 53*B)*a*c^2*e^(3*I*f*x + 3*I*e) + (12*I*A - 3*B)*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^(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
797,1,429,0,1.072202," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{A^{2} a^{3} 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 a c e^{\left(3 i \, f x + 3 i \, e\right)} + A 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^{2} 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 a c e^{\left(2 i \, f x + 2 i \, e\right)} + A a c}\right) - 3 \, \sqrt{\frac{A^{2} a^{3} 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 a c e^{\left(3 i \, f x + 3 i \, e\right)} + A 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^{2} 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 a c e^{\left(2 i \, f x + 2 i \, e\right)} + A a c}\right) - 2 \, {\left(-6 i \, A a c e^{\left(5 i \, f x + 5 i \, e\right)} + 16 \, B a c e^{\left(3 i \, f x + 3 i \, e\right)} + 6 i \, A 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}}}{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^2*a^3*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*a*c*e^(3*I*f*x + 3*I*e) + A*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^2*a^3*c^3/f^2)*(4*I*f*e^(2*I*f*x + 2*I*e) - 4*I*f))/(A*a*c*e^(2*I*f*x + 2*I*e) + A*a*c)) - 3*sqrt(A^2*a^3*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*a*c*e^(3*I*f*x + 3*I*e) + A*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^2*a^3*c^3/f^2)*(-4*I*f*e^(2*I*f*x + 2*I*e) + 4*I*f))/(A*a*c*e^(2*I*f*x + 2*I*e) + A*a*c)) - 2*(-6*I*A*a*c*e^(5*I*f*x + 5*I*e) + 16*B*a*c*e^(3*I*f*x + 3*I*e) + 6*I*A*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^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
798,1,458,0,0.723111," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)),x, algorithm=""fricas"")","\frac{\sqrt{\frac{{\left(4 \, A^{2} - 4 i \, A B - B^{2}\right)} a^{3} c}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{2 \, {\left({\left({\left(8 i \, A + 4 \, B\right)} a e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(8 i \, A + 4 \, B\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}} + 2 \, \sqrt{\frac{{\left(4 \, A^{2} - 4 i \, A B - B^{2}\right)} a^{3} c}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(2 i \, A + B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, A + B\right)} a}\right) - \sqrt{\frac{{\left(4 \, A^{2} - 4 i \, A B - B^{2}\right)} a^{3} c}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{2 \, {\left({\left({\left(8 i \, A + 4 \, B\right)} a e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(8 i \, A + 4 \, B\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}} - 2 \, \sqrt{\frac{{\left(4 \, A^{2} - 4 i \, A B - B^{2}\right)} a^{3} c}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(2 i \, A + B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, A + B\right)} a}\right) + 2 \, {\left({\left(4 i \, A + 6 \, B\right)} a e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(4 i \, A + 2 \, B\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}}}{4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/4*(sqrt((4*A^2 - 4*I*A*B - B^2)*a^3*c/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log(2*(((8*I*A + 4*B)*a*e^(3*I*f*x + 3*I*e) + (8*I*A + 4*B)*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*sqrt((4*A^2 - 4*I*A*B - B^2)*a^3*c/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((2*I*A + B)*a*e^(2*I*f*x + 2*I*e) + (2*I*A + B)*a)) - sqrt((4*A^2 - 4*I*A*B - B^2)*a^3*c/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log(2*(((8*I*A + 4*B)*a*e^(3*I*f*x + 3*I*e) + (8*I*A + 4*B)*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*sqrt((4*A^2 - 4*I*A*B - B^2)*a^3*c/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((2*I*A + B)*a*e^(2*I*f*x + 2*I*e) + (2*I*A + B)*a)) + 2*((4*I*A + 6*B)*a*e^(3*I*f*x + 3*I*e) + (4*I*A + 2*B)*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)))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
799,1,446,0,1.045208," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{c \sqrt{\frac{{\left(4 \, A^{2} - 16 i \, A B - 16 \, B^{2}\right)} a^{3}}{c f^{2}}} f \log\left(\frac{2 \, {\left({\left({\left(4 i \, A + 8 \, B\right)} a e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(4 i \, A + 8 \, B\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(c f e^{\left(2 i \, f x + 2 i \, e\right)} - c f\right)} \sqrt{\frac{{\left(4 \, A^{2} - 16 i \, A B - 16 \, B^{2}\right)} a^{3}}{c f^{2}}}\right)}}{{\left(i \, A + 2 \, B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A + 2 \, B\right)} a}\right) - c \sqrt{\frac{{\left(4 \, A^{2} - 16 i \, A B - 16 \, B^{2}\right)} a^{3}}{c f^{2}}} f \log\left(\frac{2 \, {\left({\left({\left(4 i \, A + 8 \, B\right)} a e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(4 i \, A + 8 \, B\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(c f e^{\left(2 i \, f x + 2 i \, e\right)} - c f\right)} \sqrt{\frac{{\left(4 \, A^{2} - 16 i \, A B - 16 \, B^{2}\right)} a^{3}}{c f^{2}}}\right)}}{{\left(i \, A + 2 \, B\right)} a e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A + 2 \, B\right)} a}\right) - 2 \, {\left({\left(-4 i \, A - 4 \, B\right)} a e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-4 i \, A - 8 \, B\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}}}{4 \, c f}"," ",0,"-1/4*(c*sqrt((4*A^2 - 16*I*A*B - 16*B^2)*a^3/(c*f^2))*f*log(2*(((4*I*A + 8*B)*a*e^(3*I*f*x + 3*I*e) + (4*I*A + 8*B)*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*e^(2*I*f*x + 2*I*e) - c*f)*sqrt((4*A^2 - 16*I*A*B - 16*B^2)*a^3/(c*f^2)))/((I*A + 2*B)*a*e^(2*I*f*x + 2*I*e) + (I*A + 2*B)*a)) - c*sqrt((4*A^2 - 16*I*A*B - 16*B^2)*a^3/(c*f^2))*f*log(2*(((4*I*A + 8*B)*a*e^(3*I*f*x + 3*I*e) + (4*I*A + 8*B)*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*e^(2*I*f*x + 2*I*e) - c*f)*sqrt((4*A^2 - 16*I*A*B - 16*B^2)*a^3/(c*f^2)))/((I*A + 2*B)*a*e^(2*I*f*x + 2*I*e) + (I*A + 2*B)*a)) - 2*((-4*I*A - 4*B)*a*e^(3*I*f*x + 3*I*e) + (-4*I*A - 8*B)*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
800,1,381,0,1.767786," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{3 \, c^{2} f \sqrt{-\frac{B^{2} a^{3}}{c^{3} f^{2}}} \log\left(\frac{4 \, {\left(2 \, {\left(B a e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{2} f\right)} \sqrt{-\frac{B^{2} a^{3}}{c^{3} f^{2}}}\right)}}{B a e^{\left(2 i \, f x + 2 i \, e\right)} + B a}\right) - 3 \, c^{2} f \sqrt{-\frac{B^{2} a^{3}}{c^{3} f^{2}}} \log\left(\frac{4 \, {\left(2 \, {\left(B a e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{2} f\right)} \sqrt{-\frac{B^{2} a^{3}}{c^{3} f^{2}}}\right)}}{B a e^{\left(2 i \, f x + 2 i \, e\right)} + B a}\right) + {\left({\left(-2 i \, A - 2 \, B\right)} a e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-2 i \, A + 10 \, B\right)} a e^{\left(3 i \, f x + 3 i \, e\right)} + 12 \, B 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}}}{6 \, c^{2} f}"," ",0,"1/6*(3*c^2*f*sqrt(-B^2*a^3/(c^3*f^2))*log(4*(2*(B*a*e^(3*I*f*x + 3*I*e) + B*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^2*f*e^(2*I*f*x + 2*I*e) - c^2*f)*sqrt(-B^2*a^3/(c^3*f^2)))/(B*a*e^(2*I*f*x + 2*I*e) + B*a)) - 3*c^2*f*sqrt(-B^2*a^3/(c^3*f^2))*log(4*(2*(B*a*e^(3*I*f*x + 3*I*e) + B*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^2*f*e^(2*I*f*x + 2*I*e) - c^2*f)*sqrt(-B^2*a^3/(c^3*f^2)))/(B*a*e^(2*I*f*x + 2*I*e) + B*a)) + ((-2*I*A - 2*B)*a*e^(5*I*f*x + 5*I*e) + (-2*I*A + 10*B)*a*e^(3*I*f*x + 3*I*e) + 12*B*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^2*f)","B",0
801,1,97,0,0.666373," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(-3 i \, A - 3 \, B\right)} a e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-8 i \, A + 2 \, B\right)} a e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-5 i \, A + 5 \, B\right)} 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 - 3*B)*a*e^(7*I*f*x + 7*I*e) + (-8*I*A + 2*B)*a*e^(5*I*f*x + 5*I*e) + (-5*I*A + 5*B)*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
802,1,115,0,2.362236," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left({\left(-15 i \, A - 15 \, B\right)} a e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-57 i \, A - 15 \, B\right)} a e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-77 i \, A + 35 \, B\right)} a e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-35 i \, A + 35 \, B\right)} 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}}}{420 \, c^{4} f}"," ",0,"1/420*((-15*I*A - 15*B)*a*e^(9*I*f*x + 9*I*e) + (-57*I*A - 15*B)*a*e^(7*I*f*x + 7*I*e) + (-77*I*A + 35*B)*a*e^(5*I*f*x + 5*I*e) + (-35*I*A + 35*B)*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^4*f)","A",0
803,1,133,0,1.345924," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{{\left({\left(-35 i \, A - 35 \, B\right)} a e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-170 i \, A - 80 \, B\right)} a e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-324 i \, A + 18 \, B\right)} a e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-294 i \, A + 168 \, B\right)} a e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-105 i \, A + 105 \, B\right)} 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}}}{2520 \, c^{5} f}"," ",0,"1/2520*((-35*I*A - 35*B)*a*e^(11*I*f*x + 11*I*e) + (-170*I*A - 80*B)*a*e^(9*I*f*x + 9*I*e) + (-324*I*A + 18*B)*a*e^(7*I*f*x + 7*I*e) + (-294*I*A + 168*B)*a*e^(5*I*f*x + 5*I*e) + (-105*I*A + 105*B)*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^5*f)","A",0
804,1,151,0,0.807807," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(11/2),x, algorithm=""fricas"")","\frac{{\left({\left(-315 i \, A - 315 \, B\right)} a e^{\left(13 i \, f x + 13 i \, e\right)} + {\left(-1855 i \, A - 1085 \, B\right)} a e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-4510 i \, A - 770 \, B\right)} a e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-5742 i \, A + 1386 \, B\right)} a e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-3927 i \, A + 2541 \, B\right)} a e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-1155 i \, A + 1155 \, B\right)} 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}}}{55440 \, c^{6} f}"," ",0,"1/55440*((-315*I*A - 315*B)*a*e^(13*I*f*x + 13*I*e) + (-1855*I*A - 1085*B)*a*e^(11*I*f*x + 11*I*e) + (-4510*I*A - 770*B)*a*e^(9*I*f*x + 9*I*e) + (-5742*I*A + 1386*B)*a*e^(7*I*f*x + 7*I*e) + (-3927*I*A + 2541*B)*a*e^(5*I*f*x + 5*I*e) + (-1155*I*A + 1155*B)*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^6*f)","A",0
