1,1,39,0,0.528934," ","integrate(sin(x)^4/(I+tan(x)),x, algorithm=""fricas"")","\frac{1}{384} \, {\left(-24 i \, x e^{\left(4 i \, x\right)} - 2 \, e^{\left(10 i \, x\right)} + 9 \, e^{\left(8 i \, x\right)} - 12 \, e^{\left(6 i \, x\right)} - 18 \, e^{\left(2 i \, x\right)} + 3\right)} e^{\left(-4 i \, x\right)}"," ",0,"1/384*(-24*I*x*e^(4*I*x) - 2*e^(10*I*x) + 9*e^(8*I*x) - 12*e^(6*I*x) - 18*e^(2*I*x) + 3)*e^(-4*I*x)","A",0
2,1,26,0,0.455986," ","integrate(sin(x)^3/(I+tan(x)),x, algorithm=""fricas"")","\frac{1}{240} \, {\left(-3 i \, e^{\left(8 i \, x\right)} + 10 i \, e^{\left(6 i \, x\right)} + 30 i \, e^{\left(2 i \, x\right)} - 5 i\right)} e^{\left(-3 i \, x\right)}"," ",0,"1/240*(-3*I*e^(8*I*x) + 10*I*e^(6*I*x) + 30*I*e^(2*I*x) - 5*I)*e^(-3*I*x)","A",0
3,1,25,0,0.482475," ","integrate(sin(x)^2/(I+tan(x)),x, algorithm=""fricas"")","\frac{1}{32} \, {\left(-4 i \, x e^{\left(2 i \, x\right)} + e^{\left(6 i \, x\right)} - 2 \, e^{\left(4 i \, x\right)} - 2\right)} e^{\left(-2 i \, x\right)}"," ",0,"1/32*(-4*I*x*e^(2*I*x) + e^(6*I*x) - 2*e^(4*I*x) - 2)*e^(-2*I*x)","A",0
4,1,14,0,0.466257," ","integrate(sin(x)/(I+tan(x)),x, algorithm=""fricas"")","\frac{1}{12} \, {\left(i \, e^{\left(4 i \, x\right)} + 3 i\right)} e^{\left(-i \, x\right)}"," ",0,"1/12*(I*e^(4*I*x) + 3*I)*e^(-I*x)","A",0
5,1,25,0,0.470924," ","integrate(csc(x)/(I+tan(x)),x, algorithm=""fricas"")","-i \, e^{\left(i \, x\right)} + i \, \log\left(e^{\left(i \, x\right)} + 1\right) - i \, \log\left(e^{\left(i \, x\right)} - 1\right)"," ",0,"-I*e^(I*x) + I*log(e^(I*x) + 1) - I*log(e^(I*x) - 1)","B",0
6,1,25,0,0.464706," ","integrate(csc(x)^2/(I+tan(x)),x, algorithm=""fricas"")","\frac{{\left(e^{\left(2 i \, x\right)} - 1\right)} \log\left(e^{\left(2 i \, x\right)} - 1\right) - 2}{e^{\left(2 i \, x\right)} - 1}"," ",0,"((e^(2*I*x) - 1)*log(e^(2*I*x) - 1) - 2)/(e^(2*I*x) - 1)","A",0
7,1,73,0,0.471235," ","integrate(csc(x)^3/(I+tan(x)),x, algorithm=""fricas"")","\frac{{\left(-i \, e^{\left(4 i \, x\right)} + 2 i \, e^{\left(2 i \, x\right)} - i\right)} \log\left(e^{\left(i \, x\right)} + 1\right) + {\left(i \, e^{\left(4 i \, x\right)} - 2 i \, e^{\left(2 i \, x\right)} + i\right)} \log\left(e^{\left(i \, x\right)} - 1\right) - 6 i \, e^{\left(3 i \, x\right)} + 2 i \, e^{\left(i \, x\right)}}{2 \, {\left(e^{\left(4 i \, x\right)} - 2 \, e^{\left(2 i \, x\right)} + 1\right)}}"," ",0,"1/2*((-I*e^(4*I*x) + 2*I*e^(2*I*x) - I)*log(e^(I*x) + 1) + (I*e^(4*I*x) - 2*I*e^(2*I*x) + I)*log(e^(I*x) - 1) - 6*I*e^(3*I*x) + 2*I*e^(I*x))/(e^(4*I*x) - 2*e^(2*I*x) + 1)","B",0
8,1,36,0,0.459271," ","integrate(csc(x)^4/(I+tan(x)),x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, e^{\left(4 i \, x\right)} - 3 \, e^{\left(2 i \, x\right)} + 1\right)}}{3 \, {\left(e^{\left(6 i \, x\right)} - 3 \, e^{\left(4 i \, x\right)} + 3 \, e^{\left(2 i \, x\right)} - 1\right)}}"," ",0,"2/3*(6*e^(4*I*x) - 3*e^(2*I*x) + 1)/(e^(6*I*x) - 3*e^(4*I*x) + 3*e^(2*I*x) - 1)","B",0
9,1,121,0,0.469077," ","integrate(csc(x)^5/(I+tan(x)),x, algorithm=""fricas"")","\frac{{\left(-3 i \, e^{\left(8 i \, x\right)} + 12 i \, e^{\left(6 i \, x\right)} - 18 i \, e^{\left(4 i \, x\right)} + 12 i \, e^{\left(2 i \, x\right)} - 3 i\right)} \log\left(e^{\left(i \, x\right)} + 1\right) + {\left(3 i \, e^{\left(8 i \, x\right)} - 12 i \, e^{\left(6 i \, x\right)} + 18 i \, e^{\left(4 i \, x\right)} - 12 i \, e^{\left(2 i \, x\right)} + 3 i\right)} \log\left(e^{\left(i \, x\right)} - 1\right) + 6 i \, e^{\left(7 i \, x\right)} + 106 i \, e^{\left(5 i \, x\right)} - 22 i \, e^{\left(3 i \, x\right)} + 6 i \, e^{\left(i \, x\right)}}{24 \, {\left(e^{\left(8 i \, x\right)} - 4 \, e^{\left(6 i \, x\right)} + 6 \, e^{\left(4 i \, x\right)} - 4 \, e^{\left(2 i \, x\right)} + 1\right)}}"," ",0,"1/24*((-3*I*e^(8*I*x) + 12*I*e^(6*I*x) - 18*I*e^(4*I*x) + 12*I*e^(2*I*x) - 3*I)*log(e^(I*x) + 1) + (3*I*e^(8*I*x) - 12*I*e^(6*I*x) + 18*I*e^(4*I*x) - 12*I*e^(2*I*x) + 3*I)*log(e^(I*x) - 1) + 6*I*e^(7*I*x) + 106*I*e^(5*I*x) - 22*I*e^(3*I*x) + 6*I*e^(I*x))/(e^(8*I*x) - 4*e^(6*I*x) + 6*e^(4*I*x) - 4*e^(2*I*x) + 1)","B",0
10,1,54,0,0.448909," ","integrate(csc(x)^6/(I+tan(x)),x, algorithm=""fricas"")","-\frac{4 \, {\left(30 \, e^{\left(6 i \, x\right)} - 10 \, e^{\left(4 i \, x\right)} + 5 \, e^{\left(2 i \, x\right)} - 1\right)}}{15 \, {\left(e^{\left(10 i \, x\right)} - 5 \, e^{\left(8 i \, x\right)} + 10 \, e^{\left(6 i \, x\right)} - 10 \, e^{\left(4 i \, x\right)} + 5 \, e^{\left(2 i \, x\right)} - 1\right)}}"," ",0,"-4/15*(30*e^(6*I*x) - 10*e^(4*I*x) + 5*e^(2*I*x) - 1)/(e^(10*I*x) - 5*e^(8*I*x) + 10*e^(6*I*x) - 10*e^(4*I*x) + 5*e^(2*I*x) - 1)","B",0
11,1,97,0,0.514518," ","integrate(sin(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, a \cos\left(d x + c\right)^{5} - 20 \, a \cos\left(d x + c\right)^{3} + 30 \, a \cos\left(d x + c\right) - 15 \, b \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, b \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, b \cos\left(d x + c\right)^{4} - 11 \, b \cos\left(d x + c\right)^{2} + 23 \, b\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(6*a*cos(d*x + c)^5 - 20*a*cos(d*x + c)^3 + 30*a*cos(d*x + c) - 15*b*log(sin(d*x + c) + 1) + 15*b*log(-sin(d*x + c) + 1) + 2*(3*b*cos(d*x + c)^4 - 11*b*cos(d*x + c)^2 + 23*b)*sin(d*x + c))/d","A",0
12,1,74,0,0.460277," ","integrate(sin(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b \cos\left(d x + c\right)^{4} - 3 \, a d x - 8 \, b \cos\left(d x + c\right)^{2} + 8 \, b \log\left(-\cos\left(d x + c\right)\right) - {\left(2 \, a \cos\left(d x + c\right)^{3} - 5 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(2*b*cos(d*x + c)^4 - 3*a*d*x - 8*b*cos(d*x + c)^2 + 8*b*log(-cos(d*x + c)) - (2*a*cos(d*x + c)^3 - 5*a*cos(d*x + c))*sin(d*x + c))/d","A",0
13,1,74,0,0.508657," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right)^{3} - 6 \, a \cos\left(d x + c\right) + 3 \, b \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, b \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(b \cos\left(d x + c\right)^{2} - 4 \, b\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*a*cos(d*x + c)^3 - 6*a*cos(d*x + c) + 3*b*log(sin(d*x + c) + 1) - 3*b*log(-sin(d*x + c) + 1) + 2*(b*cos(d*x + c)^2 - 4*b)*sin(d*x + c))/d","A",0
14,1,47,0,0.543810," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{a d x + b \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, b \log\left(-\cos\left(d x + c\right)\right)}{2 \, d}"," ",0,"1/2*(a*d*x + b*cos(d*x + c)^2 - a*cos(d*x + c)*sin(d*x + c) - 2*b*log(-cos(d*x + c)))/d","A",0
15,1,49,0,0.453473," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a \cos\left(d x + c\right) - b \log\left(\sin\left(d x + c\right) + 1\right) + b \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, b \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*a*cos(d*x + c) - b*log(sin(d*x + c) + 1) + b*log(-sin(d*x + c) + 1) + 2*b*sin(d*x + c))/d","A",0
16,1,58,0,0.523098," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - b \log\left(\sin\left(d x + c\right) + 1\right) + b \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, d}"," ",0,"-1/2*(a*log(1/2*cos(d*x + c) + 1/2) - a*log(-1/2*cos(d*x + c) + 1/2) - b*log(sin(d*x + c) + 1) + b*log(-sin(d*x + c) + 1))/d","B",0
17,1,62,0,0.551956," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{b \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - b \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) + 2 \, a \cos\left(d x + c\right)}{2 \, d \sin\left(d x + c\right)}"," ",0,"-1/2*(b*log(cos(d*x + c)^2)*sin(d*x + c) - b*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) + 2*a*cos(d*x + c))/(d*sin(d*x + c))","B",0
18,1,142,0,0.462802," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, b \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/4*(2*a*cos(d*x + c) - (a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2) + (a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2) + 2*(b*cos(d*x + c)^2 - b)*log(sin(d*x + c) + 1) - 2*(b*cos(d*x + c)^2 - b)*log(-sin(d*x + c) + 1) + 4*b*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","B",0
19,1,122,0,0.521266," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a \cos\left(d x + c\right)^{3} + 3 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - 3 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) - 6 \, a \cos\left(d x + c\right) - 3 \, b \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(4*a*cos(d*x + c)^3 + 3*(b*cos(d*x + c)^2 - b)*log(cos(d*x + c)^2)*sin(d*x + c) - 3*(b*cos(d*x + c)^2 - b)*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) - 6*a*cos(d*x + c) - 3*b*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
20,1,213,0,0.514533," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{18 \, a \cos\left(d x + c\right)^{3} - 30 \, a \cos\left(d x + c\right) - 9 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 9 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 24 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 24 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 16 \, {\left(3 \, b \cos\left(d x + c\right)^{2} - 4 \, b\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/48*(18*a*cos(d*x + c)^3 - 30*a*cos(d*x + c) - 9*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2) + 9*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2) + 24*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(sin(d*x + c) + 1) - 24*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(-sin(d*x + c) + 1) + 16*(3*b*cos(d*x + c)^2 - 4*b)*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
21,1,174,0,0.486842," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{32 \, a \cos\left(d x + c\right)^{5} - 80 \, a \cos\left(d x + c\right)^{3} + 30 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - 30 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) + 60 \, a \cos\left(d x + c\right) - 15 \, {\left(2 \, b \cos\left(d x + c\right)^{2} - 3 \, b\right)} \sin\left(d x + c\right)}{60 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(32*a*cos(d*x + c)^5 - 80*a*cos(d*x + c)^3 + 30*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(cos(d*x + c)^2)*sin(d*x + c) - 30*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) + 60*a*cos(d*x + c) - 15*(2*b*cos(d*x + c)^2 - 3*b)*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
22,1,137,0,0.550299," ","integrate(sin(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8 \, a b \cos\left(d x + c\right)^{5} - 32 \, a b \cos\left(d x + c\right)^{3} + 32 \, a b \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) - {\left(6 \, {\left(a^{2} - 5 \, b^{2}\right)} d x - 13 \, a b\right)} \cos\left(d x + c\right) - 2 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} - {\left(5 \, a^{2} - 9 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, b^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)}"," ",0,"-1/16*(8*a*b*cos(d*x + c)^5 - 32*a*b*cos(d*x + c)^3 + 32*a*b*cos(d*x + c)*log(-cos(d*x + c)) - (6*(a^2 - 5*b^2)*d*x - 13*a*b)*cos(d*x + c) - 2*(2*(a^2 - b^2)*cos(d*x + c)^4 - (5*a^2 - 9*b^2)*cos(d*x + c)^2 + 8*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
23,1,126,0,0.468940," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - 3 \, {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, b^{2} + 2 \, {\left(a b \cos\left(d x + c\right)^{3} - 4 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)}"," ",0,"1/3*((a^2 - b^2)*cos(d*x + c)^4 + 3*a*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*a*b*cos(d*x + c)*log(-sin(d*x + c) + 1) - 3*(a^2 - 2*b^2)*cos(d*x + c)^2 + 3*b^2 + 2*(a*b*cos(d*x + c)^3 - 4*a*b*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
24,1,101,0,0.502520," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a b \cos\left(d x + c\right)^{3} - 4 \, a b \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) + {\left({\left(a^{2} - 3 \, b^{2}\right)} d x - a b\right)} \cos\left(d x + c\right) - {\left({\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*a*b*cos(d*x + c)^3 - 4*a*b*cos(d*x + c)*log(-cos(d*x + c)) + ((a^2 - 3*b^2)*d*x - a*b)*cos(d*x + c) - ((a^2 - b^2)*cos(d*x + c)^2 - 2*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
25,1,90,0,0.515223," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\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}}{d \cos\left(d x + c\right)}"," ",0,"(a*b*cos(d*x + c)*log(sin(d*x + c) + 1) - a*b*cos(d*x + c)*log(-sin(d*x + c) + 1) - 2*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 + b^2)/(d*cos(d*x + c))","A",0
26,1,102,0,0.451515," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - a^{2} \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, b^{2}}{2 \, d \cos\left(d x + c\right)}"," ",0,"-1/2*(a^2*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2) - a^2*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2) - 2*a*b*cos(d*x + c)*log(sin(d*x + c) + 1) + 2*a*b*cos(d*x + c)*log(-sin(d*x + c) + 1) - 2*b^2)/(d*cos(d*x + c))","B",0
