1,1,53,0,0.364814," ","integrate(sin(x)^4/(I+tan(x)),x, algorithm=""giac"")","-\frac{3 i \, \tan\left(x\right)^{4} + 21 \, \tan\left(x\right)^{3} + 13 i \, \tan\left(x\right)^{2} + 11 \, \tan\left(x\right) + 8 i}{48 \, {\left(\tan\left(x\right) + i\right)}^{3} {\left(\tan\left(x\right) - i\right)}^{2}} + \frac{1}{32} \, \log\left(\tan\left(x\right) + i\right) - \frac{1}{32} \, \log\left(\tan\left(x\right) - i\right)"," ",0,"-1/48*(3*I*tan(x)^4 + 21*tan(x)^3 + 13*I*tan(x)^2 + 11*tan(x) + 8*I)/((tan(x) + I)^3*(tan(x) - I)^2) + 1/32*log(tan(x) + I) - 1/32*log(tan(x) - I)","A",0
2,1,71,0,0.341703," ","integrate(sin(x)^3/(I+tan(x)),x, algorithm=""giac"")","-\frac{-3 i \, \tan\left(\frac{1}{2} \, x\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, x\right) + 5 i}{24 \, {\left(-i \, \tan\left(\frac{1}{2} \, x\right) - 1\right)}^{3}} - \frac{15 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 60 i \, \tan\left(\frac{1}{2} \, x\right)^{3} - 10 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 20 i \, \tan\left(\frac{1}{2} \, x\right) + 7}{120 \, {\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}^{5}}"," ",0,"-1/24*(-3*I*tan(1/2*x)^2 - 12*tan(1/2*x) + 5*I)/(-I*tan(1/2*x) - 1)^3 - 1/120*(15*tan(1/2*x)^4 + 60*I*tan(1/2*x)^3 - 10*tan(1/2*x)^2 - 20*I*tan(1/2*x) + 7)/(tan(1/2*x) + I)^5","B",0
3,1,41,0,0.447587," ","integrate(sin(x)^2/(I+tan(x)),x, algorithm=""giac"")","-\frac{i \, \tan\left(x\right)^{2} + 3 \, \tan\left(x\right) + 2 i}{8 \, {\left(\tan\left(x\right) + i\right)}^{2} {\left(\tan\left(x\right) - i\right)}} + \frac{1}{16} \, \log\left(\tan\left(x\right) + i\right) - \frac{1}{16} \, \log\left(\tan\left(x\right) - i\right)"," ",0,"-1/8*(I*tan(x)^2 + 3*tan(x) + 2*I)/((tan(x) + I)^2*(tan(x) - I)) + 1/16*log(tan(x) + I) - 1/16*log(tan(x) - I)","A",0
4,1,33,0,0.757383," ","integrate(sin(x)/(I+tan(x)),x, algorithm=""giac"")","-\frac{i}{2 \, {\left(-i \, \tan\left(\frac{1}{2} \, x\right) - 1\right)}} - \frac{3 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}{6 \, {\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}^{3}}"," ",0,"-1/2*I/(-I*tan(1/2*x) - 1) - 1/6*(3*tan(1/2*x)^2 - 1)/(tan(1/2*x) + I)^3","B",0
5,1,22,0,0.308815," ","integrate(csc(x)/(I+tan(x)),x, algorithm=""giac"")","-\frac{2 i}{-i \, \tan\left(\frac{1}{2} \, x\right) + 1} - i \, \log\left(-i \, \tan\left(\frac{1}{2} \, x\right)\right)"," ",0,"-2*I/(-I*tan(1/2*x) + 1) - I*log(-I*tan(1/2*x))","A",0
6,1,18,0,0.315721," ","integrate(csc(x)^2/(I+tan(x)),x, algorithm=""giac"")","\frac{i}{\tan\left(x\right)} - \log\left(\tan\left(x\right) + i\right) + \log\left({\left| \tan\left(x\right) \right|}\right)"," ",0,"I/tan(x) - log(tan(x) + I) + log(abs(tan(x)))","A",0
7,1,46,0,0.303063," ","integrate(csc(x)^3/(I+tan(x)),x, algorithm=""giac"")","-\frac{1}{8} i \, \tan\left(\frac{1}{2} \, x\right)^{2} - \frac{6 i \, \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, x\right) - i}{8 \, \tan\left(\frac{1}{2} \, x\right)^{2}} + \frac{1}{2} i \, \log\left(\tan\left(\frac{1}{2} \, x\right)\right) - \frac{1}{2} \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"-1/8*I*tan(1/2*x)^2 - 1/8*(6*I*tan(1/2*x)^2 + 4*tan(1/2*x) - I)/tan(1/2*x)^2 + 1/2*I*log(tan(1/2*x)) - 1/2*tan(1/2*x)","B",0
8,1,12,0,0.292126," ","integrate(csc(x)^4/(I+tan(x)),x, algorithm=""giac"")","-\frac{3 \, \tan\left(x\right) - 2 i}{6 \, \tan\left(x\right)^{3}}"," ",0,"-1/6*(3*tan(x) - 2*I)/tan(x)^3","A",0
9,1,62,0,0.199577," ","integrate(csc(x)^5/(I+tan(x)),x, algorithm=""giac"")","-\frac{1}{64} i \, \tan\left(\frac{1}{2} \, x\right)^{4} - \frac{1}{24} \, \tan\left(\frac{1}{2} \, x\right)^{3} - \frac{50 i \, \tan\left(\frac{1}{2} \, x\right)^{4} + 24 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 8 \, \tan\left(\frac{1}{2} \, x\right) - 3 i}{192 \, \tan\left(\frac{1}{2} \, x\right)^{4}} + \frac{1}{8} i \, \log\left(\tan\left(\frac{1}{2} \, x\right)\right) - \frac{1}{8} \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"-1/64*I*tan(1/2*x)^4 - 1/24*tan(1/2*x)^3 - 1/192*(50*I*tan(1/2*x)^4 + 24*tan(1/2*x)^3 + 8*tan(1/2*x) - 3*I)/tan(1/2*x)^4 + 1/8*I*log(tan(1/2*x)) - 1/8*tan(1/2*x)","B",0
10,1,24,0,0.322593," ","integrate(csc(x)^6/(I+tan(x)),x, algorithm=""giac"")","-\frac{30 \, \tan\left(x\right)^{3} - 20 i \, \tan\left(x\right)^{2} + 15 \, \tan\left(x\right) - 12 i}{60 \, \tan\left(x\right)^{5}}"," ",0,"-1/60*(30*tan(x)^3 - 20*I*tan(x)^2 + 15*tan(x) - 12*I)/tan(x)^5","A",0
11,-1,0,0,0.000000," ","integrate(sin(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
12,1,1066,0,0.884426," ","integrate(sin(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{12 \, a d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 16 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 24 \, a d x \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 24 \, a d x \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 11 \, b \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 32 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 12 \, a \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 32 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 12 \, a \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 12 \, a d x \tan\left(d x\right)^{4} + 48 \, a d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 6 \, b \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 32 \, b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 12 \, a d x \tan\left(c\right)^{4} + 6 \, b \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 16 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} + 20 \, a \tan\left(d x\right)^{4} \tan\left(c\right) - 64 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 24 \, a \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 24 \, a \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 16 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(c\right)^{4} + 20 \, a \tan\left(d x\right) \tan\left(c\right)^{4} + 24 \, a d x \tan\left(d x\right)^{2} - 13 \, b \tan\left(d x\right)^{4} - 64 \, b \tan\left(d x\right)^{3} \tan\left(c\right) + 24 \, a d x \tan\left(c\right)^{2} - 36 \, b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 64 \, b \tan\left(d x\right) \tan\left(c\right)^{3} - 13 \, b \tan\left(c\right)^{4} - 32 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} - 20 \, a \tan\left(d x\right)^{3} - 24 \, a \tan\left(d x\right)^{2} \tan\left(c\right) - 32 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(c\right)^{2} - 24 \, a \tan\left(d x\right) \tan\left(c\right)^{2} - 20 \, a \tan\left(c\right)^{3} + 12 \, a d x + 6 \, b \tan\left(d x\right)^{2} - 32 \, b \tan\left(d x\right) \tan\left(c\right) + 6 \, b \tan\left(c\right)^{2} - 16 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) - 12 \, a \tan\left(d x\right) - 12 \, a \tan\left(c\right) + 11 \, b}{32 \, {\left(d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 2 \, d \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 2 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + d \tan\left(d x\right)^{4} + 4 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(c\right)^{4} + 2 \, d \tan\left(d x\right)^{2} + 2 \, d \tan\left(c\right)^{2} + d\right)}}"," ",0,"1/32*(12*a*d*x*tan(d*x)^4*tan(c)^4 - 16*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^4 + 24*a*d*x*tan(d*x)^4*tan(c)^2 + 24*a*d*x*tan(d*x)^2*tan(c)^4 + 11*b*tan(d*x)^4*tan(c)^4 - 32*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^2 + 12*a*tan(d*x)^4*tan(c)^3 - 32*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^4 + 12*a*tan(d*x)^3*tan(c)^4 + 12*a*d*x*tan(d*x)^4 + 48*a*d*x*tan(d*x)^2*tan(c)^2 + 6*b*tan(d*x)^4*tan(c)^2 - 32*b*tan(d*x)^3*tan(c)^3 + 12*a*d*x*tan(c)^4 + 6*b*tan(d*x)^2*tan(c)^4 - 16*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4 + 20*a*tan(d*x)^4*tan(c) - 64*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 + 24*a*tan(d*x)^3*tan(c)^2 + 24*a*tan(d*x)^2*tan(c)^3 - 16*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(c)^4 + 20*a*tan(d*x)*tan(c)^4 + 24*a*d*x*tan(d*x)^2 - 13*b*tan(d*x)^4 - 64*b*tan(d*x)^3*tan(c) + 24*a*d*x*tan(c)^2 - 36*b*tan(d*x)^2*tan(c)^2 - 64*b*tan(d*x)*tan(c)^3 - 13*b*tan(c)^4 - 32*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2 - 20*a*tan(d*x)^3 - 24*a*tan(d*x)^2*tan(c) - 32*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(c)^2 - 24*a*tan(d*x)*tan(c)^2 - 20*a*tan(c)^3 + 12*a*d*x + 6*b*tan(d*x)^2 - 32*b*tan(d*x)*tan(c) + 6*b*tan(c)^2 - 16*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) - 12*a*tan(d*x) - 12*a*tan(c) + 11*b)/(d*tan(d*x)^4*tan(c)^4 + 2*d*tan(d*x)^4*tan(c)^2 + 2*d*tan(d*x)^2*tan(c)^4 + d*tan(d*x)^4 + 4*d*tan(d*x)^2*tan(c)^2 + d*tan(c)^4 + 2*d*tan(d*x)^2 + 2*d*tan(c)^2 + d)","B",0
13,1,5350,0,31.086032," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} - 3 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} + 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} - 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} - 12 \, b \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{5} + 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} - 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} - 12 \, b \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{6} + 12 \, a \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} + 12 \, a \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} - 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} - 40 \, b \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{3} + 27 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 27 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 60 \, b \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{4} - 60 \, b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{5} + 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} - 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} - 40 \, b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} - 12 \, a \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} - 96 \, a \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{3} - 108 \, a \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 96 \, a \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} - 12 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{6} - 3 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{6} - 12 \, b \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right) + 27 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 27 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 60 \, b \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{2} + 120 \, b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} + 27 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} - 27 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 120 \, b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} + 60 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{5} + 3 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{6} - 3 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{6} - 12 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{6} - 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{6} + 108 \, a \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 128 \, a \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 108 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} - 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} + 12 \, b \tan\left(\frac{1}{2} \, d x\right)^{5} - 60 \, b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 27 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 27 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 120 \, b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 120 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} + 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 60 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} + 12 \, b \tan\left(\frac{1}{2} \, c\right)^{5} - 12 \, a \tan\left(\frac{1}{2} \, d x\right)^{4} - 96 \, a \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 108 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 96 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 12 \, a \tan\left(\frac{1}{2} \, c\right)^{4} + 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 40 \, b \tan\left(\frac{1}{2} \, d x\right)^{3} + 60 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 9 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 60 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 40 \, b \tan\left(\frac{1}{2} \, c\right)^{3} + 12 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} + 12 \, a \tan\left(\frac{1}{2} \, c\right)^{2} + 3 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) - 3 \, b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) + 12 \, b \tan\left(\frac{1}{2} \, d x\right) + 12 \, b \tan\left(\frac{1}{2} \, c\right) + 4 \, a}{6 \, {\left(d \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + d \tan\left(\frac{1}{2} \, d x\right)^{6} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + d \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, c\right)^{2} + d\right)}}"," ",0,"-1/6*(3*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^6*tan(1/2*c)^6 - 3*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^6*tan(1/2*c)^6 + 4*a*tan(1/2*d*x)^6*tan(1/2*c)^6 + 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^6*tan(1/2*c)^4 - 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^6*tan(1/2*c)^4 - 12*b*tan(1/2*d*x)^6*tan(1/2*c)^5 + 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4*tan(1/2*c)^6 - 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4*tan(1/2*c)^6 - 12*b*tan(1/2*d*x)^5*tan(1/2*c)^6 + 12*a*tan(1/2*d*x)^6*tan(1/2*c)^4 + 12*a*tan(1/2*d*x)^4*tan(1/2*c)^6 + 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^6*tan(1/2*c)^2 - 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^6*tan(1/2*c)^2 - 40*b*tan(1/2*d*x)^6*tan(1/2*c)^3 + 27*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4*tan(1/2*c)^4 - 27*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4*tan(1/2*c)^4 - 60*b*tan(1/2*d*x)^5*tan(1/2*c)^4 - 60*b*tan(1/2*d*x)^4*tan(1/2*c)^5 + 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^6 - 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^6 - 40*b*tan(1/2*d*x)^3*tan(1/2*c)^6 - 12*a*tan(1/2*d*x)^6*tan(1/2*c)^2 - 96*a*tan(1/2*d*x)^5*tan(1/2*c)^3 - 108*a*tan(1/2*d*x)^4*tan(1/2*c)^4 - 96*a*tan(1/2*d*x)^3*tan(1/2*c)^5 - 12*a*tan(1/2*d*x)^2*tan(1/2*c)^6 + 3*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^6 - 3*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^6 - 12*b*tan(1/2*d*x)^6*tan(1/2*c) + 27*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4*tan(1/2*c)^2 - 27*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4*tan(1/2*c)^2 + 60*b*tan(1/2*d*x)^5*tan(1/2*c)^2 + 120*b*tan(1/2*d*x)^4*tan(1/2*c)^3 + 27*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^4 - 27*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^4 + 120*b*tan(1/2*d*x)^3*tan(1/2*c)^4 + 60*b*tan(1/2*d*x)^2*tan(1/2*c)^5 + 3*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^6 - 3*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^6 - 12*b*tan(1/2*d*x)*tan(1/2*c)^6 - 4*a*tan(1/2*d*x)^6 + 108*a*tan(1/2*d*x)^4*tan(1/2*c)^2 + 128*a*tan(1/2*d*x)^3*tan(1/2*c)^3 + 108*a*tan(1/2*d*x)^2*tan(1/2*c)^4 - 4*a*tan(1/2*c)^6 + 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4 - 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4 + 12*b*tan(1/2*d*x)^5 - 60*b*tan(1/2*d*x)^4*tan(1/2*c) + 27*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 27*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 120*b*tan(1/2*d*x)^3*tan(1/2*c)^2 - 120*b*tan(1/2*d*x)^2*tan(1/2*c)^3 + 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^4 - 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^4 - 60*b*tan(1/2*d*x)*tan(1/2*c)^4 + 12*b*tan(1/2*c)^5 - 12*a*tan(1/2*d*x)^4 - 96*a*tan(1/2*d*x)^3*tan(1/2*c) - 108*a*tan(1/2*d*x)^2*tan(1/2*c)^2 - 96*a*tan(1/2*d*x)*tan(1/2*c)^3 - 12*a*tan(1/2*c)^4 + 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2 - 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2 + 40*b*tan(1/2*d*x)^3 + 60*b*tan(1/2*d*x)^2*tan(1/2*c) + 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2 - 9*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2 + 60*b*tan(1/2*d*x)*tan(1/2*c)^2 + 40*b*tan(1/2*c)^3 + 12*a*tan(1/2*d*x)^2 + 12*a*tan(1/2*c)^2 + 3*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) - 3*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) + 12*b*tan(1/2*d*x) + 12*b*tan(1/2*c) + 4*a)/(d*tan(1/2*d*x)^6*tan(1/2*c)^6 + 3*d*tan(1/2*d*x)^6*tan(1/2*c)^4 + 3*d*tan(1/2*d*x)^4*tan(1/2*c)^6 + 3*d*tan(1/2*d*x)^6*tan(1/2*c)^2 + 9*d*tan(1/2*d*x)^4*tan(1/2*c)^4 + 3*d*tan(1/2*d*x)^2*tan(1/2*c)^6 + d*tan(1/2*d*x)^6 + 9*d*tan(1/2*d*x)^4*tan(1/2*c)^2 + 9*d*tan(1/2*d*x)^2*tan(1/2*c)^4 + d*tan(1/2*c)^6 + 3*d*tan(1/2*d*x)^4 + 9*d*tan(1/2*d*x)^2*tan(1/2*c)^2 + 3*d*tan(1/2*c)^4 + 3*d*tan(1/2*d*x)^2 + 3*d*tan(1/2*c)^2 + d)","B",0
14,1,413,0,0.543556," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{2 \, a d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 2 \, a d x \tan\left(d x\right)^{2} + 2 \, a d x \tan\left(c\right)^{2} + b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} + 2 \, a \tan\left(d x\right)^{2} \tan\left(c\right) - 2 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(c\right)^{2} + 2 \, a \tan\left(d x\right) \tan\left(c\right)^{2} + 2 \, a d x - b \tan\left(d x\right)^{2} - 4 \, b \tan\left(d x\right) \tan\left(c\right) - b \tan\left(c\right)^{2} - 2 \, b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) - 2 \, a \tan\left(d x\right) - 2 \, a \tan\left(c\right) + b}{4 \, {\left(d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} + d \tan\left(c\right)^{2} + d\right)}}"," ",0,"1/4*(2*a*d*x*tan(d*x)^2*tan(c)^2 - 2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 + 2*a*d*x*tan(d*x)^2 + 2*a*d*x*tan(c)^2 + b*tan(d*x)^2*tan(c)^2 - 2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2 + 2*a*tan(d*x)^2*tan(c) - 2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(c)^2 + 2*a*tan(d*x)*tan(c)^2 + 2*a*d*x - b*tan(d*x)^2 - 4*b*tan(d*x)*tan(c) - b*tan(c)^2 - 2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) - 2*a*tan(d*x) - 2*a*tan(c) + b)/(d*tan(d*x)^2*tan(c)^2 + d*tan(d*x)^2 + d*tan(c)^2 + d)","B",0
15,1,1236,0,0.797765," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} - b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a \tan\left(\frac{1}{2} \, c\right)^{2} + b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) - b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) + 4 \, b \tan\left(\frac{1}{2} \, d x\right) + 4 \, b \tan\left(\frac{1}{2} \, c\right) + 2 \, a}{2 \, {\left(d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} + d\right)}}"," ",0,"-1/2*(b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 - b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*tan(1/2*d*x)^2*tan(1/2*c)^2 + b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2 - b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2 - 4*b*tan(1/2*d*x)^2*tan(1/2*c) + b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2 - b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2 - 4*b*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a*tan(1/2*d*x)^2 - 8*a*tan(1/2*d*x)*tan(1/2*c) - 2*a*tan(1/2*c)^2 + b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) - b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) + 4*b*tan(1/2*d*x) + 4*b*tan(1/2*c) + 2*a)/(d*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(1/2*d*x)^2 + d*tan(1/2*c)^2 + d)","B",0