805,1,753,0,0.660604," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{{\left(36 \, A^{2} + 12 i \, A B - B^{2}\right)} a^{5} c^{7}}{f^{2}}} {\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)} \log\left(\frac{2 \, {\left({\left({\left(-24 i \, A + 4 \, B\right)} a^{2} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-24 i \, A + 4 \, B\right)} a^{2} c^{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}} + 2 \, \sqrt{\frac{{\left(36 \, A^{2} + 12 i \, A B - B^{2}\right)} a^{5} c^{7}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-6 i \, A + B\right)} a^{2} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-6 i \, A + B\right)} a^{2} c^{3}}\right) - 15 \, \sqrt{\frac{{\left(36 \, A^{2} + 12 i \, A B - B^{2}\right)} a^{5} c^{7}}{f^{2}}} {\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)} \log\left(\frac{2 \, {\left({\left({\left(-24 i \, A + 4 \, B\right)} a^{2} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-24 i \, A + 4 \, B\right)} a^{2} c^{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}} - 2 \, \sqrt{\frac{{\left(36 \, A^{2} + 12 i \, A B - B^{2}\right)} a^{5} c^{7}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-6 i \, A + B\right)} a^{2} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-6 i \, A + B\right)} a^{2} c^{3}}\right) - 4 \, {\left({\left(-90 i \, A + 15 \, B\right)} a^{2} c^{3} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-510 i \, A + 85 \, B\right)} a^{2} c^{3} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-1188 i \, A + 198 \, B\right)} a^{2} c^{3} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-348 i \, A + 1338 \, B\right)} a^{2} c^{3} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(510 i \, A - 85 \, B\right)} a^{2} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(90 i \, A - 15 \, B\right)} a^{2} c^{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}}}{480 \, {\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,"-1/480*(15*sqrt((36*A^2 + 12*I*A*B - B^2)*a^5*c^7/f^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)*log(2*(((-24*I*A + 4*B)*a^2*c^3*e^(3*I*f*x + 3*I*e) + (-24*I*A + 4*B)*a^2*c^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*sqrt((36*A^2 + 12*I*A*B - B^2)*a^5*c^7/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-6*I*A + B)*a^2*c^3*e^(2*I*f*x + 2*I*e) + (-6*I*A + B)*a^2*c^3)) - 15*sqrt((36*A^2 + 12*I*A*B - B^2)*a^5*c^7/f^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)*log(2*(((-24*I*A + 4*B)*a^2*c^3*e^(3*I*f*x + 3*I*e) + (-24*I*A + 4*B)*a^2*c^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*sqrt((36*A^2 + 12*I*A*B - B^2)*a^5*c^7/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-6*I*A + B)*a^2*c^3*e^(2*I*f*x + 2*I*e) + (-6*I*A + B)*a^2*c^3)) - 4*((-90*I*A + 15*B)*a^2*c^3*e^(11*I*f*x + 11*I*e) + (-510*I*A + 85*B)*a^2*c^3*e^(9*I*f*x + 9*I*e) + (-1188*I*A + 198*B)*a^2*c^3*e^(7*I*f*x + 7*I*e) + (-348*I*A + 1338*B)*a^2*c^3*e^(5*I*f*x + 5*I*e) + (510*I*A - 85*B)*a^2*c^3*e^(3*I*f*x + 3*I*e) + (90*I*A - 15*B)*a^2*c^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)))/(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
806,1,583,0,0.947036," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{A^{2} a^{5} c^{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{32 \, {\left(A a^{2} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + A 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^{2} 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 a^{2} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + A a^{2} c^{2}\right)}}\right) - 15 \, \sqrt{\frac{A^{2} a^{5} c^{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{32 \, {\left(A a^{2} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + A 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^{2} 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 a^{2} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + A a^{2} c^{2}\right)}}\right) - 4 \, {\left(-15 i \, A a^{2} c^{2} e^{\left(9 i \, f x + 9 i \, e\right)} - 70 i \, A a^{2} c^{2} e^{\left(7 i \, f x + 7 i \, e\right)} + 128 \, B a^{2} c^{2} e^{\left(5 i \, f x + 5 i \, e\right)} + 70 i \, A a^{2} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + 15 i \, A 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}}}{80 \, {\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,"-1/80*(15*sqrt(A^2*a^5*c^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*(32*(A*a^2*c^2*e^(3*I*f*x + 3*I*e) + A*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^2*a^5*c^5/f^2)*(16*I*f*e^(2*I*f*x + 2*I*e) - 16*I*f))/(A*a^2*c^2*e^(2*I*f*x + 2*I*e) + A*a^2*c^2)) - 15*sqrt(A^2*a^5*c^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*(32*(A*a^2*c^2*e^(3*I*f*x + 3*I*e) + A*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^2*a^5*c^5/f^2)*(-16*I*f*e^(2*I*f*x + 2*I*e) + 16*I*f))/(A*a^2*c^2*e^(2*I*f*x + 2*I*e) + A*a^2*c^2)) - 4*(-15*I*A*a^2*c^2*e^(9*I*f*x + 9*I*e) - 70*I*A*a^2*c^2*e^(7*I*f*x + 7*I*e) + 128*B*a^2*c^2*e^(5*I*f*x + 5*I*e) + 70*I*A*a^2*c^2*e^(3*I*f*x + 3*I*e) + 15*I*A*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^(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
807,1,611,0,0.966693," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{{\left(16 \, A^{2} - 8 i \, A B - B^{2}\right)} a^{5} c^{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{2 \, {\left({\left({\left(16 i \, A + 4 \, B\right)} a^{2} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(16 i \, A + 4 \, B\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}} + 2 \, \sqrt{\frac{{\left(16 \, A^{2} - 8 i \, A B - B^{2}\right)} a^{5} c^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(4 i \, A + B\right)} a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 i \, A + B\right)} a^{2} c}\right) - 3 \, \sqrt{\frac{{\left(16 \, A^{2} - 8 i \, A B - B^{2}\right)} a^{5} c^{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{2 \, {\left({\left({\left(16 i \, A + 4 \, B\right)} a^{2} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(16 i \, A + 4 \, B\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}} - 2 \, \sqrt{\frac{{\left(16 \, A^{2} - 8 i \, A B - B^{2}\right)} a^{5} c^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(4 i \, A + B\right)} a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 i \, A + B\right)} a^{2} c}\right) + 4 \, {\left({\left(-12 i \, A - 3 \, B\right)} a^{2} c e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(20 i \, A + 53 \, B\right)} a^{2} c e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(44 i \, A + 11 \, B\right)} a^{2} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(12 i \, A + 3 \, B\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}}}{48 \, {\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,"1/48*(3*sqrt((16*A^2 - 8*I*A*B - B^2)*a^5*c^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(2*(((16*I*A + 4*B)*a^2*c*e^(3*I*f*x + 3*I*e) + (16*I*A + 4*B)*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)) + 2*sqrt((16*A^2 - 8*I*A*B - B^2)*a^5*c^3/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((4*I*A + B)*a^2*c*e^(2*I*f*x + 2*I*e) + (4*I*A + B)*a^2*c)) - 3*sqrt((16*A^2 - 8*I*A*B - B^2)*a^5*c^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(2*(((16*I*A + 4*B)*a^2*c*e^(3*I*f*x + 3*I*e) + (16*I*A + 4*B)*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)) - 2*sqrt((16*A^2 - 8*I*A*B - B^2)*a^5*c^3/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((4*I*A + B)*a^2*c*e^(2*I*f*x + 2*I*e) + (4*I*A + B)*a^2*c)) + 4*((-12*I*A - 3*B)*a^2*c*e^(7*I*f*x + 7*I*e) + (20*I*A + 53*B)*a^2*c*e^(5*I*f*x + 5*I*e) + (44*I*A + 11*B)*a^2*c*e^(3*I*f*x + 3*I*e) + (12*I*A + 3*B)*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^(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
808,1,543,0,1.726707," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{{\left(9 \, A^{2} - 12 i \, A B - 4 \, B^{2}\right)} a^{5} c}{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{2 \, {\left({\left({\left(12 i \, A + 8 \, B\right)} a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(12 i \, A + 8 \, B\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}} + 2 \, \sqrt{\frac{{\left(9 \, A^{2} - 12 i \, A B - 4 \, B^{2}\right)} a^{5} c}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(3 i \, A + 2 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(3 i \, A + 2 \, B\right)} a^{2}}\right) - 3 \, \sqrt{\frac{{\left(9 \, A^{2} - 12 i \, A B - 4 \, B^{2}\right)} a^{5} c}{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{2 \, {\left({\left({\left(12 i \, A + 8 \, B\right)} a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(12 i \, A + 8 \, B\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}} - 2 \, \sqrt{\frac{{\left(9 \, A^{2} - 12 i \, A B - 4 \, B^{2}\right)} a^{5} c}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(3 i \, A + 2 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(3 i \, A + 2 \, B\right)} a^{2}}\right) + 2 \, {\left({\left(30 i \, A + 36 \, B\right)} a^{2} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(48 i \, A + 32 \, B\right)} a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(18 i \, A + 12 \, B\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}}}{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((9*A^2 - 12*I*A*B - 4*B^2)*a^5*c/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log(2*(((12*I*A + 8*B)*a^2*e^(3*I*f*x + 3*I*e) + (12*I*A + 8*B)*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*sqrt((9*A^2 - 12*I*A*B - 4*B^2)*a^5*c/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((3*I*A + 2*B)*a^2*e^(2*I*f*x + 2*I*e) + (3*I*A + 2*B)*a^2)) - 3*sqrt((9*A^2 - 12*I*A*B - 4*B^2)*a^5*c/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log(2*(((12*I*A + 8*B)*a^2*e^(3*I*f*x + 3*I*e) + (12*I*A + 8*B)*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*sqrt((9*A^2 - 12*I*A*B - 4*B^2)*a^5*c/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((3*I*A + 2*B)*a^2*e^(2*I*f*x + 2*I*e) + (3*I*A + 2*B)*a^2)) + 2*((30*I*A + 36*B)*a^2*e^(5*I*f*x + 5*I*e) + (48*I*A + 32*B)*a^2*e^(3*I*f*x + 3*I*e) + (18*I*A + 12*B)*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^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
809,1,527,0,0.820525," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{{\left(36 \, A^{2} - 108 i \, A B - 81 \, B^{2}\right)} a^{5}}{c f^{2}}} {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} + c f\right)} \log\left(\frac{2 \, {\left({\left({\left(24 i \, A + 36 \, B\right)} a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(24 i \, A + 36 \, B\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}} + 2 \, \sqrt{\frac{{\left(36 \, A^{2} - 108 i \, A B - 81 \, B^{2}\right)} a^{5}}{c f^{2}}} {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} - c f\right)}\right)}}{{\left(6 i \, A + 9 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 i \, A + 9 \, B\right)} a^{2}}\right) - \sqrt{\frac{{\left(36 \, A^{2} - 108 i \, A B - 81 \, B^{2}\right)} a^{5}}{c f^{2}}} {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} + c f\right)} \log\left(\frac{2 \, {\left({\left({\left(24 i \, A + 36 \, B\right)} a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(24 i \, A + 36 \, B\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}} - 2 \, \sqrt{\frac{{\left(36 \, A^{2} - 108 i \, A B - 81 \, B^{2}\right)} a^{5}}{c f^{2}}} {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} - c f\right)}\right)}}{{\left(6 i \, A + 9 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 i \, A + 9 \, B\right)} a^{2}}\right) - 2 \, {\left({\left(-8 i \, A - 8 \, B\right)} a^{2} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-20 i \, A - 30 \, B\right)} a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-12 i \, A - 18 \, B\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}}}{4 \, {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} + c f\right)}}"," ",0,"-1/4*(sqrt((36*A^2 - 108*I*A*B - 81*B^2)*a^5/(c*f^2))*(c*f*e^(2*I*f*x + 2*I*e) + c*f)*log(2*(((24*I*A + 36*B)*a^2*e^(3*I*f*x + 3*I*e) + (24*I*A + 36*B)*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*sqrt((36*A^2 - 108*I*A*B - 81*B^2)*a^5/(c*f^2))*(c*f*e^(2*I*f*x + 2*I*e) - c*f))/((6*I*A + 9*B)*a^2*e^(2*I*f*x + 2*I*e) + (6*I*A + 9*B)*a^2)) - sqrt((36*A^2 - 108*I*A*B - 81*B^2)*a^5/(c*f^2))*(c*f*e^(2*I*f*x + 2*I*e) + c*f)*log(2*(((24*I*A + 36*B)*a^2*e^(3*I*f*x + 3*I*e) + (24*I*A + 36*B)*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*sqrt((36*A^2 - 108*I*A*B - 81*B^2)*a^5/(c*f^2))*(c*f*e^(2*I*f*x + 2*I*e) - c*f))/((6*I*A + 9*B)*a^2*e^(2*I*f*x + 2*I*e) + (6*I*A + 9*B)*a^2)) - 2*((-8*I*A - 8*B)*a^2*e^(5*I*f*x + 5*I*e) + (-20*I*A - 30*B)*a^2*e^(3*I*f*x + 3*I*e) + (-12*I*A - 18*B)*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*e^(2*I*f*x + 2*I*e) + c*f)","B",0