27,1,96,0,0.463558," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a b \cos\left(d x + c\right) \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - a b \cos\left(d x + c\right) \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2}}{d \cos\left(d x + c\right) \sin\left(d x + c\right)}"," ",0,"-(a*b*cos(d*x + c)*log(cos(d*x + c)^2)*sin(d*x + c) - a*b*cos(d*x + c)*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) + (a^2 + b^2)*cos(d*x + c)^2 - b^2)/(d*cos(d*x + c)*sin(d*x + c))","B",0
28,1,230,0,0.625988," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 4 \, b^{2} - {\left({\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(a b \cos\left(d x + c\right)^{3} - a b \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 4 \, {\left(a b \cos\left(d x + c\right)^{3} - a b \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{4 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*(8*a*b*cos(d*x + c)*sin(d*x + c) + 2*(a^2 + 2*b^2)*cos(d*x + c)^2 - 4*b^2 - ((a^2 + 2*b^2)*cos(d*x + c)^3 - (a^2 + 2*b^2)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + ((a^2 + 2*b^2)*cos(d*x + c)^3 - (a^2 + 2*b^2)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 4*(a*b*cos(d*x + c)^3 - a*b*cos(d*x + c))*log(sin(d*x + c) + 1) - 4*(a*b*cos(d*x + c)^3 - a*b*cos(d*x + c))*log(-sin(d*x + c) + 1))/(d*cos(d*x + c)^3 - d*cos(d*x + c))","B",0
29,1,174,0,0.446679," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 3 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, {\left(a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a b \cos\left(d x + c\right)^{3} - a b \cos\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - 3 \, {\left(a b \cos\left(d x + c\right)^{3} - a b \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) + 3 \, b^{2}}{3 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}"," ",0,"-1/3*(2*(a^2 + 3*b^2)*cos(d*x + c)^4 - 3*a*b*cos(d*x + c)*sin(d*x + c) - 3*(a^2 + 3*b^2)*cos(d*x + c)^2 + 3*(a*b*cos(d*x + c)^3 - a*b*cos(d*x + c))*log(cos(d*x + c)^2)*sin(d*x + c) - 3*(a*b*cos(d*x + c)^3 - a*b*cos(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) + 3*b^2)/((d*cos(d*x + c)^3 - d*cos(d*x + c))*sin(d*x + c))","B",0
30,1,333,0,0.512993," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{18 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 30 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 48 \, b^{2} - 9 \, {\left({\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 9 \, {\left({\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 48 \, {\left(a b \cos\left(d x + c\right)^{5} - 2 \, a b \cos\left(d x + c\right)^{3} + a b \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 48 \, {\left(a b \cos\left(d x + c\right)^{5} - 2 \, a b \cos\left(d x + c\right)^{3} + a b \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 32 \, {\left(3 \, a b \cos\left(d x + c\right)^{3} - 4 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{5} - 2 \, d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/48*(18*(a^2 + 4*b^2)*cos(d*x + c)^4 - 30*(a^2 + 4*b^2)*cos(d*x + c)^2 + 48*b^2 - 9*((a^2 + 4*b^2)*cos(d*x + c)^5 - 2*(a^2 + 4*b^2)*cos(d*x + c)^3 + (a^2 + 4*b^2)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 9*((a^2 + 4*b^2)*cos(d*x + c)^5 - 2*(a^2 + 4*b^2)*cos(d*x + c)^3 + (a^2 + 4*b^2)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 48*(a*b*cos(d*x + c)^5 - 2*a*b*cos(d*x + c)^3 + a*b*cos(d*x + c))*log(sin(d*x + c) + 1) - 48*(a*b*cos(d*x + c)^5 - 2*a*b*cos(d*x + c)^3 + a*b*cos(d*x + c))*log(-sin(d*x + c) + 1) + 32*(3*a*b*cos(d*x + c)^3 - 4*a*b*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5 - 2*d*cos(d*x + c)^3 + d*cos(d*x + c))","B",0
31,1,240,0,0.444102," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{16 \, {\left(a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 40 \, {\left(a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(a b \cos\left(d x + c\right)^{5} - 2 \, a b \cos\left(d x + c\right)^{3} + a b \cos\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - 30 \, {\left(a b \cos\left(d x + c\right)^{5} - 2 \, a b \cos\left(d x + c\right)^{3} + a b \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) - 30 \, b^{2} - 15 \, {\left(2 \, a b \cos\left(d x + c\right)^{3} - 3 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{30 \, {\left(d \cos\left(d x + c\right)^{5} - 2 \, d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}"," ",0,"-1/30*(16*(a^2 + 5*b^2)*cos(d*x + c)^6 - 40*(a^2 + 5*b^2)*cos(d*x + c)^4 + 30*(a^2 + 5*b^2)*cos(d*x + c)^2 + 30*(a*b*cos(d*x + c)^5 - 2*a*b*cos(d*x + c)^3 + a*b*cos(d*x + c))*log(cos(d*x + c)^2)*sin(d*x + c) - 30*(a*b*cos(d*x + c)^5 - 2*a*b*cos(d*x + c)^3 + a*b*cos(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) - 30*b^2 - 15*(2*a*b*cos(d*x + c)^3 - 3*a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^5 - 2*d*cos(d*x + c)^3 + d*cos(d*x + c))*sin(d*x + c))","B",0
32,1,188,0,0.474230," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 36 \, a b^{2} \cos\left(d x + c\right) - 12 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{2} b - 5 \, b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(6 \, a^{2} b - 5 \, b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{4} + 3 \, b^{3} - 2 \, {\left(12 \, a^{2} b - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(4*(a^3 - 3*a*b^2)*cos(d*x + c)^5 + 36*a*b^2*cos(d*x + c) - 12*(a^3 - 6*a*b^2)*cos(d*x + c)^3 + 3*(6*a^2*b - 5*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*(6*a^2*b - 5*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*(3*a^2*b - b^3)*cos(d*x + c)^4 + 3*b^3 - 2*(12*a^2*b - 7*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
33,1,149,0,0.455185," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) + 2 \, b^{3} - {\left(3 \, a^{2} b - b^{3} - 2 \, {\left(a^{3} - 9 \, a b^{2}\right)} d x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a b^{2} \cos\left(d x + c\right) - {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*(3*a^2*b - b^3)*cos(d*x + c)^4 - 4*(3*a^2*b - 2*b^3)*cos(d*x + c)^2*log(-cos(d*x + c)) + 2*b^3 - (3*a^2*b - b^3 - 2*(a^3 - 9*a*b^2)*d*x)*cos(d*x + c)^2 + 2*(6*a*b^2*cos(d*x + c) - (a^3 - 3*a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
34,1,144,0,0.449263," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{12 \, a b^{2} \cos\left(d x + c\right) - 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(b^{3} - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(12*a*b^2*cos(d*x + c) - 4*(a^3 - 3*a*b^2)*cos(d*x + c)^3 + 3*(2*a^2*b - b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*(2*a^2*b - b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(b^3 - 2*(3*a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
35,1,148,0,0.529819," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 12 \, a b^{2} \cos\left(d x + c\right) - {\left(6 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(6 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, b^{3} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/4*(2*a^3*cos(d*x + c)^2*log(1/2*cos(d*x + c) + 1/2) - 2*a^3*cos(d*x + c)^2*log(-1/2*cos(d*x + c) + 1/2) - 12*a*b^2*cos(d*x + c) - (6*a^2*b - b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (6*a^2*b - b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*b^3*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
36,1,127,0,0.475265," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, a^{2} b \cos\left(d x + c\right)^{2} \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - 3 \, a^{2} b \cos\left(d x + c\right)^{2} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) - 6 \, a b^{2} \cos\left(d x + c\right) + 2 \, {\left(a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - b^{3} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)}"," ",0,"-1/2*(3*a^2*b*cos(d*x + c)^2*log(cos(d*x + c)^2)*sin(d*x + c) - 3*a^2*b*cos(d*x + c)^2*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) - 6*a*b^2*cos(d*x + c) + 2*(a^3 + 3*a*b^2)*cos(d*x + c)^3 - b^3*sin(d*x + c))/(d*cos(d*x + c)^2*sin(d*x + c))","B",0
37,1,299,0,0.557190," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{12 \, a b^{2} \cos\left(d x + c\right) - 2 \, {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left({\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left({\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(b^{3} - {\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/4*(12*a*b^2*cos(d*x + c) - 2*(a^3 + 6*a*b^2)*cos(d*x + c)^3 + ((a^3 + 6*a*b^2)*cos(d*x + c)^4 - (a^3 + 6*a*b^2)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - ((a^3 + 6*a*b^2)*cos(d*x + c)^4 - (a^3 + 6*a*b^2)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - ((6*a^2*b + b^3)*cos(d*x + c)^4 - (6*a^2*b + b^3)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((6*a^2*b + b^3)*cos(d*x + c)^4 - (6*a^2*b + b^3)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(b^3 - (6*a^2*b + b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4 - d*cos(d*x + c)^2)","B",0
38,1,237,0,0.456326," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 18 \, a b^{2} \cos\left(d x + c\right) - 6 \, {\left(a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) + 3 \, {\left(b^{3} - {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(4*(a^3 + 9*a*b^2)*cos(d*x + c)^5 + 18*a*b^2*cos(d*x + c) - 6*(a^3 + 9*a*b^2)*cos(d*x + c)^3 + 3*((3*a^2*b + b^3)*cos(d*x + c)^4 - (3*a^2*b + b^3)*cos(d*x + c)^2)*log(cos(d*x + c)^2)*sin(d*x + c) - 3*((3*a^2*b + b^3)*cos(d*x + c)^4 - (3*a^2*b + b^3)*cos(d*x + c)^2)*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) + 3*(b^3 - (3*a^2*b + b^3)*cos(d*x + c)^2)*sin(d*x + c))/((d*cos(d*x + c)^4 - d*cos(d*x + c)^2)*sin(d*x + c))","B",0
39,1,427,0,0.565871," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 48 \, a b^{2} \cos\left(d x + c\right) - 10 \, {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left({\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 12 \, {\left({\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, {\left({\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 8 \, {\left(3 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} + b^{3} - 4 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{6} - 2 \, d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(6*(a^3 + 12*a*b^2)*cos(d*x + c)^5 + 48*a*b^2*cos(d*x + c) - 10*(a^3 + 12*a*b^2)*cos(d*x + c)^3 - 3*((a^3 + 12*a*b^2)*cos(d*x + c)^6 - 2*(a^3 + 12*a*b^2)*cos(d*x + c)^4 + (a^3 + 12*a*b^2)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + 3*((a^3 + 12*a*b^2)*cos(d*x + c)^6 - 2*(a^3 + 12*a*b^2)*cos(d*x + c)^4 + (a^3 + 12*a*b^2)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) + 12*((2*a^2*b + b^3)*cos(d*x + c)^6 - 2*(2*a^2*b + b^3)*cos(d*x + c)^4 + (2*a^2*b + b^3)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 12*((2*a^2*b + b^3)*cos(d*x + c)^6 - 2*(2*a^2*b + b^3)*cos(d*x + c)^4 + (2*a^2*b + b^3)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 8*(3*(2*a^2*b + b^3)*cos(d*x + c)^4 + b^3 - 4*(2*a^2*b + b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^6 - 2*d*cos(d*x + c)^4 + d*cos(d*x + c)^2)","B",0
40,1,343,0,0.463956," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{32 \, {\left(a^{3} + 15 \, a b^{2}\right)} \cos\left(d x + c\right)^{7} - 80 \, {\left(a^{3} + 15 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} - 180 \, a b^{2} \cos\left(d x + c\right) + 60 \, {\left(a^{3} + 15 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 30 \, {\left({\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - 30 \, {\left({\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) - 15 \, {\left(2 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + 2 \, b^{3} - 3 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, {\left(d \cos\left(d x + c\right)^{6} - 2 \, d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(32*(a^3 + 15*a*b^2)*cos(d*x + c)^7 - 80*(a^3 + 15*a*b^2)*cos(d*x + c)^5 - 180*a*b^2*cos(d*x + c) + 60*(a^3 + 15*a*b^2)*cos(d*x + c)^3 + 30*((3*a^2*b + 2*b^3)*cos(d*x + c)^6 - 2*(3*a^2*b + 2*b^3)*cos(d*x + c)^4 + (3*a^2*b + 2*b^3)*cos(d*x + c)^2)*log(cos(d*x + c)^2)*sin(d*x + c) - 30*((3*a^2*b + 2*b^3)*cos(d*x + c)^6 - 2*(3*a^2*b + 2*b^3)*cos(d*x + c)^4 + (3*a^2*b + 2*b^3)*cos(d*x + c)^2)*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) - 15*(2*(3*a^2*b + 2*b^3)*cos(d*x + c)^4 + 2*b^3 - 3*(3*a^2*b + 2*b^3)*cos(d*x + c)^2)*sin(d*x + c))/((d*cos(d*x + c)^6 - 2*d*cos(d*x + c)^4 + d*cos(d*x + c)^2)*sin(d*x + c))","B",0
41,1,224,0,0.494121," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{4} - 12 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, a^{3} b - 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, a^{3} b - 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + b^{4} + 9 \, {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{5} + 3 \, a b^{3} \cos\left(d x + c\right) - 2 \, {\left(4 \, a^{3} b - 7 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/3*((a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^6 - 3*(a^4 - 12*a^2*b^2 + 3*b^4)*cos(d*x + c)^4 + 3*(2*a^3*b - 5*a*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*a^3*b - 5*a*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + b^4 + 9*(2*a^2*b^2 - b^4)*cos(d*x + c)^2 + 2*(2*(a^3*b - a*b^3)*cos(d*x + c)^5 + 3*a*b^3*cos(d*x + c) - 2*(4*a^3*b - 7*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