16,1,49,0,0.488825," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{d}"," ",0,"(b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + a*log(abs(tan(1/2*d*x + 1/2*c))))/d","A",0
17,1,35,0,0.387584," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{b \log\left({\left| \tan\left(d x + c\right) \right|}\right) - \frac{b \tan\left(d x + c\right) + a}{\tan\left(d x + c\right)}}{d}"," ",0,"(b*log(abs(tan(d*x + c))) - (b*tan(d*x + c) + a)/tan(d*x + c))/d","A",0
18,1,118,0,0.512010," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 8 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 4 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a*tan(1/2*d*x + 1/2*c)^2 + 8*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 8*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 4*a*log(abs(tan(1/2*d*x + 1/2*c))) - 4*b*tan(1/2*d*x + 1/2*c) - (6*a*tan(1/2*d*x + 1/2*c)^2 + 4*b*tan(1/2*d*x + 1/2*c) + a)/tan(1/2*d*x + 1/2*c)^2)/d","B",0
19,1,62,0,0.501560," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{6 \, b \log\left({\left| \tan\left(d x + c\right) \right|}\right) - \frac{11 \, b \tan\left(d x + c\right)^{3} + 6 \, a \tan\left(d x + c\right)^{2} + 3 \, b \tan\left(d x + c\right) + 2 \, a}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*b*log(abs(tan(d*x + c))) - (11*b*tan(d*x + c)^3 + 6*a*tan(d*x + c)^2 + 3*b*tan(d*x + c) + 2*a)/tan(d*x + c)^3)/d","A",0
20,1,177,0,2.925981," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 192 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 192 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 72 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 120 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{150 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a*tan(1/2*d*x + 1/2*c)^4 - 8*b*tan(1/2*d*x + 1/2*c)^3 + 24*a*tan(1/2*d*x + 1/2*c)^2 + 192*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 192*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 72*a*log(abs(tan(1/2*d*x + 1/2*c))) - 120*b*tan(1/2*d*x + 1/2*c) - (150*a*tan(1/2*d*x + 1/2*c)^4 + 120*b*tan(1/2*d*x + 1/2*c)^3 + 24*a*tan(1/2*d*x + 1/2*c)^2 + 8*b*tan(1/2*d*x + 1/2*c) + 3*a)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
21,1,84,0,1.803424," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{60 \, b \log\left({\left| \tan\left(d x + c\right) \right|}\right) - \frac{137 \, b \tan\left(d x + c\right)^{5} + 60 \, a \tan\left(d x + c\right)^{4} + 60 \, b \tan\left(d x + c\right)^{3} + 40 \, a \tan\left(d x + c\right)^{2} + 15 \, b \tan\left(d x + c\right) + 12 \, a}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*b*log(abs(tan(d*x + c))) - (137*b*tan(d*x + c)^5 + 60*a*tan(d*x + c)^4 + 60*b*tan(d*x + c)^3 + 40*a*tan(d*x + c)^2 + 15*b*tan(d*x + c) + 12*a)/tan(d*x + c)^5)/d","A",0
22,-2,0,0,0.000000," ","integrate(sin(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)(24*a^2*d*x*tan(c)^5*tan(d*x)^5+48*a^2*d*x*tan(c)^5*tan(d*x)^3+24*a^2*d*x*tan(c)^5*tan(d*x)-24*a^2*d*x*tan(c)^4*tan(d*x)^4-48*a^2*d*x*tan(c)^4*tan(d*x)^2-24*a^2*d*x*tan(c)^4+48*a^2*d*x*tan(c)^3*tan(d*x)^5+96*a^2*d*x*tan(c)^3*tan(d*x)^3+48*a^2*d*x*tan(c)^3*tan(d*x)-48*a^2*d*x*tan(c)^2*tan(d*x)^4-96*a^2*d*x*tan(c)^2*tan(d*x)^2-48*a^2*d*x*tan(c)^2+24*a^2*d*x*tan(c)*tan(d*x)^5+48*a^2*d*x*tan(c)*tan(d*x)^3+24*a^2*d*x*tan(c)*tan(d*x)-24*a^2*d*x*tan(d*x)^4-48*a^2*d*x*tan(d*x)^2-24*a^2*d*x+24*a^2*tan(c)^5*tan(d*x)^4+40*a^2*tan(c)^5*tan(d*x)^2+24*a^2*tan(c)^4*tan(d*x)^5+24*a^2*tan(c)^4*tan(d*x)^3-80*a^2*tan(c)^4*tan(d*x)+24*a^2*tan(c)^3*tan(d*x)^4-96*a^2*tan(c)^3*tan(d*x)^2+40*a^2*tan(c)^3+40*a^2*tan(c)^2*tan(d*x)^5-96*a^2*tan(c)^2*tan(d*x)^3+24*a^2*tan(c)^2*tan(d*x)-80*a^2*tan(c)*tan(d*x)^4+24*a^2*tan(c)*tan(d*x)^2+24*a^2*tan(c)+40*a^2*tan(d*x)^3+24*a^2*tan(d*x)-64*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^5*tan(d*x)^5-128*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^5*tan(d*x)^3-64*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^5*tan(d*x)+64*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^4*tan(d*x)^4+128*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^4*tan(d*x)^2+64*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^4-128*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^3*tan(d*x)^5-256*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^3*tan(d*x)^3-128*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^3*tan(d*x)+128*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^2*tan(d*x)^4+256*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^2*tan(d*x)^2+128*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)^2-64*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)*tan(d*x)^5-128*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)*tan(d*x)^3-64*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(c)*tan(d*x)+64*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(d*x)^4+128*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))*tan(d*x)^2+64*a*b*ln((4*tan(c)^2*tan(d*x)^4+4*tan(c)^2*tan(d*x)^2-8*tan(c)*tan(d*x)^3-8*tan(c)*tan(d*x)+4*tan(d*x)^2+4)/(tan(c)^2+1))+44*a*b*tan(c)^5*tan(d*x)^5+24*a*b*tan(c)^5*tan(d*x)^3-52*a*b*tan(c)^5*tan(d*x)-172*a*b*tan(c)^4*tan(d*x)^4-280*a*b*tan(c)^4*tan(d*x)^2+52*a*b*tan(c)^4+24*a*b*tan(c)^3*tan(d*x)^5-16*a*b*tan(c)^3*tan(d*x)^3+280*a*b*tan(c)^3*tan(d*x)-280*a*b*tan(c)^2*tan(d*x)^4+16*a*b*tan(c)^2*tan(d*x)^2-24*a*b*tan(c)^2-52*a*b*tan(c)*tan(d*x)^5+280*a*b*tan(c)*tan(d*x)^3+172*a*b*tan(c)*tan(d*x)+52*a*b*tan(d*x)^4-24*a*b*tan(d*x)^2-44*a*b-120*b^2*d*x*tan(c)^5*tan(d*x)^5-240*b^2*d*x*tan(c)^5*tan(d*x)^3-120*b^2*d*x*tan(c)^5*tan(d*x)+120*b^2*d*x*tan(c)^4*tan(d*x)^4+240*b^2*d*x*tan(c)^4*tan(d*x)^2+120*b^2*d*x*tan(c)^4-240*b^2*d*x*tan(c)^3*tan(d*x)^5-480*b^2*d*x*tan(c)^3*tan(d*x)^3-240*b^2*d*x*tan(c)^3*tan(d*x)+240*b^2*d*x*tan(c)^2*tan(d*x)^4+480*b^2*d*x*tan(c)^2*tan(d*x)^2+240*b^2*d*x*tan(c)^2-120*b^2*d*x*tan(c)*tan(d*x)^5-240*b^2*d*x*tan(c)*tan(d*x)^3-120*b^2*d*x*tan(c)*tan(d*x)+120*b^2*d*x*tan(d*x)^4+240*b^2*d*x*tan(d*x)^2+120*b^2*d*x+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^5*tan(d*x)^5+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^5*tan(d*x)^3+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^5*tan(d*x)-3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^4*tan(d*x)^4-6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^4*tan(d*x)^2-3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^4+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^3*tan(d*x)^5+12*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^3*tan(d*x)^3+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^3*tan(d*x)-6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^2*tan(d*x)^4-12*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^2*tan(d*x)^2-6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^2+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)*tan(d*x)^5+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)*tan(d*x)^3+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)*tan(d*x)-3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(d*x)^4-6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(d*x)^2-3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^5*tan(d*x)^5+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^5*tan(d*x)^3+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^5*tan(d*x)-3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^4*tan(d*x)^4-6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^4*tan(d*x)^2-3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^4+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^3*tan(d*x)^5+12*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^3*tan(d*x)^3+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^3*tan(d*x)-6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^2*tan(d*x)^4-12*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^2*tan(d*x)^2-6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^2+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)*tan(d*x)^5+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)*tan(d*x)^3+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)*tan(d*x)-3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(d*x)^4-6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(d*x)^2-3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))+6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^5*tan(d*x)^5+12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^5*tan(d*x)^3+6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^5*tan(d*x)-6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^4*tan(d*x)^4-12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^4*tan(d*x)^2-6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^4+12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^3*tan(d*x)^5+24*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^3*tan(d*x)^3+12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^3*tan(d*x)-12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^2*tan(d*x)^4-24*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^2*tan(d*x)^2-12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^2+6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)*tan(d*x)^5+12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)*tan(d*x)^3+6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)*tan(d*x)-6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(d*x)^4-12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(d*x)^2-6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))-6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^5*tan(d*x)^5-12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^5*tan(d*x)^3-6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^5*tan(d*x)+6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^4*tan(d*x)^4+12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^4*tan(d*x)^2+6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^4-12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^3*tan(d*x)^5-24*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^3*tan(d*x)^3-12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^3*tan(d*x)+12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^2*tan(d*x)^4+24*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^2*tan(d*x)^2+12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^2-6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)*tan(d*x)^5-12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)*tan(d*x)^3-6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)*tan(d*x)+6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(d*x)^4+12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(d*x)^2+6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))-120*b^2*tan(c)^5*tan(d*x)^4-200*b^2*tan(c)^5*tan(d*x)^2-64*b^2*tan(c)^5-120*b^2*tan(c)^4*tan(d*x)^5-120*b^2*tan(c)^4*tan(d*x)^3+80*b^2*tan(c)^4*tan(d*x)-120*b^2*tan(c)^3*tan(d*x)^4-160*b^2*tan(c)^3*tan(d*x)^2-200*b^2*tan(c)^3-200*b^2*tan(c)^2*tan(d*x)^5-160*b^2*tan(c)^2*tan(d*x)^3-120*b^2*tan(c)^2*tan(d*x)+80*b^2*tan(c)*tan(d*x)^4-120*b^2*tan(c)*tan(d*x)^2-120*b^2*tan(c)-64*b^2*tan(d*x)^5-200*b^2*tan(d*x)^3-120*b^2*tan(d*x))/(64*d*tan(c)^5*tan(d*x)^5+128*d*tan(c)^5*tan(d*x)^3+64*d*tan(c)^5*tan(d*x)-64*d*tan(c)^4*tan(d*x)^4-128*d*tan(c)^4*tan(d*x)^2-64*d*tan(c)^4+128*d*tan(c)^3*tan(d*x)^5+256*d*tan(c)^3*tan(d*x)^3+128*d*tan(c)^3*tan(d*x)-128*d*tan(c)^2*tan(d*x)^4-256*d*tan(c)^2*tan(d*x)^2-128*d*tan(c)^2+64*d*tan(c)*tan(d*x)^5+128*d*tan(c)*tan(d*x)^3+64*d*tan(c)*tan(d*x)-64*d*tan(d*x)^4-128*d*tan(d*x)^2-64*d)","F(-2)",0
23,-1,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,1,1061,0,2.171139," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 2 \, a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + a^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right) - 3 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right) - a^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + a^{2} d x \tan\left(d x\right) \tan\left(c\right)^{3} - 3 \, b^{2} d x \tan\left(d x\right) \tan\left(c\right)^{3} + a b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 2 \, a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right) + 2 \, a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 3 \, b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 2 \, a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right)^{3} + a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 3 \, b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - a^{2} d x \tan\left(d x\right)^{2} + 3 \, b^{2} d x \tan\left(d x\right)^{2} + a^{2} d x \tan\left(d x\right) \tan\left(c\right) - 3 \, b^{2} d x \tan\left(d x\right) \tan\left(c\right) - a b \tan\left(d x\right)^{3} \tan\left(c\right) - a^{2} d x \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(c\right)^{2} - 5 \, a b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - a b \tan\left(d x\right) \tan\left(c\right)^{3} + 2 \, a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} - 2 \, b^{2} \tan\left(d x\right)^{3} - 2 \, a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) - 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right) + 2 \, a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(c\right)^{2} - 2 \, a^{2} \tan\left(d x\right) \tan\left(c\right)^{2} - 2 \, b^{2} \tan\left(c\right)^{3} - a^{2} d x + 3 \, b^{2} d x + a b \tan\left(d x\right)^{2} + 5 \, a b \tan\left(d x\right) \tan\left(c\right) + a b \tan\left(c\right)^{2} + 2 \, a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) + a^{2} \tan\left(d x\right) - 3 \, b^{2} \tan\left(d x\right) + a^{2} \tan\left(c\right) - 3 \, b^{2} \tan\left(c\right) - a b}{2 \, {\left(d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + d \tan\left(d x\right)^{3} \tan\left(c\right) - d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right) \tan\left(c\right)^{3} - d \tan\left(d x\right)^{2} + d \tan\left(d x\right) \tan\left(c\right) - d \tan\left(c\right)^{2} - d\right)}}"," ",0,"1/2*(a^2*d*x*tan(d*x)^3*tan(c)^3 - 3*b^2*d*x*tan(d*x)^3*tan(c)^3 - 2*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 + a^2*d*x*tan(d*x)^3*tan(c) - 3*b^2*d*x*tan(d*x)^3*tan(c) - a^2*d*x*tan(d*x)^2*tan(c)^2 + 3*b^2*d*x*tan(d*x)^2*tan(c)^2 + a^2*d*x*tan(d*x)*tan(c)^3 - 3*b^2*d*x*tan(d*x)*tan(c)^3 + a*b*tan(d*x)^3*tan(c)^3 - 2*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c) + 2*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 + a^2*tan(d*x)^3*tan(c)^2 - 3*b^2*tan(d*x)^3*tan(c)^2 - 2*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c)^3 + a^2*tan(d*x)^2*tan(c)^3 - 3*b^2*tan(d*x)^2*tan(c)^3 - a^2*d*x*tan(d*x)^2 + 3*b^2*d*x*tan(d*x)^2 + a^2*d*x*tan(d*x)*tan(c) - 3*b^2*d*x*tan(d*x)*tan(c) - a*b*tan(d*x)^3*tan(c) - a^2*d*x*tan(c)^2 + 3*b^2*d*x*tan(c)^2 - 5*a*b*tan(d*x)^2*tan(c)^2 - a*b*tan(d*x)*tan(c)^3 + 2*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2 - 2*b^2*tan(d*x)^3 - 2*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) - 2*a^2*tan(d*x)^2*tan(c) + 2*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(c)^2 - 2*a^2*tan(d*x)*tan(c)^2 - 2*b^2*tan(c)^3 - a^2*d*x + 3*b^2*d*x + a*b*tan(d*x)^2 + 5*a*b*tan(d*x)*tan(c) + a*b*tan(c)^2 + 2*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) + a^2*tan(d*x) - 3*b^2*tan(d*x) + a^2*tan(c) - 3*b^2*tan(c) - a*b)/(d*tan(d*x)^3*tan(c)^3 + d*tan(d*x)^3*tan(c) - d*tan(d*x)^2*tan(c)^2 + d*tan(d*x)*tan(c)^3 - d*tan(d*x)^2 + d*tan(d*x)*tan(c) - d*tan(c)^2 - d)","B",0
25,1,2837,0,11.780161," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 4 \, a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 8 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{4} - 4 \, a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 4 \, a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 4 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 24 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 4 \, a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 24 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{4} + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{4} + 4 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} + a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} - 2 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 8 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 20 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 8 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + a^{2} \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, b^{2} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} - 4 \, a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 24 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 8 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) + 4 \, a b \tan\left(\frac{1}{2} \, d x\right) + 4 \, a b \tan\left(\frac{1}{2} \, c\right) + a^{2} - 2 \, b^{2}}{d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, d \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - d \tan\left(\frac{1}{2} \, d x\right)^{4} - 4 \, d \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 4 \, d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - d \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + d}"," ",0,"-(a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4*tan(1/2*c)^4 - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4*tan(1/2*c)^4 + a^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 2*b^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 4*a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^3*tan(1/2*c)^3 + 4*a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^3*tan(1/2*c)^3 - 4*a*b*tan(1/2*d*x)^4*tan(1/2*c)^3 - 4*a*b*tan(1/2*d*x)^3*tan(1/2*c)^4 - 2*a^2*tan(1/2*d*x)^4*tan(1/2*c)^2 - 8*a^2*tan(1/2*d*x)^3*tan(1/2*c)^3 + 8*b^2*tan(1/2*d*x)^3*tan(1/2*c)^3 - 2*a^2*tan(1/2*d*x)^2*tan(1/2*c)^4 - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4 + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^4 - 4*a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^3*tan(1/2*c) + 4*a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^3*tan(1/2*c) + 4*a*b*tan(1/2*d*x)^4*tan(1/2*c) + 24*a*b*tan(1/2*d*x)^3*tan(1/2*c)^2 - 4*a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)*tan(1/2*c)^3 + 4*a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)*tan(1/2*c)^3 + 24*a*b*tan(1/2*d*x)^2*tan(1/2*c)^3 - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^4 + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^4 + 4*a*b*tan(1/2*d*x)*tan(1/2*c)^4 + a^2*tan(1/2*d*x)^4 - 2*b^2*tan(1/2*d*x)^4 + 8*a^2*tan(1/2*d*x)^3*tan(1/2*c) - 8*b^2*tan(1/2*d*x)^3*tan(1/2*c) + 20*a^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 24*b^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 8*a^2*tan(1/2*d*x)*tan(1/2*c)^3 - 8*b^2*tan(1/2*d*x)*tan(1/2*c)^3 + a^2*tan(1/2*c)^4 - 2*b^2*tan(1/2*c)^4 - 4*a*b*tan(1/2*d*x)^3 - 4*a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)*tan(1/2*c) + 4*a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)*tan(1/2*c) - 24*a*b*tan(1/2*d*x)^2*tan(1/2*c) - 24*a*b*tan(1/2*d*x)*tan(1/2*c)^2 - 4*a*b*tan(1/2*c)^3 - 2*a^2*tan(1/2*d*x)^2 - 8*a^2*tan(1/2*d*x)*tan(1/2*c) + 8*b^2*tan(1/2*d*x)*tan(1/2*c) - 2*a^2*tan(1/2*c)^2 + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) + 4*a*b*tan(1/2*d*x) + 4*a*b*tan(1/2*c) + a^2 - 2*b^2)/(d*tan(1/2*d*x)^4*tan(1/2*c)^4 - 4*d*tan(1/2*d*x)^3*tan(1/2*c)^3 - d*tan(1/2*d*x)^4 - 4*d*tan(1/2*d*x)^3*tan(1/2*c) - 4*d*tan(1/2*d*x)*tan(1/2*c)^3 - d*tan(1/2*c)^4 - 4*d*tan(1/2*d*x)*tan(1/2*c) + d)","B",0
26,1,74,0,0.933482," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"(2*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 2*b^2/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","A",0