810,1,499,0,0.833021," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{3 \, c^{2} \sqrt{\frac{{\left(4 \, A^{2} - 32 i \, A B - 64 \, B^{2}\right)} a^{5}}{c^{3} f^{2}}} f \log\left(\frac{2 \, {\left({\left({\left(4 i \, A + 16 \, B\right)} a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(4 i \, A + 16 \, B\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(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{2} f\right)} \sqrt{\frac{{\left(4 \, A^{2} - 32 i \, A B - 64 \, B^{2}\right)} a^{5}}{c^{3} f^{2}}}\right)}}{{\left(i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A + 4 \, B\right)} a^{2}}\right) - 3 \, c^{2} \sqrt{\frac{{\left(4 \, A^{2} - 32 i \, A B - 64 \, B^{2}\right)} a^{5}}{c^{3} f^{2}}} f \log\left(\frac{2 \, {\left({\left({\left(4 i \, A + 16 \, B\right)} a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(4 i \, A + 16 \, B\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(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{2} f\right)} \sqrt{\frac{{\left(4 \, A^{2} - 32 i \, A B - 64 \, B^{2}\right)} a^{5}}{c^{3} f^{2}}}\right)}}{{\left(i \, A + 4 \, B\right)} a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A + 4 \, B\right)} a^{2}}\right) + 2 \, {\left({\left(-4 i \, A - 4 \, B\right)} a^{2} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(8 i \, A + 32 \, B\right)} a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(12 i \, A + 48 \, B\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}}}{12 \, c^{2} f}"," ",0,"1/12*(3*c^2*sqrt((4*A^2 - 32*I*A*B - 64*B^2)*a^5/(c^3*f^2))*f*log(2*(((4*I*A + 16*B)*a^2*e^(3*I*f*x + 3*I*e) + (4*I*A + 16*B)*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*e^(2*I*f*x + 2*I*e) - c^2*f)*sqrt((4*A^2 - 32*I*A*B - 64*B^2)*a^5/(c^3*f^2)))/((I*A + 4*B)*a^2*e^(2*I*f*x + 2*I*e) + (I*A + 4*B)*a^2)) - 3*c^2*sqrt((4*A^2 - 32*I*A*B - 64*B^2)*a^5/(c^3*f^2))*f*log(2*(((4*I*A + 16*B)*a^2*e^(3*I*f*x + 3*I*e) + (4*I*A + 16*B)*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*e^(2*I*f*x + 2*I*e) - c^2*f)*sqrt((4*A^2 - 32*I*A*B - 64*B^2)*a^5/(c^3*f^2)))/((I*A + 4*B)*a^2*e^(2*I*f*x + 2*I*e) + (I*A + 4*B)*a^2)) + 2*((-4*I*A - 4*B)*a^2*e^(5*I*f*x + 5*I*e) + (8*I*A + 32*B)*a^2*e^(3*I*f*x + 3*I*e) + (12*I*A + 48*B)*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
811,1,419,0,1.415045," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{15 \, c^{3} f \sqrt{-\frac{B^{2} a^{5}}{c^{5} f^{2}}} \log\left(\frac{4 \, {\left(2 \, {\left(B a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{3} f\right)} \sqrt{-\frac{B^{2} a^{5}}{c^{5} f^{2}}}\right)}}{B a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + B a^{2}}\right) - 15 \, c^{3} f \sqrt{-\frac{B^{2} a^{5}}{c^{5} f^{2}}} \log\left(\frac{4 \, {\left(2 \, {\left(B a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{3} f\right)} \sqrt{-\frac{B^{2} a^{5}}{c^{5} f^{2}}}\right)}}{B a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + B a^{2}}\right) - {\left({\left(-6 i \, A - 6 \, B\right)} a^{2} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-6 i \, A + 14 \, B\right)} a^{2} e^{\left(5 i \, f x + 5 i \, e\right)} - 40 \, B a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} - 60 \, B 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}}}{30 \, c^{3} f}"," ",0,"-1/30*(15*c^3*f*sqrt(-B^2*a^5/(c^5*f^2))*log(4*(2*(B*a^2*e^(3*I*f*x + 3*I*e) + B*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^3*f*e^(2*I*f*x + 2*I*e) - c^3*f)*sqrt(-B^2*a^5/(c^5*f^2)))/(B*a^2*e^(2*I*f*x + 2*I*e) + B*a^2)) - 15*c^3*f*sqrt(-B^2*a^5/(c^5*f^2))*log(4*(2*(B*a^2*e^(3*I*f*x + 3*I*e) + B*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^3*f*e^(2*I*f*x + 2*I*e) - c^3*f)*sqrt(-B^2*a^5/(c^5*f^2)))/(B*a^2*e^(2*I*f*x + 2*I*e) + B*a^2)) - ((-6*I*A - 6*B)*a^2*e^(7*I*f*x + 7*I*e) + (-6*I*A + 14*B)*a^2*e^(5*I*f*x + 5*I*e) - 40*B*a^2*e^(3*I*f*x + 3*I*e) - 60*B*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^3*f)","B",0
812,1,103,0,1.889737," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left({\left(-5 i \, A - 5 \, B\right)} a^{2} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-12 i \, A + 2 \, B\right)} a^{2} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-7 i \, A + 7 \, B\right)} 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}}}{70 \, c^{4} f}"," ",0,"1/70*((-5*I*A - 5*B)*a^2*e^(9*I*f*x + 9*I*e) + (-12*I*A + 2*B)*a^2*e^(7*I*f*x + 7*I*e) + (-7*I*A + 7*B)*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^4*f)","A",0
813,1,123,0,0.886829," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{{\left({\left(-35 i \, A - 35 \, B\right)} a^{2} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-125 i \, A - 35 \, B\right)} a^{2} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-153 i \, A + 63 \, B\right)} a^{2} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-63 i \, A + 63 \, B\right)} 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}}}{1260 \, c^{5} f}"," ",0,"1/1260*((-35*I*A - 35*B)*a^2*e^(11*I*f*x + 11*I*e) + (-125*I*A - 35*B)*a^2*e^(9*I*f*x + 9*I*e) + (-153*I*A + 63*B)*a^2*e^(7*I*f*x + 7*I*e) + (-63*I*A + 63*B)*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^5*f)","A",0
814,1,143,0,0.993765," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(11/2),x, algorithm=""fricas"")","\frac{{\left({\left(-315 i \, A - 315 \, B\right)} a^{2} e^{\left(13 i \, f x + 13 i \, e\right)} + {\left(-1470 i \, A - 700 \, B\right)} a^{2} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-2640 i \, A + 110 \, B\right)} a^{2} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-2178 i \, A + 1188 \, B\right)} a^{2} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-693 i \, A + 693 \, B\right)} 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}}}{27720 \, c^{6} f}"," ",0,"1/27720*((-315*I*A - 315*B)*a^2*e^(13*I*f*x + 13*I*e) + (-1470*I*A - 700*B)*a^2*e^(11*I*f*x + 11*I*e) + (-2640*I*A + 110*B)*a^2*e^(9*I*f*x + 9*I*e) + (-2178*I*A + 1188*B)*a^2*e^(7*I*f*x + 7*I*e) + (-693*I*A + 693*B)*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^6*f)","A",0
815,1,163,0,1.390867," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(13/2),x, algorithm=""fricas"")","\frac{{\left({\left(-1155 i \, A - 1155 \, B\right)} a^{2} e^{\left(15 i \, f x + 15 i \, e\right)} + {\left(-6615 i \, A - 3885 \, B\right)} a^{2} e^{\left(13 i \, f x + 13 i \, e\right)} + {\left(-15470 i \, A - 2730 \, B\right)} a^{2} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-18590 i \, A + 4290 \, B\right)} a^{2} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-11583 i \, A + 7293 \, B\right)} a^{2} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-3003 i \, A + 3003 \, B\right)} 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}}}{240240 \, c^{7} f}"," ",0,"1/240240*((-1155*I*A - 1155*B)*a^2*e^(15*I*f*x + 15*I*e) + (-6615*I*A - 3885*B)*a^2*e^(13*I*f*x + 13*I*e) + (-15470*I*A - 2730*B)*a^2*e^(11*I*f*x + 11*I*e) + (-18590*I*A + 4290*B)*a^2*e^(9*I*f*x + 9*I*e) + (-11583*I*A + 7293*B)*a^2*e^(7*I*f*x + 7*I*e) + (-3003*I*A + 3003*B)*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^7*f)","A",0
816,1,879,0,2.101056," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2),x, algorithm=""fricas"")","-\frac{21 \, \sqrt{\frac{{\left(1600 \, A^{2} + 400 i \, A B - 25 \, B^{2}\right)} a^{7} c^{9}}{f^{2}}} {\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)} \log\left(\frac{2 \, {\left({\left({\left(-160 i \, A + 20 \, B\right)} a^{3} c^{4} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-160 i \, A + 20 \, B\right)} a^{3} c^{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}} + 2 \, \sqrt{\frac{{\left(1600 \, A^{2} + 400 i \, A B - 25 \, B^{2}\right)} a^{7} c^{9}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-40 i \, A + 5 \, B\right)} a^{3} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-40 i \, A + 5 \, B\right)} a^{3} c^{4}}\right) - 21 \, \sqrt{\frac{{\left(1600 \, A^{2} + 400 i \, A B - 25 \, B^{2}\right)} a^{7} c^{9}}{f^{2}}} {\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)} \log\left(\frac{2 \, {\left({\left({\left(-160 i \, A + 20 \, B\right)} a^{3} c^{4} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-160 i \, A + 20 \, B\right)} a^{3} c^{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}} - 2 \, \sqrt{\frac{{\left(1600 \, A^{2} + 400 i \, A B - 25 \, B^{2}\right)} a^{7} c^{9}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(-40 i \, A + 5 \, B\right)} a^{3} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-40 i \, A + 5 \, B\right)} a^{3} c^{4}}\right) - 4 \, {\left({\left(-840 i \, A + 105 \, B\right)} a^{3} c^{4} e^{\left(15 i \, f x + 15 i \, e\right)} + {\left(-6440 i \, A + 805 \, B\right)} a^{3} c^{4} e^{\left(13 i \, f x + 13 i \, e\right)} + {\left(-21448 i \, A + 2681 \, B\right)} a^{3} c^{4} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-40424 i \, A + 5053 \, B\right)} a^{3} c^{4} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-8728 i \, A + 44099 \, B\right)} a^{3} c^{4} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(21448 i \, A - 2681 \, B\right)} a^{3} c^{4} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(6440 i \, A - 805 \, B\right)} a^{3} c^{4} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(840 i \, A - 105 \, B\right)} a^{3} c^{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}}}{5376 \, {\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,"-1/5376*(21*sqrt((1600*A^2 + 400*I*A*B - 25*B^2)*a^7*c^9/f^2)*(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)*log(2*(((-160*I*A + 20*B)*a^3*c^4*e^(3*I*f*x + 3*I*e) + (-160*I*A + 20*B)*a^3*c^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*sqrt((1600*A^2 + 400*I*A*B - 25*B^2)*a^7*c^9/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-40*I*A + 5*B)*a^3*c^4*e^(2*I*f*x + 2*I*e) + (-40*I*A + 5*B)*a^3*c^4)) - 21*sqrt((1600*A^2 + 400*I*A*B - 25*B^2)*a^7*c^9/f^2)*(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)*log(2*(((-160*I*A + 20*B)*a^3*c^4*e^(3*I*f*x + 3*I*e) + (-160*I*A + 20*B)*a^3*c^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*sqrt((1600*A^2 + 400*I*A*B - 25*B^2)*a^7*c^9/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((-40*I*A + 5*B)*a^3*c^4*e^(2*I*f*x + 2*I*e) + (-40*I*A + 5*B)*a^3*c^4)) - 4*((-840*I*A + 105*B)*a^3*c^4*e^(15*I*f*x + 15*I*e) + (-6440*I*A + 805*B)*a^3*c^4*e^(13*I*f*x + 13*I*e) + (-21448*I*A + 2681*B)*a^3*c^4*e^(11*I*f*x + 11*I*e) + (-40424*I*A + 5053*B)*a^3*c^4*e^(9*I*f*x + 9*I*e) + (-8728*I*A + 44099*B)*a^3*c^4*e^(7*I*f*x + 7*I*e) + (21448*I*A - 2681*B)*a^3*c^4*e^(5*I*f*x + 5*I*e) + (6440*I*A - 805*B)*a^3*c^4*e^(3*I*f*x + 3*I*e) + (840*I*A - 105*B)*a^3*c^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)))/(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
817,1,691,0,0.954095," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{\frac{A^{2} a^{7} c^{7}}{f^{2}}} {\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)} \log\left(\frac{64 \, {\left(A a^{3} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + A a^{3} c^{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^{2} a^{7} c^{7}}{f^{2}}} {\left(32 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - 32 i \, f\right)}}{8 \, {\left(A a^{3} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + A a^{3} c^{3}\right)}}\right) - 105 \, \sqrt{\frac{A^{2} a^{7} c^{7}}{f^{2}}} {\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)} \log\left(\frac{64 \, {\left(A a^{3} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + A a^{3} c^{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^{2} a^{7} c^{7}}{f^{2}}} {\left(-32 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + 32 i \, f\right)}}{8 \, {\left(A a^{3} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + A a^{3} c^{3}\right)}}\right) - 4 \, {\left(-105 i \, A a^{3} c^{3} e^{\left(13 i \, f x + 13 i \, e\right)} - 700 i \, A a^{3} c^{3} e^{\left(11 i \, f x + 11 i \, e\right)} - 1981 i \, A a^{3} c^{3} e^{\left(9 i \, f x + 9 i \, e\right)} + 3072 \, B a^{3} c^{3} e^{\left(7 i \, f x + 7 i \, e\right)} + 1981 i \, A a^{3} c^{3} e^{\left(5 i \, f x + 5 i \, e\right)} + 700 i \, A a^{3} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + 105 i \, A a^{3} c^{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}}}{672 \, {\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,"-1/672*(105*sqrt(A^2*a^7*c^7/f^2)*(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)*log(1/8*(64*(A*a^3*c^3*e^(3*I*f*x + 3*I*e) + A*a^3*c^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^2*a^7*c^7/f^2)*(32*I*f*e^(2*I*f*x + 2*I*e) - 32*I*f))/(A*a^3*c^3*e^(2*I*f*x + 2*I*e) + A*a^3*c^3)) - 105*sqrt(A^2*a^7*c^7/f^2)*(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)*log(1/8*(64*(A*a^3*c^3*e^(3*I*f*x + 3*I*e) + A*a^3*c^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^2*a^7*c^7/f^2)*(-32*I*f*e^(2*I*f*x + 2*I*e) + 32*I*f))/(A*a^3*c^3*e^(2*I*f*x + 2*I*e) + A*a^3*c^3)) - 4*(-105*I*A*a^3*c^3*e^(13*I*f*x + 13*I*e) - 700*I*A*a^3*c^3*e^(11*I*f*x + 11*I*e) - 1981*I*A*a^3*c^3*e^(9*I*f*x + 9*I*e) + 3072*B*a^3*c^3*e^(7*I*f*x + 7*I*e) + 1981*I*A*a^3*c^3*e^(5*I*f*x + 5*I*e) + 700*I*A*a^3*c^3*e^(3*I*f*x + 3*I*e) + 105*I*A*a^3*c^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)))/(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)","B",0