42,1,186,0,0.468007," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{12 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{5} + 12 \, a b^{3} \cos\left(d x + c\right) - 24 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\cos\left(d x + c\right)\right) - 3 \, {\left(2 \, a^{3} b - 2 \, a b^{3} - {\left(a^{4} - 18 \, a^{2} b^{2} + 5 \, b^{4}\right)} d x\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, b^{4} - 2 \, {\left(18 \, a^{2} b^{2} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(12*(a^3*b - a*b^3)*cos(d*x + c)^5 + 12*a*b^3*cos(d*x + c) - 24*(a^3*b - 2*a*b^3)*cos(d*x + c)^3*log(-cos(d*x + c)) - 3*(2*a^3*b - 2*a*b^3 - (a^4 - 18*a^2*b^2 + 5*b^4)*d*x)*cos(d*x + c)^3 - (3*(a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^4 - 2*b^4 - 2*(18*a^2*b^2 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
43,1,176,0,0.504538," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) - b^{4} - 6 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left(a b^{3} \cos\left(d x + c\right) - 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"-1/3*(3*(a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^4 - 3*(2*a^3*b - 3*a*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(2*a^3*b - 3*a*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - b^4 - 6*(3*a^2*b^2 - b^4)*cos(d*x + c)^2 - 6*(a*b^3*cos(d*x + c) - 2*(a^3*b - a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
44,1,175,0,0.514467," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{3 \, a^{4} \cos\left(d x + c\right)^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, a^{4} \cos\left(d x + c\right)^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 12 \, a b^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, b^{4} - 6 \, {\left(6 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2}}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*a^4*cos(d*x + c)^3*log(1/2*cos(d*x + c) + 1/2) - 3*a^4*cos(d*x + c)^3*log(-1/2*cos(d*x + c) + 1/2) - 12*a*b^3*cos(d*x + c)*sin(d*x + c) - 6*(2*a^3*b - a*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 6*(2*a^3*b - a*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - 2*b^4 - 6*(6*a^2*b^2 - b^4)*cos(d*x + c)^2)/(d*cos(d*x + c)^3)","A",0
45,1,159,0,0.453363," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{6 \, a^{3} b \cos\left(d x + c\right)^{3} \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - 6 \, a^{3} b \cos\left(d x + c\right)^{3} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) - 6 \, a b^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(3 \, a^{4} + 18 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{4} - b^{4} - 2 \, {\left(9 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2}}{3 \, d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right)}"," ",0,"-1/3*(6*a^3*b*cos(d*x + c)^3*log(cos(d*x + c)^2)*sin(d*x + c) - 6*a^3*b*cos(d*x + c)^3*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) - 6*a*b^3*cos(d*x + c)*sin(d*x + c) + (3*a^4 + 18*a^2*b^2 - b^4)*cos(d*x + c)^4 - b^4 - 2*(9*a^2*b^2 - b^4)*cos(d*x + c)^2)/(d*cos(d*x + c)^3*sin(d*x + c))","A",0
46,1,346,0,0.553775," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{6 \, {\left(a^{4} + 12 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{4} - 4 \, b^{4} - 4 \, {\left(18 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left({\left(a^{4} + 12 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{4} + 12 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left({\left(a^{4} + 12 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{4} + 12 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 12 \, {\left({\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{5} - {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, {\left({\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{5} - {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 24 \, {\left(a b^{3} \cos\left(d x + c\right) - {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{5} - d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/12*(6*(a^4 + 12*a^2*b^2)*cos(d*x + c)^4 - 4*b^4 - 4*(18*a^2*b^2 - b^4)*cos(d*x + c)^2 - 3*((a^4 + 12*a^2*b^2)*cos(d*x + c)^5 - (a^4 + 12*a^2*b^2)*cos(d*x + c)^3)*log(1/2*cos(d*x + c) + 1/2) + 3*((a^4 + 12*a^2*b^2)*cos(d*x + c)^5 - (a^4 + 12*a^2*b^2)*cos(d*x + c)^3)*log(-1/2*cos(d*x + c) + 1/2) + 12*((2*a^3*b + a*b^3)*cos(d*x + c)^5 - (2*a^3*b + a*b^3)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 12*((2*a^3*b + a*b^3)*cos(d*x + c)^5 - (2*a^3*b + a*b^3)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 24*(a*b^3*cos(d*x + c) - (2*a^3*b + a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^5 - d*cos(d*x + c)^3)","B",0
47,1,267,0,0.459985," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{4} + 18 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{6} + 18 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{4} + 18 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + b^{4} + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - 6 \, {\left({\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) + 6 \, {\left(a b^{3} \cos\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{5} - d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}"," ",0,"-1/3*(2*(a^4 + 18*a^2*b^2 + b^4)*cos(d*x + c)^6 + 18*a^2*b^2*cos(d*x + c)^2 - 3*(a^4 + 18*a^2*b^2 + b^4)*cos(d*x + c)^4 + b^4 + 6*((a^3*b + a*b^3)*cos(d*x + c)^5 - (a^3*b + a*b^3)*cos(d*x + c)^3)*log(cos(d*x + c)^2)*sin(d*x + c) - 6*((a^3*b + a*b^3)*cos(d*x + c)^5 - (a^3*b + a*b^3)*cos(d*x + c)^3)*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) + 6*(a*b^3*cos(d*x + c) - (a^3*b + a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/((d*cos(d*x + c)^5 - d*cos(d*x + c)^3)*sin(d*x + c))","B",0
48,1,547,0,0.685142," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{6 \, {\left(3 \, a^{4} + 72 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{6} - 10 \, {\left(3 \, a^{4} + 72 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 16 \, b^{4} + 16 \, {\left(18 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left({\left(3 \, a^{4} + 72 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{7} - 2 \, {\left(3 \, a^{4} + 72 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 72 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left({\left(3 \, a^{4} + 72 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{7} - 2 \, {\left(3 \, a^{4} + 72 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 72 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 48 \, {\left({\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{7} - 2 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} + {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 48 \, {\left({\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{7} - 2 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} + {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 32 \, {\left(3 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} + 3 \, a b^{3} \cos\left(d x + c\right) - 4 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{7} - 2 \, d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/48*(6*(3*a^4 + 72*a^2*b^2 + 8*b^4)*cos(d*x + c)^6 - 10*(3*a^4 + 72*a^2*b^2 + 8*b^4)*cos(d*x + c)^4 + 16*b^4 + 16*(18*a^2*b^2 + b^4)*cos(d*x + c)^2 - 3*((3*a^4 + 72*a^2*b^2 + 8*b^4)*cos(d*x + c)^7 - 2*(3*a^4 + 72*a^2*b^2 + 8*b^4)*cos(d*x + c)^5 + (3*a^4 + 72*a^2*b^2 + 8*b^4)*cos(d*x + c)^3)*log(1/2*cos(d*x + c) + 1/2) + 3*((3*a^4 + 72*a^2*b^2 + 8*b^4)*cos(d*x + c)^7 - 2*(3*a^4 + 72*a^2*b^2 + 8*b^4)*cos(d*x + c)^5 + (3*a^4 + 72*a^2*b^2 + 8*b^4)*cos(d*x + c)^3)*log(-1/2*cos(d*x + c) + 1/2) + 48*((2*a^3*b + 3*a*b^3)*cos(d*x + c)^7 - 2*(2*a^3*b + 3*a*b^3)*cos(d*x + c)^5 + (2*a^3*b + 3*a*b^3)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 48*((2*a^3*b + 3*a*b^3)*cos(d*x + c)^7 - 2*(2*a^3*b + 3*a*b^3)*cos(d*x + c)^5 + (2*a^3*b + 3*a*b^3)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) + 32*(3*(2*a^3*b + 3*a*b^3)*cos(d*x + c)^5 + 3*a*b^3*cos(d*x + c) - 4*(2*a^3*b + 3*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^7 - 2*d*cos(d*x + c)^5 + d*cos(d*x + c)^3)","B",0
49,1,386,0,0.478621," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{8 \, {\left(a^{4} + 30 \, a^{2} b^{2} + 5 \, b^{4}\right)} \cos\left(d x + c\right)^{8} - 20 \, {\left(a^{4} + 30 \, a^{2} b^{2} + 5 \, b^{4}\right)} \cos\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 30 \, a^{2} b^{2} + 5 \, b^{4}\right)} \cos\left(d x + c\right)^{4} - 5 \, b^{4} - 10 \, {\left(9 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left({\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{7} - 2 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} + {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\cos\left(d x + c\right)^{2}\right) \sin\left(d x + c\right) - 30 \, {\left({\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{7} - 2 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} + {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) - 15 \, {\left(2 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} + 2 \, a b^{3} \cos\left(d x + c\right) - 3 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{7} - 2 \, d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}"," ",0,"-1/15*(8*(a^4 + 30*a^2*b^2 + 5*b^4)*cos(d*x + c)^8 - 20*(a^4 + 30*a^2*b^2 + 5*b^4)*cos(d*x + c)^6 + 15*(a^4 + 30*a^2*b^2 + 5*b^4)*cos(d*x + c)^4 - 5*b^4 - 10*(9*a^2*b^2 + b^4)*cos(d*x + c)^2 + 30*((a^3*b + 2*a*b^3)*cos(d*x + c)^7 - 2*(a^3*b + 2*a*b^3)*cos(d*x + c)^5 + (a^3*b + 2*a*b^3)*cos(d*x + c)^3)*log(cos(d*x + c)^2)*sin(d*x + c) - 30*((a^3*b + 2*a*b^3)*cos(d*x + c)^7 - 2*(a^3*b + 2*a*b^3)*cos(d*x + c)^5 + (a^3*b + 2*a*b^3)*cos(d*x + c)^3)*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) - 15*(2*(a^3*b + 2*a*b^3)*cos(d*x + c)^5 + 2*a*b^3*cos(d*x + c) - 3*(a^3*b + 2*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/((d*cos(d*x + c)^7 - 2*d*cos(d*x + c)^5 + d*cos(d*x + c)^3)*sin(d*x + c))","B",0
50,1,697,0,0.709017," ","integrate(csc(d*x+c)^7*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{150 \, {\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{8} - 400 \, {\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{6} + 330 \, {\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} - 160 \, b^{4} - 480 \, {\left(6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 75 \, {\left({\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{9} - 3 \, {\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 75 \, {\left({\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{9} - 3 \, {\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 480 \, {\left({\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{9} - 3 \, {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} - {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 480 \, {\left({\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{9} - 3 \, {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} - {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 64 \, {\left(15 \, {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{7} - 35 \, {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} - 15 \, a b^{3} \cos\left(d x + c\right) + 23 \, {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{9} - 3 \, d \cos\left(d x + c\right)^{7} + 3 \, d \cos\left(d x + c\right)^{5} - d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/480*(150*(a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^8 - 400*(a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^6 + 330*(a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^4 - 160*b^4 - 480*(6*a^2*b^2 + b^4)*cos(d*x + c)^2 - 75*((a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^9 - 3*(a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^7 + 3*(a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^5 - (a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^3)*log(1/2*cos(d*x + c) + 1/2) + 75*((a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^9 - 3*(a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^7 + 3*(a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^5 - (a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^3)*log(-1/2*cos(d*x + c) + 1/2) + 480*((2*a^3*b + 5*a*b^3)*cos(d*x + c)^9 - 3*(2*a^3*b + 5*a*b^3)*cos(d*x + c)^7 + 3*(2*a^3*b + 5*a*b^3)*cos(d*x + c)^5 - (2*a^3*b + 5*a*b^3)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 480*((2*a^3*b + 5*a*b^3)*cos(d*x + c)^9 - 3*(2*a^3*b + 5*a*b^3)*cos(d*x + c)^7 + 3*(2*a^3*b + 5*a*b^3)*cos(d*x + c)^5 - (2*a^3*b + 5*a*b^3)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) + 64*(15*(2*a^3*b + 5*a*b^3)*cos(d*x + c)^7 - 35*(2*a^3*b + 5*a*b^3)*cos(d*x + c)^5 - 15*a*b^3*cos(d*x + c) + 23*(2*a^3*b + 5*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^9 - 3*d*cos(d*x + c)^7 + 3*d*cos(d*x + c)^5 - d*cos(d*x + c)^3)","A",0