27,1,51,0,0.870392," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, a b \log\left({\left| \tan\left(d x + c\right) \right|}\right) + b^{2} \tan\left(d x + c\right) - \frac{2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)}}{d}"," ",0,"(2*a*b*log(abs(tan(d*x + c))) + b^2*tan(d*x + c) - (2*a*b*tan(d*x + c) + a^2)/tan(d*x + c))/d","A",0
28,1,172,0,1.592947," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 16 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, {\left(a^{2} + 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{16 \, b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a^2*tan(1/2*d*x + 1/2*c)^2 + 16*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 16*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 8*a*b*tan(1/2*d*x + 1/2*c) + 4*(a^2 + 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - 16*b^2/(tan(1/2*d*x + 1/2*c)^2 - 1) - (6*a^2*tan(1/2*d*x + 1/2*c)^2 + 12*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*a*b*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
29,1,91,0,0.783296," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, a b \log\left({\left| \tan\left(d x + c\right) \right|}\right) + 3 \, b^{2} \tan\left(d x + c\right) - \frac{11 \, a b \tan\left(d x + c\right)^{3} + 3 \, a^{2} \tan\left(d x + c\right)^{2} + 3 \, b^{2} \tan\left(d x + c\right)^{2} + 3 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(6*a*b*log(abs(tan(d*x + c))) + 3*b^2*tan(d*x + c) - (11*a*b*tan(d*x + c)^3 + 3*a^2*tan(d*x + c)^2 + 3*b^2*tan(d*x + c)^2 + 3*a*b*tan(d*x + c) + a^2)/tan(d*x + c)^3)/d","A",0
30,1,269,0,0.810908," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 384 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 384 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, {\left(a^{2} + 4 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{384 \, b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 600 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a^2*tan(1/2*d*x + 1/2*c)^4 - 16*a*b*tan(1/2*d*x + 1/2*c)^3 + 24*a^2*tan(1/2*d*x + 1/2*c)^2 + 24*b^2*tan(1/2*d*x + 1/2*c)^2 + 384*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 384*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 240*a*b*tan(1/2*d*x + 1/2*c) + 72*(a^2 + 4*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - 384*b^2/(tan(1/2*d*x + 1/2*c)^2 - 1) - (150*a^2*tan(1/2*d*x + 1/2*c)^4 + 600*b^2*tan(1/2*d*x + 1/2*c)^4 + 240*a*b*tan(1/2*d*x + 1/2*c)^3 + 24*a^2*tan(1/2*d*x + 1/2*c)^2 + 24*b^2*tan(1/2*d*x + 1/2*c)^2 + 16*a*b*tan(1/2*d*x + 1/2*c) + 3*a^2)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
31,1,131,0,0.706117," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{60 \, a b \log\left({\left| \tan\left(d x + c\right) \right|}\right) + 30 \, b^{2} \tan\left(d x + c\right) - \frac{137 \, a b \tan\left(d x + c\right)^{5} + 30 \, a^{2} \tan\left(d x + c\right)^{4} + 60 \, b^{2} \tan\left(d x + c\right)^{4} + 60 \, a b \tan\left(d x + c\right)^{3} + 20 \, a^{2} \tan\left(d x + c\right)^{2} + 10 \, b^{2} \tan\left(d x + c\right)^{2} + 15 \, a b \tan\left(d x + c\right) + 6 \, a^{2}}{\tan\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"1/30*(60*a*b*log(abs(tan(d*x + c))) + 30*b^2*tan(d*x + c) - (137*a*b*tan(d*x + c)^5 + 30*a^2*tan(d*x + c)^4 + 60*b^2*tan(d*x + c)^4 + 60*a*b*tan(d*x + c)^3 + 20*a^2*tan(d*x + c)^2 + 10*b^2*tan(d*x + c)^2 + 15*a*b*tan(d*x + c) + 6*a^2)/tan(d*x + c)^5)/d","A",0
32,-1,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,1,2590,0,7.280668," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, a^{3} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 18 \, a b^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 6 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 4 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 2 \, a^{3} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 18 \, a b^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 4 \, a^{3} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 36 \, a b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 2 \, a^{3} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 18 \, a b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 3 \, a^{2} b \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 6 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 4 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 12 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 8 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 2 \, a^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 18 \, a b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 6 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 4 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 2 \, a^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 18 \, a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 4 \, a^{3} d x \tan\left(d x\right)^{3} \tan\left(c\right) + 36 \, a b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right) + 4 \, a^{3} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 36 \, a b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 3 \, a^{2} b \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 5 \, b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 4 \, a^{3} d x \tan\left(d x\right) \tan\left(c\right)^{3} + 36 \, a b^{2} d x \tan\left(d x\right) \tan\left(c\right)^{3} - 18 \, a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 6 \, b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 5 \, b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 12 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right) - 8 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right) - 12 \, a b^{2} \tan\left(d x\right)^{4} \tan\left(c\right) - 12 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 8 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 6 \, a^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 18 \, a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 12 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right)^{3} - 8 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right)^{3} - 6 \, a^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 18 \, a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 12 \, a b^{2} \tan\left(d x\right) \tan\left(c\right)^{4} + 2 \, a^{3} d x \tan\left(d x\right)^{2} - 18 \, a b^{2} d x \tan\left(d x\right)^{2} + 2 \, b^{3} \tan\left(d x\right)^{4} - 4 \, a^{3} d x \tan\left(d x\right) \tan\left(c\right) + 36 \, a b^{2} d x \tan\left(d x\right) \tan\left(c\right) + 6 \, a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right) - 2 \, b^{3} \tan\left(d x\right)^{3} \tan\left(c\right) + 2 \, a^{3} d x \tan\left(c\right)^{2} - 18 \, a b^{2} d x \tan\left(c\right)^{2} + 30 \, a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 6 \, a^{2} b \tan\left(d x\right) \tan\left(c\right)^{3} - 2 \, b^{3} \tan\left(d x\right) \tan\left(c\right)^{3} + 2 \, b^{3} \tan\left(c\right)^{4} - 6 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} + 4 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} + 12 \, a b^{2} \tan\left(d x\right)^{3} + 12 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) - 8 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) + 6 \, a^{3} \tan\left(d x\right)^{2} \tan\left(c\right) - 18 \, a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 6 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(c\right)^{2} + 4 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(c\right)^{2} + 6 \, a^{3} \tan\left(d x\right) \tan\left(c\right)^{2} - 18 \, a b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + 12 \, a b^{2} \tan\left(c\right)^{3} + 2 \, a^{3} d x - 18 \, a b^{2} d x - 3 \, a^{2} b \tan\left(d x\right)^{2} + 5 \, b^{3} \tan\left(d x\right)^{2} - 18 \, a^{2} b \tan\left(d x\right) \tan\left(c\right) + 6 \, b^{3} \tan\left(d x\right) \tan\left(c\right) - 3 \, a^{2} b \tan\left(c\right)^{2} + 5 \, b^{3} \tan\left(c\right)^{2} - 6 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) + 4 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) - 2 \, a^{3} \tan\left(d x\right) + 18 \, a b^{2} \tan\left(d x\right) - 2 \, a^{3} \tan\left(c\right) + 18 \, a b^{2} \tan\left(c\right) + 3 \, a^{2} b + b^{3}}{4 \, {\left(d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + d \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + d \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 2 \, d \tan\left(d x\right)^{3} \tan\left(c\right) + 2 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, d \tan\left(d x\right) \tan\left(c\right)^{3} + d \tan\left(d x\right)^{2} - 2 \, d \tan\left(d x\right) \tan\left(c\right) + d \tan\left(c\right)^{2} + d\right)}}"," ",0,"1/4*(2*a^3*d*x*tan(d*x)^4*tan(c)^4 - 18*a*b^2*d*x*tan(d*x)^4*tan(c)^4 - 6*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^4 + 4*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^4 + 2*a^3*d*x*tan(d*x)^4*tan(c)^2 - 18*a*b^2*d*x*tan(d*x)^4*tan(c)^2 - 4*a^3*d*x*tan(d*x)^3*tan(c)^3 + 36*a*b^2*d*x*tan(d*x)^3*tan(c)^3 + 2*a^3*d*x*tan(d*x)^2*tan(c)^4 - 18*a*b^2*d*x*tan(d*x)^2*tan(c)^4 + 3*a^2*b*tan(d*x)^4*tan(c)^4 + b^3*tan(d*x)^4*tan(c)^4 - 6*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^2 + 4*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^2 + 12*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 - 8*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 + 2*a^3*tan(d*x)^4*tan(c)^3 - 18*a*b^2*tan(d*x)^4*tan(c)^3 - 6*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^4 + 4*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^4 + 2*a^3*tan(d*x)^3*tan(c)^4 - 18*a*b^2*tan(d*x)^3*tan(c)^4 - 4*a^3*d*x*tan(d*x)^3*tan(c) + 36*a*b^2*d*x*tan(d*x)^3*tan(c) + 4*a^3*d*x*tan(d*x)^2*tan(c)^2 - 36*a*b^2*d*x*tan(d*x)^2*tan(c)^2 - 3*a^2*b*tan(d*x)^4*tan(c)^2 + 5*b^3*tan(d*x)^4*tan(c)^2 - 4*a^3*d*x*tan(d*x)*tan(c)^3 + 36*a*b^2*d*x*tan(d*x)*tan(c)^3 - 18*a^2*b*tan(d*x)^3*tan(c)^3 + 6*b^3*tan(d*x)^3*tan(c)^3 - 3*a^2*b*tan(d*x)^2*tan(c)^4 + 5*b^3*tan(d*x)^2*tan(c)^4 + 12*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c) - 8*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c) - 12*a*b^2*tan(d*x)^4*tan(c) - 12*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 + 8*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 - 6*a^3*tan(d*x)^3*tan(c)^2 + 18*a*b^2*tan(d*x)^3*tan(c)^2 + 12*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c)^3 - 8*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c)^3 - 6*a^3*tan(d*x)^2*tan(c)^3 + 18*a*b^2*tan(d*x)^2*tan(c)^3 - 12*a*b^2*tan(d*x)*tan(c)^4 + 2*a^3*d*x*tan(d*x)^2 - 18*a*b^2*d*x*tan(d*x)^2 + 2*b^3*tan(d*x)^4 - 4*a^3*d*x*tan(d*x)*tan(c) + 36*a*b^2*d*x*tan(d*x)*tan(c) + 6*a^2*b*tan(d*x)^3*tan(c) - 2*b^3*tan(d*x)^3*tan(c) + 2*a^3*d*x*tan(c)^2 - 18*a*b^2*d*x*tan(c)^2 + 30*a^2*b*tan(d*x)^2*tan(c)^2 - 2*b^3*tan(d*x)^2*tan(c)^2 + 6*a^2*b*tan(d*x)*tan(c)^3 - 2*b^3*tan(d*x)*tan(c)^3 + 2*b^3*tan(c)^4 - 6*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2 + 4*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2 + 12*a*b^2*tan(d*x)^3 + 12*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) - 8*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) + 6*a^3*tan(d*x)^2*tan(c) - 18*a*b^2*tan(d*x)^2*tan(c) - 6*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(c)^2 + 4*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(c)^2 + 6*a^3*tan(d*x)*tan(c)^2 - 18*a*b^2*tan(d*x)*tan(c)^2 + 12*a*b^2*tan(c)^3 + 2*a^3*d*x - 18*a*b^2*d*x - 3*a^2*b*tan(d*x)^2 + 5*b^3*tan(d*x)^2 - 18*a^2*b*tan(d*x)*tan(c) + 6*b^3*tan(d*x)*tan(c) - 3*a^2*b*tan(c)^2 + 5*b^3*tan(c)^2 - 6*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) + 4*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) - 2*a^3*tan(d*x) + 18*a*b^2*tan(d*x) - 2*a^3*tan(c) + 18*a*b^2*tan(c) + 3*a^2*b + b^3)/(d*tan(d*x)^4*tan(c)^4 + d*tan(d*x)^4*tan(c)^2 - 2*d*tan(d*x)^3*tan(c)^3 + d*tan(d*x)^2*tan(c)^4 - 2*d*tan(d*x)^3*tan(c) + 2*d*tan(d*x)^2*tan(c)^2 - 2*d*tan(d*x)*tan(c)^3 + d*tan(d*x)^2 - 2*d*tan(d*x)*tan(c) + d*tan(c)^2 + d)","B",0
34,-2,0,0,0.000000," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)(-4*a^3*tan(c/2)^6*tan(d*x/2)^6+12*a^3*tan(c/2)^6*tan(d*x/2)^4-12*a^3*tan(c/2)^6*tan(d*x/2)^2+4*a^3*tan(c/2)^6+48*a^3*tan(c/2)^5*tan(d*x/2)^5-96*a^3*tan(c/2)^5*tan(d*x/2)^3+48*a^3*tan(c/2)^5*tan(d*x/2)+12*a^3*tan(c/2)^4*tan(d*x/2)^6-228*a^3*tan(c/2)^4*tan(d*x/2)^4+228*a^3*tan(c/2)^4*tan(d*x/2)^2-12*a^3*tan(c/2)^4-96*a^3*tan(c/2)^3*tan(d*x/2)^5+448*a^3*tan(c/2)^3*tan(d*x/2)^3-96*a^3*tan(c/2)^3*tan(d*x/2)-12*a^3*tan(c/2)^2*tan(d*x/2)^6+228*a^3*tan(c/2)^2*tan(d*x/2)^4-228*a^3*tan(c/2)^2*tan(d*x/2)^2+12*a^3*tan(c/2)^2+48*a^3*tan(c/2)*tan(d*x/2)^5-96*a^3*tan(c/2)*tan(d*x/2)^3+48*a^3*tan(c/2)*tan(d*x/2)+4*a^3*tan(d*x/2)^6-12*a^3*tan(d*x/2)^4+12*a^3*tan(d*x/2)^2-4*a^3-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^6+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^4+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^2-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6+48*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^5*tan(d*x/2)^5-48*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^5*tan(d*x/2)+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^6-102*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^4-102*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^2+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^6-102*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^4-102*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^2+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2-48*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)^5+48*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^6+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^4+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^2-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^6-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^4-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^2+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6-48*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^5*tan(d*x/2)^5+48*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^5*tan(d*x/2)-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^6+102*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^4+102*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^2-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^6+102*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^4+102*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^2-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2+48*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)^5-48*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^6-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^4-6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^2+6*a^2*b*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))+24*a^2*b*tan(c/2)^6*tan(d*x/2)^5-48*a^2*b*tan(c/2)^6*tan(d*x/2)^3+24*a^2*b*tan(c/2)^6*tan(d*x/2)+24*a^2*b*tan(c/2)^5*tan(d*x/2)^6-264*a^2*b*tan(c/2)^5*tan(d*x/2)^4+264*a^2*b*tan(c/2)^5*tan(d*x/2)^2-24*a^2*b*tan(c/2)^5-264*a^2*b*tan(c/2)^4*tan(d*x/2)^5+912*a^2*b*tan(c/2)^4*tan(d*x/2)^3-264*a^2*b*tan(c/2)^4*tan(d*x/2)-48*a^2*b*tan(c/2)^3*tan(d*x/2)^6+912*a^2*b*tan(c/2)^3*tan(d*x/2)^4-912*a^2*b*tan(c/2)^3*tan(d*x/2)^2+48*a^2*b*tan(c/2)^3+264*a^2*b*tan(c/2)^2*tan(d*x/2)^5-912*a^2*b*tan(c/2)^2*tan(d*x/2)^3+264*a^2*b*tan(c/2)^2*tan(d*x/2)+24*a^2*b*tan(c/2)*tan(d*x/2)^6-264*a^2*b*tan(c/2)*tan(d*x/2)^4+264*a^2*b*tan(c/2)*tan(d*x/2)^2-24*a^2*b*tan(c/2)-24*a^2*b*tan(d*x/2)^5+48*a^2*b*tan(d*x/2)^3-24*a^2*b*tan(d*x/2)+9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^6-9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^4-9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^2+9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6-72*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^5*tan(d*x/2)^5+72*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^5*tan(d*x/2)-9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^6+153*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^4+153*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^2-9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4-9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^6+153*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^4+153*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^2-9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2+72*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)*tan(d*x/2)^5-72*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)*tan(d*x/2)+9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^6-9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^4-9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^2+9*a*b^2*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)+24*a*b^2*tan(c/2)^6*tan(d*x/2)^6-24*a*b^2*tan(c/2)^6*tan(d*x/2)^4+24*a*b^2*tan(c/2)^6*tan(d*x/2)^2-24*a*b^2*tan(c/2)^6-192*a*b^2*tan(c/2)^5*tan(d*x/2)^5+192*a*b^2*tan(c/2)^5*tan(d*x/2)^3-192*a*b^2*tan(c/2)^5*tan(d*x/2)-24*a*b^2*tan(c/2)^4*tan(d*x/2)^6+696*a*b^2*tan(c/2)^4*tan(d*x/2)^4-696*a*b^2*tan(c/2)^4*tan(d*x/2)^2+24*a*b^2*tan(c/2)^4+192*a*b^2*tan(c/2)^3*tan(d*x/2)^5-1536*a*b^2*tan(c/2)^3*tan(d*x/2)^3+192*a*b^2*tan(c/2)^3*tan(d*x/2)+24*a*b^2*tan(c/2)^2*tan(d*x/2)^6-696*a*b^2*tan(c/2)^2*tan(d*x/2)^4+696*a*b^2*tan(c/2)^2*tan(d*x/2)^2-24*a*b^2*tan(c/2)^2-192*a*b^2*tan(c/2)*tan(d*x/2)^5+192*a*b^2*tan(c/2)*tan(d*x/2)^3-192*a*b^2*tan(c/2)*tan(d*x/2)-24*a*b^2*tan(d*x/2)^6+24*a*b^2*tan(d*x/2)^4-24*a*b^2*tan(d*x/2)^2+24*a*b^2+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^6-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^4-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^2+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6-24*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^5*tan(d*x/2)^5+24*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^5*tan(d*x/2)-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^6+51*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^4+51*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^2-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^6+51*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^4+51*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^2-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2+24*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)^5-24*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^6-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^4-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^2+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^6+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^4+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6*tan(d*x/2)^2-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^6+24*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^5*tan(d*x/2)^5-24*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^5*tan(d*x/2)+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^6-51*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^4-51*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^2+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^6-51*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^4-51*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2*tan(d*x/2)^2+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^2-24*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)^5+24*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^6+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^4+3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^2-3*b^3*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))-12*b^3*tan(c/2)^6*tan(d*x/2)^5+8*b^3*tan(c/2)^6*tan(d*x/2)^3-12*b^3*tan(c/2)^6*tan(d*x/2)-12*b^3*tan(c/2)^5*tan(d*x/2)^6+84*b^3*tan(c/2)^5*tan(d*x/2)^4-84*b^3*tan(c/2)^5*tan(d*x/2)^2+12*b^3*tan(c/2)^5+84*b^3*tan(c/2)^4*tan(d*x/2)^5-312*b^3*tan(c/2)^4*tan(d*x/2)^3+84*b^3*tan(c/2)^4*tan(d*x/2)+8*b^3*tan(c/2)^3*tan(d*x/2)^6-312*b^3*tan(c/2)^3*tan(d*x/2)^4+312*b^3*tan(c/2)^3*tan(d*x/2)^2-8*b^3*tan(c/2)^3-84*b^3*tan(c/2)^2*tan(d*x/2)^5+312*b^3*tan(c/2)^2*tan(d*x/2)^3-84*b^3*tan(c/2)^2*tan(d*x/2)-12*b^3*tan(c/2)*tan(d*x/2)^6+84*b^3*tan(c/2)*tan(d*x/2)^4-84*b^3*tan(c/2)*tan(d*x/2)^2+12*b^3*tan(c/2)+12*b^3*tan(d*x/2)^5-8*b^3*tan(d*x/2)^3+12*b^3*tan(d*x/2))/(4*d*tan(c/2)^6*tan(d*x/2)^6-4*d*tan(c/2)^6*tan(d*x/2)^4-4*d*tan(c/2)^6*tan(d*x/2)^2+4*d*tan(c/2)^6-32*d*tan(c/2)^5*tan(d*x/2)^5+32*d*tan(c/2)^5*tan(d*x/2)-4*d*tan(c/2)^4*tan(d*x/2)^6+68*d*tan(c/2)^4*tan(d*x/2)^4+68*d*tan(c/2)^4*tan(d*x/2)^2-4*d*tan(c/2)^4-4*d*tan(c/2)^2*tan(d*x/2)^6+68*d*tan(c/2)^2*tan(d*x/2)^4+68*d*tan(c/2)^2*tan(d*x/2)^2-4*d*tan(c/2)^2+32*d*tan(c/2)*tan(d*x/2)^5-32*d*tan(c/2)*tan(d*x/2)+4*d*tan(d*x/2)^6-4*d*tan(d*x/2)^4-4*d*tan(d*x/2)^2+4*d)","F(-2)",0