818,1,753,0,0.695610," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{\frac{{\left(36 \, A^{2} - 12 i \, A B - B^{2}\right)} a^{7} c^{5}}{f^{2}}} {\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)} \log\left(\frac{2 \, {\left({\left({\left(24 i \, A + 4 \, B\right)} a^{3} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(24 i \, A + 4 \, B\right)} a^{3} 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}} + 2 \, \sqrt{\frac{{\left(36 \, A^{2} - 12 i \, A B - B^{2}\right)} a^{7} c^{5}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(6 i \, A + B\right)} a^{3} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 i \, A + B\right)} a^{3} c^{2}}\right) - 15 \, \sqrt{\frac{{\left(36 \, A^{2} - 12 i \, A B - B^{2}\right)} a^{7} c^{5}}{f^{2}}} {\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)} \log\left(\frac{2 \, {\left({\left({\left(24 i \, A + 4 \, B\right)} a^{3} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(24 i \, A + 4 \, B\right)} a^{3} 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}} - 2 \, \sqrt{\frac{{\left(36 \, A^{2} - 12 i \, A B - B^{2}\right)} a^{7} c^{5}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(6 i \, A + B\right)} a^{3} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 i \, A + B\right)} a^{3} c^{2}}\right) + 4 \, {\left({\left(-90 i \, A - 15 \, B\right)} a^{3} c^{2} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-510 i \, A - 85 \, B\right)} a^{3} c^{2} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(348 i \, A + 1338 \, B\right)} a^{3} c^{2} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(1188 i \, A + 198 \, B\right)} a^{3} c^{2} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(510 i \, A + 85 \, B\right)} a^{3} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(90 i \, A + 15 \, B\right)} a^{3} 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}}}{480 \, {\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,"1/480*(15*sqrt((36*A^2 - 12*I*A*B - B^2)*a^7*c^5/f^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)*log(2*(((24*I*A + 4*B)*a^3*c^2*e^(3*I*f*x + 3*I*e) + (24*I*A + 4*B)*a^3*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*sqrt((36*A^2 - 12*I*A*B - B^2)*a^7*c^5/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((6*I*A + B)*a^3*c^2*e^(2*I*f*x + 2*I*e) + (6*I*A + B)*a^3*c^2)) - 15*sqrt((36*A^2 - 12*I*A*B - B^2)*a^7*c^5/f^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)*log(2*(((24*I*A + 4*B)*a^3*c^2*e^(3*I*f*x + 3*I*e) + (24*I*A + 4*B)*a^3*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*sqrt((36*A^2 - 12*I*A*B - B^2)*a^7*c^5/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((6*I*A + B)*a^3*c^2*e^(2*I*f*x + 2*I*e) + (6*I*A + B)*a^3*c^2)) + 4*((-90*I*A - 15*B)*a^3*c^2*e^(11*I*f*x + 11*I*e) + (-510*I*A - 85*B)*a^3*c^2*e^(9*I*f*x + 9*I*e) + (348*I*A + 1338*B)*a^3*c^2*e^(7*I*f*x + 7*I*e) + (1188*I*A + 198*B)*a^3*c^2*e^(5*I*f*x + 5*I*e) + (510*I*A + 85*B)*a^3*c^2*e^(3*I*f*x + 3*I*e) + (90*I*A + 15*B)*a^3*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^(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
819,1,676,0,1.012197," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{\frac{{\left(25 \, A^{2} - 20 i \, A B - 4 \, B^{2}\right)} a^{7} c^{3}}{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{2 \, {\left({\left({\left(20 i \, A + 8 \, B\right)} a^{3} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(20 i \, A + 8 \, B\right)} a^{3} 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}} + 2 \, \sqrt{\frac{{\left(25 \, A^{2} - 20 i \, A B - 4 \, B^{2}\right)} a^{7} c^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(5 i \, A + 2 \, B\right)} a^{3} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(5 i \, A + 2 \, B\right)} a^{3} c}\right) - 15 \, \sqrt{\frac{{\left(25 \, A^{2} - 20 i \, A B - 4 \, B^{2}\right)} a^{7} c^{3}}{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{2 \, {\left({\left({\left(20 i \, A + 8 \, B\right)} a^{3} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(20 i \, A + 8 \, B\right)} a^{3} 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}} - 2 \, \sqrt{\frac{{\left(25 \, A^{2} - 20 i \, A B - 4 \, B^{2}\right)} a^{7} c^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(5 i \, A + 2 \, B\right)} a^{3} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(5 i \, A + 2 \, B\right)} a^{3} c}\right) + 4 \, {\left({\left(-75 i \, A - 30 \, B\right)} a^{3} c e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(290 i \, A + 500 \, B\right)} a^{3} c e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(640 i \, A + 256 \, B\right)} a^{3} c e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(350 i \, A + 140 \, B\right)} a^{3} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(75 i \, A + 30 \, B\right)} a^{3} 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}}}{240 \, {\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,"1/240*(15*sqrt((25*A^2 - 20*I*A*B - 4*B^2)*a^7*c^3/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(2*(((20*I*A + 8*B)*a^3*c*e^(3*I*f*x + 3*I*e) + (20*I*A + 8*B)*a^3*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*sqrt((25*A^2 - 20*I*A*B - 4*B^2)*a^7*c^3/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((5*I*A + 2*B)*a^3*c*e^(2*I*f*x + 2*I*e) + (5*I*A + 2*B)*a^3*c)) - 15*sqrt((25*A^2 - 20*I*A*B - 4*B^2)*a^7*c^3/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(2*(((20*I*A + 8*B)*a^3*c*e^(3*I*f*x + 3*I*e) + (20*I*A + 8*B)*a^3*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*sqrt((25*A^2 - 20*I*A*B - 4*B^2)*a^7*c^3/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((5*I*A + 2*B)*a^3*c*e^(2*I*f*x + 2*I*e) + (5*I*A + 2*B)*a^3*c)) + 4*((-75*I*A - 30*B)*a^3*c*e^(9*I*f*x + 9*I*e) + (290*I*A + 500*B)*a^3*c*e^(7*I*f*x + 7*I*e) + (640*I*A + 256*B)*a^3*c*e^(5*I*f*x + 5*I*e) + (350*I*A + 140*B)*a^3*c*e^(3*I*f*x + 3*I*e) + (75*I*A + 30*B)*a^3*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^(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
820,1,599,0,1.740398," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{{\left(400 \, A^{2} - 600 i \, A B - 225 \, B^{2}\right)} a^{7} c}{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{2 \, {\left({\left({\left(80 i \, A + 60 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(80 i \, A + 60 \, B\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}} + 2 \, \sqrt{\frac{{\left(400 \, A^{2} - 600 i \, A B - 225 \, B^{2}\right)} a^{7} c}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(20 i \, A + 15 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(20 i \, A + 15 \, B\right)} a^{3}}\right) - 3 \, \sqrt{\frac{{\left(400 \, A^{2} - 600 i \, A B - 225 \, B^{2}\right)} a^{7} c}{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{2 \, {\left({\left({\left(80 i \, A + 60 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(80 i \, A + 60 \, B\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}} - 2 \, \sqrt{\frac{{\left(400 \, A^{2} - 600 i \, A B - 225 \, B^{2}\right)} a^{7} c}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} - f\right)}\right)}}{{\left(20 i \, A + 15 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(20 i \, A + 15 \, B\right)} a^{3}}\right) + 4 \, {\left({\left(132 i \, A + 147 \, B\right)} a^{3} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(292 i \, A + 219 \, B\right)} a^{3} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(220 i \, A + 165 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(60 i \, A + 45 \, B\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}}}{48 \, {\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,"1/48*(3*sqrt((400*A^2 - 600*I*A*B - 225*B^2)*a^7*c/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(2*(((80*I*A + 60*B)*a^3*e^(3*I*f*x + 3*I*e) + (80*I*A + 60*B)*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*sqrt((400*A^2 - 600*I*A*B - 225*B^2)*a^7*c/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((20*I*A + 15*B)*a^3*e^(2*I*f*x + 2*I*e) + (20*I*A + 15*B)*a^3)) - 3*sqrt((400*A^2 - 600*I*A*B - 225*B^2)*a^7*c/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(2*(((80*I*A + 60*B)*a^3*e^(3*I*f*x + 3*I*e) + (80*I*A + 60*B)*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*sqrt((400*A^2 - 600*I*A*B - 225*B^2)*a^7*c/f^2)*(f*e^(2*I*f*x + 2*I*e) - f))/((20*I*A + 15*B)*a^3*e^(2*I*f*x + 2*I*e) + (20*I*A + 15*B)*a^3)) + 4*((132*I*A + 147*B)*a^3*e^(7*I*f*x + 7*I*e) + (292*I*A + 219*B)*a^3*e^(5*I*f*x + 5*I*e) + (220*I*A + 165*B)*a^3*e^(3*I*f*x + 3*I*e) + (60*I*A + 45*B)*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)))/(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
821,1,587,0,1.191472," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{{\left(225 \, A^{2} - 600 i \, A B - 400 \, B^{2}\right)} a^{7}}{c f^{2}}} {\left(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\right)} \log\left(\frac{2 \, {\left({\left({\left(60 i \, A + 80 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(60 i \, A + 80 \, B\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}} + 2 \, \sqrt{\frac{{\left(225 \, A^{2} - 600 i \, A B - 400 \, B^{2}\right)} a^{7}}{c f^{2}}} {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} - c f\right)}\right)}}{{\left(15 i \, A + 20 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(15 i \, A + 20 \, B\right)} a^{3}}\right) - 3 \, \sqrt{\frac{{\left(225 \, A^{2} - 600 i \, A B - 400 \, B^{2}\right)} a^{7}}{c f^{2}}} {\left(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\right)} \log\left(\frac{2 \, {\left({\left({\left(60 i \, A + 80 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(60 i \, A + 80 \, B\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}} - 2 \, \sqrt{\frac{{\left(225 \, A^{2} - 600 i \, A B - 400 \, B^{2}\right)} a^{7}}{c f^{2}}} {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} - c f\right)}\right)}}{{\left(15 i \, A + 20 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(15 i \, A + 20 \, B\right)} a^{3}}\right) - 2 \, {\left({\left(-48 i \, A - 48 \, B\right)} a^{3} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-198 i \, A - 264 \, B\right)} a^{3} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-240 i \, A - 320 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-90 i \, A - 120 \, B\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}}}{12 \, {\left(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\right)}}"," ",0,"-1/12*(3*sqrt((225*A^2 - 600*I*A*B - 400*B^2)*a^7/(c*f^2))*(c*f*e^(4*I*f*x + 4*I*e) + 2*c*f*e^(2*I*f*x + 2*I*e) + c*f)*log(2*(((60*I*A + 80*B)*a^3*e^(3*I*f*x + 3*I*e) + (60*I*A + 80*B)*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*sqrt((225*A^2 - 600*I*A*B - 400*B^2)*a^7/(c*f^2))*(c*f*e^(2*I*f*x + 2*I*e) - c*f))/((15*I*A + 20*B)*a^3*e^(2*I*f*x + 2*I*e) + (15*I*A + 20*B)*a^3)) - 3*sqrt((225*A^2 - 600*I*A*B - 400*B^2)*a^7/(c*f^2))*(c*f*e^(4*I*f*x + 4*I*e) + 2*c*f*e^(2*I*f*x + 2*I*e) + c*f)*log(2*(((60*I*A + 80*B)*a^3*e^(3*I*f*x + 3*I*e) + (60*I*A + 80*B)*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*sqrt((225*A^2 - 600*I*A*B - 400*B^2)*a^7/(c*f^2))*(c*f*e^(2*I*f*x + 2*I*e) - c*f))/((15*I*A + 20*B)*a^3*e^(2*I*f*x + 2*I*e) + (15*I*A + 20*B)*a^3)) - 2*((-48*I*A - 48*B)*a^3*e^(7*I*f*x + 7*I*e) + (-198*I*A - 264*B)*a^3*e^(5*I*f*x + 5*I*e) + (-240*I*A - 320*B)*a^3*e^(3*I*f*x + 3*I*e) + (-90*I*A - 120*B)*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^(4*I*f*x + 4*I*e) + 2*c*f*e^(2*I*f*x + 2*I*e) + c*f)","B",0