51,1,370,0,0.492577," ","integrate(sin(d*x+c)^5/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, \sqrt{a^{2} + b^{2}} a^{5} b \log\left(\frac{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} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\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) - 6 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{7} + 5 \, a^{5} b^{2} + 4 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(a^{7} + a^{5} b^{2}\right)} \cos\left(d x + c\right) + 2 \, {\left(23 \, a^{6} b + 34 \, a^{4} b^{3} + 14 \, a^{2} b^{5} + 3 \, b^{7} + 3 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(11 \, a^{6} b + 28 \, a^{4} b^{3} + 23 \, a^{2} b^{5} + 6 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d}"," ",0,"1/30*(15*sqrt(a^2 + b^2)*a^5*b*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(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)) - 6*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(d*x + c)^5 + 10*(2*a^7 + 5*a^5*b^2 + 4*a^3*b^4 + a*b^6)*cos(d*x + c)^3 - 30*(a^7 + a^5*b^2)*cos(d*x + c) + 2*(23*a^6*b + 34*a^4*b^3 + 14*a^2*b^5 + 3*b^7 + 3*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^4 - (11*a^6*b + 28*a^4*b^3 + 23*a^2*b^5 + 6*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d)","A",0
52,1,216,0,0.463187," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, a^{4} b \log\left(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) + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{5} - 6 \, a^{3} b^{2} - a b^{4}\right)} d x - 4 \, {\left(2 \, a^{4} b + 3 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{3} - {\left(5 \, a^{5} + 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d}"," ",0,"1/8*(4*a^4*b*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^4 + (3*a^5 - 6*a^3*b^2 - a*b^4)*d*x - 4*(2*a^4*b + 3*a^2*b^3 + b^5)*cos(d*x + c)^2 + (2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^3 - (5*a^5 + 6*a^3*b^2 + a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)","A",0
53,1,261,0,0.462915," ","integrate(sin(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{a^{2} + b^{2}} a^{3} b \log\left(\frac{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} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\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) + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(a^{5} + a^{3} b^{2}\right)} \cos\left(d x + c\right) + 2 \, {\left(4 \, a^{4} b + 5 \, a^{2} b^{3} + b^{5} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d}"," ",0,"1/6*(3*sqrt(a^2 + b^2)*a^3*b*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(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)) + 2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^3 - 6*(a^5 + a^3*b^2)*cos(d*x + c) + 2*(4*a^4*b + 5*a^2*b^3 + b^5 - (a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)","A",0
54,1,122,0,0.457076," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{a^{2} b \log\left(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) + {\left(a^{3} - a b^{2}\right)} d x - {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d}"," ",0,"1/2*(a^2*b*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) + (a^3 - a*b^2)*d*x - (a^2*b + b^3)*cos(d*x + c)^2 - (a^3 + a*b^2)*cos(d*x + c)*sin(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d)","A",0
55,1,185,0,0.475563," ","integrate(sin(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} a b \log\left(\frac{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} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\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) - 2 \, {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + 2 \, {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d}"," ",0,"1/2*(sqrt(a^2 + b^2)*a*b*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(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)) - 2*(a^3 + a*b^2)*cos(d*x + c) + 2*(a^2*b + b^3)*sin(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d)","B",0
56,1,183,0,0.483118," ","integrate(csc(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} b \log\left(\frac{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} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\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) - {\left(a^{2} + b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{2} + b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{3} + a b^{2}\right)} d}"," ",0,"1/2*(sqrt(a^2 + b^2)*b*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - (a^2 + b^2)*log(1/2*cos(d*x + c) + 1/2) + (a^2 + b^2)*log(-1/2*cos(d*x + c) + 1/2))/((a^3 + a*b^2)*d)","B",0
57,1,95,0,0.442482," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{b \log\left(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) \sin\left(d x + c\right) - b \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right)}{2 \, a^{2} d \sin\left(d x + c\right)}"," ",0,"1/2*(b*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)*sin(d*x + c) - b*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) - 2*a*cos(d*x + c))/(a^2*d*sin(d*x + c))","A",0
58,1,270,0,0.532302," ","integrate(csc(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a^{2} \cos\left(d x + c\right) - 4 \, a b \sin\left(d x + c\right) + 2 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{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} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\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) - {\left({\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} - 2 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} - 2 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}"," ",0,"1/4*(2*a^2*cos(d*x + c) - 4*a*b*sin(d*x + c) + 2*(b*cos(d*x + c)^2 - b)*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - ((a^2 + 2*b^2)*cos(d*x + c)^2 - a^2 - 2*b^2)*log(1/2*cos(d*x + c) + 1/2) + ((a^2 + 2*b^2)*cos(d*x + c)^2 - a^2 - 2*b^2)*log(-1/2*cos(d*x + c) + 1/2))/(a^3*d*cos(d*x + c)^2 - a^3*d)","B",0
59,1,208,0,0.461009," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, a^{2} b \sin\left(d x + c\right) + 3 \, {\left(a^{2} b + b^{3} - {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(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) \sin\left(d x + c\right) - 3 \, {\left(a^{2} b + b^{3} - {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) - 6 \, {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right)}{6 \, {\left(a^{4} d \cos\left(d x + c\right)^{2} - a^{4} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(2*(2*a^3 + 3*a*b^2)*cos(d*x + c)^3 + 3*a^2*b*sin(d*x + c) + 3*(a^2*b + b^3 - (a^2*b + b^3)*cos(d*x + c)^2)*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)*sin(d*x + c) - 3*(a^2*b + b^3 - (a^2*b + b^3)*cos(d*x + c)^2)*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) - 6*(a^3 + a*b^2)*cos(d*x + c))/((a^4*d*cos(d*x + c)^2 - a^4*d)*sin(d*x + c))","A",0
60,1,385,0,0.469358," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(8 \, a^{5} + 25 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} - 20 \, {\left(4 \, a^{5} + 11 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(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) \sin\left(d x + c\right) + 30 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) \sin\left(d x + c\right) + 60 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - 15 \, {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, {\left(a^{6} d \cos\left(d x + c\right)^{4} - 2 \, a^{6} d \cos\left(d x + c\right)^{2} + a^{6} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(4*(8*a^5 + 25*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5 - 20*(4*a^5 + 11*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^3 - 30*(a^4*b + 2*a^2*b^3 + b^5 + (a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^4 - 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^2)*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)*sin(d*x + c) + 30*(a^4*b + 2*a^2*b^3 + b^5 + (a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^4 - 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^2)*log(-1/4*cos(d*x + c)^2 + 1/4)*sin(d*x + c) + 60*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c) - 15*(3*a^4*b + 2*a^2*b^3 - 2*(a^4*b + a^2*b^3)*cos(d*x + c)^2)*sin(d*x + c))/((a^6*d*cos(d*x + c)^4 - 2*a^6*d*cos(d*x + c)^2 + a^6*d)*sin(d*x + c))","B",0
61,1,619,0,0.540334," ","integrate(sin(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8 \, {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{7} - 2 \, {\left(19 \, a^{8} b + 68 \, a^{6} b^{3} + 90 \, a^{4} b^{5} + 52 \, a^{2} b^{7} + 11 \, b^{9}\right)} \cos\left(d x + c\right)^{5} + {\left(85 \, a^{8} b + 224 \, a^{6} b^{3} + 210 \, a^{4} b^{5} + 88 \, a^{2} b^{7} + 17 \, b^{9}\right)} \cos\left(d x + c\right)^{3} - {\left(17 \, a^{8} b + 72 \, a^{6} b^{3} + 120 \, a^{4} b^{5} + 20 \, a^{2} b^{7} + 3 \, b^{9} + 3 \, {\left(5 \, a^{9} - 80 \, a^{7} b^{2} + 50 \, a^{5} b^{4} + 8 \, a^{3} b^{6} + a b^{8}\right)} d x\right)} \cos\left(d x + c\right) - 48 \, {\left({\left(a^{8} b - 3 \, a^{6} b^{3}\right)} \cos\left(d x + c\right) + {\left(a^{7} b^{2} - 3 \, a^{5} b^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(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) - {\left(98 \, a^{7} b^{2} + 24 \, a^{5} b^{4} - 30 \, a^{3} b^{6} - 4 \, a b^{8} - 8 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(13 \, a^{9} + 44 \, a^{7} b^{2} + 54 \, a^{5} b^{4} + 28 \, a^{3} b^{6} + 5 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{8} b - 80 \, a^{6} b^{3} + 50 \, a^{4} b^{5} + 8 \, a^{2} b^{7} + b^{9}\right)} d x - 3 \, {\left(11 \, a^{9} + 16 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - a b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{48 \, {\left({\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{10} b + 5 \, a^{8} b^{3} + 10 \, a^{6} b^{5} + 10 \, a^{4} b^{7} + 5 \, a^{2} b^{9} + b^{11}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"-1/48*(8*(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*cos(d*x + c)^7 - 2*(19*a^8*b + 68*a^6*b^3 + 90*a^4*b^5 + 52*a^2*b^7 + 11*b^9)*cos(d*x + c)^5 + (85*a^8*b + 224*a^6*b^3 + 210*a^4*b^5 + 88*a^2*b^7 + 17*b^9)*cos(d*x + c)^3 - (17*a^8*b + 72*a^6*b^3 + 120*a^4*b^5 + 20*a^2*b^7 + 3*b^9 + 3*(5*a^9 - 80*a^7*b^2 + 50*a^5*b^4 + 8*a^3*b^6 + a*b^8)*d*x)*cos(d*x + c) - 48*((a^8*b - 3*a^6*b^3)*cos(d*x + c) + (a^7*b^2 - 3*a^5*b^4)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (98*a^7*b^2 + 24*a^5*b^4 - 30*a^3*b^6 - 4*a*b^8 - 8*(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*cos(d*x + c)^6 + 2*(13*a^9 + 44*a^7*b^2 + 54*a^5*b^4 + 28*a^3*b^6 + 5*a*b^8)*cos(d*x + c)^4 + 3*(5*a^8*b - 80*a^6*b^3 + 50*a^4*b^5 + 8*a^2*b^7 + b^9)*d*x - 3*(11*a^9 + 16*a^7*b^2 - 2*a^5*b^4 - 8*a^3*b^6 - a*b^8)*cos(d*x + c)^2)*sin(d*x + c))/((a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d*cos(d*x + c) + (a^10*b + 5*a^8*b^3 + 10*a^6*b^5 + 10*a^4*b^7 + 5*a^2*b^9 + b^11)*d*sin(d*x + c))","B",0
62,1,444,0,0.522216," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{5} - 6 \, {\left(3 \, a^{6} b + 7 \, a^{4} b^{3} + 5 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{6} b + 8 \, a^{4} b^{3} + 23 \, a^{2} b^{5} + 2 \, b^{7} + 2 \, {\left(3 \, a^{7} - 33 \, a^{5} b^{2} + 13 \, a^{3} b^{4} + a b^{6}\right)} d x\right)} \cos\left(d x + c\right) + 16 \, {\left({\left(a^{6} b - 2 \, a^{4} b^{3}\right)} \cos\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(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) + {\left(29 \, a^{5} b^{2} + 10 \, a^{3} b^{4} - 3 \, a b^{6} + 4 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b - 33 \, a^{4} b^{3} + 13 \, a^{2} b^{5} + b^{7}\right)} d x - 2 \, {\left(5 \, a^{7} + 9 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"1/16*(4*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^5 - 6*(3*a^6*b + 7*a^4*b^3 + 5*a^2*b^5 + b^7)*cos(d*x + c)^3 + (3*a^6*b + 8*a^4*b^3 + 23*a^2*b^5 + 2*b^7 + 2*(3*a^7 - 33*a^5*b^2 + 13*a^3*b^4 + a*b^6)*d*x)*cos(d*x + c) + 16*((a^6*b - 2*a^4*b^3)*cos(d*x + c) + (a^5*b^2 - 2*a^3*b^4)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) + (29*a^5*b^2 + 10*a^3*b^4 - 3*a*b^6 + 4*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(d*x + c)^4 + 2*(3*a^6*b - 33*a^4*b^3 + 13*a^2*b^5 + b^7)*d*x - 2*(5*a^7 + 9*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d*cos(d*x + c) + (a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d*sin(d*x + c))","B",0
