1,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))*tan(d*x+c)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))*tan(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3,1,1456,0,1.175188," ","integrate((a+a*sin(d*x+c))*tan(d*x+c),x, algorithm=""giac"")","-\frac{a \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} - a \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} + a \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a \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} - a \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} + a \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(\frac{1}{2} \, d x\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a \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} - a \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} + a \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(\frac{1}{2} \, c\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + a \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 \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 \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 \, a \tan\left(\frac{1}{2} \, d x\right) + 4 \, a \tan\left(\frac{1}{2} \, c\right)}{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*(a*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 - a*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 + a*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(1/2*d*x)^2*tan(1/2*c)^2 + a*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 - a*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 + a*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(1/2*d*x)^2 - 4*a*tan(1/2*d*x)^2*tan(1/2*c) + a*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 - a*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 + a*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(1/2*c)^2 - 4*a*tan(1/2*d*x)*tan(1/2*c)^2 + a*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*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*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*a*tan(1/2*d*x) + 4*a*tan(1/2*c))/(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
4,1,23,0,0.219482," ","integrate(cot(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + a \sin\left(d x + c\right)}{d}"," ",0,"(a*log(abs(sin(d*x + c))) + a*sin(d*x + c))/d","A",0
5,1,60,0,0.413005," ","integrate(cot(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 2 \, a \sin\left(d x + c\right) - \frac{3 \, a \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right) - a}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*a*log(abs(sin(d*x + c))) + 2*a*sin(d*x + c) - (3*a*sin(d*x + c)^2 - 2*a*sin(d*x + c) - a)/sin(d*x + c)^2)/d","A",0
6,1,82,0,0.547627," ","integrate(cot(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{12 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 12 \, a \sin\left(d x + c\right) - \frac{25 \, a \sin\left(d x + c\right)^{4} - 24 \, a \sin\left(d x + c\right)^{3} - 12 \, a \sin\left(d x + c\right)^{2} + 4 \, a \sin\left(d x + c\right) + 3 \, a}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*a*log(abs(sin(d*x + c))) + 12*a*sin(d*x + c) - (25*a*sin(d*x + c)^4 - 24*a*sin(d*x + c)^3 - 12*a*sin(d*x + c)^2 + 4*a*sin(d*x + c) + 3*a)/sin(d*x + c)^4)/d","A",0
7,1,104,0,1.463567," ","integrate(cot(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{60 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 60 \, a \sin\left(d x + c\right) - \frac{147 \, a \sin\left(d x + c\right)^{6} - 180 \, a \sin\left(d x + c\right)^{5} - 90 \, a \sin\left(d x + c\right)^{4} + 60 \, a \sin\left(d x + c\right)^{3} + 45 \, a \sin\left(d x + c\right)^{2} - 12 \, a \sin\left(d x + c\right) - 10 \, a}{\sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(60*a*log(abs(sin(d*x + c))) + 60*a*sin(d*x + c) - (147*a*sin(d*x + c)^6 - 180*a*sin(d*x + c)^5 - 90*a*sin(d*x + c)^4 + 60*a*sin(d*x + c)^3 + 45*a*sin(d*x + c)^2 - 12*a*sin(d*x + c) - 10*a)/sin(d*x + c)^6)/d","A",0
8,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))*tan(d*x+c)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))*tan(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,1,1008,0,4.948836," ","integrate((a+a*sin(d*x+c))*tan(d*x+c)^2,x, algorithm=""giac"")","-\frac{a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - a d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 2 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + a \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 4 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 8 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 4 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + a d x \tan\left(\frac{1}{2} \, d x\right)^{4} + 4 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 8 \, a \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + a d x \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 8 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 24 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 8 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 2 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} - 4 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 4 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - a \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} - a \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - a \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 2 \, a \tan\left(\frac{1}{2} \, d x\right)^{4} + 4 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 24 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, c\right)^{4} + a d x \tan\left(d x\right) \tan\left(c\right) + 8 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - a d x - 8 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a \tan\left(d x\right) \tan\left(c\right) + a \tan\left(d x\right) + a \tan\left(c\right) + 2 \, a}{d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 4 \, d \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 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(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) + 4 \, d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + d \tan\left(d x\right) \tan\left(c\right) - d}"," ",0,"-(a*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - a*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4 - 4*a*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 2*a*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + a*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4 + a*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 4*a*d*x*tan(1/2*d*x)^3*tan(1/2*c)^3 + 2*a*tan(1/2*d*x)^4*tan(1/2*c)^4 - a*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 4*a*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 4*a*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) + 8*a*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - a*d*x*tan(d*x)*tan(1/2*c)^4*tan(c) - 4*a*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3 - 4*a*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + a*d*x*tan(1/2*d*x)^4 + 4*a*d*x*tan(1/2*d*x)^3*tan(1/2*c) + 4*a*d*x*tan(1/2*d*x)*tan(1/2*c)^3 - 8*a*tan(1/2*d*x)^3*tan(1/2*c)^3 + a*d*x*tan(1/2*c)^4 - 2*a*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 4*a*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 8*a*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 24*a*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - 8*a*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 2*a*tan(d*x)*tan(1/2*c)^4*tan(c) - a*tan(d*x)*tan(1/2*d*x)^4 - 4*a*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c) - 4*a*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3 - a*tan(d*x)*tan(1/2*c)^4 - a*tan(1/2*d*x)^4*tan(c) - 4*a*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 4*a*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - a*tan(1/2*c)^4*tan(c) + 2*a*tan(1/2*d*x)^4 + 4*a*d*x*tan(1/2*d*x)*tan(1/2*c) + 8*a*tan(1/2*d*x)^3*tan(1/2*c) + 24*a*tan(1/2*d*x)^2*tan(1/2*c)^2 + 8*a*tan(1/2*d*x)*tan(1/2*c)^3 + 2*a*tan(1/2*c)^4 + a*d*x*tan(d*x)*tan(c) + 8*a*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 4*a*tan(d*x)*tan(1/2*d*x)*tan(1/2*c) - 4*a*tan(1/2*d*x)*tan(1/2*c)*tan(c) - a*d*x - 8*a*tan(1/2*d*x)*tan(1/2*c) - 2*a*tan(d*x)*tan(c) + a*tan(d*x) + a*tan(c) + 2*a)/(d*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - d*tan(1/2*d*x)^4*tan(1/2*c)^4 - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + 4*d*tan(1/2*d*x)^3*tan(1/2*c)^3 - d*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - d*tan(d*x)*tan(1/2*c)^4*tan(c) + 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(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) + 4*d*tan(1/2*d*x)*tan(1/2*c) + d*tan(d*x)*tan(c) - d)","B",0
11,1,108,0,0.564888," ","integrate(cot(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{6 \, {\left(d x + c\right)} a - 6 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, a \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)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*a - 6*a*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a*tan(1/2*d*x + 1/2*c) + (2*a*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c)^2 - 10*a*tan(1/2*d*x + 1/2*c) + 3*a)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c)))/d","B",0
12,1,141,0,0.356479," ","integrate(cot(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, {\left(d x + c\right)} a - 36 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{48 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{66 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a \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)^{3}}}{24 \, d}"," ",0,"1/24*(a*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c)^2 + 24*(d*x + c)*a - 36*a*log(abs(tan(1/2*d*x + 1/2*c))) - 15*a*tan(1/2*d*x + 1/2*c) - 48*a/(tan(1/2*d*x + 1/2*c)^2 + 1) + (66*a*tan(1/2*d*x + 1/2*c)^3 + 15*a*tan(1/2*d*x + 1/2*c)^2 - 3*a*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
13,1,199,0,0.458824," ","integrate(cot(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 960 \, {\left(d x + c\right)} a + 1800 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 660 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1920 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - \frac{4110 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 660 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 70 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a*tan(1/2*d*x + 1/2*c)^5 + 15*a*tan(1/2*d*x + 1/2*c)^4 - 70*a*tan(1/2*d*x + 1/2*c)^3 - 240*a*tan(1/2*d*x + 1/2*c)^2 - 960*(d*x + c)*a + 1800*a*log(abs(tan(1/2*d*x + 1/2*c))) + 660*a*tan(1/2*d*x + 1/2*c) + 1920*a/(tan(1/2*d*x + 1/2*c)^2 + 1) - (4110*a*tan(1/2*d*x + 1/2*c)^5 + 660*a*tan(1/2*d*x + 1/2*c)^4 - 240*a*tan(1/2*d*x + 1/2*c)^3 - 70*a*tan(1/2*d*x + 1/2*c)^2 + 15*a*tan(1/2*d*x + 1/2*c) + 6*a)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
14,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,1,6695,0,19.303445," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c),x, algorithm=""giac"")","-\frac{4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 4 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} - 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 4 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} - 16 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 4 \, a^{2} \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(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - 16 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 4 \, a^{2} \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} \tan\left(c\right)^{2} - 4 \, a^{2} \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} \tan\left(c\right)^{2} + 4 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} - a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} - 16 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} \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(\frac{1}{2} \, c\right)^{2} - 16 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} \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} - 4 \, a^{2} \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} + 4 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} \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(d x\right)^{2} \tan\left(c\right)^{2} - 4 \, a^{2} \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(d x\right)^{2} \tan\left(c\right)^{2} + 4 \, a^{2} \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} + 16 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(c\right)^{2} + 4 \, a^{2} \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(c\right)^{2} - 