822,1,568,0,0.984806," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{3 \, {\left(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} f\right)} \sqrt{\frac{{\left(100 \, A^{2} - 500 i \, A B - 625 \, B^{2}\right)} a^{7}}{c^{3} f^{2}}} \log\left(\frac{2 \, {\left({\left({\left(40 i \, A + 100 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(40 i \, A + 100 \, B\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}} + 2 \, {\left(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{2} f\right)} \sqrt{\frac{{\left(100 \, A^{2} - 500 i \, A B - 625 \, B^{2}\right)} a^{7}}{c^{3} f^{2}}}\right)}}{{\left(10 i \, A + 25 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(10 i \, A + 25 \, B\right)} a^{3}}\right) - 3 \, {\left(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} f\right)} \sqrt{\frac{{\left(100 \, A^{2} - 500 i \, A B - 625 \, B^{2}\right)} a^{7}}{c^{3} f^{2}}} \log\left(\frac{2 \, {\left({\left({\left(40 i \, A + 100 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(40 i \, A + 100 \, B\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}} - 2 \, {\left(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{2} f\right)} \sqrt{\frac{{\left(100 \, A^{2} - 500 i \, A B - 625 \, B^{2}\right)} a^{7}}{c^{3} f^{2}}}\right)}}{{\left(10 i \, A + 25 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(10 i \, A + 25 \, B\right)} a^{3}}\right) + 2 \, {\left({\left(-8 i \, A - 8 \, B\right)} a^{3} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(32 i \, A + 80 \, B\right)} a^{3} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(100 i \, A + 250 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(60 i \, A + 150 \, B\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}}}{12 \, {\left(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} f\right)}}"," ",0,"1/12*(3*(c^2*f*e^(2*I*f*x + 2*I*e) + c^2*f)*sqrt((100*A^2 - 500*I*A*B - 625*B^2)*a^7/(c^3*f^2))*log(2*(((40*I*A + 100*B)*a^3*e^(3*I*f*x + 3*I*e) + (40*I*A + 100*B)*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*(c^2*f*e^(2*I*f*x + 2*I*e) - c^2*f)*sqrt((100*A^2 - 500*I*A*B - 625*B^2)*a^7/(c^3*f^2)))/((10*I*A + 25*B)*a^3*e^(2*I*f*x + 2*I*e) + (10*I*A + 25*B)*a^3)) - 3*(c^2*f*e^(2*I*f*x + 2*I*e) + c^2*f)*sqrt((100*A^2 - 500*I*A*B - 625*B^2)*a^7/(c^3*f^2))*log(2*(((40*I*A + 100*B)*a^3*e^(3*I*f*x + 3*I*e) + (40*I*A + 100*B)*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*(c^2*f*e^(2*I*f*x + 2*I*e) - c^2*f)*sqrt((100*A^2 - 500*I*A*B - 625*B^2)*a^7/(c^3*f^2)))/((10*I*A + 25*B)*a^3*e^(2*I*f*x + 2*I*e) + (10*I*A + 25*B)*a^3)) + 2*((-8*I*A - 8*B)*a^3*e^(7*I*f*x + 7*I*e) + (32*I*A + 80*B)*a^3*e^(5*I*f*x + 5*I*e) + (100*I*A + 250*B)*a^3*e^(3*I*f*x + 3*I*e) + (60*I*A + 150*B)*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*e^(2*I*f*x + 2*I*e) + c^2*f)","B",0
823,1,519,0,2.897335," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{15 \, c^{3} \sqrt{\frac{{\left(4 \, A^{2} - 48 i \, A B - 144 \, B^{2}\right)} a^{7}}{c^{5} f^{2}}} f \log\left(\frac{2 \, {\left({\left({\left(4 i \, A + 24 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(4 i \, A + 24 \, B\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(c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{3} f\right)} \sqrt{\frac{{\left(4 \, A^{2} - 48 i \, A B - 144 \, B^{2}\right)} a^{7}}{c^{5} f^{2}}}\right)}}{{\left(i \, A + 6 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A + 6 \, B\right)} a^{3}}\right) - 15 \, c^{3} \sqrt{\frac{{\left(4 \, A^{2} - 48 i \, A B - 144 \, B^{2}\right)} a^{7}}{c^{5} f^{2}}} f \log\left(\frac{2 \, {\left({\left({\left(4 i \, A + 24 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(4 i \, A + 24 \, B\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(c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{3} f\right)} \sqrt{\frac{{\left(4 \, A^{2} - 48 i \, A B - 144 \, B^{2}\right)} a^{7}}{c^{5} f^{2}}}\right)}}{{\left(i \, A + 6 \, B\right)} a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, A + 6 \, B\right)} a^{3}}\right) - 2 \, {\left({\left(-12 i \, A - 12 \, B\right)} a^{3} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(8 i \, A + 48 \, B\right)} a^{3} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-40 i \, A - 240 \, B\right)} a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-60 i \, A - 360 \, B\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}}}{60 \, c^{3} f}"," ",0,"-1/60*(15*c^3*sqrt((4*A^2 - 48*I*A*B - 144*B^2)*a^7/(c^5*f^2))*f*log(2*(((4*I*A + 24*B)*a^3*e^(3*I*f*x + 3*I*e) + (4*I*A + 24*B)*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*e^(2*I*f*x + 2*I*e) - c^3*f)*sqrt((4*A^2 - 48*I*A*B - 144*B^2)*a^7/(c^5*f^2)))/((I*A + 6*B)*a^3*e^(2*I*f*x + 2*I*e) + (I*A + 6*B)*a^3)) - 15*c^3*sqrt((4*A^2 - 48*I*A*B - 144*B^2)*a^7/(c^5*f^2))*f*log(2*(((4*I*A + 24*B)*a^3*e^(3*I*f*x + 3*I*e) + (4*I*A + 24*B)*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*e^(2*I*f*x + 2*I*e) - c^3*f)*sqrt((4*A^2 - 48*I*A*B - 144*B^2)*a^7/(c^5*f^2)))/((I*A + 6*B)*a^3*e^(2*I*f*x + 2*I*e) + (I*A + 6*B)*a^3)) - 2*((-12*I*A - 12*B)*a^3*e^(7*I*f*x + 7*I*e) + (8*I*A + 48*B)*a^3*e^(5*I*f*x + 5*I*e) + (-40*I*A - 240*B)*a^3*e^(3*I*f*x + 3*I*e) + (-60*I*A - 360*B)*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
824,1,433,0,0.857064," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{105 \, c^{4} f \sqrt{-\frac{B^{2} a^{7}}{c^{7} f^{2}}} \log\left(\frac{4 \, {\left(2 \, {\left(B a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(c^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{4} f\right)} \sqrt{-\frac{B^{2} a^{7}}{c^{7} f^{2}}}\right)}}{B a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + B a^{3}}\right) - 105 \, c^{4} f \sqrt{-\frac{B^{2} a^{7}}{c^{7} f^{2}}} \log\left(\frac{4 \, {\left(2 \, {\left(B a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(c^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - c^{4} f\right)} \sqrt{-\frac{B^{2} a^{7}}{c^{7} f^{2}}}\right)}}{B a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + B a^{3}}\right) + {\left({\left(-30 i \, A - 30 \, B\right)} a^{3} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-30 i \, A + 54 \, B\right)} a^{3} e^{\left(7 i \, f x + 7 i \, e\right)} - 56 \, B a^{3} e^{\left(5 i \, f x + 5 i \, e\right)} + 280 \, B a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + 420 \, B 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}}}{210 \, c^{4} f}"," ",0,"1/210*(105*c^4*f*sqrt(-B^2*a^7/(c^7*f^2))*log(4*(2*(B*a^3*e^(3*I*f*x + 3*I*e) + B*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^4*f*e^(2*I*f*x + 2*I*e) - c^4*f)*sqrt(-B^2*a^7/(c^7*f^2)))/(B*a^3*e^(2*I*f*x + 2*I*e) + B*a^3)) - 105*c^4*f*sqrt(-B^2*a^7/(c^7*f^2))*log(4*(2*(B*a^3*e^(3*I*f*x + 3*I*e) + B*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^4*f*e^(2*I*f*x + 2*I*e) - c^4*f)*sqrt(-B^2*a^7/(c^7*f^2)))/(B*a^3*e^(2*I*f*x + 2*I*e) + B*a^3)) + ((-30*I*A - 30*B)*a^3*e^(9*I*f*x + 9*I*e) + (-30*I*A + 54*B)*a^3*e^(7*I*f*x + 7*I*e) - 56*B*a^3*e^(5*I*f*x + 5*I*e) + 280*B*a^3*e^(3*I*f*x + 3*I*e) + 420*B*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^4*f)","B",0
825,1,103,0,0.587835," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{{\left({\left(-7 i \, A - 7 \, B\right)} a^{3} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-16 i \, A + 2 \, B\right)} a^{3} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-9 i \, A + 9 \, B\right)} a^{3} e^{\left(7 i \, f x + 7 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}}}{126 \, c^{5} f}"," ",0,"1/126*((-7*I*A - 7*B)*a^3*e^(11*I*f*x + 11*I*e) + (-16*I*A + 2*B)*a^3*e^(9*I*f*x + 9*I*e) + (-9*I*A + 9*B)*a^3*e^(7*I*f*x + 7*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^5*f)","A",0
826,1,123,0,2.052453," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(11/2),x, algorithm=""fricas"")","\frac{{\left({\left(-63 i \, A - 63 \, B\right)} a^{3} e^{\left(13 i \, f x + 13 i \, e\right)} + {\left(-217 i \, A - 63 \, B\right)} a^{3} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-253 i \, A + 99 \, B\right)} a^{3} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-99 i \, A + 99 \, B\right)} a^{3} e^{\left(7 i \, f x + 7 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}}}{2772 \, c^{6} f}"," ",0,"1/2772*((-63*I*A - 63*B)*a^3*e^(13*I*f*x + 13*I*e) + (-217*I*A - 63*B)*a^3*e^(11*I*f*x + 11*I*e) + (-253*I*A + 99*B)*a^3*e^(9*I*f*x + 9*I*e) + (-99*I*A + 99*B)*a^3*e^(7*I*f*x + 7*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^6*f)","A",0
827,1,143,0,1.098101," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(13/2),x, algorithm=""fricas"")","\frac{{\left({\left(-693 i \, A - 693 \, B\right)} a^{3} e^{\left(15 i \, f x + 15 i \, e\right)} + {\left(-3150 i \, A - 1512 \, B\right)} a^{3} e^{\left(13 i \, f x + 13 i \, e\right)} + {\left(-5460 i \, A + 182 \, B\right)} a^{3} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-4290 i \, A + 2288 \, B\right)} a^{3} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-1287 i \, A + 1287 \, B\right)} a^{3} e^{\left(7 i \, f x + 7 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}}}{72072 \, c^{7} f}"," ",0,"1/72072*((-693*I*A - 693*B)*a^3*e^(15*I*f*x + 15*I*e) + (-3150*I*A - 1512*B)*a^3*e^(13*I*f*x + 13*I*e) + (-5460*I*A + 182*B)*a^3*e^(11*I*f*x + 11*I*e) + (-4290*I*A + 2288*B)*a^3*e^(9*I*f*x + 9*I*e) + (-1287*I*A + 1287*B)*a^3*e^(7*I*f*x + 7*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^7*f)","A",0
828,1,163,0,0.589016," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(15/2),x, algorithm=""fricas"")","\frac{{\left({\left(-3003 i \, A - 3003 \, B\right)} a^{3} e^{\left(17 i \, f x + 17 i \, e\right)} + {\left(-16863 i \, A - 9933 \, B\right)} a^{3} e^{\left(15 i \, f x + 15 i \, e\right)} + {\left(-38430 i \, A - 6930 \, B\right)} a^{3} e^{\left(13 i \, f x + 13 i \, e\right)} + {\left(-44590 i \, A + 10010 \, B\right)} a^{3} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-26455 i \, A + 16445 \, B\right)} a^{3} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-6435 i \, A + 6435 \, B\right)} a^{3} e^{\left(7 i \, f x + 7 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}}}{720720 \, c^{8} f}"," ",0,"1/720720*((-3003*I*A - 3003*B)*a^3*e^(17*I*f*x + 17*I*e) + (-16863*I*A - 9933*B)*a^3*e^(15*I*f*x + 15*I*e) + (-38430*I*A - 6930*B)*a^3*e^(13*I*f*x + 13*I*e) + (-44590*I*A + 10010*B)*a^3*e^(11*I*f*x + 11*I*e) + (-26455*I*A + 16445*B)*a^3*e^(9*I*f*x + 9*I*e) + (-6435*I*A + 6435*B)*a^3*e^(7*I*f*x + 7*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^8*f)","A",0
829,1,183,0,0.798802," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(17/2),x, algorithm=""fricas"")","\frac{{\left({\left(-45045 i \, A - 45045 \, B\right)} a^{3} e^{\left(19 i \, f x + 19 i \, e\right)} + {\left(-300300 i \, A - 198198 \, B\right)} a^{3} e^{\left(17 i \, f x + 17 i \, e\right)} + {\left(-844305 i \, A - 270963 \, B\right)} a^{3} e^{\left(15 i \, f x + 15 i \, e\right)} + {\left(-1285200 i \, A + 21420 \, B\right)} a^{3} e^{\left(13 i \, f x + 13 i \, e\right)} + {\left(-1121575 i \, A + 394485 \, B\right)} a^{3} e^{\left(11 i \, f x + 11 i \, e\right)} + {\left(-534820 i \, A + 364650 \, B\right)} a^{3} e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-109395 i \, A + 109395 \, B\right)} a^{3} e^{\left(7 i \, f x + 7 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}}}{24504480 \, c^{9} f}"," ",0,"1/24504480*((-45045*I*A - 45045*B)*a^3*e^(19*I*f*x + 19*I*e) + (-300300*I*A - 198198*B)*a^3*e^(17*I*f*x + 17*I*e) + (-844305*I*A - 270963*B)*a^3*e^(15*I*f*x + 15*I*e) + (-1285200*I*A + 21420*B)*a^3*e^(13*I*f*x + 13*I*e) + (-1121575*I*A + 394485*B)*a^3*e^(11*I*f*x + 11*I*e) + (-534820*I*A + 364650*B)*a^3*e^(9*I*f*x + 9*I*e) + (-109395*I*A + 109395*B)*a^3*e^(7*I*f*x + 7*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^9*f)","A",0