63,1,292,0,0.468759," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{2} b^{3} - b^{5} - {\left(a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} d x\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right) + {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(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) - {\left(3 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} d x - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*((a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^3 + (a^2*b^3 - b^5 - (a^5 - 6*a^3*b^2 + a*b^4)*d*x)*cos(d*x + c) - 2*((a^4*b - a^2*b^3)*cos(d*x + c) + (a^3*b^2 - a*b^4)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (3*a^3*b^2 + a*b^4 + (a^4*b - 6*a^2*b^3 + b^5)*d*x - (a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d*sin(d*x + c))","B",0
64,1,293,0,0.462719," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} b^{2} - {\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4} - {\left(a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(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) - {\left(a^{2} b^{2} + b^{4} - {\left(a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right)}{{\left(a^{5} b + a^{3} b^{3}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} + a^{4} b^{2}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{5} b + a^{3} b^{3}\right)} d}"," ",0,"-(a^2*b^2 - (a^4 + 2*a^2*b^2)*cos(d*x + c)^2 - (a^3*b + 2*a*b^3)*cos(d*x + c)*sin(d*x + c) + (a^2*b^2 + b^4 - (a^2*b^2 + b^4)*cos(d*x + c)^2 + (a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (a^2*b^2 + b^4 - (a^2*b^2 + b^4)*cos(d*x + c)^2 + (a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4))/((a^5*b + a^3*b^3)*d*cos(d*x + c)^2 - (a^6 + a^4*b^2)*d*cos(d*x + c)*sin(d*x + c) - (a^5*b + a^3*b^3)*d)","B",0
65,1,442,0,0.503474," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{4} + 6 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{4} + 6 \, a^{2} b^{2} - 3 \, {\left(a^{4} + 6 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{2} b^{2} + 2 \, b^{4} - 2 \, {\left(a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 3 \, {\left({\left(a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{2} b^{2} + 2 \, b^{4} - 2 \, {\left(a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) - 2 \, {\left(6 \, a b^{3} \cos\left(d x + c\right) - {\left(a^{3} b + 6 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{5} b d \cos\left(d x + c\right)^{4} - 2 \, a^{5} b d \cos\left(d x + c\right)^{2} + a^{5} b d - {\left(a^{6} d \cos\left(d x + c\right)^{3} - a^{6} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/3*(2*(a^4 + 6*a^2*b^2)*cos(d*x + c)^4 + 6*a^2*b^2 - 3*(a^4 + 6*a^2*b^2)*cos(d*x + c)^2 + 3*((a^2*b^2 + 2*b^4)*cos(d*x + c)^4 + a^2*b^2 + 2*b^4 - 2*(a^2*b^2 + 2*b^4)*cos(d*x + c)^2 - ((a^3*b + 2*a*b^3)*cos(d*x + c)^3 - (a^3*b + 2*a*b^3)*cos(d*x + c))*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 3*((a^2*b^2 + 2*b^4)*cos(d*x + c)^4 + a^2*b^2 + 2*b^4 - 2*(a^2*b^2 + 2*b^4)*cos(d*x + c)^2 - ((a^3*b + 2*a*b^3)*cos(d*x + c)^3 - (a^3*b + 2*a*b^3)*cos(d*x + c))*sin(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4) - 2*(6*a*b^3*cos(d*x + c) - (a^3*b + 6*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(a^5*b*d*cos(d*x + c)^4 - 2*a^5*b*d*cos(d*x + c)^2 + a^5*b*d - (a^6*d*cos(d*x + c)^3 - a^6*d*cos(d*x + c))*sin(d*x + c))","B",0
66,1,787,0,0.526509," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(4 \, a^{6} + 45 \, a^{4} b^{2} + 45 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{6} - 75 \, a^{4} b^{2} - 90 \, a^{2} b^{4} - 10 \, {\left(4 \, a^{6} + 45 \, a^{4} b^{2} + 45 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(2 \, a^{6} + 23 \, a^{4} b^{2} + 24 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left({\left(a^{4} b^{2} + 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{4} b^{2} - 4 \, a^{2} b^{4} - 3 \, b^{6} - 3 \, {\left(a^{4} b^{2} + 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b^{2} + 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(a^{5} b + 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} - 2 \, {\left(a^{5} b + 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{5} b + 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(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) - 30 \, {\left({\left(a^{4} b^{2} + 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{4} b^{2} - 4 \, a^{2} b^{4} - 3 \, b^{6} - 3 \, {\left(a^{4} b^{2} + 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b^{2} + 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(a^{5} b + 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} - 2 \, {\left(a^{5} b + 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{5} b + 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) + {\left(4 \, {\left(4 \, a^{5} b + 45 \, a^{3} b^{3} + 45 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(a^{5} b + 33 \, a^{3} b^{3} + 36 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(a^{5} b - 10 \, a^{3} b^{3} - 12 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{7} b d \cos\left(d x + c\right)^{6} - 3 \, a^{7} b d \cos\left(d x + c\right)^{4} + 3 \, a^{7} b d \cos\left(d x + c\right)^{2} - a^{7} b d - {\left(a^{8} d \cos\left(d x + c\right)^{5} - 2 \, a^{8} d \cos\left(d x + c\right)^{3} + a^{8} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/30*(4*(4*a^6 + 45*a^4*b^2 + 45*a^2*b^4)*cos(d*x + c)^6 - 75*a^4*b^2 - 90*a^2*b^4 - 10*(4*a^6 + 45*a^4*b^2 + 45*a^2*b^4)*cos(d*x + c)^4 + 15*(2*a^6 + 23*a^4*b^2 + 24*a^2*b^4)*cos(d*x + c)^2 + 30*((a^4*b^2 + 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^6 - a^4*b^2 - 4*a^2*b^4 - 3*b^6 - 3*(a^4*b^2 + 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^4 + 3*(a^4*b^2 + 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^2 - ((a^5*b + 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^5 - 2*(a^5*b + 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3 + (a^5*b + 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c))*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 30*((a^4*b^2 + 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^6 - a^4*b^2 - 4*a^2*b^4 - 3*b^6 - 3*(a^4*b^2 + 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^4 + 3*(a^4*b^2 + 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^2 - ((a^5*b + 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^5 - 2*(a^5*b + 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3 + (a^5*b + 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c))*sin(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4) + (4*(4*a^5*b + 45*a^3*b^3 + 45*a*b^5)*cos(d*x + c)^5 - 10*(a^5*b + 33*a^3*b^3 + 36*a*b^5)*cos(d*x + c)^3 - 15*(a^5*b - 10*a^3*b^3 - 12*a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^7*b*d*cos(d*x + c)^6 - 3*a^7*b*d*cos(d*x + c)^4 + 3*a^7*b*d*cos(d*x + c)^2 - a^7*b*d - (a^8*d*cos(d*x + c)^5 - 2*a^8*d*cos(d*x + c)^3 + a^8*d*cos(d*x + c))*sin(d*x + c))","B",0
67,1,932,0,0.625875," ","integrate(sin(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{195 \, a^{8} b^{3} - 427 \, a^{6} b^{5} - 165 \, a^{4} b^{7} + 27 \, a^{2} b^{9} + 2 \, b^{11} - 8 \, {\left(a^{10} b + 5 \, a^{8} b^{3} + 10 \, a^{6} b^{5} + 10 \, a^{4} b^{7} + 5 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{8} + 20 \, {\left(2 \, a^{10} b + 9 \, a^{8} b^{3} + 16 \, a^{6} b^{5} + 14 \, a^{4} b^{7} + 6 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(49 \, a^{10} b + 162 \, a^{8} b^{3} + 198 \, a^{6} b^{5} + 112 \, a^{4} b^{7} + 33 \, a^{2} b^{9} + 6 \, b^{11}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{9} b^{2} - 180 \, a^{7} b^{4} + 390 \, a^{5} b^{6} - 68 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d x + {\left(9 \, a^{10} b - 46 \, a^{8} b^{3} + 994 \, a^{6} b^{5} + 144 \, a^{4} b^{7} - 43 \, a^{2} b^{9} - 2 \, b^{11} + 3 \, {\left(5 \, a^{11} - 185 \, a^{9} b^{2} + 570 \, a^{7} b^{4} - 458 \, a^{5} b^{6} + 65 \, a^{3} b^{8} + 3 \, a b^{10}\right)} d x\right)} \cos\left(d x + c\right)^{2} + 24 \, {\left(3 \, a^{8} b^{3} - 22 \, a^{6} b^{5} + 15 \, a^{4} b^{7} + {\left(3 \, a^{10} b - 25 \, a^{8} b^{3} + 37 \, a^{6} b^{5} - 15 \, a^{4} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{9} b^{2} - 22 \, a^{7} b^{4} + 15 \, a^{5} b^{6}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(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) - {\left(8 \, {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{7} - 2 \, {\left(13 \, a^{11} + 55 \, a^{9} b^{2} + 90 \, a^{7} b^{4} + 70 \, a^{5} b^{6} + 25 \, a^{3} b^{8} + 3 \, a b^{10}\right)} \cos\left(d x + c\right)^{5} + {\left(33 \, a^{11} + 49 \, a^{9} b^{2} - 54 \, a^{7} b^{4} - 126 \, a^{5} b^{6} - 59 \, a^{3} b^{8} - 3 \, a b^{10}\right)} \cos\left(d x + c\right)^{3} - {\left(261 \, a^{9} b^{2} - 338 \, a^{7} b^{4} + 120 \, a^{5} b^{6} - 150 \, a^{3} b^{8} - 5 \, a b^{10} + 6 \, {\left(5 \, a^{10} b - 180 \, a^{8} b^{3} + 390 \, a^{6} b^{5} - 68 \, a^{4} b^{7} - 3 \, a^{2} b^{9}\right)} d x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\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 \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{2} + 6 \, a^{10} b^{4} + 15 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 6 \, a^{2} b^{12} + b^{14}\right)} d\right)}}"," ",0,"1/48*(195*a^8*b^3 - 427*a^6*b^5 - 165*a^4*b^7 + 27*a^2*b^9 + 2*b^11 - 8*(a^10*b + 5*a^8*b^3 + 10*a^6*b^5 + 10*a^4*b^7 + 5*a^2*b^9 + b^11)*cos(d*x + c)^8 + 20*(2*a^10*b + 9*a^8*b^3 + 16*a^6*b^5 + 14*a^4*b^7 + 6*a^2*b^9 + b^11)*cos(d*x + c)^6 - 2*(49*a^10*b + 162*a^8*b^3 + 198*a^6*b^5 + 112*a^4*b^7 + 33*a^2*b^9 + 6*b^11)*cos(d*x + c)^4 + 3*(5*a^9*b^2 - 180*a^7*b^4 + 390*a^5*b^6 - 68*a^3*b^8 - 3*a*b^10)*d*x + (9*a^10*b - 46*a^8*b^3 + 994*a^6*b^5 + 144*a^4*b^7 - 43*a^2*b^9 - 2*b^11 + 3*(5*a^11 - 185*a^9*b^2 + 570*a^7*b^4 - 458*a^5*b^6 + 65*a^3*b^8 + 3*a*b^10)*d*x)*cos(d*x + c)^2 + 24*(3*a^8*b^3 - 22*a^6*b^5 + 15*a^4*b^7 + (3*a^10*b - 25*a^8*b^3 + 37*a^6*b^5 - 15*a^4*b^7)*cos(d*x + c)^2 + 2*(3*a^9*b^2 - 22*a^7*b^4 + 15*a^5*b^6)*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (8*(a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*cos(d*x + c)^7 - 2*(13*a^11 + 55*a^9*b^2 + 90*a^7*b^4 + 70*a^5*b^6 + 25*a^3*b^8 + 3*a*b^10)*cos(d*x + c)^5 + (33*a^11 + 49*a^9*b^2 - 54*a^7*b^4 - 126*a^5*b^6 - 59*a^3*b^8 - 3*a*b^10)*cos(d*x + c)^3 - (261*a^9*b^2 - 338*a^7*b^4 + 120*a^5*b^6 - 150*a^3*b^8 - 5*a*b^10 + 6*(5*a^10*b - 180*a^8*b^3 + 390*a^6*b^5 - 68*a^4*b^7 - 3*a^2*b^9)*d*x)*cos(d*x + c))*sin(d*x + c))/((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*cos(d*x + c)^2 + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d*cos(d*x + c)*sin(d*x + c) + (a^12*b^2 + 6*a^10*b^4 + 15*a^8*b^6 + 20*a^6*b^8 + 15*a^4*b^10 + 6*a^2*b^12 + b^14)*d)","B",0
68,1,705,0,0.568516," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{119 \, a^{6} b^{3} - 159 \, a^{4} b^{5} - 51 \, a^{2} b^{7} + 3 \, b^{9} + 8 \, {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{6} - 8 \, {\left(5 \, a^{8} b + 16 \, a^{6} b^{3} + 18 \, a^{4} b^{5} + 8 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{4} + 12 \, {\left(a^{7} b^{2} - 25 \, a^{5} b^{4} + 35 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d x - {\left(a^{8} b + 110 \, a^{6} b^{3} - 420 \, a^{4} b^{5} - 78 \, a^{2} b^{7} + 3 \, b^{9} - 12 \, {\left(a^{9} - 26 \, a^{7} b^{2} + 60 \, a^{5} b^{4} - 38 \, a^{3} b^{6} + 3 \, a b^{8}\right)} d x\right)} \cos\left(d x + c\right)^{2} + 48 \, {\left(a^{6} b^{3} - 5 \, a^{4} b^{5} + 2 \, a^{2} b^{7} + {\left(a^{8} b - 6 \, a^{6} b^{3} + 7 \, a^{4} b^{5} - 2 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{2} - 5 \, a^{5} b^{4} + 2 \, a^{3} b^{6}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(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) + 2 \, {\left(4 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right)^{5} - 2 \, {\left(5 \, a^{9} + 12 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} - 3 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + {\left(77 \, a^{7} b^{2} - 69 \, a^{5} b^{4} + 63 \, a^{3} b^{6} - 15 \, a b^{8} + 12 \, {\left(a^{8} b - 25 \, a^{6} b^{3} + 35 \, a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} d x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{32 \, {\left({\left(a^{12} + 4 \, a^{10} b^{2} + 5 \, a^{8} b^{4} - 5 \, a^{4} b^{8} - 4 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\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)} d \cos\left(d x + c\right) \sin\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)} d\right)}}"," ",0,"1/32*(119*a^6*b^3 - 159*a^4*b^5 - 51*a^2*b^7 + 3*b^9 + 8*(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*cos(d*x + c)^6 - 8*(5*a^8*b + 16*a^6*b^3 + 18*a^4*b^5 + 8*a^2*b^7 + b^9)*cos(d*x + c)^4 + 12*(a^7*b^2 - 25*a^5*b^4 + 35*a^3*b^6 - 3*a*b^8)*d*x - (a^8*b + 110*a^6*b^3 - 420*a^4*b^5 - 78*a^2*b^7 + 3*b^9 - 12*(a^9 - 26*a^7*b^2 + 60*a^5*b^4 - 38*a^3*b^6 + 3*a*b^8)*d*x)*cos(d*x + c)^2 + 48*(a^6*b^3 - 5*a^4*b^5 + 2*a^2*b^7 + (a^8*b - 6*a^6*b^3 + 7*a^4*b^5 - 2*a^2*b^7)*cos(d*x + c)^2 + 2*(a^7*b^2 - 5*a^5*b^4 + 2*a^3*b^6)*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) + 2*(4*(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*cos(d*x + c)^5 - 2*(5*a^9 + 12*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 - 3*a*b^8)*cos(d*x + c)^3 + (77*a^7*b^2 - 69*a^5*b^4 + 63*a^3*b^6 - 15*a*b^8 + 12*(a^8*b - 25*a^6*b^3 + 35*a^4*b^5 - 3*a^2*b^7)*d*x)*cos(d*x + c))*sin(d*x + c))/((a^12 + 4*a^10*b^2 + 5*a^8*b^4 - 5*a^4*b^8 - 4*a^2*b^10 - b^12)*d*cos(d*x + c)^2 + 2*(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)*d*cos(d*x + c)*sin(d*x + c) + (a^10*b^2 + 5*a^8*b^4 + 10*a^6*b^6 + 10*a^4*b^8 + 5*a^2*b^10 + b^12)*d)","B",0