35,1,144,0,7.583355," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + {\left(6 \, a^{2} b - b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(6 \, a^{2} b - b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + (6*a^2*b - b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (6*a^2*b - b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c)^2 + b^3*tan(1/2*d*x + 1/2*c) + 6*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
36,1,70,0,1.795745," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{b^{3} \tan\left(d x + c\right)^{2} + 6 \, a^{2} b \log\left({\left| \tan\left(d x + c\right) \right|}\right) + 6 \, a b^{2} \tan\left(d x + c\right) - \frac{2 \, {\left(3 \, a^{2} b \tan\left(d x + c\right) + a^{3}\right)}}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(b^3*tan(d*x + c)^2 + 6*a^2*b*log(abs(tan(d*x + c))) + 6*a*b^2*tan(d*x + c) - 2*(3*a^2*b*tan(d*x + c) + a^3)/tan(d*x + c))/d","A",0
37,1,304,0,2.106447," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, {\left(6 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 4 \, {\left(a^{3} + 6 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2}}}{8 \, d}"," ",0,"1/8*(a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) + 4*(6*a^2*b + b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 4*(6*a^2*b + b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 4*(a^3 + 6*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - (2*a^3*tan(1/2*d*x + 1/2*c)^6 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 8*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*a^3*tan(1/2*d*x + 1/2*c)^4 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 24*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 8*b^3*tan(1/2*d*x + 1/2*c)^3 - 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 12*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c))^2)/d","B",0
38,1,133,0,2.512214," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, b^{3} \tan\left(d x + c\right)^{2} + 18 \, a b^{2} \tan\left(d x + c\right) + 6 \, {\left(3 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right) - \frac{33 \, a^{2} b \tan\left(d x + c\right)^{3} + 11 \, b^{3} \tan\left(d x + c\right)^{3} + 6 \, a^{3} \tan\left(d x + c\right)^{2} + 18 \, a b^{2} \tan\left(d x + c\right)^{2} + 9 \, a^{2} b \tan\left(d x + c\right) + 2 \, a^{3}}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(3*b^3*tan(d*x + c)^2 + 18*a*b^2*tan(d*x + c) + 6*(3*a^2*b + b^3)*log(abs(tan(d*x + c))) - (33*a^2*b*tan(d*x + c)^3 + 11*b^3*tan(d*x + c)^3 + 6*a^3*tan(d*x + c)^2 + 18*a*b^2*tan(d*x + c)^2 + 9*a^2*b*tan(d*x + c) + 2*a^3)/tan(d*x + c)^3)/d","A",0
39,1,373,0,5.325542," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 32 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, {\left(2 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 96 \, {\left(2 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 24 \, {\left(a^{3} + 12 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{64 \, {\left(b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} - \frac{50 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 600 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{64 \, d}"," ",0,"1/64*(a^3*tan(1/2*d*x + 1/2*c)^4 - 8*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 8*a^3*tan(1/2*d*x + 1/2*c)^2 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 120*a^2*b*tan(1/2*d*x + 1/2*c) - 32*b^3*tan(1/2*d*x + 1/2*c) + 96*(2*a^2*b + b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 96*(2*a^2*b + b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 24*(a^3 + 12*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + 64*(b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c)^2 + b^3*tan(1/2*d*x + 1/2*c) + 6*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 - (50*a^3*tan(1/2*d*x + 1/2*c)^4 + 600*a*b^2*tan(1/2*d*x + 1/2*c)^4 + 120*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 32*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*a^3*tan(1/2*d*x + 1/2*c)^2 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
40,1,189,0,1.849816," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{30 \, b^{3} \tan\left(d x + c\right)^{2} + 180 \, a b^{2} \tan\left(d x + c\right) + 60 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right) - \frac{411 \, a^{2} b \tan\left(d x + c\right)^{5} + 274 \, b^{3} \tan\left(d x + c\right)^{5} + 60 \, a^{3} \tan\left(d x + c\right)^{4} + 360 \, a b^{2} \tan\left(d x + c\right)^{4} + 180 \, a^{2} b \tan\left(d x + c\right)^{3} + 30 \, b^{3} \tan\left(d x + c\right)^{3} + 40 \, a^{3} \tan\left(d x + c\right)^{2} + 60 \, a b^{2} \tan\left(d x + c\right)^{2} + 45 \, a^{2} b \tan\left(d x + c\right) + 12 \, a^{3}}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(30*b^3*tan(d*x + c)^2 + 180*a*b^2*tan(d*x + c) + 60*(3*a^2*b + 2*b^3)*log(abs(tan(d*x + c))) - (411*a^2*b*tan(d*x + c)^5 + 274*b^3*tan(d*x + c)^5 + 60*a^3*tan(d*x + c)^4 + 360*a*b^2*tan(d*x + c)^4 + 180*a^2*b*tan(d*x + c)^3 + 30*b^3*tan(d*x + c)^3 + 40*a^3*tan(d*x + c)^2 + 60*a*b^2*tan(d*x + c)^2 + 45*a^2*b*tan(d*x + c) + 12*a^3)/tan(d*x + c)^5)/d","A",0
41,-1,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,1,3931,0,22.339095," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 54 \, a^{2} b^{2} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 15 \, b^{4} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 12 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 24 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 3 \, a^{4} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{3} - 54 \, a^{2} b^{2} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{3} + 15 \, b^{4} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{3} - 9 \, a^{4} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 162 \, a^{2} b^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 45 \, b^{4} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 3 \, a^{4} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{5} - 54 \, a^{2} b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{5} + 15 \, b^{4} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{5} + 6 \, a^{3} b \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 6 \, a b^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 12 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{5} \tan\left(c\right)^{3} + 24 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{5} \tan\left(c\right)^{3} + 36 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 72 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 3 \, a^{4} \tan\left(d x\right)^{5} \tan\left(c\right)^{4} - 54 \, a^{2} b^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{4} + 15 \, b^{4} \tan\left(d x\right)^{5} \tan\left(c\right)^{4} - 12 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{5} + 24 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{5} + 3 \, a^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{5} - 54 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{5} + 15 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{5} - 9 \, a^{4} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 162 \, a^{2} b^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 45 \, b^{4} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 12 \, a^{4} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 216 \, a^{2} b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 60 \, b^{4} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 6 \, a^{3} b \tan\left(d x\right)^{5} \tan\left(c\right)^{3} + 30 \, a b^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{3} - 9 \, a^{4} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 162 \, a^{2} b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 45 \, b^{4} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 42 \, a^{3} b \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 30 \, a b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 6 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right)^{5} + 30 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{5} + 36 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 72 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 36 \, a^{2} b^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{2} + 10 \, b^{4} \tan\left(d x\right)^{5} \tan\left(c\right)^{2} - 48 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 96 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 12 \, a^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 108 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 30 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 36 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 72 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 12 \, a^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 108 \, a^{2} b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 30 \, b^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 36 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{5} + 10 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{5} + 9 \, a^{4} d x \tan\left(d x\right)^{3} \tan\left(c\right) - 162 \, a^{2} b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right) + 45 \, b^{4} d x \tan\left(d x\right)^{3} \tan\left(c\right) + 12 \, a b^{3} \tan\left(d x\right)^{5} \tan\left(c\right) - 12 \, a^{4} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 216 \, a^{2} b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 60 \, b^{4} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 18 \, a^{3} b \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 42 \, a b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 9 \, a^{4} d x \tan\left(d x\right) \tan\left(c\right)^{3} - 162 \, a^{2} b^{2} d x \tan\left(d x\right) \tan\left(c\right)^{3} + 45 \, b^{4} d x \tan\left(d x\right) \tan\left(c\right)^{3} + 96 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 48 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 18 \, a^{3} b \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 42 \, a b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 12 \, a b^{3} \tan\left(d x\right) \tan\left(c\right)^{5} - 2 \, b^{4} \tan\left(d x\right)^{5} - 36 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right) + 72 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right) + 72 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right) - 30 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right) + 48 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 96 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 18 \, a^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 108 \, a^{2} b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 10 \, b^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 36 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right)^{3} + 72 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right)^{3} + 18 \, a^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 108 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 10 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 72 \, a^{2} b^{2} \tan\left(d x\right) \tan\left(c\right)^{4} - 30 \, b^{4} \tan\left(d x\right) \tan\left(c\right)^{4} - 2 \, b^{4} \tan\left(c\right)^{5} - 3 \, a^{4} d x \tan\left(d x\right)^{2} + 54 \, a^{2} b^{2} d x \tan\left(d x\right)^{2} - 15 \, b^{4} d x \tan\left(d x\right)^{2} - 12 \, a b^{3} \tan\left(d x\right)^{4} + 9 \, a^{4} d x \tan\left(d x\right) \tan\left(c\right) - 162 \, a^{2} b^{2} d x \tan\left(d x\right) \tan\left(c\right) + 45 \, b^{4} d x \tan\left(d x\right) \tan\left(c\right) - 18 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right) + 42 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right) - 3 \, a^{4} d x \tan\left(c\right)^{2} + 54 \, a^{2} b^{2} d x \tan\left(c\right)^{2} - 15 \, b^{4} d x \tan\left(c\right)^{2} - 96 \, a^{3} b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 48 \, a b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 18 \, a^{3} b \tan\left(d x\right) \tan\left(c\right)^{3} + 42 \, a b^{3} \tan\left(d x\right) \tan\left(c\right)^{3} - 12 \, a b^{3} \tan\left(c\right)^{4} + 12 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} - 24 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} - 36 \, a^{2} b^{2} \tan\left(d x\right)^{3} + 10 \, b^{4} \tan\left(d x\right)^{3} - 36 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) + 72 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) - 12 \, a^{4} \tan\left(d x\right)^{2} \tan\left(c\right) + 108 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 30 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right) + 12 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(c\right)^{2} - 24 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(c\right)^{2} - 12 \, a^{4} \tan\left(d x\right) \tan\left(c\right)^{2} + 108 \, a^{2} b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} - 30 \, b^{4} \tan\left(d x\right) \tan\left(c\right)^{2} - 36 \, a^{2} b^{2} \tan\left(c\right)^{3} + 10 \, b^{4} \tan\left(c\right)^{3} - 3 \, a^{4} d x + 54 \, a^{2} b^{2} d x - 15 \, b^{4} d x + 6 \, a^{3} b \tan\left(d x\right)^{2} - 30 \, a b^{3} \tan\left(d x\right)^{2} + 42 \, a^{3} b \tan\left(d x\right) \tan\left(c\right) - 30 \, a b^{3} \tan\left(d x\right) \tan\left(c\right) + 6 \, a^{3} b \tan\left(c\right)^{2} - 30 \, a b^{3} \tan\left(c\right)^{2} + 12 \, a^{3} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) - 24 \, a b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) + 3 \, a^{4} \tan\left(d x\right) - 54 \, a^{2} b^{2} \tan\left(d x\right) + 15 \, b^{4} \tan\left(d x\right) + 3 \, a^{4} \tan\left(c\right) - 54 \, a^{2} b^{2} \tan\left(c\right) + 15 \, b^{4} \tan\left(c\right) - 6 \, a^{3} b - 6 \, a b^{3}}{6 \, {\left(d \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + d \tan\left(d x\right)^{5} \tan\left(c\right)^{3} - 3 \, d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + d \tan\left(d x\right)^{3} \tan\left(c\right)^{5} - 3 \, d \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 4 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 3 \, d \tan\left(d x\right)^{3} \tan\left(c\right) - 4 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right) \tan\left(c\right)^{3} - d \tan\left(d x\right)^{2} + 3 \, d \tan\left(d x\right) \tan\left(c\right) - d \tan\left(c\right)^{2} - d\right)}}"," ",0,"1/6*(3*a^4*d*x*tan(d*x)^5*tan(c)^5 - 54*a^2*b^2*d*x*tan(d*x)^5*tan(c)^5 + 15*b^4*d*x*tan(d*x)^5*tan(c)^5 - 12*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^5*tan(c)^5 + 24*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^5*tan(c)^5 + 3*a^4*d*x*tan(d*x)^5*tan(c)^3 - 54*a^2*b^2*d*x*tan(d*x)^5*tan(c)^3 + 15*b^4*d*x*tan(d*x)^5*tan(c)^3 - 9*a^4*d*x*tan(d*x)^4*tan(c)^4 + 162*a^2*b^2*d*x*tan(d*x)^4*tan(c)^4 - 45*b^4*d*x*tan(d*x)^4*tan(c)^4 + 3*a^4*d*x*tan(d*x)^3*tan(c)^5 - 54*a^2*b^2*d*x*tan(d*x)^3*tan(c)^5 + 15*b^4*d*x*tan(d*x)^3*tan(c)^5 + 6*a^3*b*tan(d*x)^5*tan(c)^5 + 6*a*b^3*tan(d*x)^5*tan(c)^5 - 12*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^5*tan(c)^3 + 24*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^5*tan(c)^3 + 36*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^4 - 72*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^4 + 3*a^4*tan(d*x)^5*tan(c)^4 - 54*a^2*b^2*tan(d*x)^5*tan(c)^4 + 15*b^4*tan(d*x)^5*tan(c)^4 - 12*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^5 + 24*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^5 + 3*a^4*tan(d*x)^4*tan(c)^5 - 54*a^2*b^2*tan(d*x)^4*tan(c)^5 + 15*b^4*tan(d*x)^4*tan(c)^5 - 9*a^4*d*x*tan(d*x)^4*tan(c)^2 + 162*a^2*b^2*d*x*tan(d*x)^4*tan(c)^2 - 45*b^4*d*x*tan(d*x)^4*tan(c)^2 + 12*a^4*d*x*tan(d*x)^3*tan(c)^3 - 216*a^2*b^2*d*x*tan(d*x)^3*tan(c)^3 + 60*b^4*d*x*tan(d*x)^3*tan(c)^3 - 6*a^3*b*tan(d*x)^5*tan(c)^3 + 30*a*b^3*tan(d*x)^5*tan(c)^3 - 9*a^4*d*x*tan(d*x)^2*tan(c)^4 + 162*a^2*b^2*d*x*tan(d*x)^2*tan(c)^4 - 45*b^4*d*x*tan(d*x)^2*tan(c)^4 - 42*a^3*b*tan(d*x)^4*tan(c)^4 + 30*a*b^3*tan(d*x)^4*tan(c)^4 - 6*a^3*b*tan(d*x)^3*tan(c)^5 + 30*a*b^3*tan(d*x)^3*tan(c)^5 + 36*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^2 - 72*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^2 - 36*a^2*b^2*tan(d*x)^5*tan(c)^2 + 10*b^4*tan(d*x)^5*tan(c)^2 - 48*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 + 96*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 - 12*a^4*tan(d*x)^4*tan(c)^3 + 108*a^2*b^2*tan(d*x)^4*tan(c)^3 - 30*b^4*tan(d*x)^4*tan(c)^3 + 36*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^4 - 72*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^4 - 12*a^4*tan(d*x)^3*tan(c)^4 + 108*a^2*b^2*tan(d*x)^3*tan(c)^4 - 30*b^4*tan(d*x)^3*tan(c)^4 - 36*a^2*b^2*tan(d*x)^2*tan(c)^5 + 10*b^4*tan(d*x)^2*tan(c)^5 + 9*a^4*d*x*tan(d*x)^3*tan(c) - 162*a^2*b^2*d*x*tan(d*x)^3*tan(c) + 45*b^4*d*x*tan(d*x)^3*tan(c) + 12*a*b^3*tan(d*x)^5*tan(c) - 12*a^4*d*x*tan(d*x)^2*tan(c)^2 + 216*a^2*b^2*d*x*tan(d*x)^2*tan(c)^2 - 60*b^4*d*x*tan(d*x)^2*tan(c)^2 + 18*a^3*b*tan(d*x)^4*tan(c)^2 - 42*a*b^3*tan(d*x)^4*tan(c)^2 + 9*a^4*d*x*tan(d*x)*tan(c)^3 - 162*a^2*b^2*d*x*tan(d*x)*tan(c)^3 + 45*b^4*d*x*tan(d*x)*tan(c)^3 + 96*a^3*b*tan(d*x)^3*tan(c)^3 - 48*a*b^3*tan(d*x)^3*tan(c)^3 + 18*a^3*b*tan(d*x)^2*tan(c)^4 - 42*a*b^3*tan(d*x)^2*tan(c)^4 + 12*a*b^3*tan(d*x)*tan(c)^5 - 2*b^4*tan(d*x)^5 - 36*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c) + 72*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c) + 72*a^2*b^2*tan(d*x)^4*tan(c) - 30*b^4*tan(d*x)^4*tan(c) + 48*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 - 96*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 + 18*a^4*tan(d*x)^3*tan(c)^2 - 108*a^2*b^2*tan(d*x)^3*tan(c)^2 + 10*b^4*tan(d*x)^3*tan(c)^2 - 36*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c)^3 + 72*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c)^3 + 18*a^4*tan(d*x)^2*tan(c)^3 - 108*a^2*b^2*tan(d*x)^2*tan(c)^3 + 10*b^4*tan(d*x)^2*tan(c)^3 + 72*a^2*b^2*tan(d*x)*tan(c)^4 - 30*b^4*tan(d*x)*tan(c)^4 - 2*b^4*tan(c)^5 - 3*a^4*d*x*tan(d*x)^2 + 54*a^2*b^2*d*x*tan(d*x)^2 - 15*b^4*d*x*tan(d*x)^2 - 12*a*b^3*tan(d*x)^4 + 9*a^4*d*x*tan(d*x)*tan(c) - 162*a^2*b^2*d*x*tan(d*x)*tan(c) + 45*b^4*d*x*tan(d*x)*tan(c) - 18*a^3*b*tan(d*x)^3*tan(c) + 42*a*b^3*tan(d*x)^3*tan(c) - 3*a^4*d*x*tan(c)^2 + 54*a^2*b^2*d*x*tan(c)^2 - 15*b^4*d*x*tan(c)^2 - 96*a^3*b*tan(d*x)^2*tan(c)^2 + 48*a*b^3*tan(d*x)^2*tan(c)^2 - 18*a^3*b*tan(d*x)*tan(c)^3 + 42*a*b^3*tan(d*x)*tan(c)^3 - 12*a*b^3*tan(c)^4 + 12*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2 - 24*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2 - 36*a^2*b^2*tan(d*x)^3 + 10*b^4*tan(d*x)^3 - 36*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) + 72*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) - 12*a^4*tan(d*x)^2*tan(c) + 108*a^2*b^2*tan(d*x)^2*tan(c) - 30*b^4*tan(d*x)^2*tan(c) + 12*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(c)^2 - 24*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(c)^2 - 12*a^4*tan(d*x)*tan(c)^2 + 108*a^2*b^2*tan(d*x)*tan(c)^2 - 30*b^4*tan(d*x)*tan(c)^2 - 36*a^2*b^2*tan(c)^3 + 10*b^4*tan(c)^3 - 3*a^4*d*x + 54*a^2*b^2*d*x - 15*b^4*d*x + 6*a^3*b*tan(d*x)^2 - 30*a*b^3*tan(d*x)^2 + 42*a^3*b*tan(d*x)*tan(c) - 30*a*b^3*tan(d*x)*tan(c) + 6*a^3*b*tan(c)^2 - 30*a*b^3*tan(c)^2 + 12*a^3*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) - 24*a*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) + 3*a^4*tan(d*x) - 54*a^2*b^2*tan(d*x) + 15*b^4*tan(d*x) + 3*a^4*tan(c) - 54*a^2*b^2*tan(c) + 15*b^4*tan(c) - 6*a^3*b - 6*a*b^3)/(d*tan(d*x)^5*tan(c)^5 + d*tan(d*x)^5*tan(c)^3 - 3*d*tan(d*x)^4*tan(c)^4 + d*tan(d*x)^3*tan(c)^5 - 3*d*tan(d*x)^4*tan(c)^2 + 4*d*tan(d*x)^3*tan(c)^3 - 3*d*tan(d*x)^2*tan(c)^4 + 3*d*tan(d*x)^3*tan(c) - 4*d*tan(d*x)^2*tan(c)^2 + 3*d*tan(d*x)*tan(c)^3 - d*tan(d*x)^2 + 3*d*tan(d*x)*tan(c) - d*tan(c)^2 - d)","B",0