830,1,545,0,1.649806," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{{\left(36 \, A^{2} + 108 i \, A B - 81 \, B^{2}\right)} c^{5}}{a f^{2}}} {\left(a f e^{\left(3 i \, f x + 3 i \, e\right)} + a f e^{\left(i \, f x + i \, e\right)}\right)} \log\left(\frac{2 \, {\left({\left({\left(-24 i \, A + 36 \, B\right)} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-24 i \, A + 36 \, B\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}} + 2 \, \sqrt{\frac{{\left(36 \, A^{2} + 108 i \, A B - 81 \, B^{2}\right)} c^{5}}{a f^{2}}} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} - a f\right)}\right)}}{{\left(-6 i \, A + 9 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-6 i \, A + 9 \, B\right)} c^{2}}\right) - \sqrt{\frac{{\left(36 \, A^{2} + 108 i \, A B - 81 \, B^{2}\right)} c^{5}}{a f^{2}}} {\left(a f e^{\left(3 i \, f x + 3 i \, e\right)} + a f e^{\left(i \, f x + i \, e\right)}\right)} \log\left(\frac{2 \, {\left({\left({\left(-24 i \, A + 36 \, B\right)} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-24 i \, A + 36 \, B\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}} - 2 \, \sqrt{\frac{{\left(36 \, A^{2} + 108 i \, A B - 81 \, B^{2}\right)} c^{5}}{a f^{2}}} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} - a f\right)}\right)}}{{\left(-6 i \, A + 9 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-6 i \, A + 9 \, B\right)} c^{2}}\right) + 2 \, {\left({\left(12 i \, A - 18 \, B\right)} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(20 i \, A - 30 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, A - 8 \, B\right)} 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}}}{4 \, {\left(a f e^{\left(3 i \, f x + 3 i \, e\right)} + a f e^{\left(i \, f x + i \, e\right)}\right)}}"," ",0,"1/4*(sqrt((36*A^2 + 108*I*A*B - 81*B^2)*c^5/(a*f^2))*(a*f*e^(3*I*f*x + 3*I*e) + a*f*e^(I*f*x + I*e))*log(2*(((-24*I*A + 36*B)*c^2*e^(3*I*f*x + 3*I*e) + (-24*I*A + 36*B)*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*sqrt((36*A^2 + 108*I*A*B - 81*B^2)*c^5/(a*f^2))*(a*f*e^(2*I*f*x + 2*I*e) - a*f))/((-6*I*A + 9*B)*c^2*e^(2*I*f*x + 2*I*e) + (-6*I*A + 9*B)*c^2)) - sqrt((36*A^2 + 108*I*A*B - 81*B^2)*c^5/(a*f^2))*(a*f*e^(3*I*f*x + 3*I*e) + a*f*e^(I*f*x + I*e))*log(2*(((-24*I*A + 36*B)*c^2*e^(3*I*f*x + 3*I*e) + (-24*I*A + 36*B)*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*sqrt((36*A^2 + 108*I*A*B - 81*B^2)*c^5/(a*f^2))*(a*f*e^(2*I*f*x + 2*I*e) - a*f))/((-6*I*A + 9*B)*c^2*e^(2*I*f*x + 2*I*e) + (-6*I*A + 9*B)*c^2)) + 2*((12*I*A - 18*B)*c^2*e^(4*I*f*x + 4*I*e) + (20*I*A - 30*B)*c^2*e^(2*I*f*x + 2*I*e) + (8*I*A - 8*B)*c^2)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(a*f*e^(3*I*f*x + 3*I*e) + a*f*e^(I*f*x + I*e))","B",0
831,1,464,0,0.777788," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a \sqrt{\frac{{\left(4 \, A^{2} + 16 i \, A B - 16 \, B^{2}\right)} c^{3}}{a f^{2}}} f e^{\left(i \, f x + i \, e\right)} \log\left(\frac{2 \, {\left({\left({\left(-4 i \, A + 8 \, B\right)} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-4 i \, A + 8 \, B\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(a f e^{\left(2 i \, f x + 2 i \, e\right)} - a f\right)} \sqrt{\frac{{\left(4 \, A^{2} + 16 i \, A B - 16 \, B^{2}\right)} c^{3}}{a f^{2}}}\right)}}{{\left(-i \, A + 2 \, B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A + 2 \, B\right)} c}\right) - a \sqrt{\frac{{\left(4 \, A^{2} + 16 i \, A B - 16 \, B^{2}\right)} c^{3}}{a f^{2}}} f e^{\left(i \, f x + i \, e\right)} \log\left(\frac{2 \, {\left({\left({\left(-4 i \, A + 8 \, B\right)} c e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-4 i \, A + 8 \, B\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(a f e^{\left(2 i \, f x + 2 i \, e\right)} - a f\right)} \sqrt{\frac{{\left(4 \, A^{2} + 16 i \, A B - 16 \, B^{2}\right)} c^{3}}{a f^{2}}}\right)}}{{\left(-i \, A + 2 \, B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A + 2 \, B\right)} c}\right) + 2 \, {\left({\left(4 i \, A - 8 \, B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 i \, A - 4 \, B\right)} 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)}}{4 \, a f}"," ",0,"1/4*(a*sqrt((4*A^2 + 16*I*A*B - 16*B^2)*c^3/(a*f^2))*f*e^(I*f*x + I*e)*log(2*(((-4*I*A + 8*B)*c*e^(3*I*f*x + 3*I*e) + (-4*I*A + 8*B)*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)) + (a*f*e^(2*I*f*x + 2*I*e) - a*f)*sqrt((4*A^2 + 16*I*A*B - 16*B^2)*c^3/(a*f^2)))/((-I*A + 2*B)*c*e^(2*I*f*x + 2*I*e) + (-I*A + 2*B)*c)) - a*sqrt((4*A^2 + 16*I*A*B - 16*B^2)*c^3/(a*f^2))*f*e^(I*f*x + I*e)*log(2*(((-4*I*A + 8*B)*c*e^(3*I*f*x + 3*I*e) + (-4*I*A + 8*B)*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)) - (a*f*e^(2*I*f*x + 2*I*e) - a*f)*sqrt((4*A^2 + 16*I*A*B - 16*B^2)*c^3/(a*f^2)))/((-I*A + 2*B)*c*e^(2*I*f*x + 2*I*e) + (-I*A + 2*B)*c)) + 2*((4*I*A - 8*B)*c*e^(2*I*f*x + 2*I*e) + (4*I*A - 4*B)*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
832,1,351,0,0.630394," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a f \sqrt{-\frac{B^{2} c}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(\frac{4 \, {\left(2 \, {\left(B e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(a f e^{\left(2 i \, f x + 2 i \, e\right)} - a f\right)} \sqrt{-\frac{B^{2} c}{a f^{2}}}\right)}}{B e^{\left(2 i \, f x + 2 i \, e\right)} + B}\right) - a f \sqrt{-\frac{B^{2} c}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(\frac{4 \, {\left(2 \, {\left(B e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(a f e^{\left(2 i \, f x + 2 i \, e\right)} - a f\right)} \sqrt{-\frac{B^{2} c}{a f^{2}}}\right)}}{B e^{\left(2 i \, f x + 2 i \, e\right)} + B}\right) + {\left({\left(2 i \, A - 2 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, A - 2 \, B\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(-B^2*c/(a*f^2))*e^(I*f*x + I*e)*log(4*(2*(B*e^(3*I*f*x + 3*I*e) + B*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)) + (a*f*e^(2*I*f*x + 2*I*e) - a*f)*sqrt(-B^2*c/(a*f^2)))/(B*e^(2*I*f*x + 2*I*e) + B)) - a*f*sqrt(-B^2*c/(a*f^2))*e^(I*f*x + I*e)*log(4*(2*(B*e^(3*I*f*x + 3*I*e) + B*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)) - (a*f*e^(2*I*f*x + 2*I*e) - a*f)*sqrt(-B^2*c/(a*f^2)))/(B*e^(2*I*f*x + 2*I*e) + B)) + ((2*I*A - 2*B)*e^(2*I*f*x + 2*I*e) + 2*I*A - 2*B)*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
833,1,114,0,1.519500," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(-i \, A - B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, B e^{\left(3 i \, f x + 3 i \, e\right)} - 2 \, B e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, B e^{\left(i \, f x + i \, e\right)} + i \, A - B\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(-i \, f x - i \, e\right)}}{2 \, a c f}"," ",0,"1/2*((-I*A - B)*e^(4*I*f*x + 4*I*e) + 2*B*e^(3*I*f*x + 3*I*e) - 2*B*e^(2*I*f*x + 2*I*e) + 2*B*e^(I*f*x + I*e) + I*A - B)*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*c*f)","A",0
834,1,146,0,0.972267," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(-i \, A - B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-7 i \, A - B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(4 i \, A + 4 \, B\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-3 i \, A - 3 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 i \, A + 4 \, B\right)} e^{\left(i \, f x + i \, e\right)} + 3 i \, A - 3 \, B\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(-i \, f x - i \, e\right)}}{12 \, a c^{2} f}"," ",0,"1/12*((-I*A - B)*e^(6*I*f*x + 6*I*e) + (-7*I*A - B)*e^(4*I*f*x + 4*I*e) + (4*I*A + 4*B)*e^(3*I*f*x + 3*I*e) + (-3*I*A - 3*B)*e^(2*I*f*x + 2*I*e) + (4*I*A + 4*B)*e^(I*f*x + I*e) + 3*I*A - 3*B)*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*c^2*f)","A",0
835,1,158,0,0.944969," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(-3 i \, A - 3 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-18 i \, A - 8 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-60 i \, A + 10 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(48 i \, A + 8 \, B\right)} e^{\left(3 i \, f x + 3 i \, e\right)} - 30 i \, A e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(48 i \, A + 8 \, B\right)} e^{\left(i \, f x + i \, e\right)} + 15 i \, A - 15 \, B\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(-i \, f x - i \, e\right)}}{120 \, a c^{3} f}"," ",0,"1/120*((-3*I*A - 3*B)*e^(8*I*f*x + 8*I*e) + (-18*I*A - 8*B)*e^(6*I*f*x + 6*I*e) + (-60*I*A + 10*B)*e^(4*I*f*x + 4*I*e) + (48*I*A + 8*B)*e^(3*I*f*x + 3*I*e) - 30*I*A*e^(2*I*f*x + 2*I*e) + (48*I*A + 8*B)*e^(I*f*x + I*e) + 15*I*A - 15*B)*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*c^3*f)","A",0
836,1,586,0,0.790829," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} f e^{\left(5 i \, f x + 5 i \, e\right)} + a^{2} f e^{\left(3 i \, f x + 3 i \, e\right)}\right)} \sqrt{\frac{{\left(100 \, A^{2} + 500 i \, A B - 625 \, B^{2}\right)} c^{7}}{a^{3} f^{2}}} \log\left(\frac{2 \, {\left({\left({\left(-40 i \, A + 100 \, B\right)} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-40 i \, A + 100 \, B\right)} c^{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}} + 2 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{2} f\right)} \sqrt{\frac{{\left(100 \, A^{2} + 500 i \, A B - 625 \, B^{2}\right)} c^{7}}{a^{3} f^{2}}}\right)}}{{\left(-10 i \, A + 25 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-10 i \, A + 25 \, B\right)} c^{3}}\right) - 3 \, {\left(a^{2} f e^{\left(5 i \, f x + 5 i \, e\right)} + a^{2} f e^{\left(3 i \, f x + 3 i \, e\right)}\right)} \sqrt{\frac{{\left(100 \, A^{2} + 500 i \, A B - 625 \, B^{2}\right)} c^{7}}{a^{3} f^{2}}} \log\left(\frac{2 \, {\left({\left({\left(-40 i \, A + 100 \, B\right)} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-40 i \, A + 100 \, B\right)} c^{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}} - 2 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{2} f\right)} \sqrt{\frac{{\left(100 \, A^{2} + 500 i \, A B - 625 \, B^{2}\right)} c^{7}}{a^{3} f^{2}}}\right)}}{{\left(-10 i \, A + 25 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-10 i \, A + 25 \, B\right)} c^{3}}\right) - 2 \, {\left({\left(-60 i \, A + 150 \, B\right)} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-100 i \, A + 250 \, B\right)} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-32 i \, A + 80 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, A - 8 \, B\right)} c^{3}\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(a^{2} f e^{\left(5 i \, f x + 5 i \, e\right)} + a^{2} f e^{\left(3 i \, f x + 3 i \, e\right)}\right)}}"," ",0,"-1/12*(3*(a^2*f*e^(5*I*f*x + 5*I*e) + a^2*f*e^(3*I*f*x + 3*I*e))*sqrt((100*A^2 + 500*I*A*B - 625*B^2)*c^7/(a^3*f^2))*log(2*(((-40*I*A + 100*B)*c^3*e^(3*I*f*x + 3*I*e) + (-40*I*A + 100*B)*c^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*(a^2*f*e^(2*I*f*x + 2*I*e) - a^2*f)*sqrt((100*A^2 + 500*I*A*B - 625*B^2)*c^7/(a^3*f^2)))/((-10*I*A + 25*B)*c^3*e^(2*I*f*x + 2*I*e) + (-10*I*A + 25*B)*c^3)) - 3*(a^2*f*e^(5*I*f*x + 5*I*e) + a^2*f*e^(3*I*f*x + 3*I*e))*sqrt((100*A^2 + 500*I*A*B - 625*B^2)*c^7/(a^3*f^2))*log(2*(((-40*I*A + 100*B)*c^3*e^(3*I*f*x + 3*I*e) + (-40*I*A + 100*B)*c^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*(a^2*f*e^(2*I*f*x + 2*I*e) - a^2*f)*sqrt((100*A^2 + 500*I*A*B - 625*B^2)*c^7/(a^3*f^2)))/((-10*I*A + 25*B)*c^3*e^(2*I*f*x + 2*I*e) + (-10*I*A + 25*B)*c^3)) - 2*((-60*I*A + 150*B)*c^3*e^(6*I*f*x + 6*I*e) + (-100*I*A + 250*B)*c^3*e^(4*I*f*x + 4*I*e) + (-32*I*A + 80*B)*c^3*e^(2*I*f*x + 2*I*e) + (8*I*A - 8*B)*c^3)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(a^2*f*e^(5*I*f*x + 5*I*e) + a^2*f*e^(3*I*f*x + 3*I*e))","B",0