69,1,526,0,0.520090," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{13 \, a^{4} b^{3} - 8 \, a^{2} b^{5} - b^{7} - 2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{5} b^{2} - 14 \, a^{3} b^{4} + 9 \, a b^{6}\right)} d x - {\left(a^{6} b + 23 \, a^{4} b^{3} - 21 \, a^{2} b^{5} - 3 \, b^{7} - 2 \, {\left(a^{7} - 15 \, a^{5} b^{2} + 23 \, a^{3} b^{4} - 9 \, a b^{6}\right)} d x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + b^{7} + {\left(3 \, a^{6} b - 11 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(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) - 2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(4 \, a^{5} b^{2} - 3 \, a^{3} b^{4} + 3 \, a b^{6} + {\left(a^{6} b - 14 \, a^{4} b^{3} + 9 \, a^{2} b^{5}\right)} d x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\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 \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 \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\right)}}"," ",0,"1/4*(13*a^4*b^3 - 8*a^2*b^5 - b^7 - 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^4 + 2*(a^5*b^2 - 14*a^3*b^4 + 9*a*b^6)*d*x - (a^6*b + 23*a^4*b^3 - 21*a^2*b^5 - 3*b^7 - 2*(a^7 - 15*a^5*b^2 + 23*a^3*b^4 - 9*a*b^6)*d*x)*cos(d*x + c)^2 + 2*(3*a^4*b^3 - 8*a^2*b^5 + b^7 + (3*a^6*b - 11*a^4*b^3 + 9*a^2*b^5 - b^7)*cos(d*x + c)^2 + 2*(3*a^5*b^2 - 8*a^3*b^4 + a*b^6)*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 2*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(d*x + c)^3 - 2*(4*a^5*b^2 - 3*a^3*b^4 + 3*a*b^6 + (a^6*b - 14*a^4*b^3 + 9*a^2*b^5)*d*x)*cos(d*x + c))*sin(d*x + c))/((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*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*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)","B",0
70,1,565,0,0.538462," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{7} + 4 \, a^{5} b^{2} - 2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{5} b^{2} - 3 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \cos\left(d x + c\right) + 3 \, {\left(2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) - {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7} + {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 3 \, {\left(2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) - {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7} + {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) - {\left(5 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - 4 \, {\left(a^{6} b + 5 \, a^{4} b^{3} + 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right) - {\left({\left(a^{10} + a^{8} b^{2} - a^{6} b^{4} - a^{4} b^{6}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} b^{2} + 2 \, a^{6} b^{4} + a^{4} b^{6}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/2*(2*(a^7 + 4*a^5*b^2 - 2*a^3*b^4 - 3*a*b^6)*cos(d*x + c)^3 - 2*(2*a^5*b^2 - 3*a^3*b^4 - 3*a*b^6)*cos(d*x + c) + 3*(2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*cos(d*x + c)^3 - 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*cos(d*x + c) - (a^4*b^3 + 2*a^2*b^5 + b^7 + (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 3*(2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*cos(d*x + c)^3 - 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*cos(d*x + c) - (a^4*b^3 + 2*a^2*b^5 + b^7 + (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4) - (5*a^4*b^3 + 3*a^2*b^5 - 4*(a^6*b + 5*a^4*b^3 + 3*a^2*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(2*(a^9*b + 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^3 - 2*(a^9*b + 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c) - ((a^10 + a^8*b^2 - a^6*b^4 - a^4*b^6)*d*cos(d*x + c)^2 + (a^8*b^2 + 2*a^6*b^4 + a^4*b^6)*d)*sin(d*x + c))","B",0
71,1,811,0,0.556424," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{7} + 27 \, a^{5} b^{2} + a^{3} b^{4} - 30 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{7} + 43 \, a^{5} b^{2} - 8 \, a^{3} b^{4} - 60 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(5 \, a^{5} b^{2} - 3 \, a^{3} b^{4} - 10 \, a b^{6}\right)} \cos\left(d x + c\right) + 3 \, {\left(2 \, {\left(3 \, a^{5} b^{2} + 13 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} - 4 \, {\left(3 \, a^{5} b^{2} + 13 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{5} b^{2} + 13 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right) + {\left(3 \, a^{4} b^{3} + 13 \, a^{2} b^{5} + 10 \, b^{7} - {\left(3 \, a^{6} b + 10 \, a^{4} b^{3} - 3 \, a^{2} b^{5} - 10 \, b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{6} b + 7 \, a^{4} b^{3} - 16 \, a^{2} b^{5} - 20 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 3 \, {\left(2 \, {\left(3 \, a^{5} b^{2} + 13 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} - 4 \, {\left(3 \, a^{5} b^{2} + 13 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{5} b^{2} + 13 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right) + {\left(3 \, a^{4} b^{3} + 13 \, a^{2} b^{5} + 10 \, b^{7} - {\left(3 \, a^{6} b + 10 \, a^{4} b^{3} - 3 \, a^{2} b^{5} - 10 \, b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{6} b + 7 \, a^{4} b^{3} - 16 \, a^{2} b^{5} - 20 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) + {\left(24 \, a^{4} b^{3} + 30 \, a^{2} b^{5} + 4 \, {\left(2 \, a^{6} b + 29 \, a^{4} b^{3} + 30 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(a^{6} b + 45 \, a^{4} b^{3} + 50 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(2 \, {\left(a^{9} b + a^{7} b^{3}\right)} d \cos\left(d x + c\right)^{5} - 4 \, {\left(a^{9} b + a^{7} b^{3}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{9} b + a^{7} b^{3}\right)} d \cos\left(d x + c\right) - {\left({\left(a^{10} - a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{10} - a^{8} b^{2} - 2 \, a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} b^{2} + a^{6} b^{4}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/6*(2*(2*a^7 + 27*a^5*b^2 + a^3*b^4 - 30*a*b^6)*cos(d*x + c)^5 - 2*(3*a^7 + 43*a^5*b^2 - 8*a^3*b^4 - 60*a*b^6)*cos(d*x + c)^3 + 6*(5*a^5*b^2 - 3*a^3*b^4 - 10*a*b^6)*cos(d*x + c) + 3*(2*(3*a^5*b^2 + 13*a^3*b^4 + 10*a*b^6)*cos(d*x + c)^5 - 4*(3*a^5*b^2 + 13*a^3*b^4 + 10*a*b^6)*cos(d*x + c)^3 + 2*(3*a^5*b^2 + 13*a^3*b^4 + 10*a*b^6)*cos(d*x + c) + (3*a^4*b^3 + 13*a^2*b^5 + 10*b^7 - (3*a^6*b + 10*a^4*b^3 - 3*a^2*b^5 - 10*b^7)*cos(d*x + c)^4 + (3*a^6*b + 7*a^4*b^3 - 16*a^2*b^5 - 20*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 3*(2*(3*a^5*b^2 + 13*a^3*b^4 + 10*a*b^6)*cos(d*x + c)^5 - 4*(3*a^5*b^2 + 13*a^3*b^4 + 10*a*b^6)*cos(d*x + c)^3 + 2*(3*a^5*b^2 + 13*a^3*b^4 + 10*a*b^6)*cos(d*x + c) + (3*a^4*b^3 + 13*a^2*b^5 + 10*b^7 - (3*a^6*b + 10*a^4*b^3 - 3*a^2*b^5 - 10*b^7)*cos(d*x + c)^4 + (3*a^6*b + 7*a^4*b^3 - 16*a^2*b^5 - 20*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4) + (24*a^4*b^3 + 30*a^2*b^5 + 4*(2*a^6*b + 29*a^4*b^3 + 30*a^2*b^5)*cos(d*x + c)^4 - 3*(a^6*b + 45*a^4*b^3 + 50*a^2*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(2*(a^9*b + a^7*b^3)*d*cos(d*x + c)^5 - 4*(a^9*b + a^7*b^3)*d*cos(d*x + c)^3 + 2*(a^9*b + a^7*b^3)*d*cos(d*x + c) - ((a^10 - a^6*b^4)*d*cos(d*x + c)^4 - (a^10 - a^8*b^2 - 2*a^6*b^4)*d*cos(d*x + c)^2 - (a^8*b^2 + a^6*b^4)*d)*sin(d*x + c))","B",0
72,1,1018,0,0.563980," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, {\left(8 \, a^{7} + 187 \, a^{5} b^{2} + 120 \, a^{3} b^{4} - 315 \, a b^{6}\right)} \cos\left(d x + c\right)^{7} - 4 \, {\left(20 \, a^{7} + 482 \, a^{5} b^{2} + 255 \, a^{3} b^{4} - 945 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(6 \, a^{7} + 157 \, a^{5} b^{2} + 60 \, a^{3} b^{4} - 378 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(13 \, a^{5} b^{2} + 2 \, a^{3} b^{4} - 42 \, a b^{6}\right)} \cos\left(d x + c\right) + 30 \, {\left(2 \, {\left(3 \, a^{5} b^{2} + 20 \, a^{3} b^{4} + 21 \, a b^{6}\right)} \cos\left(d x + c\right)^{7} - 6 \, {\left(3 \, a^{5} b^{2} + 20 \, a^{3} b^{4} + 21 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{5} b^{2} + 20 \, a^{3} b^{4} + 21 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(3 \, a^{5} b^{2} + 20 \, a^{3} b^{4} + 21 \, a b^{6}\right)} \cos\left(d x + c\right) - {\left(3 \, a^{4} b^{3} + 20 \, a^{2} b^{5} + 21 \, b^{7} + {\left(3 \, a^{6} b + 17 \, a^{4} b^{3} + a^{2} b^{5} - 21 \, b^{7}\right)} \cos\left(d x + c\right)^{6} - {\left(6 \, a^{6} b + 31 \, a^{4} b^{3} - 18 \, a^{2} b^{5} - 63 \, b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{6} b + 11 \, a^{4} b^{3} - 39 \, a^{2} b^{5} - 63 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(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) - 30 \, {\left(2 \, {\left(3 \, a^{5} b^{2} + 20 \, a^{3} b^{4} + 21 \, a b^{6}\right)} \cos\left(d x + c\right)^{7} - 6 \, {\left(3 \, a^{5} b^{2} + 20 \, a^{3} b^{4} + 21 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{5} b^{2} + 20 \, a^{3} b^{4} + 21 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(3 \, a^{5} b^{2} + 20 \, a^{3} b^{4} + 21 \, a b^{6}\right)} \cos\left(d x + c\right) - {\left(3 \, a^{4} b^{3} + 20 \, a^{2} b^{5} + 21 \, b^{7} + {\left(3 \, a^{6} b + 17 \, a^{4} b^{3} + a^{2} b^{5} - 21 \, b^{7}\right)} \cos\left(d x + c\right)^{6} - {\left(6 \, a^{6} b + 31 \, a^{4} b^{3} - 18 \, a^{2} b^{5} - 63 \, b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{6} b + 11 \, a^{4} b^{3} - 39 \, a^{2} b^{5} - 63 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) - {\left(285 \, a^{4} b^{3} + 630 \, a^{2} b^{5} - 8 \, {\left(8 \, a^{6} b + 195 \, a^{4} b^{3} + 315 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{6} + 10 \, {\left(7 \, a^{6} b + 330 \, a^{4} b^{3} + 567 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(a^{6} b - 135 \, a^{4} b^{3} - 252 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, {\left(2 \, a^{9} b d \cos\left(d x + c\right)^{7} - 6 \, a^{9} b d \cos\left(d x + c\right)^{5} + 6 \, a^{9} b d \cos\left(d x + c\right)^{3} - 2 \, a^{9} b d \cos\left(d x + c\right) - {\left(a^{8} b^{2} d + {\left(a^{10} - a^{8} b^{2}\right)} d \cos\left(d x + c\right)^{6} - {\left(2 \, a^{10} - 3 \, a^{8} b^{2}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{10} - 3 \, a^{8} b^{2}\right)} d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/60*(4*(8*a^7 + 187*a^5*b^2 + 120*a^3*b^4 - 315*a*b^6)*cos(d*x + c)^7 - 4*(20*a^7 + 482*a^5*b^2 + 255*a^3*b^4 - 945*a*b^6)*cos(d*x + c)^5 + 10*(6*a^7 + 157*a^5*b^2 + 60*a^3*b^4 - 378*a*b^6)*cos(d*x + c)^3 - 30*(13*a^5*b^2 + 2*a^3*b^4 - 42*a*b^6)*cos(d*x + c) + 30*(2*(3*a^5*b^2 + 20*a^3*b^4 + 21*a*b^6)*cos(d*x + c)^7 - 6*(3*a^5*b^2 + 20*a^3*b^4 + 21*a*b^6)*cos(d*x + c)^5 + 6*(3*a^5*b^2 + 20*a^3*b^4 + 21*a*b^6)*cos(d*x + c)^3 - 2*(3*a^5*b^2 + 20*a^3*b^4 + 21*a*b^6)*cos(d*x + c) - (3*a^4*b^3 + 20*a^2*b^5 + 21*b^7 + (3*a^6*b + 17*a^4*b^3 + a^2*b^5 - 21*b^7)*cos(d*x + c)^6 - (6*a^6*b + 31*a^4*b^3 - 18*a^2*b^5 - 63*b^7)*cos(d*x + c)^4 + (3*a^6*b + 11*a^4*b^3 - 39*a^2*b^5 - 63*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 30*(2*(3*a^5*b^2 + 20*a^3*b^4 + 21*a*b^6)*cos(d*x + c)^7 - 6*(3*a^5*b^2 + 20*a^3*b^4 + 21*a*b^6)*cos(d*x + c)^5 + 6*(3*a^5*b^2 + 20*a^3*b^4 + 21*a*b^6)*cos(d*x + c)^3 - 2*(3*a^5*b^2 + 20*a^3*b^4 + 21*a*b^6)*cos(d*x + c) - (3*a^4*b^3 + 20*a^2*b^5 + 21*b^7 + (3*a^6*b + 17*a^4*b^3 + a^2*b^5 - 21*b^7)*cos(d*x + c)^6 - (6*a^6*b + 31*a^4*b^3 - 18*a^2*b^5 - 63*b^7)*cos(d*x + c)^4 + (3*a^6*b + 11*a^4*b^3 - 39*a^2*b^5 - 63*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4) - (285*a^4*b^3 + 630*a^2*b^5 - 8*(8*a^6*b + 195*a^4*b^3 + 315*a^2*b^5)*cos(d*x + c)^6 + 10*(7*a^6*b + 330*a^4*b^3 + 567*a^2*b^5)*cos(d*x + c)^4 + 15*(a^6*b - 135*a^4*b^3 - 252*a^2*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(2*a^9*b*d*cos(d*x + c)^7 - 6*a^9*b*d*cos(d*x + c)^5 + 6*a^9*b*d*cos(d*x + c)^3 - 2*a^9*b*d*cos(d*x + c) - (a^8*b^2*d + (a^10 - a^8*b^2)*d*cos(d*x + c)^6 - (2*a^10 - 3*a^8*b^2)*d*cos(d*x + c)^4 + (a^10 - 3*a^8*b^2)*d*cos(d*x + c)^2)*sin(d*x + c))","B",0