43,-1,0,0,0.000000," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,1,193,0,6.000656," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 6 \, {\left(2 \, a^{3} b - a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, {\left(2 \, a^{3} b - a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{4 \, {\left(3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, a^{2} b^{2} + b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*a^4*log(abs(tan(1/2*d*x + 1/2*c))) + 6*(2*a^3*b - a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*(2*a^3*b - a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 4*(3*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 9*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 18*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*b^4*tan(1/2*d*x + 1/2*c)^2 - 3*a*b^3*tan(1/2*d*x + 1/2*c) - 9*a^2*b^2 + b^4)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
45,1,86,0,4.037579," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{b^{4} \tan\left(d x + c\right)^{3} + 6 \, a b^{3} \tan\left(d x + c\right)^{2} + 12 \, a^{3} b \log\left({\left| \tan\left(d x + c\right) \right|}\right) + 18 \, a^{2} b^{2} \tan\left(d x + c\right) - \frac{3 \, {\left(4 \, a^{3} b \tan\left(d x + c\right) + a^{4}\right)}}{\tan\left(d x + c\right)}}{3 \, d}"," ",0,"1/3*(b^4*tan(d*x + c)^3 + 6*a*b^3*tan(d*x + c)^2 + 12*a^3*b*log(abs(tan(d*x + c))) + 18*a^2*b^2*tan(d*x + c) - 3*(4*a^3*b*tan(d*x + c) + a^4)/tan(d*x + c))/d","A",0
46,1,300,0,12.817986," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, {\left(2 \, a^{3} b + a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 48 \, {\left(2 \, a^{3} b + a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 12 \, {\left(a^{4} + 12 \, a^{2} b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{3 \, {\left(6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{4}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{16 \, {\left(6 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 36 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a^{2} b^{2} - b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{24 \, d}"," ",0,"1/24*(3*a^4*tan(1/2*d*x + 1/2*c)^2 - 48*a^3*b*tan(1/2*d*x + 1/2*c) + 48*(2*a^3*b + a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 48*(2*a^3*b + a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 12*(a^4 + 12*a^2*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - 3*(6*a^4*tan(1/2*d*x + 1/2*c)^2 + 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 16*a^3*b*tan(1/2*d*x + 1/2*c) + a^4)/tan(1/2*d*x + 1/2*c)^2 + 16*(6*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 18*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 - 3*b^4*tan(1/2*d*x + 1/2*c)^4 + 36*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*a*b^3*tan(1/2*d*x + 1/2*c) - 18*a^2*b^2 - b^4)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
47,1,161,0,7.802495," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{b^{4} \tan\left(d x + c\right)^{3} + 6 \, a b^{3} \tan\left(d x + c\right)^{2} + 18 \, a^{2} b^{2} \tan\left(d x + c\right) + 3 \, b^{4} \tan\left(d x + c\right) + 12 \, {\left(a^{3} b + a b^{3}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right) - \frac{22 \, a^{3} b \tan\left(d x + c\right)^{3} + 22 \, a b^{3} \tan\left(d x + c\right)^{3} + 3 \, a^{4} \tan\left(d x + c\right)^{2} + 18 \, a^{2} b^{2} \tan\left(d x + c\right)^{2} + 6 \, a^{3} b \tan\left(d x + c\right) + a^{4}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(b^4*tan(d*x + c)^3 + 6*a*b^3*tan(d*x + c)^2 + 18*a^2*b^2*tan(d*x + c) + 3*b^4*tan(d*x + c) + 12*(a^3*b + a*b^3)*log(abs(tan(d*x + c))) - (22*a^3*b*tan(d*x + c)^3 + 22*a*b^3*tan(d*x + c)^3 + 3*a^4*tan(d*x + c)^2 + 18*a^2*b^2*tan(d*x + c)^2 + 6*a^3*b*tan(d*x + c) + a^4)/tan(d*x + c)^3)/d","A",0
48,1,479,0,8.970392," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 32 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 144 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 480 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 384 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 384 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 384 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 24 \, {\left(3 \, a^{4} + 72 \, a^{2} b^{2} + 8 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{256 \, {\left(3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, a^{2} b^{2} - 2 \, b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}} - \frac{150 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3600 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 400 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 480 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 384 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 144 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 32 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a^4*tan(1/2*d*x + 1/2*c)^4 - 32*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 24*a^4*tan(1/2*d*x + 1/2*c)^2 + 144*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 480*a^3*b*tan(1/2*d*x + 1/2*c) - 384*a*b^3*tan(1/2*d*x + 1/2*c) + 384*(2*a^3*b + 3*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 384*(2*a^3*b + 3*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 24*(3*a^4 + 72*a^2*b^2 + 8*b^4)*log(abs(tan(1/2*d*x + 1/2*c))) + 256*(3*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 9*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 - 3*b^4*tan(1/2*d*x + 1/2*c)^4 + 18*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 3*b^4*tan(1/2*d*x + 1/2*c)^2 - 3*a*b^3*tan(1/2*d*x + 1/2*c) - 9*a^2*b^2 - 2*b^4)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3 - (150*a^4*tan(1/2*d*x + 1/2*c)^4 + 3600*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 400*b^4*tan(1/2*d*x + 1/2*c)^4 + 480*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 384*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 24*a^4*tan(1/2*d*x + 1/2*c)^2 + 144*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 32*a^3*b*tan(1/2*d*x + 1/2*c) + 3*a^4)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
49,1,235,0,3.635965," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{5 \, b^{4} \tan\left(d x + c\right)^{3} + 30 \, a b^{3} \tan\left(d x + c\right)^{2} + 90 \, a^{2} b^{2} \tan\left(d x + c\right) + 30 \, b^{4} \tan\left(d x + c\right) + 60 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right) - \frac{137 \, a^{3} b \tan\left(d x + c\right)^{5} + 274 \, a b^{3} \tan\left(d x + c\right)^{5} + 15 \, a^{4} \tan\left(d x + c\right)^{4} + 180 \, a^{2} b^{2} \tan\left(d x + c\right)^{4} + 15 \, b^{4} \tan\left(d x + c\right)^{4} + 60 \, a^{3} b \tan\left(d x + c\right)^{3} + 30 \, a b^{3} \tan\left(d x + c\right)^{3} + 10 \, a^{4} \tan\left(d x + c\right)^{2} + 30 \, a^{2} b^{2} \tan\left(d x + c\right)^{2} + 15 \, a^{3} b \tan\left(d x + c\right) + 3 \, a^{4}}{\tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*(5*b^4*tan(d*x + c)^3 + 30*a*b^3*tan(d*x + c)^2 + 90*a^2*b^2*tan(d*x + c) + 30*b^4*tan(d*x + c) + 60*(a^3*b + 2*a*b^3)*log(abs(tan(d*x + c))) - (137*a^3*b*tan(d*x + c)^5 + 274*a*b^3*tan(d*x + c)^5 + 15*a^4*tan(d*x + c)^4 + 180*a^2*b^2*tan(d*x + c)^4 + 15*b^4*tan(d*x + c)^4 + 60*a^3*b*tan(d*x + c)^3 + 30*a*b^3*tan(d*x + c)^3 + 10*a^4*tan(d*x + c)^2 + 30*a^2*b^2*tan(d*x + c)^2 + 15*a^3*b*tan(d*x + c) + 3*a^4)/tan(d*x + c)^5)/d","A",0
50,1,647,0,3.186635," ","integrate(csc(d*x+c)^7*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{5 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 48 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 180 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 560 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 225 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2880 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 240 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5280 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8640 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3840 \, {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3840 \, {\left(2 \, a^{3} b + 5 \, a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 600 \, {\left(a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{1280 \, {\left(6 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 9 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 36 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a^{2} b^{2} - 7 \, b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}} - \frac{1470 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 52920 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 11760 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 5280 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8640 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 225 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2880 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 240 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 560 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 180 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^4*tan(1/2*d*x + 1/2*c)^6 - 48*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 45*a^4*tan(1/2*d*x + 1/2*c)^4 + 180*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 - 560*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 320*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 225*a^4*tan(1/2*d*x + 1/2*c)^2 + 2880*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 240*b^4*tan(1/2*d*x + 1/2*c)^2 - 5280*a^3*b*tan(1/2*d*x + 1/2*c) - 8640*a*b^3*tan(1/2*d*x + 1/2*c) + 3840*(2*a^3*b + 5*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3840*(2*a^3*b + 5*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 600*(a^4 + 36*a^2*b^2 + 8*b^4)*log(abs(tan(1/2*d*x + 1/2*c))) + 1280*(6*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 18*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 - 9*b^4*tan(1/2*d*x + 1/2*c)^4 + 36*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 12*b^4*tan(1/2*d*x + 1/2*c)^2 - 6*a*b^3*tan(1/2*d*x + 1/2*c) - 18*a^2*b^2 - 7*b^4)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3 - (1470*a^4*tan(1/2*d*x + 1/2*c)^6 + 52920*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 + 11760*b^4*tan(1/2*d*x + 1/2*c)^6 + 5280*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 8640*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 225*a^4*tan(1/2*d*x + 1/2*c)^4 + 2880*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 240*b^4*tan(1/2*d*x + 1/2*c)^4 + 560*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 320*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 45*a^4*tan(1/2*d*x + 1/2*c)^2 + 180*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 48*a^3*b*tan(1/2*d*x + 1/2*c) + 5*a^4)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
51,1,464,0,2.842432," ","integrate(sin(d*x+c)^5/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{15 \, a^{5} b \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(15 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 15 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 80 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 20 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 90 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 30 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 178 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 136 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 80 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 30 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{5} + 9 \, a^{3} b^{2} + 2 \, a b^{4}\right)}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{15 \, d}"," ",0,"1/15*(15*a^5*b*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) + 2*(15*a^4*b*tan(1/2*d*x + 1/2*c)^9 + 15*a^3*b^2*tan(1/2*d*x + 1/2*c)^8 + 80*a^4*b*tan(1/2*d*x + 1/2*c)^7 + 20*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 90*a^3*b^2*tan(1/2*d*x + 1/2*c)^6 + 30*a*b^4*tan(1/2*d*x + 1/2*c)^6 + 178*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 136*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 48*b^5*tan(1/2*d*x + 1/2*c)^5 - 80*a^5*tan(1/2*d*x + 1/2*c)^4 - 10*a*b^4*tan(1/2*d*x + 1/2*c)^4 + 80*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 20*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 40*a^5*tan(1/2*d*x + 1/2*c)^2 + 30*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 10*a*b^4*tan(1/2*d*x + 1/2*c)^2 + 15*a^4*b*tan(1/2*d*x + 1/2*c) - 8*a^5 + 9*a^3*b^2 + 2*a*b^4)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(1/2*d*x + 1/2*c)^2 + 1)^5))/d","A",0
52,1,334,0,3.867287," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{8 \, a^{4} b^{2} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{4 \, a^{4} b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{5} - 6 \, a^{3} b^{2} - a b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{6 \, a^{4} b \tan\left(d x + c\right)^{4} - 5 \, a^{5} \tan\left(d x + c\right)^{3} - 6 \, a^{3} b^{2} \tan\left(d x + c\right)^{3} - a b^{4} \tan\left(d x + c\right)^{3} + 4 \, a^{4} b \tan\left(d x + c\right)^{2} - 12 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} - 4 \, b^{5} \tan\left(d x + c\right)^{2} - 3 \, a^{5} \tan\left(d x + c\right) - 2 \, a^{3} b^{2} \tan\left(d x + c\right) + a b^{4} \tan\left(d x + c\right) - 8 \, a^{2} b^{3} - 2 \, b^{5}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*(8*a^4*b^2*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - 4*a^4*b*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*a^5 - 6*a^3*b^2 - a*b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (6*a^4*b*tan(d*x + c)^4 - 5*a^5*tan(d*x + c)^3 - 6*a^3*b^2*tan(d*x + c)^3 - a*b^4*tan(d*x + c)^3 + 4*a^4*b*tan(d*x + c)^2 - 12*a^2*b^3*tan(d*x + c)^2 - 4*b^5*tan(d*x + c)^2 - 3*a^5*tan(d*x + c) - 2*a^3*b^2*tan(d*x + c) + a*b^4*tan(d*x + c) - 8*a^2*b^3 - 2*b^5)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(d*x + c)^2 + 1)^2))/d","B",0
53,1,241,0,0.984781," ","integrate(sin(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, a^{3} b \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{3} + a b^{2}\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*a^3*b*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + 2*(3*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 3*a*b^2*tan(1/2*d*x + 1/2*c)^4 + 10*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 4*b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^2*b*tan(1/2*d*x + 1/2*c) - 2*a^3 + a*b^2)/((a^4 + 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 + 1)^3))/d","A",0
54,1,184,0,0.617228," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, a^{2} b^{2} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} - \frac{a^{2} b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{3} - a b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{a^{2} b \tan\left(d x + c\right)^{2} - a^{3} \tan\left(d x + c\right) - a b^{2} \tan\left(d x + c\right) - b^{3}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}}}{2 \, d}"," ",0,"1/2*(2*a^2*b^2*log(abs(b*tan(d*x + c) + a))/(a^4*b + 2*a^2*b^3 + b^5) - a^2*b*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^3 - a*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + (a^2*b*tan(d*x + c)^2 - a^3*tan(d*x + c) - a*b^2*tan(d*x + c) - b^3)/((a^4 + 2*a^2*b^2 + b^4)*(tan(d*x + c)^2 + 1)))/d","B",0
55,1,118,0,0.611943," ","integrate(sin(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{a b \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}{{\left(a^{2} + b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}}}{d}"," ",0,"(a*b*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) + 2*(b*tan(1/2*d*x + 1/2*c) - a)/((a^2 + b^2)*(tan(1/2*d*x + 1/2*c)^2 + 1)))/d","A",0
56,1,94,0,1.618692," ","integrate(csc(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{b \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} a} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a}}{d}"," ",0,"(b*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a) + log(abs(tan(1/2*d*x + 1/2*c)))/a)/d","A",0
57,1,60,0,0.702379," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{b \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2}} - \frac{b \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{2}} + \frac{b \tan\left(d x + c\right) - a}{a^{2} \tan\left(d x + c\right)}}{d}"," ",0,"(b*log(abs(b*tan(d*x + c) + a))/a^2 - b*log(abs(tan(d*x + c)))/a^2 + (b*tan(d*x + c) - a)/(a^2*tan(d*x + c)))/d","A",0
58,1,209,0,2.071229," ","integrate(csc(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} + \frac{4 \, {\left(a^{2} + 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{8 \, {\left(a^{2} b + b^{3}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} a^{3}} - \frac{6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*((a*tan(1/2*d*x + 1/2*c)^2 + 4*b*tan(1/2*d*x + 1/2*c))/a^2 + 4*(a^2 + 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 8*(a^2*b + b^3)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a^3) - (6*a^2*tan(1/2*d*x + 1/2*c)^2 + 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 4*a*b*tan(1/2*d*x + 1/2*c) + a^2)/(a^3*tan(1/2*d*x + 1/2*c)^2))/d","A",0
59,1,144,0,2.925507," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{4}} - \frac{6 \, {\left(a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b} - \frac{11 \, a^{2} b \tan\left(d x + c\right)^{3} + 11 \, b^{3} \tan\left(d x + c\right)^{3} - 6 \, a^{3} \tan\left(d x + c\right)^{2} - 6 \, a b^{2} \tan\left(d x + c\right)^{2} + 3 \, a^{2} b \tan\left(d x + c\right) - 2 \, a^{3}}{a^{4} \tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(6*(a^2*b + b^3)*log(abs(tan(d*x + c)))/a^4 - 6*(a^2*b^2 + b^4)*log(abs(b*tan(d*x + c) + a))/(a^4*b) - (11*a^2*b*tan(d*x + c)^3 + 11*b^3*tan(d*x + c)^3 - 6*a^3*tan(d*x + c)^2 - 6*a*b^2*tan(d*x + c)^2 + 3*a^2*b*tan(d*x + c) - 2*a^3)/(a^4*tan(d*x + c)^3))/d","A",0