837,1,517,0,0.931132," ","integrate((A+B*tan(f*x+e))*(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} \sqrt{\frac{{\left(4 \, A^{2} + 32 i \, A B - 64 \, B^{2}\right)} c^{5}}{a^{3} f^{2}}} f e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(\frac{2 \, {\left({\left({\left(-4 i \, A + 16 \, B\right)} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-4 i \, A + 16 \, B\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(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{2} f\right)} \sqrt{\frac{{\left(4 \, A^{2} + 32 i \, A B - 64 \, B^{2}\right)} c^{5}}{a^{3} f^{2}}}\right)}}{{\left(-i \, A + 4 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A + 4 \, B\right)} c^{2}}\right) - 3 \, a^{2} \sqrt{\frac{{\left(4 \, A^{2} + 32 i \, A B - 64 \, B^{2}\right)} c^{5}}{a^{3} f^{2}}} f e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(\frac{2 \, {\left({\left({\left(-4 i \, A + 16 \, B\right)} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-4 i \, A + 16 \, B\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(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{2} f\right)} \sqrt{\frac{{\left(4 \, A^{2} + 32 i \, A B - 64 \, B^{2}\right)} c^{5}}{a^{3} f^{2}}}\right)}}{{\left(-i \, A + 4 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A + 4 \, B\right)} c^{2}}\right) - 2 \, {\left({\left(-12 i \, A + 48 \, B\right)} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-8 i \, A + 32 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 i \, A - 4 \, B\right)} 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)}}{12 \, a^{2} f}"," ",0,"-1/12*(3*a^2*sqrt((4*A^2 + 32*I*A*B - 64*B^2)*c^5/(a^3*f^2))*f*e^(3*I*f*x + 3*I*e)*log(2*(((-4*I*A + 16*B)*c^2*e^(3*I*f*x + 3*I*e) + (-4*I*A + 16*B)*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)) + (a^2*f*e^(2*I*f*x + 2*I*e) - a^2*f)*sqrt((4*A^2 + 32*I*A*B - 64*B^2)*c^5/(a^3*f^2)))/((-I*A + 4*B)*c^2*e^(2*I*f*x + 2*I*e) + (-I*A + 4*B)*c^2)) - 3*a^2*sqrt((4*A^2 + 32*I*A*B - 64*B^2)*c^5/(a^3*f^2))*f*e^(3*I*f*x + 3*I*e)*log(2*(((-4*I*A + 16*B)*c^2*e^(3*I*f*x + 3*I*e) + (-4*I*A + 16*B)*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)) - (a^2*f*e^(2*I*f*x + 2*I*e) - a^2*f)*sqrt((4*A^2 + 32*I*A*B - 64*B^2)*c^5/(a^3*f^2)))/((-I*A + 4*B)*c^2*e^(2*I*f*x + 2*I*e) + (-I*A + 4*B)*c^2)) - 2*((-12*I*A + 48*B)*c^2*e^(4*I*f*x + 4*I*e) + (-8*I*A + 32*B)*c^2*e^(2*I*f*x + 2*I*e) + (4*I*A - 4*B)*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
838,1,400,0,1.770911," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{2} f \sqrt{-\frac{B^{2} c^{3}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(\frac{4 \, {\left(2 \, {\left(B c e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{2} f\right)} \sqrt{-\frac{B^{2} c^{3}}{a^{3} f^{2}}}\right)}}{B c e^{\left(2 i \, f x + 2 i \, e\right)} + B c}\right) - 3 \, a^{2} f \sqrt{-\frac{B^{2} c^{3}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(\frac{4 \, {\left(2 \, {\left(B c e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{2} f\right)} \sqrt{-\frac{B^{2} c^{3}}{a^{3} f^{2}}}\right)}}{B c e^{\left(2 i \, f x + 2 i \, e\right)} + B c}\right) - {\left(12 \, B c e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(2 i \, A + 10 \, B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, A - 2 \, B\right)} 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(-3 i \, f x - 3 i \, e\right)}}{6 \, a^{2} f}"," ",0,"-1/6*(3*a^2*f*sqrt(-B^2*c^3/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(4*(2*(B*c*e^(3*I*f*x + 3*I*e) + B*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)) + (a^2*f*e^(2*I*f*x + 2*I*e) - a^2*f)*sqrt(-B^2*c^3/(a^3*f^2)))/(B*c*e^(2*I*f*x + 2*I*e) + B*c)) - 3*a^2*f*sqrt(-B^2*c^3/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(4*(2*(B*c*e^(3*I*f*x + 3*I*e) + B*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)) - (a^2*f*e^(2*I*f*x + 2*I*e) - a^2*f)*sqrt(-B^2*c^3/(a^3*f^2)))/(B*c*e^(2*I*f*x + 2*I*e) + B*c)) - (12*B*c*e^(4*I*f*x + 4*I*e) + (2*I*A + 10*B)*c*e^(2*I*f*x + 2*I*e) + (2*I*A - 2*B)*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
839,1,92,0,0.685357," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(3 i \, A + 3 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(4 i \, A + 2 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\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)}}{6 \, a^{2} f}"," ",0,"1/6*((3*I*A + 3*B)*e^(4*I*f*x + 4*I*e) + (4*I*A + 2*B)*e^(2*I*f*x + 2*I*e) + I*A - B)*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)","A",0
840,1,146,0,0.497734," ","integrate((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(-3 i \, A - 3 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-4 i \, A + 4 \, B\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(3 i \, A - 3 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-4 i \, A + 4 \, B\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(7 i \, A - B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\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)}}{12 \, a^{2} c f}"," ",0,"1/12*((-3*I*A - 3*B)*e^(6*I*f*x + 6*I*e) + (-4*I*A + 4*B)*e^(5*I*f*x + 5*I*e) + (3*I*A - 3*B)*e^(4*I*f*x + 4*I*e) + (-4*I*A + 4*B)*e^(3*I*f*x + 3*I*e) + (7*I*A - B)*e^(2*I*f*x + 2*I*e) + I*A - B)*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*c*f)","A",0
841,1,148,0,1.319227," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(-i \, A - B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-10 i \, A - 4 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + 8 \, B e^{\left(5 i \, f x + 5 i \, e\right)} - 6 \, B e^{\left(4 i \, f x + 4 i \, e\right)} + 8 \, B e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(10 i \, A - 4 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, A - B\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)}}{24 \, a^{2} c^{2} f}"," ",0,"1/24*((-I*A - B)*e^(8*I*f*x + 8*I*e) + (-10*I*A - 4*B)*e^(6*I*f*x + 6*I*e) + 8*B*e^(5*I*f*x + 5*I*e) - 6*B*e^(4*I*f*x + 4*I*e) + 8*B*e^(3*I*f*x + 3*I*e) + (10*I*A - 4*B)*e^(2*I*f*x + 2*I*e) + I*A - B)*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*c^2*f)","A",0
842,1,180,0,0.661892," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(-3 i \, A - 3 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-23 i \, A - 13 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-110 i \, A - 10 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(48 i \, A + 48 \, B\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-30 i \, A - 30 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(48 i \, A + 48 \, B\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(65 i \, A - 35 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 5 i \, A - 5 \, B\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)}}{240 \, a^{2} c^{3} f}"," ",0,"1/240*((-3*I*A - 3*B)*e^(10*I*f*x + 10*I*e) + (-23*I*A - 13*B)*e^(8*I*f*x + 8*I*e) + (-110*I*A - 10*B)*e^(6*I*f*x + 6*I*e) + (48*I*A + 48*B)*e^(5*I*f*x + 5*I*e) + (-30*I*A - 30*B)*e^(4*I*f*x + 4*I*e) + (48*I*A + 48*B)*e^(3*I*f*x + 3*I*e) + (65*I*A - 35*B)*e^(2*I*f*x + 2*I*e) + 5*I*A - 5*B)*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*c^3*f)","A",0
843,1,606,0,0.734178," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{15 \, {\left(a^{3} f e^{\left(7 i \, f x + 7 i \, e\right)} + a^{3} f e^{\left(5 i \, f x + 5 i \, e\right)}\right)} \sqrt{\frac{{\left(196 \, A^{2} + 1372 i \, A B - 2401 \, B^{2}\right)} c^{9}}{a^{5} f^{2}}} \log\left(\frac{2 \, {\left({\left({\left(-56 i \, A + 196 \, B\right)} c^{4} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-56 i \, A + 196 \, B\right)} c^{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}} + 2 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{3} f\right)} \sqrt{\frac{{\left(196 \, A^{2} + 1372 i \, A B - 2401 \, B^{2}\right)} c^{9}}{a^{5} f^{2}}}\right)}}{{\left(-14 i \, A + 49 \, B\right)} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-14 i \, A + 49 \, B\right)} c^{4}}\right) - 15 \, {\left(a^{3} f e^{\left(7 i \, f x + 7 i \, e\right)} + a^{3} f e^{\left(5 i \, f x + 5 i \, e\right)}\right)} \sqrt{\frac{{\left(196 \, A^{2} + 1372 i \, A B - 2401 \, B^{2}\right)} c^{9}}{a^{5} f^{2}}} \log\left(\frac{2 \, {\left({\left({\left(-56 i \, A + 196 \, B\right)} c^{4} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-56 i \, A + 196 \, B\right)} c^{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}} - 2 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{3} f\right)} \sqrt{\frac{{\left(196 \, A^{2} + 1372 i \, A B - 2401 \, B^{2}\right)} c^{9}}{a^{5} f^{2}}}\right)}}{{\left(-14 i \, A + 49 \, B\right)} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-14 i \, A + 49 \, B\right)} c^{4}}\right) + 2 \, {\left({\left(420 i \, A - 1470 \, B\right)} c^{4} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(700 i \, A - 2450 \, B\right)} c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(224 i \, A - 784 \, B\right)} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-32 i \, A + 112 \, B\right)} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(24 i \, A - 24 \, B\right)} c^{4}\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}}}{60 \, {\left(a^{3} f e^{\left(7 i \, f x + 7 i \, e\right)} + a^{3} f e^{\left(5 i \, f x + 5 i \, e\right)}\right)}}"," ",0,"1/60*(15*(a^3*f*e^(7*I*f*x + 7*I*e) + a^3*f*e^(5*I*f*x + 5*I*e))*sqrt((196*A^2 + 1372*I*A*B - 2401*B^2)*c^9/(a^5*f^2))*log(2*(((-56*I*A + 196*B)*c^4*e^(3*I*f*x + 3*I*e) + (-56*I*A + 196*B)*c^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*(a^3*f*e^(2*I*f*x + 2*I*e) - a^3*f)*sqrt((196*A^2 + 1372*I*A*B - 2401*B^2)*c^9/(a^5*f^2)))/((-14*I*A + 49*B)*c^4*e^(2*I*f*x + 2*I*e) + (-14*I*A + 49*B)*c^4)) - 15*(a^3*f*e^(7*I*f*x + 7*I*e) + a^3*f*e^(5*I*f*x + 5*I*e))*sqrt((196*A^2 + 1372*I*A*B - 2401*B^2)*c^9/(a^5*f^2))*log(2*(((-56*I*A + 196*B)*c^4*e^(3*I*f*x + 3*I*e) + (-56*I*A + 196*B)*c^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*(a^3*f*e^(2*I*f*x + 2*I*e) - a^3*f)*sqrt((196*A^2 + 1372*I*A*B - 2401*B^2)*c^9/(a^5*f^2)))/((-14*I*A + 49*B)*c^4*e^(2*I*f*x + 2*I*e) + (-14*I*A + 49*B)*c^4)) + 2*((420*I*A - 1470*B)*c^4*e^(8*I*f*x + 8*I*e) + (700*I*A - 2450*B)*c^4*e^(6*I*f*x + 6*I*e) + (224*I*A - 784*B)*c^4*e^(4*I*f*x + 4*I*e) + (-32*I*A + 112*B)*c^4*e^(2*I*f*x + 2*I*e) + (24*I*A - 24*B)*c^4)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(a^3*f*e^(7*I*f*x + 7*I*e) + a^3*f*e^(5*I*f*x + 5*I*e))","B",0
844,1,537,0,0.711392," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, a^{3} \sqrt{\frac{{\left(4 \, A^{2} + 48 i \, A B - 144 \, B^{2}\right)} c^{7}}{a^{5} f^{2}}} f e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(\frac{2 \, {\left({\left({\left(-4 i \, A + 24 \, B\right)} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-4 i \, A + 24 \, B\right)} c^{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(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{3} f\right)} \sqrt{\frac{{\left(4 \, A^{2} + 48 i \, A B - 144 \, B^{2}\right)} c^{7}}{a^{5} f^{2}}}\right)}}{{\left(-i \, A + 6 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A + 6 \, B\right)} c^{3}}\right) - 15 \, a^{3} \sqrt{\frac{{\left(4 \, A^{2} + 48 i \, A B - 144 \, B^{2}\right)} c^{7}}{a^{5} f^{2}}} f e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(\frac{2 \, {\left({\left({\left(-4 i \, A + 24 \, B\right)} c^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-4 i \, A + 24 \, B\right)} c^{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(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{3} f\right)} \sqrt{\frac{{\left(4 \, A^{2} + 48 i \, A B - 144 \, B^{2}\right)} c^{7}}{a^{5} f^{2}}}\right)}}{{\left(-i \, A + 6 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, A + 6 \, B\right)} c^{3}}\right) + 2 \, {\left({\left(60 i \, A - 360 \, B\right)} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(40 i \, A - 240 \, B\right)} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-8 i \, A + 48 \, B\right)} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(12 i \, A - 12 \, B\right)} c^{3}\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(-5 i \, f x - 5 i \, e\right)}}{60 \, a^{3} f}"," ",0,"1/60*(15*a^3*sqrt((4*A^2 + 48*I*A*B - 144*B^2)*c^7/(a^5*f^2))*f*e^(5*I*f*x + 5*I*e)*log(2*(((-4*I*A + 24*B)*c^3*e^(3*I*f*x + 3*I*e) + (-4*I*A + 24*B)*c^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)) + (a^3*f*e^(2*I*f*x + 2*I*e) - a^3*f)*sqrt((4*A^2 + 48*I*A*B - 144*B^2)*c^7/(a^5*f^2)))/((-I*A + 6*B)*c^3*e^(2*I*f*x + 2*I*e) + (-I*A + 6*B)*c^3)) - 15*a^3*sqrt((4*A^2 + 48*I*A*B - 144*B^2)*c^7/(a^5*f^2))*f*e^(5*I*f*x + 5*I*e)*log(2*(((-4*I*A + 24*B)*c^3*e^(3*I*f*x + 3*I*e) + (-4*I*A + 24*B)*c^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)) - (a^3*f*e^(2*I*f*x + 2*I*e) - a^3*f)*sqrt((4*A^2 + 48*I*A*B - 144*B^2)*c^7/(a^5*f^2)))/((-I*A + 6*B)*c^3*e^(2*I*f*x + 2*I*e) + (-I*A + 6*B)*c^3)) + 2*((60*I*A - 360*B)*c^3*e^(6*I*f*x + 6*I*e) + (40*I*A - 240*B)*c^3*e^(4*I*f*x + 4*I*e) + (-8*I*A + 48*B)*c^3*e^(2*I*f*x + 2*I*e) + (12*I*A - 12*B)*c^3)*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