73,1,1053,0,0.665639," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{6 \, {\left(a^{10} b + 5 \, a^{8} b^{3} + 10 \, a^{6} b^{5} + 10 \, a^{4} b^{7} + 5 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{7} - 3 \, {\left(11 \, a^{10} b + 45 \, a^{8} b^{3} + 70 \, a^{6} b^{5} + 50 \, a^{4} b^{7} + 15 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{5} - {\left(6 \, a^{10} b + 342 \, a^{8} b^{3} - 1830 \, a^{6} b^{5} + 614 \, a^{4} b^{7} - 216 \, a^{2} b^{9} + 12 \, b^{11} - 3 \, {\left(3 \, a^{11} - 141 \, a^{9} b^{2} + 766 \, a^{7} b^{4} - 1242 \, a^{5} b^{6} + 399 \, a^{3} b^{8} - 9 \, a b^{10}\right)} d x\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(114 \, a^{8} b^{3} - 381 \, a^{6} b^{5} + 187 \, a^{4} b^{7} - 67 \, a^{2} b^{9} + 3 \, b^{11} + 3 \, {\left(3 \, a^{9} b^{2} - 132 \, a^{7} b^{4} + 370 \, a^{5} b^{6} - 132 \, a^{3} b^{8} + 3 \, a b^{10}\right)} d x\right)} \cos\left(d x + c\right) + 48 \, {\left({\left(a^{10} b - 12 \, a^{8} b^{3} + 36 \, a^{6} b^{5} - 28 \, a^{4} b^{7} + 3 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{8} b^{3} - 9 \, a^{6} b^{5} + 9 \, a^{4} b^{7} - a^{2} b^{9}\right)} \cos\left(d x + c\right) + {\left(a^{7} b^{4} - 9 \, a^{5} b^{6} + 9 \, a^{3} b^{8} - a b^{10} + {\left(3 \, a^{9} b^{2} - 28 \, a^{7} b^{4} + 36 \, a^{5} b^{6} - 12 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(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) + {\left(143 \, a^{7} b^{4} - 537 \, a^{5} b^{6} + 105 \, a^{3} b^{8} + 33 \, a b^{10} + 6 \, {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{6} - 15 \, {\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{8} b^{3} - 132 \, a^{6} b^{5} + 370 \, a^{4} b^{7} - 132 \, a^{2} b^{9} + 3 \, b^{11}\right)} d x + {\left(216 \, a^{9} b^{2} - 734 \, a^{7} b^{4} + 1590 \, a^{5} b^{6} - 522 \, a^{3} b^{8} - 54 \, a b^{10} + 3 \, {\left(9 \, a^{10} b - 399 \, a^{8} b^{3} + 1242 \, a^{6} b^{5} - 766 \, a^{4} b^{7} + 141 \, a^{2} b^{9} - 3 \, b^{11}\right)} d x\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{24 \, {\left({\left(a^{15} + 3 \, a^{13} b^{2} - 3 \, a^{11} b^{4} - 25 \, a^{9} b^{6} - 45 \, a^{7} b^{8} - 39 \, a^{5} b^{10} - 17 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} d \cos\left(d x + c\right) + {\left({\left(3 \, a^{14} b + 17 \, a^{12} b^{3} + 39 \, a^{10} b^{5} + 45 \, a^{8} b^{7} + 25 \, a^{6} b^{9} + 3 \, a^{4} b^{11} - 3 \, a^{2} b^{13} - b^{15}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} b^{3} + 6 \, a^{10} b^{5} + 15 \, a^{8} b^{7} + 20 \, a^{6} b^{9} + 15 \, a^{4} b^{11} + 6 \, a^{2} b^{13} + b^{15}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/24*(6*(a^10*b + 5*a^8*b^3 + 10*a^6*b^5 + 10*a^4*b^7 + 5*a^2*b^9 + b^11)*cos(d*x + c)^7 - 3*(11*a^10*b + 45*a^8*b^3 + 70*a^6*b^5 + 50*a^4*b^7 + 15*a^2*b^9 + b^11)*cos(d*x + c)^5 - (6*a^10*b + 342*a^8*b^3 - 1830*a^6*b^5 + 614*a^4*b^7 - 216*a^2*b^9 + 12*b^11 - 3*(3*a^11 - 141*a^9*b^2 + 766*a^7*b^4 - 1242*a^5*b^6 + 399*a^3*b^8 - 9*a*b^10)*d*x)*cos(d*x + c)^3 + 3*(114*a^8*b^3 - 381*a^6*b^5 + 187*a^4*b^7 - 67*a^2*b^9 + 3*b^11 + 3*(3*a^9*b^2 - 132*a^7*b^4 + 370*a^5*b^6 - 132*a^3*b^8 + 3*a*b^10)*d*x)*cos(d*x + c) + 48*((a^10*b - 12*a^8*b^3 + 36*a^6*b^5 - 28*a^4*b^7 + 3*a^2*b^9)*cos(d*x + c)^3 + 3*(a^8*b^3 - 9*a^6*b^5 + 9*a^4*b^7 - a^2*b^9)*cos(d*x + c) + (a^7*b^4 - 9*a^5*b^6 + 9*a^3*b^8 - a*b^10 + (3*a^9*b^2 - 28*a^7*b^4 + 36*a^5*b^6 - 12*a^3*b^8 + a*b^10)*cos(d*x + c)^2)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) + (143*a^7*b^4 - 537*a^5*b^6 + 105*a^3*b^8 + 33*a*b^10 + 6*(a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*cos(d*x + c)^6 - 15*(a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*cos(d*x + c)^4 + 3*(3*a^8*b^3 - 132*a^6*b^5 + 370*a^4*b^7 - 132*a^2*b^9 + 3*b^11)*d*x + (216*a^9*b^2 - 734*a^7*b^4 + 1590*a^5*b^6 - 522*a^3*b^8 - 54*a*b^10 + 3*(9*a^10*b - 399*a^8*b^3 + 1242*a^6*b^5 - 766*a^4*b^7 + 141*a^2*b^9 - 3*b^11)*d*x)*cos(d*x + c)^2)*sin(d*x + c))/((a^15 + 3*a^13*b^2 - 3*a^11*b^4 - 25*a^9*b^6 - 45*a^7*b^8 - 39*a^5*b^10 - 17*a^3*b^12 - 3*a*b^14)*d*cos(d*x + c)^3 + 3*(a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*d*cos(d*x + c) + ((3*a^14*b + 17*a^12*b^3 + 39*a^10*b^5 + 45*a^8*b^7 + 25*a^6*b^9 + 3*a^4*b^11 - 3*a^2*b^13 - b^15)*d*cos(d*x + c)^2 + (a^12*b^3 + 6*a^10*b^5 + 15*a^8*b^7 + 20*a^6*b^9 + 15*a^4*b^11 + 6*a^2*b^13 + b^15)*d)*sin(d*x + c))","B",0
74,1,802,0,0.564202," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{5} + {\left(3 \, a^{8} b + 111 \, a^{6} b^{3} - 231 \, a^{4} b^{5} + 65 \, a^{2} b^{7} - 12 \, b^{9} - 3 \, {\left(a^{9} - 28 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 108 \, a^{3} b^{6} + 9 \, a b^{8}\right)} d x\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(25 \, a^{6} b^{3} - 51 \, a^{4} b^{5} + 25 \, a^{2} b^{7} - 3 \, b^{9} + 3 \, {\left(a^{7} b^{2} - 25 \, a^{5} b^{4} + 35 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d x\right)} \cos\left(d x + c\right) - 12 \, {\left({\left(a^{8} b - 8 \, a^{6} b^{3} + 17 \, a^{4} b^{5} - 6 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{6} b^{3} - 5 \, a^{4} b^{5} + 2 \, a^{2} b^{7}\right)} \cos\left(d x + c\right) + {\left(a^{5} b^{4} - 5 \, a^{3} b^{6} + 2 \, a b^{8} + {\left(3 \, a^{7} b^{2} - 16 \, a^{5} b^{4} + 11 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(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) - {\left(32 \, a^{5} b^{4} - 66 \, a^{3} b^{6} + 6 \, a b^{8} - 3 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{6} b^{3} - 25 \, a^{4} b^{5} + 35 \, a^{2} b^{7} - 3 \, b^{9}\right)} d x + {\left(45 \, a^{7} b^{2} - 143 \, a^{5} b^{4} + 219 \, a^{3} b^{6} - 9 \, a b^{8} + 3 \, {\left(3 \, a^{8} b - 76 \, a^{6} b^{3} + 130 \, a^{4} b^{5} - 44 \, a^{2} b^{7} + 3 \, b^{9}\right)} d x\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{13} + 2 \, a^{11} b^{2} - 5 \, a^{9} b^{4} - 20 \, a^{7} b^{6} - 25 \, a^{5} b^{8} - 14 \, a^{3} b^{10} - 3 \, a b^{12}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{11} b^{2} + 5 \, a^{9} b^{4} + 10 \, a^{7} b^{6} + 10 \, a^{5} b^{8} + 5 \, a^{3} b^{10} + a b^{12}\right)} d \cos\left(d x + c\right) + {\left({\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{10} b^{3} + 5 \, a^{8} b^{5} + 10 \, a^{6} b^{7} + 10 \, a^{4} b^{9} + 5 \, a^{2} b^{11} + b^{13}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/6*(3*(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*cos(d*x + c)^5 + (3*a^8*b + 111*a^6*b^3 - 231*a^4*b^5 + 65*a^2*b^7 - 12*b^9 - 3*(a^9 - 28*a^7*b^2 + 110*a^5*b^4 - 108*a^3*b^6 + 9*a*b^8)*d*x)*cos(d*x + c)^3 - 3*(25*a^6*b^3 - 51*a^4*b^5 + 25*a^2*b^7 - 3*b^9 + 3*(a^7*b^2 - 25*a^5*b^4 + 35*a^3*b^6 - 3*a*b^8)*d*x)*cos(d*x + c) - 12*((a^8*b - 8*a^6*b^3 + 17*a^4*b^5 - 6*a^2*b^7)*cos(d*x + c)^3 + 3*(a^6*b^3 - 5*a^4*b^5 + 2*a^2*b^7)*cos(d*x + c) + (a^5*b^4 - 5*a^3*b^6 + 2*a*b^8 + (3*a^7*b^2 - 16*a^5*b^4 + 11*a^3*b^6 - 2*a*b^8)*cos(d*x + c)^2)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (32*a^5*b^4 - 66*a^3*b^6 + 6*a*b^8 - 3*(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*cos(d*x + c)^4 + 3*(a^6*b^3 - 25*a^4*b^5 + 35*a^2*b^7 - 3*b^9)*d*x + (45*a^7*b^2 - 143*a^5*b^4 + 219*a^3*b^6 - 9*a*b^8 + 3*(3*a^8*b - 76*a^6*b^3 + 130*a^4*b^5 - 44*a^2*b^7 + 3*b^9)*d*x)*cos(d*x + c)^2)*sin(d*x + c))/((a^13 + 2*a^11*b^2 - 5*a^9*b^4 - 20*a^7*b^6 - 25*a^5*b^8 - 14*a^3*b^10 - 3*a*b^12)*d*cos(d*x + c)^3 + 3*(a^11*b^2 + 5*a^9*b^4 + 10*a^7*b^6 + 10*a^5*b^8 + 5*a^3*b^10 + a*b^12)*d*cos(d*x + c) + ((3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d*cos(d*x + c)^2 + (a^10*b^3 + 5*a^8*b^5 + 10*a^6*b^7 + 10*a^4*b^9 + 5*a^2*b^11 + b^13)*d)*sin(d*x + c))","B",0
75,1,874,0,0.543671," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{13 \, a^{6} b^{4} + 15 \, a^{4} b^{6} + 6 \, a^{2} b^{8} - {\left(3 \, a^{10} + 18 \, a^{8} b^{2} - 49 \, a^{6} b^{4} - 84 \, a^{4} b^{6} - 36 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(9 \, a^{8} b^{2} - 71 \, a^{6} b^{4} - 102 \, a^{4} b^{6} - 42 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10} - {\left(3 \, a^{8} b^{2} + 8 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - b^{10}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{8} b^{2} + 7 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - 2 \, b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{9} b - 6 \, a^{5} b^{5} - 8 \, a^{3} b^{7} - 3 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(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) - 6 \, {\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10} - {\left(3 \, a^{8} b^{2} + 8 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - b^{10}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{8} b^{2} + 7 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - 2 \, b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{9} b - 6 \, a^{5} b^{5} - 8 \, a^{3} b^{7} - 3 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) - {\left({\left(9 \, a^{9} b + 78 \, a^{7} b^{3} + 69 \, a^{5} b^{5} + 4 \, a^{3} b^{7} - 12 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(9 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - 6 \, a^{3} b^{7} - 4 \, a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(3 \, a^{13} b + 8 \, a^{11} b^{3} + 6 \, a^{9} b^{5} - a^{5} b^{9}\right)} d \cos\left(d x + c\right)^{4} - {\left(3 \, a^{13} b + 7 \, a^{11} b^{3} + 3 \, a^{9} b^{5} - 3 \, a^{7} b^{7} - 2 \, a^{5} b^{9}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{11} b^{3} + 3 \, a^{9} b^{5} + 3 \, a^{7} b^{7} + a^{5} b^{9}\right)} d - {\left({\left(a^{14} - 6 \, a^{10} b^{4} - 8 \, a^{8} b^{6} - 3 \, a^{6} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{12} b^{2} + 3 \, a^{10} b^{4} + 3 \, a^{8} b^{6} + a^{6} b^{8}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*(13*a^6*b^4 + 15*a^4*b^6 + 6*a^2*b^8 - (3*a^10 + 18*a^8*b^2 - 49*a^6*b^4 - 84*a^4*b^6 - 36*a^2*b^8)*cos(d*x + c)^4 + (9*a^8*b^2 - 71*a^6*b^4 - 102*a^4*b^6 - 42*a^2*b^8)*cos(d*x + c)^2 + 6*(a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10 - (3*a^8*b^2 + 8*a^6*b^4 + 6*a^4*b^6 - b^10)*cos(d*x + c)^4 + (3*a^8*b^2 + 7*a^6*b^4 + 3*a^4*b^6 - 3*a^2*b^8 - 2*b^10)*cos(d*x + c)^2 + ((a^9*b - 6*a^5*b^5 - 8*a^3*b^7 - 3*a*b^9)*cos(d*x + c)^3 + 3*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*cos(d*x + c))*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 6*(a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10 - (3*a^8*b^2 + 8*a^6*b^4 + 6*a^4*b^6 - b^10)*cos(d*x + c)^4 + (3*a^8*b^2 + 7*a^6*b^4 + 3*a^4*b^6 - 3*a^2*b^8 - 2*b^10)*cos(d*x + c)^2 + ((a^9*b - 6*a^5*b^5 - 8*a^3*b^7 - 3*a*b^9)*cos(d*x + c)^3 + 3*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*cos(d*x + c))*sin(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4) - ((9*a^9*b + 78*a^7*b^3 + 69*a^5*b^5 + 4*a^3*b^7 - 12*a*b^9)*cos(d*x + c)^3 - 3*(9*a^7*b^3 + 3*a^5*b^5 - 6*a^3*b^7 - 4*a*b^9)*cos(d*x + c))*sin(d*x + c))/((3*a^13*b + 8*a^11*b^3 + 6*a^9*b^5 - a^5*b^9)*d*cos(d*x + c)^4 - (3*a^13*b + 7*a^11*b^3 + 3*a^9*b^5 - 3*a^7*b^7 - 2*a^5*b^9)*d*cos(d*x + c)^2 - (a^11*b^3 + 3*a^9*b^5 + 3*a^7*b^7 + a^5*b^9)*d - ((a^14 - 6*a^10*b^4 - 8*a^8*b^6 - 3*a^6*b^8)*d*cos(d*x + c)^3 + 3*(a^12*b^2 + 3*a^10*b^4 + 3*a^8*b^6 + a^6*b^8)*d*cos(d*x + c))*sin(d*x + c))","B",0
76,1,1235,0,0.600502," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{19 \, a^{6} b^{4} + 51 \, a^{4} b^{6} + 30 \, a^{2} b^{8} + 2 \, {\left(a^{10} + 23 \, a^{8} b^{2} - 22 \, a^{6} b^{4} - 138 \, a^{4} b^{6} - 90 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{10} + 25 \, a^{8} b^{2} - 46 \, a^{6} b^{4} - 206 \, a^{4} b^{6} - 130 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(9 \, a^{8} b^{2} - 38 \, a^{6} b^{4} - 131 \, a^{4} b^{6} - 80 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(a^{6} b^{4} + 7 \, a^{4} b^{6} + 11 \, a^{2} b^{8} + 5 \, b^{10} + {\left(3 \, a^{8} b^{2} + 20 \, a^{6} b^{4} + 26 \, a^{4} b^{6} + 4 \, a^{2} b^{8} - 5 \, b^{10}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(2 \, a^{8} b^{2} + 13 \, a^{6} b^{4} + 15 \, a^{4} b^{6} - a^{2} b^{8} - 5 \, b^{10}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{8} b^{2} + 6 \, a^{6} b^{4} + 4 \, a^{4} b^{6} - 6 \, a^{2} b^{8} - 5 \, b^{10}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(a^{9} b + 4 \, a^{7} b^{3} - 10 \, a^{5} b^{5} - 28 \, a^{3} b^{7} - 15 \, a b^{9}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{9} b + a^{7} b^{3} - 31 \, a^{5} b^{5} - 61 \, a^{3} b^{7} - 30 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{7} b^{3} + 7 \, a^{5} b^{5} + 11 \, a^{3} b^{7} + 5 \, a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(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) - 6 \, {\left(a^{6} b^{4} + 7 \, a^{4} b^{6} + 11 \, a^{2} b^{8} + 5 \, b^{10} + {\left(3 \, a^{8} b^{2} + 20 \, a^{6} b^{4} + 26 \, a^{4} b^{6} + 4 \, a^{2} b^{8} - 5 \, b^{10}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(2 \, a^{8} b^{2} + 13 \, a^{6} b^{4} + 15 \, a^{4} b^{6} - a^{2} b^{8} - 5 \, b^{10}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{8} b^{2} + 6 \, a^{6} b^{4} + 4 \, a^{4} b^{6} - 6 \, a^{2} b^{8} - 5 \, b^{10}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(a^{9} b + 4 \, a^{7} b^{3} - 10 \, a^{5} b^{5} - 28 \, a^{3} b^{7} - 15 \, a b^{9}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{9} b + a^{7} b^{3} - 31 \, a^{5} b^{5} - 61 \, a^{3} b^{7} - 30 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{7} b^{3} + 7 \, a^{5} b^{5} + 11 \, a^{3} b^{7} + 5 \, a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) + {\left(2 \, {\left(3 \, a^{9} b + 77 \, a^{7} b^{3} + 142 \, a^{5} b^{5} + 34 \, a^{3} b^{7} - 30 \, a b^{9}\right)} \cos\left(d x + c\right)^{5} - {\left(3 \, a^{9} b + 193 \, a^{7} b^{3} + 350 \, a^{5} b^{5} + 26 \, a^{3} b^{7} - 120 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{7} b^{3} + 23 \, a^{5} b^{5} - 14 \, a^{3} b^{7} - 20 \, a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(3 \, a^{13} b + 5 \, a^{11} b^{3} + a^{9} b^{5} - a^{7} b^{7}\right)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(2 \, a^{13} b + 3 \, a^{11} b^{3} - a^{7} b^{7}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{13} b + a^{11} b^{3} - a^{9} b^{5} - a^{7} b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{11} b^{3} + 2 \, a^{9} b^{5} + a^{7} b^{7}\right)} d - {\left({\left(a^{14} - a^{12} b^{2} - 5 \, a^{10} b^{4} - 3 \, a^{8} b^{6}\right)} d \cos\left(d x + c\right)^{5} - {\left(a^{14} - 4 \, a^{12} b^{2} - 11 \, a^{10} b^{4} - 6 \, a^{8} b^{6}\right)} d \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{12} b^{2} + 2 \, a^{10} b^{4} + a^{8} b^{6}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/3*(19*a^6*b^4 + 51*a^4*b^6 + 30*a^2*b^8 + 2*(a^10 + 23*a^8*b^2 - 22*a^6*b^4 - 138*a^4*b^6 - 90*a^2*b^8)*cos(d*x + c)^6 - 3*(a^10 + 25*a^8*b^2 - 46*a^6*b^4 - 206*a^4*b^6 - 130*a^2*b^8)*cos(d*x + c)^4 + 3*(9*a^8*b^2 - 38*a^6*b^4 - 131*a^4*b^6 - 80*a^2*b^8)*cos(d*x + c)^2 + 6*(a^6*b^4 + 7*a^4*b^6 + 11*a^2*b^8 + 5*b^10 + (3*a^8*b^2 + 20*a^6*b^4 + 26*a^4*b^6 + 4*a^2*b^8 - 5*b^10)*cos(d*x + c)^6 - 3*(2*a^8*b^2 + 13*a^6*b^4 + 15*a^4*b^6 - a^2*b^8 - 5*b^10)*cos(d*x + c)^4 + 3*(a^8*b^2 + 6*a^6*b^4 + 4*a^4*b^6 - 6*a^2*b^8 - 5*b^10)*cos(d*x + c)^2 - ((a^9*b + 4*a^7*b^3 - 10*a^5*b^5 - 28*a^3*b^7 - 15*a*b^9)*cos(d*x + c)^5 - (a^9*b + a^7*b^3 - 31*a^5*b^5 - 61*a^3*b^7 - 30*a*b^9)*cos(d*x + c)^3 - 3*(a^7*b^3 + 7*a^5*b^5 + 11*a^3*b^7 + 5*a*b^9)*cos(d*x + c))*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 6*(a^6*b^4 + 7*a^4*b^6 + 11*a^2*b^8 + 5*b^10 + (3*a^8*b^2 + 20*a^6*b^4 + 26*a^4*b^6 + 4*a^2*b^8 - 5*b^10)*cos(d*x + c)^6 - 3*(2*a^8*b^2 + 13*a^6*b^4 + 15*a^4*b^6 - a^2*b^8 - 5*b^10)*cos(d*x + c)^4 + 3*(a^8*b^2 + 6*a^6*b^4 + 4*a^4*b^6 - 6*a^2*b^8 - 5*b^10)*cos(d*x + c)^2 - ((a^9*b + 4*a^7*b^3 - 10*a^5*b^5 - 28*a^3*b^7 - 15*a*b^9)*cos(d*x + c)^5 - (a^9*b + a^7*b^3 - 31*a^5*b^5 - 61*a^3*b^7 - 30*a*b^9)*cos(d*x + c)^3 - 3*(a^7*b^3 + 7*a^5*b^5 + 11*a^3*b^7 + 5*a*b^9)*cos(d*x + c))*sin(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4) + (2*(3*a^9*b + 77*a^7*b^3 + 142*a^5*b^5 + 34*a^3*b^7 - 30*a*b^9)*cos(d*x + c)^5 - (3*a^9*b + 193*a^7*b^3 + 350*a^5*b^5 + 26*a^3*b^7 - 120*a*b^9)*cos(d*x + c)^3 + 3*(15*a^7*b^3 + 23*a^5*b^5 - 14*a^3*b^7 - 20*a*b^9)*cos(d*x + c))*sin(d*x + c))/((3*a^13*b + 5*a^11*b^3 + a^9*b^5 - a^7*b^7)*d*cos(d*x + c)^6 - 3*(2*a^13*b + 3*a^11*b^3 - a^7*b^7)*d*cos(d*x + c)^4 + 3*(a^13*b + a^11*b^3 - a^9*b^5 - a^7*b^7)*d*cos(d*x + c)^2 + (a^11*b^3 + 2*a^9*b^5 + a^7*b^7)*d - ((a^14 - a^12*b^2 - 5*a^10*b^4 - 3*a^8*b^6)*d*cos(d*x + c)^5 - (a^14 - 4*a^12*b^2 - 11*a^10*b^4 - 6*a^8*b^6)*d*cos(d*x + c)^3 - 3*(a^12*b^2 + 2*a^10*b^4 + a^8*b^6)*d*cos(d*x + c))*sin(d*x + c))","B",0
77,1,1536,0,0.651744," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{110 \, a^{6} b^{4} + 510 \, a^{4} b^{6} + 420 \, a^{2} b^{8} - 4 \, {\left(2 \, a^{10} + 81 \, a^{8} b^{2} + 29 \, a^{6} b^{4} - 660 \, a^{4} b^{6} - 630 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{8} + 2 \, {\left(10 \, a^{10} + 423 \, a^{8} b^{2} - 47 \, a^{6} b^{4} - 4320 \, a^{4} b^{6} - 3990 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{6} - 15 \, {\left(a^{10} + 47 \, a^{8} b^{2} - 44 \, a^{6} b^{4} - 658 \, a^{4} b^{6} - 588 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + 20 \, {\left(9 \, a^{8} b^{2} - 28 \, a^{6} b^{4} - 219 \, a^{4} b^{6} - 189 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(a^{6} b^{4} + 11 \, a^{4} b^{6} + 24 \, a^{2} b^{8} + 14 \, b^{10} - {\left(3 \, a^{8} b^{2} + 32 \, a^{6} b^{4} + 61 \, a^{4} b^{6} + 18 \, a^{2} b^{8} - 14 \, b^{10}\right)} \cos\left(d x + c\right)^{8} + {\left(9 \, a^{8} b^{2} + 95 \, a^{6} b^{4} + 172 \, a^{4} b^{6} + 30 \, a^{2} b^{8} - 56 \, b^{10}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(3 \, a^{8} b^{2} + 31 \, a^{6} b^{4} + 50 \, a^{4} b^{6} - 6 \, a^{2} b^{8} - 28 \, b^{10}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{8} b^{2} + 29 \, a^{6} b^{4} + 28 \, a^{4} b^{6} - 54 \, a^{2} b^{8} - 56 \, b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{9} b + 8 \, a^{7} b^{3} - 9 \, a^{5} b^{5} - 58 \, a^{3} b^{7} - 42 \, a b^{9}\right)} \cos\left(d x + c\right)^{7} - {\left(2 \, a^{9} b + 13 \, a^{7} b^{3} - 51 \, a^{5} b^{5} - 188 \, a^{3} b^{7} - 126 \, a b^{9}\right)} \cos\left(d x + c\right)^{5} + {\left(a^{9} b + 2 \, a^{7} b^{3} - 75 \, a^{5} b^{5} - 202 \, a^{3} b^{7} - 126 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{3} + 11 \, a^{5} b^{5} + 24 \, a^{3} b^{7} + 14 \, a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(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) - 30 \, {\left(a^{6} b^{4} + 11 \, a^{4} b^{6} + 24 \, a^{2} b^{8} + 14 \, b^{10} - {\left(3 \, a^{8} b^{2} + 32 \, a^{6} b^{4} + 61 \, a^{4} b^{6} + 18 \, a^{2} b^{8} - 14 \, b^{10}\right)} \cos\left(d x + c\right)^{8} + {\left(9 \, a^{8} b^{2} + 95 \, a^{6} b^{4} + 172 \, a^{4} b^{6} + 30 \, a^{2} b^{8} - 56 \, b^{10}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(3 \, a^{8} b^{2} + 31 \, a^{6} b^{4} + 50 \, a^{4} b^{6} - 6 \, a^{2} b^{8} - 28 \, b^{10}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{8} b^{2} + 29 \, a^{6} b^{4} + 28 \, a^{4} b^{6} - 54 \, a^{2} b^{8} - 56 \, b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{9} b + 8 \, a^{7} b^{3} - 9 \, a^{5} b^{5} - 58 \, a^{3} b^{7} - 42 \, a b^{9}\right)} \cos\left(d x + c\right)^{7} - {\left(2 \, a^{9} b + 13 \, a^{7} b^{3} - 51 \, a^{5} b^{5} - 188 \, a^{3} b^{7} - 126 \, a b^{9}\right)} \cos\left(d x + c\right)^{5} + {\left(a^{9} b + 2 \, a^{7} b^{3} - 75 \, a^{5} b^{5} - 202 \, a^{3} b^{7} - 126 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{3} + 11 \, a^{5} b^{5} + 24 \, a^{3} b^{7} + 14 \, a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(d x + c\right)^{2} + \frac{1}{4}\right) - 2 \, {\left(2 \, {\left(6 \, a^{9} b + 259 \, a^{7} b^{3} + 783 \, a^{5} b^{5} + 340 \, a^{3} b^{7} - 210 \, a b^{9}\right)} \cos\left(d x + c\right)^{7} - {\left(15 \, a^{9} b + 1141 \, a^{7} b^{3} + 3546 \, a^{5} b^{5} + 1270 \, a^{3} b^{7} - 1260 \, a b^{9}\right)} \cos\left(d x + c\right)^{5} + 5 \, {\left(151 \, a^{7} b^{3} + 483 \, a^{5} b^{5} + 100 \, a^{3} b^{7} - 252 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(9 \, a^{7} b^{3} + 29 \, a^{5} b^{5} - 6 \, a^{3} b^{7} - 28 \, a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{15 \, {\left({\left(3 \, a^{13} b + 2 \, a^{11} b^{3} - a^{9} b^{5}\right)} d \cos\left(d x + c\right)^{8} - {\left(9 \, a^{13} b + 5 \, a^{11} b^{3} - 4 \, a^{9} b^{5}\right)} d \cos\left(d x + c\right)^{6} + 3 \, {\left(3 \, a^{13} b + a^{11} b^{3} - 2 \, a^{9} b^{5}\right)} d \cos\left(d x + c\right)^{4} - {\left(3 \, a^{13} b - a^{11} b^{3} - 4 \, a^{9} b^{5}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{11} b^{3} + a^{9} b^{5}\right)} d - {\left({\left(a^{14} - 2 \, a^{12} b^{2} - 3 \, a^{10} b^{4}\right)} d \cos\left(d x + c\right)^{7} - {\left(2 \, a^{14} - 7 \, a^{12} b^{2} - 9 \, a^{10} b^{4}\right)} d \cos\left(d x + c\right)^{5} + {\left(a^{14} - 8 \, a^{12} b^{2} - 9 \, a^{10} b^{4}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{12} b^{2} + a^{10} b^{4}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/15*(110*a^6*b^4 + 510*a^4*b^6 + 420*a^2*b^8 - 4*(2*a^10 + 81*a^8*b^2 + 29*a^6*b^4 - 660*a^4*b^6 - 630*a^2*b^8)*cos(d*x + c)^8 + 2*(10*a^10 + 423*a^8*b^2 - 47*a^6*b^4 - 4320*a^4*b^6 - 3990*a^2*b^8)*cos(d*x + c)^6 - 15*(a^10 + 47*a^8*b^2 - 44*a^6*b^4 - 658*a^4*b^6 - 588*a^2*b^8)*cos(d*x + c)^4 + 20*(9*a^8*b^2 - 28*a^6*b^4 - 219*a^4*b^6 - 189*a^2*b^8)*cos(d*x + c)^2 + 30*(a^6*b^4 + 11*a^4*b^6 + 24*a^2*b^8 + 14*b^10 - (3*a^8*b^2 + 32*a^6*b^4 + 61*a^4*b^6 + 18*a^2*b^8 - 14*b^10)*cos(d*x + c)^8 + (9*a^8*b^2 + 95*a^6*b^4 + 172*a^4*b^6 + 30*a^2*b^8 - 56*b^10)*cos(d*x + c)^6 - 3*(3*a^8*b^2 + 31*a^6*b^4 + 50*a^4*b^6 - 6*a^2*b^8 - 28*b^10)*cos(d*x + c)^4 + (3*a^8*b^2 + 29*a^6*b^4 + 28*a^4*b^6 - 54*a^2*b^8 - 56*b^10)*cos(d*x + c)^2 + ((a^9*b + 8*a^7*b^3 - 9*a^5*b^5 - 58*a^3*b^7 - 42*a*b^9)*cos(d*x + c)^7 - (2*a^9*b + 13*a^7*b^3 - 51*a^5*b^5 - 188*a^3*b^7 - 126*a*b^9)*cos(d*x + c)^5 + (a^9*b + 2*a^7*b^3 - 75*a^5*b^5 - 202*a^3*b^7 - 126*a*b^9)*cos(d*x + c)^3 + 3*(a^7*b^3 + 11*a^5*b^5 + 24*a^3*b^7 + 14*a*b^9)*cos(d*x + c))*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 30*(a^6*b^4 + 11*a^4*b^6 + 24*a^2*b^8 + 14*b^10 - (3*a^8*b^2 + 32*a^6*b^4 + 61*a^4*b^6 + 18*a^2*b^8 - 14*b^10)*cos(d*x + c)^8 + (9*a^8*b^2 + 95*a^6*b^4 + 172*a^4*b^6 + 30*a^2*b^8 - 56*b^10)*cos(d*x + c)^6 - 3*(3*a^8*b^2 + 31*a^6*b^4 + 50*a^4*b^6 - 6*a^2*b^8 - 28*b^10)*cos(d*x + c)^4 + (3*a^8*b^2 + 29*a^6*b^4 + 28*a^4*b^6 - 54*a^2*b^8 - 56*b^10)*cos(d*x + c)^2 + ((a^9*b + 8*a^7*b^3 - 9*a^5*b^5 - 58*a^3*b^7 - 42*a*b^9)*cos(d*x + c)^7 - (2*a^9*b + 13*a^7*b^3 - 51*a^5*b^5 - 188*a^3*b^7 - 126*a*b^9)*cos(d*x + c)^5 + (a^9*b + 2*a^7*b^3 - 75*a^5*b^5 - 202*a^3*b^7 - 126*a*b^9)*cos(d*x + c)^3 + 3*(a^7*b^3 + 11*a^5*b^5 + 24*a^3*b^7 + 14*a*b^9)*cos(d*x + c))*sin(d*x + c))*log(-1/4*cos(d*x + c)^2 + 1/4) - 2*(2*(6*a^9*b + 259*a^7*b^3 + 783*a^5*b^5 + 340*a^3*b^7 - 210*a*b^9)*cos(d*x + c)^7 - (15*a^9*b + 1141*a^7*b^3 + 3546*a^5*b^5 + 1270*a^3*b^7 - 1260*a*b^9)*cos(d*x + c)^5 + 5*(151*a^7*b^3 + 483*a^5*b^5 + 100*a^3*b^7 - 252*a*b^9)*cos(d*x + c)^3 - 15*(9*a^7*b^3 + 29*a^5*b^5 - 6*a^3*b^7 - 28*a*b^9)*cos(d*x + c))*sin(d*x + c))/((3*a^13*b + 2*a^11*b^3 - a^9*b^5)*d*cos(d*x + c)^8 - (9*a^13*b + 5*a^11*b^3 - 4*a^9*b^5)*d*cos(d*x + c)^6 + 3*(3*a^13*b + a^11*b^3 - 2*a^9*b^5)*d*cos(d*x + c)^4 - (3*a^13*b - a^11*b^3 - 4*a^9*b^5)*d*cos(d*x + c)^2 - (a^11*b^3 + a^9*b^5)*d - ((a^14 - 2*a^12*b^2 - 3*a^10*b^4)*d*cos(d*x + c)^7 - (2*a^14 - 7*a^12*b^2 - 9*a^10*b^4)*d*cos(d*x + c)^5 + (a^14 - 8*a^12*b^2 - 9*a^10*b^4)*d*cos(d*x + c)^3 + 3*(a^12*b^2 + a^10*b^4)*d*cos(d*x + c))*sin(d*x + c))","B",0
78,1,55,0,0.432574," ","integrate(csc(x)/(1+tan(x)),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{2 \, {\left(\sqrt{2} + \cos\left(x\right)\right)} \sin\left(x\right) - 2 \, \sqrt{2} \cos\left(x\right) - 3}{2 \, \cos\left(x\right) \sin\left(x\right) + 1}\right) - \frac{1}{2} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{2} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"1/4*sqrt(2)*log((2*(sqrt(2) + cos(x))*sin(x) - 2*sqrt(2)*cos(x) - 3)/(2*cos(x)*sin(x) + 1)) - 1/2*log(1/2*cos(x) + 1/2) + 1/2*log(-1/2*cos(x) + 1/2)","B",0
79,0,0,0,0.435380," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(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}\right)} \sin\left(d x + c\right)^{m}, x\right)"," ",0,"integral((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)*sin(d*x + c)^m, x)","F",0
80,0,0,0,0.433864," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}\right)} \sin\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)*sin(d*x + c)^m, x)","F",0
81,0,0,0,0.430025," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)*sin(d*x + c)^m, x)","F",0
82,0,0,0,0.437003," ","integrate(sin(d*x+c)^m/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)^{m}}{b \tan\left(d x + c\right) + a}, x\right)"," ",0,"integral(sin(d*x + c)^m/(b*tan(d*x + c) + a), x)","F",0
83,0,0,0,0.528611," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*sin(d*x + c)^m, x)","F",0
84,0,0,0,0.454014," ","integrate(sin(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*(b*tan(d*x + c) + a)^n, x)","F",0
85,0,0,0,0.436963," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(d x + c\right)^{2} - 1\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)*(b*tan(d*x + c) + a)^n, x)","F",0
86,0,0,0,0.467359," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
87,0,0,0,0.482908," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*csc(d*x + c)^4, x)","F",0
88,0,0,0,0.443405," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(d x + c\right)^{2} - 1\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right), x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)*(b*tan(d*x + c) + a)^n*sin(d*x + c), x)","F",0
89,0,0,0,0.441603," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right), x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*sin(d*x + c), x)","F",0
90,0,0,0,0.437507," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right), x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*csc(d*x + c), x)","F",0
91,0,0,0,0.444737," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{3}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*csc(d*x + c)^3, x)","F",0