60,1,251,0,2.931901," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{6}} - \frac{60 \, {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b} - \frac{137 \, a^{4} b \tan\left(d x + c\right)^{5} + 274 \, a^{2} b^{3} \tan\left(d x + c\right)^{5} + 137 \, b^{5} \tan\left(d x + c\right)^{5} - 60 \, a^{5} \tan\left(d x + c\right)^{4} - 120 \, a^{3} b^{2} \tan\left(d x + c\right)^{4} - 60 \, a b^{4} \tan\left(d x + c\right)^{4} + 60 \, a^{4} b \tan\left(d x + c\right)^{3} + 30 \, a^{2} b^{3} \tan\left(d x + c\right)^{3} - 40 \, a^{5} \tan\left(d x + c\right)^{2} - 20 \, a^{3} b^{2} \tan\left(d x + c\right)^{2} + 15 \, a^{4} b \tan\left(d x + c\right) - 12 \, a^{5}}{a^{6} \tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*(a^4*b + 2*a^2*b^3 + b^5)*log(abs(tan(d*x + c)))/a^6 - 60*(a^4*b^2 + 2*a^2*b^4 + b^6)*log(abs(b*tan(d*x + c) + a))/(a^6*b) - (137*a^4*b*tan(d*x + c)^5 + 274*a^2*b^3*tan(d*x + c)^5 + 137*b^5*tan(d*x + c)^5 - 60*a^5*tan(d*x + c)^4 - 120*a^3*b^2*tan(d*x + c)^4 - 60*a*b^4*tan(d*x + c)^4 + 60*a^4*b*tan(d*x + c)^3 + 30*a^2*b^3*tan(d*x + c)^3 - 40*a^5*tan(d*x + c)^2 - 20*a^3*b^2*tan(d*x + c)^2 + 15*a^4*b*tan(d*x + c) - 12*a^5)/(a^6*tan(d*x + c)^5))/d","A",0
61,1,735,0,1.530046," ","integrate(sin(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(5 \, a^{8} - 80 \, a^{6} b^{2} + 50 \, a^{4} b^{4} + 8 \, a^{2} b^{6} + b^{8}\right)} {\left(d x + c\right)}}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{48 \, {\left(a^{7} b - 3 \, a^{5} b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} + \frac{96 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{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}} - \frac{48 \, {\left(2 \, a^{7} b^{2} \tan\left(d x + c\right) - 6 \, a^{5} b^{4} \tan\left(d x + c\right) + 3 \, a^{8} b - 5 \, a^{6} b^{3}\right)}}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} {\left(b \tan\left(d x + c\right) + a\right)}} + \frac{88 \, a^{7} b \tan\left(d x + c\right)^{6} - 264 \, a^{5} b^{3} \tan\left(d x + c\right)^{6} - 33 \, a^{8} \tan\left(d x + c\right)^{5} + 96 \, a^{6} b^{2} \tan\left(d x + c\right)^{5} + 150 \, a^{4} b^{4} \tan\left(d x + c\right)^{5} + 24 \, a^{2} b^{6} \tan\left(d x + c\right)^{5} + 3 \, b^{8} \tan\left(d x + c\right)^{5} + 120 \, a^{7} b \tan\left(d x + c\right)^{4} - 936 \, a^{5} b^{3} \tan\left(d x + c\right)^{4} - 40 \, a^{8} \tan\left(d x + c\right)^{3} + 208 \, a^{6} b^{2} \tan\left(d x + c\right)^{3} + 240 \, a^{4} b^{4} \tan\left(d x + c\right)^{3} - 16 \, a^{2} b^{6} \tan\left(d x + c\right)^{3} - 8 \, b^{8} \tan\left(d x + c\right)^{3} + 48 \, a^{7} b \tan\left(d x + c\right)^{2} - 912 \, a^{5} b^{3} \tan\left(d x + c\right)^{2} + 120 \, a^{3} b^{5} \tan\left(d x + c\right)^{2} + 24 \, a b^{7} \tan\left(d x + c\right)^{2} - 15 \, a^{8} \tan\left(d x + c\right) + 96 \, a^{6} b^{2} \tan\left(d x + c\right) + 90 \, a^{4} b^{4} \tan\left(d x + c\right) - 24 \, a^{2} b^{6} \tan\left(d x + c\right) - 3 \, b^{8} \tan\left(d x + c\right) - 288 \, a^{5} b^{3} + 72 \, a^{3} b^{5} + 8 \, a b^{7}}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}^{3}}}{48 \, d}"," ",0,"1/48*(3*(5*a^8 - 80*a^6*b^2 + 50*a^4*b^4 + 8*a^2*b^6 + b^8)*(d*x + c)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - 48*(a^7*b - 3*a^5*b^3)*log(tan(d*x + c)^2 + 1)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) + 96*(a^7*b^2 - 3*a^5*b^4)*log(abs(b*tan(d*x + c) + a))/(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) - 48*(2*a^7*b^2*tan(d*x + c) - 6*a^5*b^4*tan(d*x + c) + 3*a^8*b - 5*a^6*b^3)/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*(b*tan(d*x + c) + a)) + (88*a^7*b*tan(d*x + c)^6 - 264*a^5*b^3*tan(d*x + c)^6 - 33*a^8*tan(d*x + c)^5 + 96*a^6*b^2*tan(d*x + c)^5 + 150*a^4*b^4*tan(d*x + c)^5 + 24*a^2*b^6*tan(d*x + c)^5 + 3*b^8*tan(d*x + c)^5 + 120*a^7*b*tan(d*x + c)^4 - 936*a^5*b^3*tan(d*x + c)^4 - 40*a^8*tan(d*x + c)^3 + 208*a^6*b^2*tan(d*x + c)^3 + 240*a^4*b^4*tan(d*x + c)^3 - 16*a^2*b^6*tan(d*x + c)^3 - 8*b^8*tan(d*x + c)^3 + 48*a^7*b*tan(d*x + c)^2 - 912*a^5*b^3*tan(d*x + c)^2 + 120*a^3*b^5*tan(d*x + c)^2 + 24*a*b^7*tan(d*x + c)^2 - 15*a^8*tan(d*x + c) + 96*a^6*b^2*tan(d*x + c) + 90*a^4*b^4*tan(d*x + c) - 24*a^2*b^6*tan(d*x + c) - 3*b^8*tan(d*x + c) - 288*a^5*b^3 + 72*a^3*b^5 + 8*a*b^7)/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*(tan(d*x + c)^2 + 1)^3))/d","B",0
62,1,513,0,1.453311," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(3 \, a^{6} - 33 \, a^{4} b^{2} + 13 \, a^{2} b^{4} + b^{6}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{8 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{16 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}} - \frac{8 \, {\left(2 \, a^{5} b^{2} \tan\left(d x + c\right) - 4 \, a^{3} b^{4} \tan\left(d x + c\right) + 3 \, a^{6} b - 3 \, a^{4} b^{3}\right)}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}} + \frac{12 \, a^{5} b \tan\left(d x + c\right)^{4} - 24 \, a^{3} b^{3} \tan\left(d x + c\right)^{4} - 5 \, a^{6} \tan\left(d x + c\right)^{3} + 7 \, a^{4} b^{2} \tan\left(d x + c\right)^{3} + 13 \, a^{2} b^{4} \tan\left(d x + c\right)^{3} + b^{6} \tan\left(d x + c\right)^{3} + 8 \, a^{5} b \tan\left(d x + c\right)^{2} - 64 \, a^{3} b^{3} \tan\left(d x + c\right)^{2} - 3 \, a^{6} \tan\left(d x + c\right) + 9 \, a^{4} b^{2} \tan\left(d x + c\right) + 11 \, a^{2} b^{4} \tan\left(d x + c\right) - b^{6} \tan\left(d x + c\right) - 32 \, a^{3} b^{3} + 4 \, a b^{5}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*((3*a^6 - 33*a^4*b^2 + 13*a^2*b^4 + b^6)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 8*(a^5*b - 2*a^3*b^3)*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 16*(a^5*b^2 - 2*a^3*b^4)*log(abs(b*tan(d*x + c) + a))/(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9) - 8*(2*a^5*b^2*tan(d*x + c) - 4*a^3*b^4*tan(d*x + c) + 3*a^6*b - 3*a^4*b^3)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(b*tan(d*x + c) + a)) + (12*a^5*b*tan(d*x + c)^4 - 24*a^3*b^3*tan(d*x + c)^4 - 5*a^6*tan(d*x + c)^3 + 7*a^4*b^2*tan(d*x + c)^3 + 13*a^2*b^4*tan(d*x + c)^3 + b^6*tan(d*x + c)^3 + 8*a^5*b*tan(d*x + c)^2 - 64*a^3*b^3*tan(d*x + c)^2 - 3*a^6*tan(d*x + c) + 9*a^4*b^2*tan(d*x + c) + 11*a^2*b^4*tan(d*x + c) - b^6*tan(d*x + c) - 32*a^3*b^3 + 4*a*b^5)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(tan(d*x + c)^2 + 1)^2))/d","B",0
63,1,263,0,0.886114," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{4 \, {\left(a^{3} b^{2} - a b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{3 \, a^{2} b \tan\left(d x + c\right)^{2} - b^{3} \tan\left(d x + c\right)^{2} + a^{3} \tan\left(d x + c\right) + a b^{2} \tan\left(d x + c\right) + 4 \, a^{2} b}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(d x + c\right)^{3} + a \tan\left(d x + c\right)^{2} + b \tan\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"1/2*((a^4 - 6*a^2*b^2 + b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(a^3*b - a*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 4*(a^3*b^2 - a*b^4)*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - (3*a^2*b*tan(d*x + c)^2 - b^3*tan(d*x + c)^2 + a^3*tan(d*x + c) + a*b^2*tan(d*x + c) + 4*a^2*b)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(d*x + c)^3 + a*tan(d*x + c)^2 + b*tan(d*x + c) + a)))/d","A",0
64,1,74,0,0.891600," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, b \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{3}} - \frac{2 \, b \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{2 \, b \tan\left(d x + c\right) + a}{{\left(b \tan\left(d x + c\right)^{2} + a \tan\left(d x + c\right)\right)} a^{2}}}{d}"," ",0,"(2*b*log(abs(b*tan(d*x + c) + a))/a^3 - 2*b*log(abs(tan(d*x + c)))/a^3 - (2*b*tan(d*x + c) + a)/((b*tan(d*x + c)^2 + a*tan(d*x + c))*a^2))/d","A",0
65,1,203,0,0.796193," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(a^{2} b + 2 \, b^{3}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{5}} - \frac{6 \, {\left(a^{2} b^{2} + 2 \, b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{5} b} + \frac{3 \, {\left(2 \, a^{2} b^{2} \tan\left(d x + c\right) + 4 \, b^{4} \tan\left(d x + c\right) + 3 \, a^{3} b + 5 \, a b^{3}\right)}}{{\left(b \tan\left(d x + c\right) + a\right)} a^{5}} - \frac{11 \, a^{2} b \tan\left(d x + c\right)^{3} + 22 \, b^{3} \tan\left(d x + c\right)^{3} - 3 \, a^{3} \tan\left(d x + c\right)^{2} - 9 \, a b^{2} \tan\left(d x + c\right)^{2} + 3 \, a^{2} b \tan\left(d x + c\right) - a^{3}}{a^{5} \tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"-1/3*(6*(a^2*b + 2*b^3)*log(abs(tan(d*x + c)))/a^5 - 6*(a^2*b^2 + 2*b^4)*log(abs(b*tan(d*x + c) + a))/(a^5*b) + 3*(2*a^2*b^2*tan(d*x + c) + 4*b^4*tan(d*x + c) + 3*a^3*b + 5*a*b^3)/((b*tan(d*x + c) + a)*a^5) - (11*a^2*b*tan(d*x + c)^3 + 22*b^3*tan(d*x + c)^3 - 3*a^3*tan(d*x + c)^2 - 9*a*b^2*tan(d*x + c)^2 + 3*a^2*b*tan(d*x + c) - a^3)/(a^5*tan(d*x + c)^3))/d","A",0
66,1,332,0,1.008838," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(a^{4} b + 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{7}} - \frac{60 \, {\left(a^{4} b^{2} + 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{7} b} + \frac{30 \, {\left(2 \, a^{4} b^{2} \tan\left(d x + c\right) + 8 \, a^{2} b^{4} \tan\left(d x + c\right) + 6 \, b^{6} \tan\left(d x + c\right) + 3 \, a^{5} b + 10 \, a^{3} b^{3} + 7 \, a b^{5}\right)}}{{\left(b \tan\left(d x + c\right) + a\right)} a^{7}} - \frac{137 \, a^{4} b \tan\left(d x + c\right)^{5} + 548 \, a^{2} b^{3} \tan\left(d x + c\right)^{5} + 411 \, b^{5} \tan\left(d x + c\right)^{5} - 30 \, a^{5} \tan\left(d x + c\right)^{4} - 180 \, a^{3} b^{2} \tan\left(d x + c\right)^{4} - 150 \, a b^{4} \tan\left(d x + c\right)^{4} + 60 \, a^{4} b \tan\left(d x + c\right)^{3} + 60 \, a^{2} b^{3} \tan\left(d x + c\right)^{3} - 20 \, a^{5} \tan\left(d x + c\right)^{2} - 30 \, a^{3} b^{2} \tan\left(d x + c\right)^{2} + 15 \, a^{4} b \tan\left(d x + c\right) - 6 \, a^{5}}{a^{7} \tan\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"-1/30*(60*(a^4*b + 4*a^2*b^3 + 3*b^5)*log(abs(tan(d*x + c)))/a^7 - 60*(a^4*b^2 + 4*a^2*b^4 + 3*b^6)*log(abs(b*tan(d*x + c) + a))/(a^7*b) + 30*(2*a^4*b^2*tan(d*x + c) + 8*a^2*b^4*tan(d*x + c) + 6*b^6*tan(d*x + c) + 3*a^5*b + 10*a^3*b^3 + 7*a*b^5)/((b*tan(d*x + c) + a)*a^7) - (137*a^4*b*tan(d*x + c)^5 + 548*a^2*b^3*tan(d*x + c)^5 + 411*b^5*tan(d*x + c)^5 - 30*a^5*tan(d*x + c)^4 - 180*a^3*b^2*tan(d*x + c)^4 - 150*a*b^4*tan(d*x + c)^4 + 60*a^4*b*tan(d*x + c)^3 + 60*a^2*b^3*tan(d*x + c)^3 - 20*a^5*tan(d*x + c)^2 - 30*a^3*b^2*tan(d*x + c)^2 + 15*a^4*b*tan(d*x + c) - 6*a^5)/(a^7*tan(d*x + c)^5))/d","A",0
67,1,923,0,6.864072," ","integrate(sin(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(5 \, a^{9} - 180 \, a^{7} b^{2} + 390 \, a^{5} b^{4} - 68 \, a^{3} b^{6} - 3 \, a b^{8}\right)} {\left(d x + c\right)}}{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}} - \frac{24 \, {\left(3 \, a^{8} b - 22 \, a^{6} b^{3} + 15 \, a^{4} b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}} + \frac{48 \, {\left(3 \, a^{8} b^{2} - 22 \, a^{6} b^{4} + 15 \, a^{4} b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{12} b + 6 \, a^{10} b^{3} + 15 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 15 \, a^{4} b^{9} + 6 \, a^{2} b^{11} + b^{13}} - \frac{24 \, {\left(9 \, a^{8} b^{3} \tan\left(d x + c\right)^{2} - 66 \, a^{6} b^{5} \tan\left(d x + c\right)^{2} + 45 \, a^{4} b^{7} \tan\left(d x + c\right)^{2} + 22 \, a^{9} b^{2} \tan\left(d x + c\right) - 140 \, a^{7} b^{4} \tan\left(d x + c\right) + 78 \, a^{5} b^{6} \tan\left(d x + c\right) + 14 \, a^{10} b - 72 \, a^{8} b^{3} + 34 \, a^{6} b^{5}\right)}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}} + \frac{132 \, a^{8} b \tan\left(d x + c\right)^{6} - 968 \, a^{6} b^{3} \tan\left(d x + c\right)^{6} + 660 \, a^{4} b^{5} \tan\left(d x + c\right)^{6} - 33 \, a^{9} \tan\left(d x + c\right)^{5} + 324 \, a^{7} b^{2} \tan\left(d x + c\right)^{5} + 162 \, a^{5} b^{4} \tan\left(d x + c\right)^{5} - 204 \, a^{3} b^{6} \tan\left(d x + c\right)^{5} - 9 \, a b^{8} \tan\left(d x + c\right)^{5} + 180 \, a^{8} b \tan\left(d x + c\right)^{4} - 2760 \, a^{6} b^{3} \tan\left(d x + c\right)^{4} + 2340 \, a^{4} b^{5} \tan\left(d x + c\right)^{4} - 40 \, a^{9} \tan\left(d x + c\right)^{3} + 576 \, a^{7} b^{2} \tan\left(d x + c\right)^{3} + 96 \, a^{5} b^{4} \tan\left(d x + c\right)^{3} - 544 \, a^{3} b^{6} \tan\left(d x + c\right)^{3} - 24 \, a b^{8} \tan\left(d x + c\right)^{3} + 72 \, a^{8} b \tan\left(d x + c\right)^{2} - 2448 \, a^{6} b^{3} \tan\left(d x + c\right)^{2} + 2700 \, a^{4} b^{5} \tan\left(d x + c\right)^{2} - 72 \, a^{2} b^{7} \tan\left(d x + c\right)^{2} - 12 \, b^{9} \tan\left(d x + c\right)^{2} - 15 \, a^{9} \tan\left(d x + c\right) + 252 \, a^{7} b^{2} \tan\left(d x + c\right) - 18 \, a^{5} b^{4} \tan\left(d x + c\right) - 276 \, a^{3} b^{6} \tan\left(d x + c\right) + 9 \, a b^{8} \tan\left(d x + c\right) - 720 \, a^{6} b^{3} + 972 \, a^{4} b^{5} - 72 \, a^{2} b^{7} - 4 \, b^{9}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}^{3}}}{48 \, d}"," ",0,"1/48*(3*(5*a^9 - 180*a^7*b^2 + 390*a^5*b^4 - 68*a^3*b^6 - 3*a*b^8)*(d*x + c)/(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12) - 24*(3*a^8*b - 22*a^6*b^3 + 15*a^4*b^5)*log(tan(d*x + c)^2 + 1)/(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12) + 48*(3*a^8*b^2 - 22*a^6*b^4 + 15*a^4*b^6)*log(abs(b*tan(d*x + c) + a))/(a^12*b + 6*a^10*b^3 + 15*a^8*b^5 + 20*a^6*b^7 + 15*a^4*b^9 + 6*a^2*b^11 + b^13) - 24*(9*a^8*b^3*tan(d*x + c)^2 - 66*a^6*b^5*tan(d*x + c)^2 + 45*a^4*b^7*tan(d*x + c)^2 + 22*a^9*b^2*tan(d*x + c) - 140*a^7*b^4*tan(d*x + c) + 78*a^5*b^6*tan(d*x + c) + 14*a^10*b - 72*a^8*b^3 + 34*a^6*b^5)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*(b*tan(d*x + c) + a)^2) + (132*a^8*b*tan(d*x + c)^6 - 968*a^6*b^3*tan(d*x + c)^6 + 660*a^4*b^5*tan(d*x + c)^6 - 33*a^9*tan(d*x + c)^5 + 324*a^7*b^2*tan(d*x + c)^5 + 162*a^5*b^4*tan(d*x + c)^5 - 204*a^3*b^6*tan(d*x + c)^5 - 9*a*b^8*tan(d*x + c)^5 + 180*a^8*b*tan(d*x + c)^4 - 2760*a^6*b^3*tan(d*x + c)^4 + 2340*a^4*b^5*tan(d*x + c)^4 - 40*a^9*tan(d*x + c)^3 + 576*a^7*b^2*tan(d*x + c)^3 + 96*a^5*b^4*tan(d*x + c)^3 - 544*a^3*b^6*tan(d*x + c)^3 - 24*a*b^8*tan(d*x + c)^3 + 72*a^8*b*tan(d*x + c)^2 - 2448*a^6*b^3*tan(d*x + c)^2 + 2700*a^4*b^5*tan(d*x + c)^2 - 72*a^2*b^7*tan(d*x + c)^2 - 12*b^9*tan(d*x + c)^2 - 15*a^9*tan(d*x + c) + 252*a^7*b^2*tan(d*x + c) - 18*a^5*b^4*tan(d*x + c) - 276*a^3*b^6*tan(d*x + c) + 9*a*b^8*tan(d*x + c) - 720*a^6*b^3 + 972*a^4*b^5 - 72*a^2*b^7 - 4*b^9)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*(tan(d*x + c)^2 + 1)^3))/d","B",0
68,1,588,0,3.868985," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a^{7} - 25 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 3 \, a b^{6}\right)} {\left(d x + c\right)}}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{12 \, {\left(a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} + \frac{24 \, {\left(a^{6} b^{2} - 5 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{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}} - \frac{21 \, a^{5} b^{2} \tan\left(d x + c\right)^{5} - 66 \, a^{3} b^{4} \tan\left(d x + c\right)^{5} + 9 \, a b^{6} \tan\left(d x + c\right)^{5} + 30 \, a^{6} b \tan\left(d x + c\right)^{4} - 72 \, a^{4} b^{3} \tan\left(d x + c\right)^{4} - 6 \, a^{2} b^{5} \tan\left(d x + c\right)^{4} + 5 \, a^{7} \tan\left(d x + c\right)^{3} + 49 \, a^{5} b^{2} \tan\left(d x + c\right)^{3} - 133 \, a^{3} b^{4} \tan\left(d x + c\right)^{3} + 15 \, a b^{6} \tan\left(d x + c\right)^{3} + 70 \, a^{6} b \tan\left(d x + c\right)^{2} - 122 \, a^{4} b^{3} \tan\left(d x + c\right)^{2} + 2 \, a^{2} b^{5} \tan\left(d x + c\right)^{2} + 2 \, b^{7} \tan\left(d x + c\right)^{2} + 3 \, a^{7} \tan\left(d x + c\right) + 22 \, a^{5} b^{2} \tan\left(d x + c\right) - 73 \, a^{3} b^{4} \tan\left(d x + c\right) + 4 \, a b^{6} \tan\left(d x + c\right) + 38 \, a^{6} b - 56 \, a^{4} b^{3} + 2 \, a^{2} b^{5}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right)^{3} + a \tan\left(d x + c\right)^{2} + b \tan\left(d x + c\right) + a\right)}^{2}}}{8 \, d}"," ",0,"1/8*(3*(a^7 - 25*a^5*b^2 + 35*a^3*b^4 - 3*a*b^6)*(d*x + c)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - 12*(a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*log(tan(d*x + c)^2 + 1)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) + 24*(a^6*b^2 - 5*a^4*b^4 + 2*a^2*b^6)*log(abs(b*tan(d*x + c) + a))/(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) - (21*a^5*b^2*tan(d*x + c)^5 - 66*a^3*b^4*tan(d*x + c)^5 + 9*a*b^6*tan(d*x + c)^5 + 30*a^6*b*tan(d*x + c)^4 - 72*a^4*b^3*tan(d*x + c)^4 - 6*a^2*b^5*tan(d*x + c)^4 + 5*a^7*tan(d*x + c)^3 + 49*a^5*b^2*tan(d*x + c)^3 - 133*a^3*b^4*tan(d*x + c)^3 + 15*a*b^6*tan(d*x + c)^3 + 70*a^6*b*tan(d*x + c)^2 - 122*a^4*b^3*tan(d*x + c)^2 + 2*a^2*b^5*tan(d*x + c)^2 + 2*b^7*tan(d*x + c)^2 + 3*a^7*tan(d*x + c) + 22*a^5*b^2*tan(d*x + c) - 73*a^3*b^4*tan(d*x + c) + 4*a*b^6*tan(d*x + c) + 38*a^6*b - 56*a^4*b^3 + 2*a^2*b^5)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(b*tan(d*x + c)^3 + a*tan(d*x + c)^2 + b*tan(d*x + c) + a)^2))/d","B",0
69,1,482,0,1.225574," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(a^{5} - 14 \, a^{3} b^{2} + 9 \, a b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{{\left(3 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{2 \, {\left(3 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}} + \frac{3 \, a^{4} b \tan\left(d x + c\right)^{2} - 8 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} + b^{5} \tan\left(d x + c\right)^{2} - a^{5} \tan\left(d x + c\right) + 2 \, a^{3} b^{2} \tan\left(d x + c\right) + 3 \, a b^{4} \tan\left(d x + c\right) - 10 \, a^{2} b^{3} + 2 \, b^{5}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}} - \frac{9 \, a^{4} b^{3} \tan\left(d x + c\right)^{2} - 24 \, a^{2} b^{5} \tan\left(d x + c\right)^{2} + 3 \, b^{7} \tan\left(d x + c\right)^{2} + 22 \, a^{5} b^{2} \tan\left(d x + c\right) - 48 \, a^{3} b^{4} \tan\left(d x + c\right) + 2 \, a b^{6} \tan\left(d x + c\right) + 14 \, a^{6} b - 22 \, a^{4} b^{3}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*((a^5 - 14*a^3*b^2 + 9*a*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - (3*a^4*b - 8*a^2*b^3 + b^5)*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 2*(3*a^4*b^2 - 8*a^2*b^4 + b^6)*log(abs(b*tan(d*x + c) + a))/(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9) + (3*a^4*b*tan(d*x + c)^2 - 8*a^2*b^3*tan(d*x + c)^2 + b^5*tan(d*x + c)^2 - a^5*tan(d*x + c) + 2*a^3*b^2*tan(d*x + c) + 3*a*b^4*tan(d*x + c) - 10*a^2*b^3 + 2*b^5)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(tan(d*x + c)^2 + 1)) - (9*a^4*b^3*tan(d*x + c)^2 - 24*a^2*b^5*tan(d*x + c)^2 + 3*b^7*tan(d*x + c)^2 + 22*a^5*b^2*tan(d*x + c) - 48*a^3*b^4*tan(d*x + c) + 2*a*b^6*tan(d*x + c) + 14*a^6*b - 22*a^4*b^3)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(b*tan(d*x + c) + a)^2))/d","B",0
70,1,113,0,1.041487," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, b \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4}} - \frac{6 \, b \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{4}} + \frac{2 \, {\left(3 \, b \tan\left(d x + c\right) - a\right)}}{a^{4} \tan\left(d x + c\right)} - \frac{9 \, b^{3} \tan\left(d x + c\right)^{2} + 22 \, a b^{2} \tan\left(d x + c\right) + 14 \, a^{2} b}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} a^{4}}}{2 \, d}"," ",0,"1/2*(6*b*log(abs(b*tan(d*x + c) + a))/a^4 - 6*b*log(abs(tan(d*x + c)))/a^4 + 2*(3*b*tan(d*x + c) - a)/(a^4*tan(d*x + c)) - (9*b^3*tan(d*x + c)^2 + 22*a*b^2*tan(d*x + c) + 14*a^2*b)/((b*tan(d*x + c) + a)^2*a^4))/d","A",0