845,1,439,0,1.205520," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, a^{3} f \sqrt{-\frac{B^{2} c^{5}}{a^{5} f^{2}}} e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(\frac{4 \, {\left(2 \, {\left(B c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{3} f\right)} \sqrt{-\frac{B^{2} c^{5}}{a^{5} f^{2}}}\right)}}{B c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + B c^{2}}\right) - 15 \, a^{3} f \sqrt{-\frac{B^{2} c^{5}}{a^{5} f^{2}}} e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(\frac{4 \, {\left(2 \, {\left(B c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + B 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(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - a^{3} f\right)} \sqrt{-\frac{B^{2} c^{5}}{a^{5} f^{2}}}\right)}}{B c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + B c^{2}}\right) - {\left(60 \, B c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + 40 \, B c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - {\left(6 i \, A + 14 \, B\right)} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(6 i \, A - 6 \, B\right)} 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(-5 i \, f x - 5 i \, e\right)}}{30 \, a^{3} f}"," ",0,"1/30*(15*a^3*f*sqrt(-B^2*c^5/(a^5*f^2))*e^(5*I*f*x + 5*I*e)*log(4*(2*(B*c^2*e^(3*I*f*x + 3*I*e) + B*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)) + (a^3*f*e^(2*I*f*x + 2*I*e) - a^3*f)*sqrt(-B^2*c^5/(a^5*f^2)))/(B*c^2*e^(2*I*f*x + 2*I*e) + B*c^2)) - 15*a^3*f*sqrt(-B^2*c^5/(a^5*f^2))*e^(5*I*f*x + 5*I*e)*log(4*(2*(B*c^2*e^(3*I*f*x + 3*I*e) + B*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)) - (a^3*f*e^(2*I*f*x + 2*I*e) - a^3*f)*sqrt(-B^2*c^5/(a^5*f^2)))/(B*c^2*e^(2*I*f*x + 2*I*e) + B*c^2)) - (60*B*c^2*e^(6*I*f*x + 6*I*e) + 40*B*c^2*e^(4*I*f*x + 4*I*e) - (6*I*A + 14*B)*c^2*e^(2*I*f*x + 2*I*e) - (6*I*A - 6*B)*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
846,1,97,0,0.930263," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(5 i \, A + 5 \, B\right)} c e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(8 i \, A + 2 \, B\right)} c e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(3 i \, A - 3 \, B\right)} 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*A + 5*B)*c*e^(4*I*f*x + 4*I*e) + (8*I*A + 2*B)*c*e^(2*I*f*x + 2*I*e) + (3*I*A - 3*B)*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
847,1,109,0,2.294902," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(15 i \, A + 15 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(25 i \, A + 15 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(13 i \, A - 3 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, A - 3 \, B\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)}}{60 \, a^{3} f}"," ",0,"1/60*((15*I*A + 15*B)*e^(6*I*f*x + 6*I*e) + (25*I*A + 15*B)*e^(4*I*f*x + 4*I*e) + (13*I*A - 3*B)*e^(2*I*f*x + 2*I*e) + 3*I*A - 3*B)*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
848,1,158,0,1.422682," ","integrate((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(-15 i \, A - 15 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-48 i \, A + 8 \, B\right)} e^{\left(7 i \, f x + 7 i \, e\right)} + 30 i \, A e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-48 i \, A + 8 \, B\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(60 i \, A + 10 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(18 i \, A - 8 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, A - 3 \, B\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)}}{120 \, a^{3} c f}"," ",0,"1/120*((-15*I*A - 15*B)*e^(8*I*f*x + 8*I*e) + (-48*I*A + 8*B)*e^(7*I*f*x + 7*I*e) + 30*I*A*e^(6*I*f*x + 6*I*e) + (-48*I*A + 8*B)*e^(5*I*f*x + 5*I*e) + (60*I*A + 10*B)*e^(4*I*f*x + 4*I*e) + (18*I*A - 8*B)*e^(2*I*f*x + 2*I*e) + 3*I*A - 3*B)*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*c*f)","A",0
849,1,180,0,0.923729," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(-5 i \, A - 5 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-65 i \, A - 35 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-48 i \, A + 48 \, B\right)} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(30 i \, A - 30 \, B\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-48 i \, A + 48 \, B\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(110 i \, A - 10 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(23 i \, A - 13 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, A - 3 \, B\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)}}{240 \, a^{3} c^{2} f}"," ",0,"1/240*((-5*I*A - 5*B)*e^(10*I*f*x + 10*I*e) + (-65*I*A - 35*B)*e^(8*I*f*x + 8*I*e) + (-48*I*A + 48*B)*e^(7*I*f*x + 7*I*e) + (30*I*A - 30*B)*e^(6*I*f*x + 6*I*e) + (-48*I*A + 48*B)*e^(5*I*f*x + 5*I*e) + (110*I*A - 10*B)*e^(4*I*f*x + 4*I*e) + (23*I*A - 13*B)*e^(2*I*f*x + 2*I*e) + 3*I*A - 3*B)*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*c^2*f)","A",0
850,1,182,0,0.584579," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(-3 i \, A - 3 \, B\right)} e^{\left(12 i \, f x + 12 i \, e\right)} + {\left(-28 i \, A - 18 \, B\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-175 i \, A - 45 \, B\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + 96 \, B e^{\left(7 i \, f x + 7 i \, e\right)} - 60 \, B e^{\left(6 i \, f x + 6 i \, e\right)} + 96 \, B e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(175 i \, A - 45 \, B\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(28 i \, A - 18 \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, A - 3 \, B\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)}}{480 \, a^{3} c^{3} f}"," ",0,"1/480*((-3*I*A - 3*B)*e^(12*I*f*x + 12*I*e) + (-28*I*A - 18*B)*e^(10*I*f*x + 10*I*e) + (-175*I*A - 45*B)*e^(8*I*f*x + 8*I*e) + 96*B*e^(7*I*f*x + 7*I*e) - 60*B*e^(6*I*f*x + 6*I*e) + 96*B*e^(5*I*f*x + 5*I*e) + (175*I*A - 45*B)*e^(4*I*f*x + 4*I*e) + (28*I*A - 18*B)*e^(2*I*f*x + 2*I*e) + 3*I*A - 3*B)*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*c^3*f)","A",0
851,0,0,0,0.687676," ","integrate((a+I*a*tan(f*x+e))^m*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + A + i \, B\right)} \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)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(((A - I*B)*e^(2*I*f*x + 2*I*e) + A + I*B)*(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)))/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
852,0,0,0,0.622529," ","integrate((a+I*a*tan(f*x+e))^(1+m)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(-1-m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - i \, B\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + A + i \, B\right)} \left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{-m - 1} e^{\left(2 i \, e m + {\left(2 i \, f m + 2 i \, f\right)} x + {\left(m + 1\right)} \log\left(\frac{a}{c}\right) + {\left(m + 1\right)} \log\left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(((A - I*B)*e^(2*I*f*x + 2*I*e) + A + I*B)*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^(-m - 1)*e^(2*I*e*m + (2*I*f*m + 2*I*f)*x + (m + 1)*log(a/c) + (m + 1)*log(2*c/(e^(2*I*f*x + 2*I*e) + 1)) + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
853,1,54,0,1.538649," ","integrate((c-I*c*tan(f*x+e))^n*(-I*(2+n)+(-2+n)*tan(f*x+e))/(-I+tan(f*x+e))^2,x, algorithm=""fricas"")","-\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 \, f}"," ",0,"-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)/f","A",0
854,1,84,0,0.724117," ","integrate((A+B*tan(f*x+e))*(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left({\left(4 \, {\left(A - i \, B\right)} c + {\left(-4 i \, A - 4 \, B\right)} d\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(i \, A - B\right)} c - {\left(A + i \, B\right)} d + {\left(4 i \, A c + 4 i \, B d\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*(A - I*B)*c + (-4*I*A - 4*B)*d)*f*x*e^(4*I*f*x + 4*I*e) + (I*A - B)*c - (A + I*B)*d + (4*I*A*c + 4*I*B*d)*e^(2*I*f*x + 2*I*e))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
855,1,625,0,0.818258," ","integrate((A+B*tan(f*x+e))*(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{{\left(A^{2} - 2 i \, A B - B^{2}\right)} c^{2} - {\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} c d - {\left(A^{2} - 2 i \, A B - B^{2}\right)} d^{2}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(-\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(4 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a^{2} f\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{{\left(A^{2} - 2 i \, A B - B^{2}\right)} c^{2} - {\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} c d - {\left(A^{2} - 2 i \, A B - B^{2}\right)} d^{2}}{a^{3} f^{2}}} - {\left(4 \, {\left(A - i \, B\right)} a c - {\left(4 i \, A + 4 \, B\right)} a d\right)} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{{\left(A - i \, B\right)} c - {\left(i \, A + B\right)} d}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{{\left(A^{2} - 2 i \, A B - B^{2}\right)} c^{2} - {\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} c d - {\left(A^{2} - 2 i \, A B - B^{2}\right)} d^{2}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(-\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-4 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, a^{2} f\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{{\left(A^{2} - 2 i \, A B - B^{2}\right)} c^{2} - {\left(2 i \, A^{2} + 4 \, A B - 2 i \, B^{2}\right)} c d - {\left(A^{2} - 2 i \, A B - B^{2}\right)} d^{2}}{a^{3} f^{2}}} - {\left(4 \, {\left(A - i \, B\right)} a c - {\left(4 i \, A + 4 \, B\right)} a d\right)} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{{\left(A - i \, B\right)} c - {\left(i \, A + B\right)} d}\right) - \sqrt{2} {\left({\left(i \, A - B\right)} c - {\left(A + i \, B\right)} d + {\left({\left(4 i \, A + 2 \, B\right)} c + 2 \, {\left(A + 4 i \, B\right)} d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left({\left(5 i \, A + B\right)} c + {\left(A + 7 i \, B\right)} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \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(-((A^2 - 2*I*A*B - B^2)*c^2 - (2*I*A^2 + 4*A*B - 2*I*B^2)*c*d - (A^2 - 2*I*A*B - B^2)*d^2)/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(-(sqrt(2)*sqrt(1/2)*(4*I*a^2*f*e^(2*I*f*x + 2*I*e) + 4*I*a^2*f)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-((A^2 - 2*I*A*B - B^2)*c^2 - (2*I*A^2 + 4*A*B - 2*I*B^2)*c*d - (A^2 - 2*I*A*B - B^2)*d^2)/(a^3*f^2)) - (4*(A - I*B)*a*c - (4*I*A + 4*B)*a*d)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/((A - I*B)*c - (I*A + B)*d)) - 3*sqrt(1/2)*a^2*f*sqrt(-((A^2 - 2*I*A*B - B^2)*c^2 - (2*I*A^2 + 4*A*B - 2*I*B^2)*c*d - (A^2 - 2*I*A*B - B^2)*d^2)/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(-(sqrt(2)*sqrt(1/2)*(-4*I*a^2*f*e^(2*I*f*x + 2*I*e) - 4*I*a^2*f)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-((A^2 - 2*I*A*B - B^2)*c^2 - (2*I*A^2 + 4*A*B - 2*I*B^2)*c*d - (A^2 - 2*I*A*B - B^2)*d^2)/(a^3*f^2)) - (4*(A - I*B)*a*c - (4*I*A + 4*B)*a*d)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/((A - I*B)*c - (I*A + B)*d)) - sqrt(2)*((I*A - B)*c - (A + I*B)*d + ((4*I*A + 2*B)*c + 2*(A + 4*I*B)*d)*e^(4*I*f*x + 4*I*e) + ((5*I*A + B)*c + (A + 7*I*B)*d)*e^(2*I*f*x + 2*I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-3*I*f*x - 3*I*e)/(a^2*f)","B",0