71,1,237,0,2.066135," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(3 \, a^{2} b + 10 \, b^{3}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{6}} - \frac{6 \, {\left(3 \, a^{2} b^{2} + 10 \, b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b} + \frac{3 \, {\left(9 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} + 30 \, b^{5} \tan\left(d x + c\right)^{2} + 22 \, a^{3} b^{2} \tan\left(d x + c\right) + 68 \, a b^{4} \tan\left(d x + c\right) + 14 \, a^{4} b + 39 \, a^{2} b^{3}\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} a^{6}} - \frac{33 \, a^{2} b \tan\left(d x + c\right)^{3} + 110 \, b^{3} \tan\left(d x + c\right)^{3} - 6 \, a^{3} \tan\left(d x + c\right)^{2} - 36 \, a b^{2} \tan\left(d x + c\right)^{2} + 9 \, a^{2} b \tan\left(d x + c\right) - 2 \, a^{3}}{a^{6} \tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(6*(3*a^2*b + 10*b^3)*log(abs(tan(d*x + c)))/a^6 - 6*(3*a^2*b^2 + 10*b^4)*log(abs(b*tan(d*x + c) + a))/(a^6*b) + 3*(9*a^2*b^3*tan(d*x + c)^2 + 30*b^5*tan(d*x + c)^2 + 22*a^3*b^2*tan(d*x + c) + 68*a*b^4*tan(d*x + c) + 14*a^4*b + 39*a^2*b^3)/((b*tan(d*x + c) + a)^2*a^6) - (33*a^2*b*tan(d*x + c)^3 + 110*b^3*tan(d*x + c)^3 - 6*a^3*tan(d*x + c)^2 - 36*a*b^2*tan(d*x + c)^2 + 9*a^2*b*tan(d*x + c) - 2*a^3)/(a^6*tan(d*x + c)^3))/d","A",0
72,1,382,0,1.356195," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(3 \, a^{4} b + 20 \, a^{2} b^{3} + 21 \, b^{5}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{8}} - \frac{60 \, {\left(3 \, a^{4} b^{2} + 20 \, a^{2} b^{4} + 21 \, b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{8} b} + \frac{30 \, {\left(9 \, a^{4} b^{3} \tan\left(d x + c\right)^{2} + 60 \, a^{2} b^{5} \tan\left(d x + c\right)^{2} + 63 \, b^{7} \tan\left(d x + c\right)^{2} + 22 \, a^{5} b^{2} \tan\left(d x + c\right) + 136 \, a^{3} b^{4} \tan\left(d x + c\right) + 138 \, a b^{6} \tan\left(d x + c\right) + 14 \, a^{6} b + 78 \, a^{4} b^{3} + 76 \, a^{2} b^{5}\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} a^{8}} - \frac{411 \, a^{4} b \tan\left(d x + c\right)^{5} + 2740 \, a^{2} b^{3} \tan\left(d x + c\right)^{5} + 2877 \, b^{5} \tan\left(d x + c\right)^{5} - 60 \, a^{5} \tan\left(d x + c\right)^{4} - 720 \, a^{3} b^{2} \tan\left(d x + c\right)^{4} - 900 \, a b^{4} \tan\left(d x + c\right)^{4} + 180 \, a^{4} b \tan\left(d x + c\right)^{3} + 300 \, a^{2} b^{3} \tan\left(d x + c\right)^{3} - 40 \, a^{5} \tan\left(d x + c\right)^{2} - 120 \, a^{3} b^{2} \tan\left(d x + c\right)^{2} + 45 \, a^{4} b \tan\left(d x + c\right) - 12 \, a^{5}}{a^{8} \tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*(3*a^4*b + 20*a^2*b^3 + 21*b^5)*log(abs(tan(d*x + c)))/a^8 - 60*(3*a^4*b^2 + 20*a^2*b^4 + 21*b^6)*log(abs(b*tan(d*x + c) + a))/(a^8*b) + 30*(9*a^4*b^3*tan(d*x + c)^2 + 60*a^2*b^5*tan(d*x + c)^2 + 63*b^7*tan(d*x + c)^2 + 22*a^5*b^2*tan(d*x + c) + 136*a^3*b^4*tan(d*x + c) + 138*a*b^6*tan(d*x + c) + 14*a^6*b + 78*a^4*b^3 + 76*a^2*b^5)/((b*tan(d*x + c) + a)^2*a^8) - (411*a^4*b*tan(d*x + c)^5 + 2740*a^2*b^3*tan(d*x + c)^5 + 2877*b^5*tan(d*x + c)^5 - 60*a^5*tan(d*x + c)^4 - 720*a^3*b^2*tan(d*x + c)^4 - 900*a*b^4*tan(d*x + c)^4 + 180*a^4*b*tan(d*x + c)^3 + 300*a^2*b^3*tan(d*x + c)^3 - 40*a^5*tan(d*x + c)^2 - 120*a^3*b^2*tan(d*x + c)^2 + 45*a^4*b*tan(d*x + c) - 12*a^5)/(a^8*tan(d*x + c)^5))/d","A",0
73,1,902,0,6.915658," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, a^{8} - 132 \, a^{6} b^{2} + 370 \, a^{4} b^{4} - 132 \, a^{2} b^{6} + 3 \, b^{8}\right)} {\left(d x + c\right)}}{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}} - \frac{48 \, {\left(a^{7} b - 9 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - a b^{7}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}} + \frac{96 \, {\left(a^{7} b^{2} - 9 \, a^{5} b^{4} + 9 \, a^{3} b^{6} - a b^{8}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{12} b + 6 \, a^{10} b^{3} + 15 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 15 \, a^{4} b^{9} + 6 \, a^{2} b^{11} + b^{13}} + \frac{3 \, {\left(24 \, a^{7} b \tan\left(d x + c\right)^{4} - 216 \, a^{5} b^{3} \tan\left(d x + c\right)^{4} + 216 \, a^{3} b^{5} \tan\left(d x + c\right)^{4} - 24 \, a b^{7} \tan\left(d x + c\right)^{4} - 5 \, a^{8} \tan\left(d x + c\right)^{3} + 60 \, a^{6} b^{2} \tan\left(d x + c\right)^{3} + 10 \, a^{4} b^{4} \tan\left(d x + c\right)^{3} - 52 \, a^{2} b^{6} \tan\left(d x + c\right)^{3} + 3 \, b^{8} \tan\left(d x + c\right)^{3} + 16 \, a^{7} b \tan\left(d x + c\right)^{2} - 384 \, a^{5} b^{3} \tan\left(d x + c\right)^{2} + 496 \, a^{3} b^{5} \tan\left(d x + c\right)^{2} - 64 \, a b^{7} \tan\left(d x + c\right)^{2} - 3 \, a^{8} \tan\left(d x + c\right) + 52 \, a^{6} b^{2} \tan\left(d x + c\right) - 10 \, a^{4} b^{4} \tan\left(d x + c\right) - 60 \, a^{2} b^{6} \tan\left(d x + c\right) + 5 \, b^{8} \tan\left(d x + c\right) - 160 \, a^{5} b^{3} + 272 \, a^{3} b^{5} - 48 \, a b^{7}\right)}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}^{2}} - \frac{8 \, {\left(22 \, a^{7} b^{4} \tan\left(d x + c\right)^{3} - 198 \, a^{5} b^{6} \tan\left(d x + c\right)^{3} + 198 \, a^{3} b^{8} \tan\left(d x + c\right)^{3} - 22 \, a b^{10} \tan\left(d x + c\right)^{3} + 75 \, a^{8} b^{3} \tan\left(d x + c\right)^{2} - 630 \, a^{6} b^{5} \tan\left(d x + c\right)^{2} + 567 \, a^{4} b^{7} \tan\left(d x + c\right)^{2} - 48 \, a^{2} b^{9} \tan\left(d x + c\right)^{2} + 87 \, a^{9} b^{2} \tan\left(d x + c\right) - 666 \, a^{7} b^{4} \tan\left(d x + c\right) + 531 \, a^{5} b^{6} \tan\left(d x + c\right) - 36 \, a^{3} b^{8} \tan\left(d x + c\right) + 35 \, a^{10} b - 231 \, a^{8} b^{3} + 165 \, a^{6} b^{5} - 9 \, a^{4} b^{7}\right)}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3}}}{24 \, d}"," ",0,"1/24*(3*(3*a^8 - 132*a^6*b^2 + 370*a^4*b^4 - 132*a^2*b^6 + 3*b^8)*(d*x + c)/(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12) - 48*(a^7*b - 9*a^5*b^3 + 9*a^3*b^5 - a*b^7)*log(tan(d*x + c)^2 + 1)/(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12) + 96*(a^7*b^2 - 9*a^5*b^4 + 9*a^3*b^6 - a*b^8)*log(abs(b*tan(d*x + c) + a))/(a^12*b + 6*a^10*b^3 + 15*a^8*b^5 + 20*a^6*b^7 + 15*a^4*b^9 + 6*a^2*b^11 + b^13) + 3*(24*a^7*b*tan(d*x + c)^4 - 216*a^5*b^3*tan(d*x + c)^4 + 216*a^3*b^5*tan(d*x + c)^4 - 24*a*b^7*tan(d*x + c)^4 - 5*a^8*tan(d*x + c)^3 + 60*a^6*b^2*tan(d*x + c)^3 + 10*a^4*b^4*tan(d*x + c)^3 - 52*a^2*b^6*tan(d*x + c)^3 + 3*b^8*tan(d*x + c)^3 + 16*a^7*b*tan(d*x + c)^2 - 384*a^5*b^3*tan(d*x + c)^2 + 496*a^3*b^5*tan(d*x + c)^2 - 64*a*b^7*tan(d*x + c)^2 - 3*a^8*tan(d*x + c) + 52*a^6*b^2*tan(d*x + c) - 10*a^4*b^4*tan(d*x + c) - 60*a^2*b^6*tan(d*x + c) + 5*b^8*tan(d*x + c) - 160*a^5*b^3 + 272*a^3*b^5 - 48*a*b^7)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*(tan(d*x + c)^2 + 1)^2) - 8*(22*a^7*b^4*tan(d*x + c)^3 - 198*a^5*b^6*tan(d*x + c)^3 + 198*a^3*b^8*tan(d*x + c)^3 - 22*a*b^10*tan(d*x + c)^3 + 75*a^8*b^3*tan(d*x + c)^2 - 630*a^6*b^5*tan(d*x + c)^2 + 567*a^4*b^7*tan(d*x + c)^2 - 48*a^2*b^9*tan(d*x + c)^2 + 87*a^9*b^2*tan(d*x + c) - 666*a^7*b^4*tan(d*x + c) + 531*a^5*b^6*tan(d*x + c) - 36*a^3*b^8*tan(d*x + c) + 35*a^10*b - 231*a^8*b^3 + 165*a^6*b^5 - 9*a^4*b^7)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*(b*tan(d*x + c) + a)^3))/d","B",0
74,1,642,0,3.891224," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a^{6} - 25 \, a^{4} b^{2} + 35 \, a^{2} b^{4} - 3 \, b^{6}\right)} {\left(d x + c\right)}}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{12 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} + \frac{24 \, {\left(a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{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}} + \frac{3 \, {\left(4 \, a^{5} b \tan\left(d x + c\right)^{2} - 20 \, a^{3} b^{3} \tan\left(d x + c\right)^{2} + 8 \, a b^{5} \tan\left(d x + c\right)^{2} - a^{6} \tan\left(d x + c\right) + 5 \, a^{4} b^{2} \tan\left(d x + c\right) + 5 \, a^{2} b^{4} \tan\left(d x + c\right) - b^{6} \tan\left(d x + c\right) - 20 \, a^{3} b^{3} + 12 \, a b^{5}\right)}}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}} - \frac{2 \, {\left(22 \, a^{5} b^{4} \tan\left(d x + c\right)^{3} - 110 \, a^{3} b^{6} \tan\left(d x + c\right)^{3} + 44 \, a b^{8} \tan\left(d x + c\right)^{3} + 75 \, a^{6} b^{3} \tan\left(d x + c\right)^{2} - 345 \, a^{4} b^{5} \tan\left(d x + c\right)^{2} + 111 \, a^{2} b^{7} \tan\left(d x + c\right)^{2} + 3 \, b^{9} \tan\left(d x + c\right)^{2} + 87 \, a^{7} b^{2} \tan\left(d x + c\right) - 357 \, a^{5} b^{4} \tan\left(d x + c\right) + 87 \, a^{3} b^{6} \tan\left(d x + c\right) + 3 \, a b^{8} \tan\left(d x + c\right) + 35 \, a^{8} b - 119 \, a^{6} b^{3} + 23 \, a^{4} b^{5} + a^{2} b^{7}\right)}}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(a^6 - 25*a^4*b^2 + 35*a^2*b^4 - 3*b^6)*(d*x + c)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - 12*(a^5*b - 5*a^3*b^3 + 2*a*b^5)*log(tan(d*x + c)^2 + 1)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) + 24*(a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*log(abs(b*tan(d*x + c) + a))/(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) + 3*(4*a^5*b*tan(d*x + c)^2 - 20*a^3*b^3*tan(d*x + c)^2 + 8*a*b^5*tan(d*x + c)^2 - a^6*tan(d*x + c) + 5*a^4*b^2*tan(d*x + c) + 5*a^2*b^4*tan(d*x + c) - b^6*tan(d*x + c) - 20*a^3*b^3 + 12*a*b^5)/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*(tan(d*x + c)^2 + 1)) - 2*(22*a^5*b^4*tan(d*x + c)^3 - 110*a^3*b^6*tan(d*x + c)^3 + 44*a*b^8*tan(d*x + c)^3 + 75*a^6*b^3*tan(d*x + c)^2 - 345*a^4*b^5*tan(d*x + c)^2 + 111*a^2*b^7*tan(d*x + c)^2 + 3*b^9*tan(d*x + c)^2 + 87*a^7*b^2*tan(d*x + c) - 357*a^5*b^4*tan(d*x + c) + 87*a^3*b^6*tan(d*x + c) + 3*a*b^8*tan(d*x + c) + 35*a^8*b - 119*a^6*b^3 + 23*a^4*b^5 + a^2*b^7)/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*(b*tan(d*x + c) + a)^3))/d","B",0
75,1,129,0,2.574667," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{12 \, b \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{5}} - \frac{12 \, b \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{5}} + \frac{3 \, {\left(4 \, b \tan\left(d x + c\right) - a\right)}}{a^{5} \tan\left(d x + c\right)} - \frac{22 \, b^{4} \tan\left(d x + c\right)^{3} + 75 \, a b^{3} \tan\left(d x + c\right)^{2} + 87 \, a^{2} b^{2} \tan\left(d x + c\right) + 35 \, a^{3} b}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} a^{5}}}{3 \, d}"," ",0,"1/3*(12*b*log(abs(b*tan(d*x + c) + a))/a^5 - 12*b*log(abs(tan(d*x + c)))/a^5 + 3*(4*b*tan(d*x + c) - a)/(a^5*tan(d*x + c)) - (22*b^4*tan(d*x + c)^3 + 75*a*b^3*tan(d*x + c)^2 + 87*a^2*b^2*tan(d*x + c) + 35*a^3*b)/((b*tan(d*x + c) + a)^3*a^5))/d","A",0
76,1,222,0,5.001288," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(a^{2} b + 5 \, b^{3}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{7}} - \frac{12 \, {\left(a^{2} b^{2} + 5 \, b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{7} b} + \frac{12 \, a^{2} b^{3} \tan\left(d x + c\right)^{5} + 60 \, b^{5} \tan\left(d x + c\right)^{5} + 30 \, a^{3} b^{2} \tan\left(d x + c\right)^{4} + 150 \, a b^{4} \tan\left(d x + c\right)^{4} + 22 \, a^{4} b \tan\left(d x + c\right)^{3} + 110 \, a^{2} b^{3} \tan\left(d x + c\right)^{3} + 3 \, a^{5} \tan\left(d x + c\right)^{2} + 15 \, a^{3} b^{2} \tan\left(d x + c\right)^{2} - 3 \, a^{4} b \tan\left(d x + c\right) + a^{5}}{{\left(b \tan\left(d x + c\right)^{2} + a \tan\left(d x + c\right)\right)}^{3} a^{6}}}{3 \, d}"," ",0,"-1/3*(12*(a^2*b + 5*b^3)*log(abs(tan(d*x + c)))/a^7 - 12*(a^2*b^2 + 5*b^4)*log(abs(b*tan(d*x + c) + a))/(a^7*b) + (12*a^2*b^3*tan(d*x + c)^5 + 60*b^5*tan(d*x + c)^5 + 30*a^3*b^2*tan(d*x + c)^4 + 150*a*b^4*tan(d*x + c)^4 + 22*a^4*b*tan(d*x + c)^3 + 110*a^2*b^3*tan(d*x + c)^3 + 3*a^5*tan(d*x + c)^2 + 15*a^3*b^2*tan(d*x + c)^2 - 3*a^4*b*tan(d*x + c) + a^5)/((b*tan(d*x + c)^2 + a*tan(d*x + c))^3*a^6))/d","A",0
77,1,428,0,1.946760," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(a^{4} b + 10 \, a^{2} b^{3} + 14 \, b^{5}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{9}} - \frac{60 \, {\left(a^{4} b^{2} + 10 \, a^{2} b^{4} + 14 \, b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{9} b} + \frac{5 \, {\left(22 \, a^{4} b^{4} \tan\left(d x + c\right)^{3} + 220 \, a^{2} b^{6} \tan\left(d x + c\right)^{3} + 308 \, b^{8} \tan\left(d x + c\right)^{3} + 75 \, a^{5} b^{3} \tan\left(d x + c\right)^{2} + 720 \, a^{3} b^{5} \tan\left(d x + c\right)^{2} + 987 \, a b^{7} \tan\left(d x + c\right)^{2} + 87 \, a^{6} b^{2} \tan\left(d x + c\right) + 792 \, a^{4} b^{4} \tan\left(d x + c\right) + 1059 \, a^{2} b^{6} \tan\left(d x + c\right) + 35 \, a^{7} b + 294 \, a^{5} b^{3} + 381 \, a^{3} b^{5}\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} a^{9}} - \frac{137 \, a^{4} b \tan\left(d x + c\right)^{5} + 1370 \, a^{2} b^{3} \tan\left(d x + c\right)^{5} + 1918 \, b^{5} \tan\left(d x + c\right)^{5} - 15 \, a^{5} \tan\left(d x + c\right)^{4} - 300 \, a^{3} b^{2} \tan\left(d x + c\right)^{4} - 525 \, a b^{4} \tan\left(d x + c\right)^{4} + 60 \, a^{4} b \tan\left(d x + c\right)^{3} + 150 \, a^{2} b^{3} \tan\left(d x + c\right)^{3} - 10 \, a^{5} \tan\left(d x + c\right)^{2} - 50 \, a^{3} b^{2} \tan\left(d x + c\right)^{2} + 15 \, a^{4} b \tan\left(d x + c\right) - 3 \, a^{5}}{a^{9} \tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*(60*(a^4*b + 10*a^2*b^3 + 14*b^5)*log(abs(tan(d*x + c)))/a^9 - 60*(a^4*b^2 + 10*a^2*b^4 + 14*b^6)*log(abs(b*tan(d*x + c) + a))/(a^9*b) + 5*(22*a^4*b^4*tan(d*x + c)^3 + 220*a^2*b^6*tan(d*x + c)^3 + 308*b^8*tan(d*x + c)^3 + 75*a^5*b^3*tan(d*x + c)^2 + 720*a^3*b^5*tan(d*x + c)^2 + 987*a*b^7*tan(d*x + c)^2 + 87*a^6*b^2*tan(d*x + c) + 792*a^4*b^4*tan(d*x + c) + 1059*a^2*b^6*tan(d*x + c) + 35*a^7*b + 294*a^5*b^3 + 381*a^3*b^5)/((b*tan(d*x + c) + a)^3*a^9) - (137*a^4*b*tan(d*x + c)^5 + 1370*a^2*b^3*tan(d*x + c)^5 + 1918*b^5*tan(d*x + c)^5 - 15*a^5*tan(d*x + c)^4 - 300*a^3*b^2*tan(d*x + c)^4 - 525*a*b^4*tan(d*x + c)^4 + 60*a^4*b*tan(d*x + c)^3 + 150*a^2*b^3*tan(d*x + c)^3 - 10*a^5*tan(d*x + c)^2 - 50*a^3*b^2*tan(d*x + c)^2 + 15*a^4*b*tan(d*x + c) - 3*a^5)/(a^9*tan(d*x + c)^5))/d","A",0
78,1,44,0,2.970184," ","integrate(csc(x)/(1+tan(x)),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) - 2 \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) - 2 \right|}}\right) + \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)"," ",0,"1/2*sqrt(2)*log(abs(-2*sqrt(2) + 2*tan(1/2*x) - 2)/abs(2*sqrt(2) + 2*tan(1/2*x) - 2)) + log(abs(tan(1/2*x)))","A",0
79,0,0,0,0.000000," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{3} \sin\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3*sin(d*x + c)^m, x)","F",0
80,0,0,0,0.000000," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2*sin(d*x + c)^m, x)","F",0
81,0,0,0,0.000000," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)*sin(d*x + c)^m, x)","F",0
82,0,0,0,0.000000," ","integrate(sin(d*x+c)^m/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{m}}{b \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^m/(b*tan(d*x + c) + a), x)","F",0
83,-2,0,0,0.000000," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming a near 0Simplification assuming a near 0Evaluation time: 0.53Unable to divide, perhaps due to rounding error%%%{-268435456,[0,10,0,10,16,0,4,0]%%%}+%%%{1073741824*i,[0,10,0,10,15,0,5,0]%%%}+%%%{1610612736,[0,10,0,10,14,0,6,0]%%%}+%%%{-1073741824*i,[0,10,0,10,13,0,7,0]%%%}+%%%{268435456,[0,10,0,10,12,0,8,0]%%%}+%%%{-2147483648*i,[0,10,0,10,11,0,9,0]%%%}+%%%{-3221225472,[0,10,0,10,10,0,10,0]%%%}+%%%{2147483648*i,[0,10,0,10,9,0,11,0]%%%}+%%%{268435456,[0,10,0,10,8,0,12,0]%%%}+%%%{1073741824*i,[0,10,0,10,7,0,13,0]%%%}+%%%{1610612736,[0,10,0,10,6,0,14,0]%%%}+%%%{-1073741824*i,[0,10,0,10,5,0,15,0]%%%}+%%%{-268435456,[0,10,0,10,4,0,16,0]%%%}+%%%{1073741824,[0,9,0,10,16,1,4,0]%%%}+%%%{-4294967296*i,[0,9,0,10,15,1,5,0]%%%}+%%%{1073741824*i,[0,9,0,10,15,0,5,1]%%%}+%%%{-6710886400,[0,9,0,10,14,1,6,0]%%%}+%%%{4026531840,[0,9,0,10,14,0,6,1]%%%}+%%%{4831838208*i,[0,9,0,10,13,1,7,0]%%%}+%%%{-4831838208*i,[0,9,0,10,13,0,7,1]%%%}+%%%{-1342177280,[0,9,0,10,12,1,8,0]%%%}+%%%{-268435456,[0,9,0,10,12,0,8,1]%%%}+%%%{9663676416*i,[0,9,0,10,11,1,9,0]%%%}+%%%{-5368709120*i,[0,9,0,10,11,0,9,1]%%%}+%%%{13421772800,[0,9,0,10,10,1,10,0]%%%}+%%%{-8053063680,[0,9,0,10,10,0,10,1]%%%}+%%%{-8589934592*i,[0,9,0,10,9,1,11,0]%%%}+%%%{6442450944*i,[0,9,0,10,9,0,11,1]%%%}+%%%{-536870912,[0,9,0,10,8,1,12,0]%%%}+%%%{536870912,[0,9,0,10,8,0,12,1]%%%}+%%%{-5368709120*i,[0,9,0,10,7,1,13,0]%%%}+%%%{4294967296*i,[0,9,0,10,7,0,13,1]%%%}+%%%{-6710886400,[0,9,0,10,6,1,14,0]%%%}+%%%{4026531840,[0,9,0,10,6,0,14,1]%%%}+%%%{3758096384*i,[0,9,0,10,5,1,15,0]%%%}+%%%{-1610612736*i,[0,9,0,10,5,0,15,1]%%%}+%%%{805306368,[0,9,0,10,4,1,16,0]%%%}+%%%{-268435456,[0,9,0,10,4,0,16,1]%%%}+%%%{-1610612736,[0,8,0,10,16,2,4,0]%%%}+%%%{536870912,[0,8,0,10,16,0,4,2]%%%}+%%%{6442450944*i,[0,8,0,10,15,2,5,0]%%%}+%%%{-4294967296*i,[0,8,0,10,15,1,5,1]%%%}+%%%{-2147483648*i,[0,8,0,10,15,0,5,2]%%%}+%%%{10468982784,[0,8,0,10,14,2,6,0]%%%}+%%%{-16106127360,[0,8,0,10,14,1,6,1]%%%}+%%%{-1879048192,[0,8,0,10,14,0,6,2]%%%}+%%%{-8053063680*i,[0,8,0,10,13,2,7,0]%%%}+%%%{19864223744*i,[0,8,0,10,13,1,7,1]%%%}+%%%{-2147483648*i,[0,8,0,10,13,0,7,2]%%%}+%%%{2348810240,[0,8,0,10,12,2,8,0]%%%}+%%%{2013265920,[0,8,0,10,12,1,8,1]%%%}+%%%{-3556769792,[0,8,0,10,12,0,8,2]%%%}+%%%{-16106127360*i,[0,8,0,10,11,2,9,0]%%%}+%%%{22548578304*i,[0,8,0,10,11,1,9,1]%%%}+%%%{-21206401024,[0,8,0,10,10,2,10,0]%%%}+%%%{34896609280,[0,8,0,10,10,1,10,1]%%%}+%%%{-1879048192,[0,8,0,10,10,0,10,2]%%%}+%%%{12884901888*i,[0,8,0,10,9,2,11,0]%%%}+%%%{-25769803776*i,[0,8,0,10,9,1,11,1]%%%}+%%%{-402653184,[0,8,0,10,8,2,12,0]%%%}+%%%{268435456,[0,8,0,10,8,1,12,1]%%%}+%%%{-2550136832,[0,8,0,10,8,0,12,2]%%%}+%%%{9663676416*i,[0,8,0,10,7,2,13,0]%%%}+%%%{-18253611008*i,[0,8,0,10,7,1,13,1]%%%}+%%%{2147483648*i,[0,8,0,10,7,0,13,2]%%%}+%%%{10200547328,[0,8,0,10,6,2,14,0]%%%}+%%%{-15569256448,[0,8,0,10,6,1,14,1]%%%}+%%%{-1073741824,[0,8,0,10,6,0,14,2]%%%}+%%%{-4831838208*i,[0,8,0,10,5,2,15,0]%%%}+%%%{5905580032*i,[0,8,0,10,5,1,15,1]%%%}+%%%{2147483648*i,[0,8,0,10,5,0,15,2]%%%}+%%%{-872415232,[0,8,0,10,4,2,16,0]%%%}+%%%{939524096,[0,8,0,10,4,1,16,1]%%%}+%%%{738197504,[0,8,0,10,4,0,16,2]%%%}+%%%{1073741824,[0,7,0,10,16,3,4,0]%%%}+%%%{-2147483648,[0,7,0,10,16,1,4,2]%%%}+%%%{-4294967296*i,[0,7,0,10,15,3,5,0]%%%}+%%%{6442450944*i,[0,7,0,10,15,2,5,1]%%%}+%%%{8589934592*i,[0,7,0,10,15,1,5,2]%%%}+%%%{-2147483648*i,[0,7,0,10,15,0,5,3]%%%}+%%%{-7247757312,[0,7,0,10,14,3,6,0]%%%}+%%%{24159191040,[0,7,0,10,14,2,6,1]%%%}+%%%{8321499136,[0,7,0,10,14,1,6,2]%%%}+%%%{-8053063680,[0,7,0,10,14,0,6,3]%%%}+%%%{5905580032*i,[0,7,0,10,13,3,7,0]%%%}+%%%{-30601641984*i,[0,7,0,10,13,2,7,1]%%%}+%%%{6979321856*i,[0,7,0,10,13,1,7,2]%%%}+%%%{9126805504*i,[0,7,0,10,13,0,7,3]%%%}+%%%{-1744830464,[0,7,0,10,12,3,8,0]%%%}+%%%{-4429185024,[0,7,0,10,12,2,8,1]%%%}+%%%{15166603264,[0,7,0,10,12,1,8,2]%%%}+%%%{-402653184,[0,7,0,10,12,0,8,3]%%%}+%%%{11811160064*i,[0,7,0,10,11,3,9,0]%%%}+%%%{-35433480192*i,[0,7,0,10,11,2,9,1]%%%}+%%%{-3221225472*i,[0,7,0,10,11,1,9,2]%%%}+%%%{9663676416*i,[0,7,0,10,11,0,9,3]%%%}+%%%{15032385536,[0,7,0,10,10,3,10,0]%%%}+%%%{-56371445760,[0,7,0,10,10,2,10,1]%%%}+%%%{6442450944,[0,7,0,10,10,1,10,2]%%%}+%%%{13421772800,[0,7,0,10,10,0,10,3]%%%}+%%%{-8589934592*i,[0,7,0,10,9,3,11,0]%%%}+%%%{38654705664*i,[0,7,0,10,9,2,11,1]%%%}+%%%{-12884901888*i,[0,7,0,10,9,0,11,3]%%%}+%%%{1342177280,[0,7,0,10,8,3,12,0]%%%}+%%%{-4026531840,[0,7,0,10,8,2,12,1]%%%}+%%%{9395240960,[0,7,0,10,8,1,12,2]%%%}+%%%{-3489660928,[0,7,0,10,8,0,12,3]%%%}+%%%{-7516192768*i,[0,7,0,10,7,3,13,0]%%%}+%%%{28991029248*i,[0,7,0,10,7,2,13,1]%%%}+%%%{-5368709120*i,[0,7,0,10,7,1,13,2]%%%}+%%%{-7516192768*i,[0,7,0,10,7,0,13,3]%%%}+%%%{-6710886400,[0,7,0,10,6,3,14,0]%%%}+%%%{22548578304,[0,7,0,10,6,2,14,1]%%%}+%%%{5637144576,[0,7,0,10,6,1,14,2]%%%}+%%%{-8589934592,[0,7,0,10,6,0,14,3]%%%}+%%%{2684354560*i,[0,7,0,10,5,3,15,0]%%%}+%%%{-8053063680*i,[0,7,0,10,5,2,15,1]%%%}+%%%{-6979321856*i,[0,7,0,10,5,1,15,2]%%%}+%%%{3758096384*i,[0,7,0,10,5,0,15,3]%%%}+%%%{402653184,[0,7,0,10,4,3,16,0]%%%}+%%%{-1207959552,[0,7,0,10,4,2,16,1]%%%}+%%%{-2013265920,[0,7,0,10,4,1,16,2]%%%}+%%%{671088640,[0,7,0,10,4,0,1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/ %%%{1024,[0,4,0,4,8,0,0,0]%%%}+%%%{-4096*i,[0,4,0,4,7,0,1,0]%%%}+%%%{-8192,[0,4,0,4,6,0,2,0]%%%}+%%%{12288*i,[0,4,0,4,5,0,3,0]%%%}+%%%{14336,[0,4,0,4,4,0,4,0]%%%}+%%%{-12288*i,[0,4,0,4,3,0,5,0]%%%}+%%%{-8192,[0,4,0,4,2,0,6,0]%%%}+%%%{4096*i,[0,4,0,4,1,0,7,0]%%%}+%%%{1024,[0,4,0,4,0,0,8,0]%%%}+%%%{-2048,[0,3,0,4,8,1,0,0]%%%}+%%%{8192*i,[0,3,0,4,7,1,1,0]%%%}+%%%{-4096*i,[0,3,0,4,7,0,1,1]%%%}+%%%{17408,[0,3,0,4,6,1,2,0]%%%}+%%%{-15360,[0,3,0,4,6,0,2,1]%%%}+%%%{-26624*i,[0,3,0,4,5,1,3,0]%%%}+%%%{26624*i,[0,3,0,4,5,0,3,1]%%%}+%%%{-29696,[0,3,0,4,4,1,4,0]%%%}+%%%{31744,[0,3,0,4,4,0,4,1]%%%}+%%%{24576*i,[0,3,0,4,3,1,5,0]%%%}+%%%{-28672*i,[0,3,0,4,3,0,5,1]%%%}+%%%{15360,[0,3,0,4,2,1,6,0]%%%}+%%%{-17408,[0,3,0,4,2,0,6,1]%%%}+%%%{-6144*i,[0,3,0,4,1,1,7,0]%%%}+%%%{6144*i,[0,3,0,4,1,0,7,1]%%%}+%%%{-1024,[0,3,0,4,0,1,8,0]%%%}+%%%{1024,[0,3,0,4,0,0,8,1]%%%}+%%%{1024,[0,2,0,4,8,2,0,0]%%%}+%%%{-4096*i,[0,2,0,4,7,2,1,0]%%%}+%%%{8192*i,[0,2,0,4,7,1,1,1]%%%}+%%%{-9216,[0,2,0,4,6,2,2,0]%%%}+%%%{30720,[0,2,0,4,6,1,2,1]%%%}+%%%{-5120,[0,2,0,4,6,0,2,2]%%%}+%%%{14336*i,[0,2,0,4,5,2,3,0]%%%}+%%%{-55296*i,[0,2,0,4,5,1,3,1]%%%}+%%%{16384*i,[0,2,0,4,5,0,3,2]%%%}+%%%{15616,[0,2,0,4,4,2,4,0]%%%}+%%%{-67072,[0,2,0,4,4,1,4,1]%%%}+%%%{21760,[0,2,0,4,4,0,4,2]%%%}+%%%{-12288*i,[0,2,0,4,3,2,5,0]%%%}+%%%{57344*i,[0,2,0,4,3,1,5,1]%%%}+%%%{-16384*i,[0,2,0,4,3,0,5,2]%%%}+%%%{-6656,[0,2,0,4,2,2,6,0]%%%}+%%%{31744,[0,2,0,4,2,1,6,1]%%%}+%%%{-6656,[0,2,0,4,2,0,6,2]%%%}+%%%{2048*i,[0,2,0,4,1,2,7,0]%%%}+%%%{-10240*i,[0,2,0,4,1,1,7,1]%%%}+%%%{256,[0,2,0,4,0,2,8,0]%%%}+%%%{-1536,[0,2,0,4,0,1,8,1]%%%}+%%%{-768,[0,2,0,4,0,0,8,2]%%%}+%%%{-4096*i,[0,1,0,4,7,2,1,1]%%%}+%%%{-15360,[0,1,0,4,6,2,2,1]%%%}+%%%{9216,[0,1,0,4,6,1,2,2]%%%}+%%%{28672*i,[0,1,0,4,5,2,3,1]%%%}+%%%{-30720*i,[0,1,0,4,5,1,3,2]%%%}+%%%{2048*i,[0,1,0,4,5,0,3,3]%%%}+%%%{35328,[0,1,0,4,4,2,4,1]%%%}+%%%{-43008,[0,1,0,4,4,1,4,2]%%%}+%%%{3584,[0,1,0,4,4,0,4,3]%%%}+%%%{-28672*i,[0,1,0,4,3,2,5,1]%%%}+%%%{32768*i,[0,1,0,4,3,1,5,2]%%%}+%%%{-14336,[0,1,0,4,2,2,6,1]%%%}+%%%{13312,[0,1,0,4,2,1,6,2]%%%}+%%%{3072,[0,1,0,4,2,0,6,3]%%%}+%%%{4096*i,[0,1,0,4,1,2,7,1]%%%}+%%%{-2048*i,[0,1,0,4,1,1,7,2]%%%}+%%%{-2048*i,[0,1,0,4,1,0,7,3]%%%}+%%%{512,[0,1,0,4,0,2,8,1]%%%}+%%%{-512,[0,1,0,4,0,0,8,3]%%%}+%%%{-4096,[0,0,0,4,6,2,2,2]%%%}+%%%{14336*i,[0,0,0,4,5,2,3,2]%%%}+%%%{-2048*i,[0,0,0,4,5,1,3,3]%%%}+%%%{20736,[0,0,0,4,4,2,4,2]%%%}+%%%{-3584,[0,0,0,4,4,1,4,3]%%%}+%%%{256,[0,0,0,4,4,0,4,4]%%%}+%%%{-16384*i,[0,0,0,4,3,2,5,2]%%%}+%%%{-7680,[0,0,0,4,2,2,6,2]%%%}+%%%{-3072,[0,0,0,4,2,1,6,3]%%%}+%%%{512,[0,0,0,4,2,0,6,4]%%%}+%%%{2048*i,[0,0,0,4,1,2,7,2]%%%}+%%%{2048*i,[0,0,0,4,1,1,7,3]%%%}+%%%{256,[0,0,0,4,0,2,8,2]%%%}+%%%{512,[0,0,0,4,0,1,8,3]%%%}+%%%{256,[0,0,0,4,0,0,8,4]%%%} Error: Bad Argument Value","F(-2)",0
84,-2,0,0,0.000000," ","integrate(sin(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.46Unable to divide, perhaps due to rounding error%%%{1048576,[2,0,10,17,20,20]%%%}+%%%{-10485760,[2,0,10,17,20,18]%%%}+%%%{47185920,[2,0,10,17,20,16]%%%}+%%%{-125829120,[2,0,10,17,20,14]%%%}+%%%{220200960,[2,0,10,17,20,12]%%%}+%%%{-264241152,[2,0,10,17,20,10]%%%}+%%%{220200960,[2,0,10,17,20,8]%%%}+%%%{-125829120,[2,0,10,17,20,6]%%%}+%%%{47185920,[2,0,10,17,20,4]%%%}+%%%{-10485760,[2,0,10,17,20,2]%%%}+%%%{1048576,[2,0,10,17,20,0]%%%}+%%%{3145728*i,[2,0,10,16,21,20]%%%}+%%%{-31457280*i,[2,0,10,16,21,18]%%%}+%%%{141557760*i,[2,0,10,16,21,16]%%%}+%%%{-377487360*i,[2,0,10,16,21,14]%%%}+%%%{660602880*i,[2,0,10,16,21,12]%%%}+%%%{-792723456*i,[2,0,10,16,21,10]%%%}+%%%{660602880*i,[2,0,10,16,21,8]%%%}+%%%{-377487360*i,[2,0,10,16,21,6]%%%}+%%%{141557760*i,[2,0,10,16,21,4]%%%}+%%%{-31457280*i,[2,0,10,16,21,2]%%%}+%%%{3145728*i,[2,0,10,16,21,0]%%%}+%%%{4194304,[2,0,10,15,22,20]%%%}+%%%{-41943040,[2,0,10,15,22,18]%%%}+%%%{188743680,[2,0,10,15,22,16]%%%}+%%%{-503316480,[2,0,10,15,22,14]%%%}+%%%{880803840,[2,0,10,15,22,12]%%%}+%%%{-1056964608,[2,0,10,15,22,10]%%%}+%%%{880803840,[2,0,10,15,22,8]%%%}+%%%{-503316480,[2,0,10,15,22,6]%%%}+%%%{188743680,[2,0,10,15,22,4]%%%}+%%%{-41943040,[2,0,10,15,22,2]%%%}+%%%{4194304,[2,0,10,15,22,0]%%%}+%%%{20971520*i,[2,0,10,14,23,20]%%%}+%%%{-209715200*i,[2,0,10,14,23,18]%%%}+%%%{943718400*i,[2,0,10,14,23,16]%%%}+%%%{-2516582400*i,[2,0,10,14,23,14]%%%}+%%%{4404019200*i,[2,0,10,14,23,12]%%%}+%%%{-5284823040*i,[2,0,10,14,23,10]%%%}+%%%{4404019200*i,[2,0,10,14,23,8]%%%}+%%%{-2516582400*i,[2,0,10,14,23,6]%%%}+%%%{943718400*i,[2,0,10,14,23,4]%%%}+%%%{-209715200*i,[2,0,10,14,23,2]%%%}+%%%{20971520*i,[2,0,10,14,23,0]%%%}+%%%{58720256*i,[2,0,10,12,25,20]%%%}+%%%{-587202560*i,[2,0,10,12,25,18]%%%}+%%%{2642411520*i,[2,0,10,12,25,16]%%%}+%%%{-7046430720*i,[2,0,10,12,25,14]%%%}+%%%{12331253760*i,[2,0,10,12,25,12]%%%}+%%%{-14797504512*i,[2,0,10,12,25,10]%%%}+%%%{12331253760*i,[2,0,10,12,25,8]%%%}+%%%{-7046430720*i,[2,0,10,12,25,6]%%%}+%%%{2642411520*i,[2,0,10,12,25,4]%%%}+%%%{-587202560*i,[2,0,10,12,25,2]%%%}+%%%{58720256*i,[2,0,10,12,25,0]%%%}+%%%{-29360128,[2,0,10,11,26,20]%%%}+%%%{293601280,[2,0,10,11,26,18]%%%}+%%%{-1321205760,[2,0,10,11,26,16]%%%}+%%%{3523215360,[2,0,10,11,26,14]%%%}+%%%{-6165626880,[2,0,10,11,26,12]%%%}+%%%{7398752256,[2,0,10,11,26,10]%%%}+%%%{-6165626880,[2,0,10,11,26,8]%%%}+%%%{3523215360,[2,0,10,11,26,6]%%%}+%%%{-1321205760,[2,0,10,11,26,4]%%%}+%%%{293601280,[2,0,10,11,26,2]%%%}+%%%{-29360128,[2,0,10,11,26,0]%%%}+%%%{88080384*i,[2,0,10,10,27,20]%%%}+%%%{-880803840*i,[2,0,10,10,27,18]%%%}+%%%{3963617280*i,[2,0,10,10,27,16]%%%}+%%%{-10569646080*i,[2,0,10,10,27,14]%%%}+%%%{18496880640*i,[2,0,10,10,27,12]%%%}+%%%{-22196256768*i,[2,0,10,10,27,10]%%%}+%%%{18496880640*i,[2,0,10,10,27,8]%%%}+%%%{-10569646080*i,[2,0,10,10,27,6]%%%}+%%%{3963617280*i,[2,0,10,10,27,4]%%%}+%%%{-880803840*i,[2,0,10,10,27,2]%%%}+%%%{88080384*i,[2,0,10,10,27,0]%%%}+%%%{-73400320,[2,0,10,9,28,20]%%%}+%%%{734003200,[2,0,10,9,28,18]%%%}+%%%{-3303014400,[2,0,10,9,28,16]%%%}+%%%{8808038400,[2,0,10,9,28,14]%%%}+%%%{-15414067200,[2,0,10,9,28,12]%%%}+%%%{18496880640,[2,0,10,9,28,10]%%%}+%%%{-15414067200,[2,0,10,9,28,8]%%%}+%%%{8808038400,[2,0,10,9,28,6]%%%}+%%%{-3303014400,[2,0,10,9,28,4]%%%}+%%%{734003200,[2,0,10,9,28,2]%%%}+%%%{-73400320,[2,0,10,9,28,0]%%%}+%%%{73400320*i,[2,0,10,8,29,20]%%%}+%%%{-734003200*i,[2,0,10,8,29,18]%%%}+%%%{3303014400*i,[2,0,10,8,29,16]%%%}+%%%{-8808038400*i,[2,0,10,8,29,14]%%%}+%%%{15414067200*i,[2,0,10,8,29,12]%%%}+%%%{-18496880640*i,[2,0,10,8,29,10]%%%}+%%%{15414067200*i,[2,0,10,8,29,8]%%%}+%%%{-8808038400*i,[2,0,10,8,29,6]%%%}+%%%{3303014400*i,[2,0,10,8,29,4]%%%}+%%%{-734003200*i,[2,0,10,8,29,2]%%%}+%%%{73400320*i,[2,0,10,8,29,0]%%%}+%%%{-88080384,[2,0,10,7,30,20]%%%}+%%%{880803840,[2,0,10,7,30,18]%%%}+%%%{-3963617280,[2,0,10,7,30,16]%%%}+%%%{10569646080,[2,0,10,7,30,14]%%%}+%%%{-18496880640,[2,0,10,7,30,12]%%%}+%%%{22196256768,[2,0,10,7,30,10]%%%}+%%%{-18496880640,[2,0,10,7,30,8]%%%}+%%%{10569646080,[2,0,10,7,30,6]%%%}+%%%{-3963617280,[2,0,10,7,30,4]%%%}+%%%{880803840,[2,0,10,7,30,2]%%%}+%%%{-88080384,[2,0,10,7,30,0]%%%}+%%%{29360128*i,[2,0,10,6,31,20]%%%}+%%%{-293601280*i,[2,0,10,6,31,18]%%%}+%%%{1321205760*i,[2,0,10,6,31,16]%%%}+%%%{-3523215360*i,[2,0,10,6,31,14]%%%}+%%%{6165626880*i,[2,0,10,6,31,12]%%%}+%%%{-7398752256*i,[2,0,10,6,31,10]%%%}+%%%{6165626880*i,[2,0,10,6,31,8]%%%}+%%%{-3523215360*i,[2,0,10,6,31,6]%%%}+%%%{1321205760*i,[2,0,10,6,31,4]%%%}+%%%{-293601280*i,[2,0,10,6,31,2]%%%}+%%%{29360128*i,[2,0,10,6,31,0]%%%}+%%%{-58720256,[2,0,10,5,32,20]%%%}+%%%{587202560,[2,0,10,5,32,18]%%%}+%%%{-2642411520,[2,0,10,5,32,16]%%%}+%%%{7046430720,[2,0,10,5,32,14]%%%}+%%%{-12331253760,[2,0,10,5,32,12]%%%}+%%%{14797504512,[2,0,10,5,32,10]%%%}+%%%{-12331253760,[2,0,10,5,32,8]%%%}+%%%{7046430720,[2,0,10,5,32,6]%%%}+%%%{-2642411520,[2,0,10,5,32,4]%%%}+%%%{587202560,[2,0,10,5,32,2]%%%}+%%%{-58720256,[2,0,10,5,32,0]%%%}+%%%{-20971520,[2,0,10,3,34,20]%%%}+%%%{209715200,[2,0,10,3,34,18]%%%}+%%%{-943718400,[2,0,10,3,34,16]%%%}+%%%{2516582400,[2,0,10,3,34,14]%%%}+%%%{-4404019200,[2,0,10,3,34,12]%%%}+%%%{5284823040,[2,0,10,3,34,10]%%%}+%%%{-4404019200,[2,0,10,3,34,8]%%%}+%%%{2516582400,[2,0,10,3,34,6]%%%}+%%%{-943718400,[2,0,10,3,34,4]%%%}+%%%{209715200,[2,0,10,3,34,2]%%%}+%%%{-20971520,[2,0,10,3,34,0]%%%}+%%%{-4194304*i,[2,0,10,2,35,20]%%%}+%%%{41943040*i,[2,0,10,2,35,18]%%%}+%%%{-188743680*i,[2,0,10,2,35,16]%%%}+%%%{503316480*i,[2,0,10,2,35,14]%%%}+%%%{-880803840*i,[2,0,10,2,35,12]%%%}+%%%{1056964608*i,[2,0,10,2,35,10]%%%}+%%%{-880803840*i,[2,0,10,2,35,8]%%%}+%%%{503316480*i,[2,0,10,2,35,6]%%%}+%%%{-188743680*i,[2,0,10,2,35,4]%%%}+%%%{41943040*i,[2,0,10,2,35,2]%%%}+%%%{-4194304*i,[2,0,10,2,35,0]%%%}+%%%{-3145728,[2,0,10,1,36,20]%%%}+%%%{31457280,[2,0,10,1,36,18]%%%}+%%%{-141557760,[2,0,10,1,36,16]%%%}+%%%{377487360,[2,0,10,1,36,14]%%%}+%%%{-660602880,[2,0,10,1,36,12]%%%}+%%%{792723456,[2,0,10,1,36,10]%%%}+%%%{-660602880,[2,0,10,1,36,8]%%%}+%%%{377487360,[2,0,10,1,36,6]%%%}+%%%{-141557760,[2,0,10,1,36,4]%%%}+%%%{31457280,[2,0,10,1,36,2]%%%}+%%%{-3145728,[2,0,10,1,36,0]%%%}+%%%{-1048576*i,[2,0,10,0,37,20]%%%}+%%%{10485760*i,[2,0,10,0,37,18]%%%}+%%%{-47185920*i,[2,0,10,0,37,16]%%%}+%%%{125829120*i,[2,0,10,0,37,14]%%%}+%%%{-220200960*i,[2,0,10,0,37,12]%%%}+%%%{264241152*i,[2,0,10,0,37,10]%%%}+%%%{-220200960*i,[2,0,10,0,37,8]%%%}+%%%{125829120*i,[2,0,10,0,37,6]%%%}+%%%{-47185920*i,[2,0,10,0,37,4]%%%}+%%%{10485760*i,[2,0,10,0,37,2]%%%}+%%%{-1048576*i,[2,0,10,0,37,0]%%%}+%%%{-6291456,[1,0,10,17,20,20]%%%}+%%%{62914560,[1,0,10,17,20,18]%%%}+%%%{-283115520,[1,0,10,17,20,16]%%%}+%%%{754974720,[1,0,10,17,20,14]%%%}+%%%{-1321205760,[1,0,10,17,20,12]%%%}+%%%{1585446912,[1,0,10,17,20,10]%%%}+%%%{-1321205760,[1,0,10,17,20,8]%%%}+%%%{754974720,[1,0,10,17,20,6]%%%}+%%%{-283115520,[1,0,10,17,20,4]%%%}+%%%{62914560,[1,0,10,17,20,2]%%%}+%%%{-6291456,[1,0,10,17,20,0]%%%}+%%%{-20971520*i,[1,0,10,16,21,20]%%%}+%%%{209715200*i,[1,0,10,16,21,18]%%%}+%%%{-943718400*i,[1,0,10,16,21,16]%%%}+%%%{2516582400*i,[1,0,10,16,21,14]%%%}+%%%{-4404019200*i,[1,0,10,16,21,12]%%%}+%%%{5284823040*i,[1,0,10,16,21,10]%%%}+%%%{-4404019200*i,[1,0,10,16,21,8]%%%}+%%%{2516582400*i,[1,0,10,16,21,6]%%%}+%%%{-943718400*i,[1,0,10,16,21,4]%%%}+%%%{209715200*i,[1,0,10,16,21,2]%%%}+%%%{-20971520*i,[1,0,10,16,21,0]%%%}+%%%{-16777216,[1,0,10,15,22,20]%%%}+%%%{167772160,[1,0,10,15,22,18]%%%}+%%%{-754974720,[1,0,10,15,22,16]%%%}+%%%{2013265920,[1,0,10,15,22,14]%%%}+%%%{-3523215360,[1,0,10,15,22,12]%%%}+%%%{4227858432,[1,0,10,15,22,10]%%%}+%%%{-3523215360,[1,0,10,15,22,8]%%%}+%%%{2013265920,[1,0,10,15,22,6]%%%}+%%%{-754974720,[1,0,10,15,22,4]%%%}+%%%{167772160,[1,0,10,15,22,2]%%%}+%%%{-16777216,[1,0,10,15,22,0]%%%}+%%%{-125829120*i,[1,0,10,14,23,20]%%%}+%%%{1258291200*i,[1,0,10,14,23,18]%%%}+%%%{-5662310400*i,[1,0,10,14,23,16]%%%}+%%%{15099494400*i,[1,0,10,14,23,14]%%%}+%%%{-26424115200*i,[1,0,10,14,23,12]%%%}+%%%{31708938240*i,[1,0,10,14,23,10]%%%}+%%%{-26424115200*i,[1,0,10,14,23,8]%%%}+%%%{15099494400*i,[1,0,10,14,23,6]%%%}+%%%{-5662310400*i,[1,0,10,14,23,4]%%%}+%%%{1258291200*i,[1,0,10,14,23,2]%%%}+%%%{-125829120*i,[1,0,10,14,23,0]%%%}+%%%{41943040,[1,0,10,13,24,20]%%%}+%%%{-419430400,[1,0,10,13,24,18]%%%}+%%%{1887436800,[1,0,10,13,24,16]%%%}+%%%{-5033164800,[1,0,10,13,24,14]%%%}+%%%{8808038400,[1,0,10,13,24,12]%%%}+%%%{-10569646080,[1,0,10,13,24,10]%%%}+%%%{8808038400,[1,0,10,13,24,8]%%%}+%%%{-5033164800,[1,0,10,13,24,6]%%%}+%%%{1887436800,[1,0,10,13,24,4]%%%}+%%%{-419430400,[1,0,10,13,24,2]%%%}+%%%{41943040,[1,0,10,13,24,0]%%%}+%%%{-310378496*i,[1,0,10,12,25,20]%%%}+%%%{3103784960*i,[1,0,10,12,25,18]%%%}+%%%{-13967032320*i,[1,0,10,12,25,16]%%%}+%%%{37245419520*i,[1,0,10,12,25,14]%%%}+%%%{-65179484160*i,[1,0,10,12,25,12]%%%}+%%%{78215380992*i,[1,0,10,12,25,10]%%%}+%%%{-65179484160*i,[1,0,10,12,25,8]%%%}+%%%{37245419520*i,[1,0,10,12,25,6]%%%}+%%%{-13967032320*i,[1,0,10,12,25,4]%%%}+%%%{3103784960*i,[1,0,10,12,25,2]%%%}+%%%{-310378496*i,[1,0,10,12,25,0]%%%}+%%%{251658240,[1,0,10,11,26,20]%%%}+%%%{-2516582400,[1,0,10,11,26,18]%%%}+%%%{11324620800,[1,0,10,11,26,16]%%%}+%%%{-30198988800,[1,0,10,11,26,14]%%%}+%%%{52848230400,[1,0,10,11,26,12]%%%}+%%%{-63417876480,[1,0,10,11,26,10]%%%}+%%%{52848230400,[1,0,10,11,26,8]%%%}+%%%{-30198988800,[1,0,10,11,26,6]%%%}+%%%{11324620800,[1,0,10,11,26,4]%%%}+%%%{-2516582400,[1,0,10,11,26,2]%%%}+%%%{251658240,[1,0,10,11,26,0]%%%}+%%%{-394264576*i,[1,0,10,10,27,20]%%%}+%%%{3942645760*i,[1,0,10,10,27,18]%%%}+%%%{-17741905920*i,[1,0,10,10,27,16]%%%}+%%%{47311749120*i,[1,0,10,10,27,14]%%%}+%%%{-82795560960*i,[1,0,10,10,27,12]%%%}+%%%{99354673152*i,[1,0,10,10,27,10]%%%}+%%%{-82795560960*i,[1,0,10,10,27,8]%%%}+%%%{47311749120*i,[1,0,10,10,27,6]%%%}+%%%{-17741905920*i,[1,0,10,10,27,4]%%%}+%%%{3942645760*i,[1,0,10,10,27,2]%%%}+%%%{-394264576*i,[1,0,10,10,27,0]%%%}+%%%{482344960,[1,0,10,9,28,20]%%%}+%%%{-4823449600,[1,0,10,9,28,18]%%%}+%%%{21705523200,[1,0,10,9,28,16]%%%}+%%%{-57881395200,[1,0,10,9,28,14]%%%}+%%%{101292441600,[1,0,10,9,28,12]%%%}+%%%{-121550929920,[1,0,10,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3,18]%%%}+%%%{-226492416*i,[0,0,10,4,33,17]%%%}+%%%{943718400*i,[0,0,10,4,33,16]%%%}+%%%{905969664*i,[0,0,10,4,33,15]%%%}+%%%{-2013265920*i,[0,0,10,4,33,14]%%%}+%%%{-2113929216*i,[0,0,10,4,33,13]%%%}+%%%{2642411520*i,[0,0,10,4,33,12]%%%}+%%%{3170893824*i,[0,0,10,4,33,11]%%%}+%%%{-2113929216*i,[0,0,10,4,33,10]%%%}+%%%{-3170893824*i,[0,0,10,4,33,9]%%%}+%%%{880803840*i,[0,0,10,4,33,8]%%%}+%%%{2113929216*i,[0,0,10,4,33,7]%%%}+%%%{-905969664*i,[0,0,10,4,33,5]%%%}+%%%{-188743680*i,[0,0,10,4,33,4]%%%}+%%%{226492416*i,[0,0,10,4,33,3]%%%}+%%%{83886080*i,[0,0,10,4,33,2]%%%}+%%%{-25165824*i,[0,0,10,4,33,1]%%%}+%%%{-12582912*i,[0,0,10,4,33,0]%%%}+%%%{8388608,[0,0,10,3,34,20]%%%}+%%%{192937984,[0,0,10,3,34,19]%%%}+%%%{109051904,[0,0,10,3,34,18]%%%}+%%%{-1736441856,[0,0,10,3,34,17]%%%}+%%%{-1358954496,[0,0,10,3,34,16]%%%}+%%%{6945767424,[0,0,10,3,34,15]%%%}+%%%{5939134464,[0,0,10,3,34,14]%%%}+%%%{-16206790656,[0,0,10,3,34,13]%%%}+%%%{-14445182976,[0,0,10,3,34,12]%%%}+%%%{24310185984,[0,0,10,3,34,11]%%%}+%%%{22196256768,[0,0,10,3,34,10]%%%}+%%%{-24310185984,[0,0,10,3,34,9]%%%}+%%%{-22548578304,[0,0,10,3,34,8]%%%}+%%%{16206790656,[0,0,10,3,34,7]%%%}+%%%{15200157696,[0,0,10,3,34,6]%%%}+%%%{-6945767424,[0,0,10,3,34,5]%%%}+%%%{-6568280064,[0,0,10,3,34,4]%%%}+%%%{1736441856,[0,0,10,3,34,3]%%%}+%%%{1652555776,[0,0,10,3,34,2]%%%}+%%%{-192937984,[0,0,10,3,34,1]%%%}+%%%{-184549376,[0,0,10,3,34,0]%%%}+%%%{8388608*i,[0,0,10,2,35,20]%%%}+%%%{41943040*i,[0,0,10,2,35,19]%%%}+%%%{-41943040*i,[0,0,10,2,35,18]%%%}+%%%{-377487360*i,[0,0,10,2,35,17]%%%}+%%%{1509949440*i,[0,0,10,2,35,15]%%%}+%%%{503316480*i,[0,0,10,2,35,14]%%%}+%%%{-3523215360*i,[0,0,10,2,35,13]%%%}+%%%{-1761607680*i,[0,0,10,2,35,12]%%%}+%%%{5284823040*i,[0,0,10,2,35,11]%%%}+%%%{3170893824*i,[0,0,10,2,35,10]%%%}+%%%{-5284823040*i,[0,0,10,2,35,9]%%%}+%%%{-3523215360*i,[0,0,10,2,35,8]%%%}+%%%{3523215360*i,[0,0,10,2,35,7]%%%}+%%%{2516582400*i,[0,0,10,2,35,6]%%%}+%%%{-1509949440*i,[0,0,10,2,35,5]%%%}+%%%{-1132462080*i,[0,0,10,2,35,4]%%%}+%%%{377487360*i,[0,0,10,2,35,3]%%%}+%%%{293601280*i,[0,0,10,2,35,2]%%%}+%%%{-41943040*i,[0,0,10,2,35,1]%%%}+%%%{-33554432*i,[0,0,10,2,35,0]%%%}+%%%{1048576,[0,0,10,1,36,20]%%%}+%%%{25165824,[0,0,10,1,36,19]%%%}+%%%{14680064,[0,0,10,1,36,18]%%%}+%%%{-226492416,[0,0,10,1,36,17]%%%}+%%%{-179306496,[0,0,10,1,36,16]%%%}+%%%{905969664,[0,0,10,1,36,15]%%%}+%%%{780140544,[0,0,10,1,36,14]%%%}+%%%{-2113929216,[0,0,10,1,36,13]%%%}+%%%{-1893728256,[0,0,10,1,36,12]%%%}+%%%{3170893824,[0,0,10,1,36,11]%%%}+%%%{2906652672,[0,0,10,1,36,10]%%%}+%%%{-3170893824,[0,0,10,1,36,9]%%%}+%%%{-2950692864,[0,0,10,1,36,8]%%%}+%%%{2113929216,[0,0,10,1,36,7]%%%}+%%%{1988100096,[0,0,10,1,36,6]%%%}+%%%{-905969664,[0,0,10,1,36,5]%%%}+%%%{-858783744,[0,0,10,1,36,4]%%%}+%%%{226492416,[0,0,10,1,36,3]%%%}+%%%{216006656,[0,0,10,1,36,2]%%%}+%%%{-25165824,[0,0,10,1,36,1]%%%}+%%%{-24117248,[0,0,10,1,36,0]%%%}+%%%{1048576*i,[0,0,10,0,37,20]%%%}+%%%{8388608*i,[0,0,10,0,37,19]%%%}+%%%{-2097152*i,[0,0,10,0,37,18]%%%}+%%%{-75497472*i,[0,0,10,0,37,17]%%%}+%%%{-28311552*i,[0,0,10,0,37,16]%%%}+%%%{301989888*i,[0,0,10,0,37,15]%%%}+%%%{176160768*i,[0,0,10,0,37,14]%%%}+%%%{-704643072*i,[0,0,10,0,37,13]%%%}+%%%{-484442112*i,[0,0,10,0,37,12]%%%}+%%%{1056964608*i,[0,0,10,0,37,11]%%%}+%%%{792723456*i,[0,0,10,0,37,10]%%%}+%%%{-1056964608*i,[0,0,10,0,37,9]%%%}+%%%{-836763648*i,[0,0,10,0,37,8]%%%}+%%%{704643072*i,[0,0,10,0,37,7]%%%}+%%%{578813952*i,[0,0,10,0,37,6]%%%}+%%%{-301989888*i,[0,0,10,0,37,5]%%%}+%%%{-254803968*i,[0,0,10,0,37,4]%%%}+%%%{75497472*i,[0,0,10,0,37,3]%%%}+%%%{65011712*i,[0,0,10,0,37,2]%%%}+%%%{-8388608*i,[0,0,10,0,37,1]%%%}+%%%{-7340032*i,[0,0,10,0,37,0]%%%} / %%%{1024,[0,0,5,9,10,10]%%%}+%%%{-5120,[0,0,5,9,10,8]%%%}+%%%{10240,[0,0,5,9,10,6]%%%}+%%%{-10240,[0,0,5,9,10,4]%%%}+%%%{5120,[0,0,5,9,10,2]%%%}+%%%{-1024,[0,0,5,9,10,0]%%%}+%%%{1024*i,[0,0,5,8,11,10]%%%}+%%%{-5120*i,[0,0,5,8,11,8]%%%}+%%%{10240*i,[0,0,5,8,11,6]%%%}+%%%{-10240*i,[0,0,5,8,11,4]%%%}+%%%{5120*i,[0,0,5,8,11,2]%%%}+%%%{-1024*i,[0,0,5,8,11,0]%%%}+%%%{4096,[0,0,5,7,12,10]%%%}+%%%{-20480,[0,0,5,7,12,8]%%%}+%%%{40960,[0,0,5,7,12,6]%%%}+%%%{-40960,[0,0,5,7,12,4]%%%}+%%%{20480,[0,0,5,7,12,2]%%%}+%%%{-4096,[0,0,5,7,12,0]%%%}+%%%{4096*i,[0,0,5,6,13,10]%%%}+%%%{-20480*i,[0,0,5,6,13,8]%%%}+%%%{40960*i,[0,0,5,6,13,6]%%%}+%%%{-40960*i,[0,0,5,6,13,4]%%%}+%%%{20480*i,[0,0,5,6,13,2]%%%}+%%%{-4096*i,[0,0,5,6,13,0]%%%}+%%%{6144,[0,0,5,5,14,10]%%%}+%%%{-30720,[0,0,5,5,14,8]%%%}+%%%{61440,[0,0,5,5,14,6]%%%}+%%%{-61440,[0,0,5,5,14,4]%%%}+%%%{30720,[0,0,5,5,14,2]%%%}+%%%{-6144,[0,0,5,5,14,0]%%%}+%%%{6144*i,[0,0,5,4,15,10]%%%}+%%%{-30720*i,[0,0,5,4,15,8]%%%}+%%%{61440*i,[0,0,5,4,15,6]%%%}+%%%{-61440*i,[0,0,5,4,15,4]%%%}+%%%{30720*i,[0,0,5,4,15,2]%%%}+%%%{-6144*i,[0,0,5,4,15,0]%%%}+%%%{4096,[0,0,5,3,16,10]%%%}+%%%{-20480,[0,0,5,3,16,8]%%%}+%%%{40960,[0,0,5,3,16,6]%%%}+%%%{-40960,[0,0,5,3,16,4]%%%}+%%%{20480,[0,0,5,3,16,2]%%%}+%%%{-4096,[0,0,5,3,16,0]%%%}+%%%{4096*i,[0,0,5,2,17,10]%%%}+%%%{-20480*i,[0,0,5,2,17,8]%%%}+%%%{40960*i,[0,0,5,2,17,6]%%%}+%%%{-40960*i,[0,0,5,2,17,4]%%%}+%%%{20480*i,[0,0,5,2,17,2]%%%}+%%%{-4096*i,[0,0,5,2,17,0]%%%}+%%%{1024,[0,0,5,1,18,10]%%%}+%%%{-5120,[0,0,5,1,18,8]%%%}+%%%{10240,[0,0,5,1,18,6]%%%}+%%%{-10240,[0,0,5,1,18,4]%%%}+%%%{5120,[0,0,5,1,18,2]%%%}+%%%{-1024,[0,0,5,1,18,0]%%%}+%%%{1024*i,[0,0,5,0,19,10]%%%}+%%%{-5120*i,[0,0,5,0,19,8]%%%}+%%%{10240*i,[0,0,5,0,19,6]%%%}+%%%{-10240*i,[0,0,5,0,19,4]%%%}+%%%{5120*i,[0,0,5,0,19,2]%%%}+%%%{-1024*i,[0,0,5,0,19,0]%%%} Error: Bad Argument Value","F(-2)",0
85,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sin(d*x + c)^2, x)","F",0
86,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
87,0,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*csc(d*x + c)^4, x)","F",0
88,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sin(d*x + c)^3, x)","F",0
89,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sin(d*x + c), x)","F",0
90,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*csc(d*x + c), x)","F",0
91,0,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*csc(d*x + c)^3, x)","F",0