4 \, a^{2} \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(c\right)^{2} + 4 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 16 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 4 \, a^{2} \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} \tan\left(c\right)^{2} - 4 \, a^{2} \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} \tan\left(c\right)^{2} + 4 \, a^{2} \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(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) + 4 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + a^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 4 \, a^{2} \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(d x\right)^{2} - 4 \, a^{2} \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(d x\right)^{2} + 4 \, a^{2} \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} + 16 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) + 4 \, a^{2} \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 \, a^{2} \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 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} + 16 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} \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 \, a^{2} \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 \, a^{2} \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(\frac{1}{2} \, c\right)^{2} - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} \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(c\right)^{2} - 4 \, a^{2} \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(c\right)^{2} + 4 \, a^{2} \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} + 16 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(c\right)^{2} + 16 \, a^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + a^{2} \tan\left(d x\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} \tan\left(d x\right) \tan\left(c\right) + a^{2} \tan\left(c\right)^{2} + 4 \, a^{2} \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^{2} \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^{2} \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) + 16 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) + 16 \, a^{2} \tan\left(\frac{1}{2} \, c\right) - a^{2}}{4 \, {\left(d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(c\right)^{2} + d\right)}}"," ",0,"-1/4*(4*a^2*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(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 - 4*a^2*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(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 4*a^2*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(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 - a^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 4*a^2*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(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a^2*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(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a^2*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(1/2*d*x)^2*tan(1/2*c)^2 + 4*a^2*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(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 - 4*a^2*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(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + 4*a^2*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(1/2*d*x)^2*tan(c)^2 - 16*a^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(c)^2 + 4*a^2*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(d*x)^2*tan(1/2*c)^2*tan(c)^2 - 4*a^2*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(d*x)^2*tan(1/2*c)^2*tan(c)^2 + 4*a^2*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(1/2*c)^2*tan(c)^2 - 16*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^2 + 4*a^2*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*tan(c)^2 - 4*a^2*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*tan(c)^2 + 4*a^2*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(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + a^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - a^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 - a^2*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + a^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 4*a^2*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(d*x)^2*tan(1/2*d*x)^2 - 4*a^2*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(d*x)^2*tan(1/2*d*x)^2 + 4*a^2*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(1/2*d*x)^2 - 16*a^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*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(d*x)^2*tan(1/2*c)^2 - 4*a^2*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(d*x)^2*tan(1/2*c)^2 + 4*a^2*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(1/2*c)^2 - 16*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^2 + 4*a^2*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 - 4*a^2*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 + 4*a^2*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(1/2*d*x)^2*tan(1/2*c)^2 + 4*a^2*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(d*x)^2*tan(c)^2 - 4*a^2*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(d*x)^2*tan(c)^2 + 4*a^2*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 + 16*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(c)^2 + 4*a^2*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(c)^2 - 4*a^2*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(c)^2 + 4*a^2*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(1/2*d*x)^2*tan(c)^2 + 16*a^2*tan(d*x)^2*tan(1/2*c)*tan(c)^2 - 16*a^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(c)^2 + 4*a^2*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*tan(c)^2 - 4*a^2*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*tan(c)^2 + 4*a^2*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(1/2*c)^2*tan(c)^2 - 16*a^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^2 + a^2*tan(d*x)^2*tan(1/2*d*x)^2 + a^2*tan(d*x)^2*tan(1/2*c)^2 - a^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a^2*tan(d*x)*tan(1/2*d*x)^2*tan(c) + 4*a^2*tan(d*x)*tan(1/2*c)^2*tan(c) - a^2*tan(d*x)^2*tan(c)^2 + a^2*tan(1/2*d*x)^2*tan(c)^2 + a^2*tan(1/2*c)^2*tan(c)^2 + 4*a^2*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(d*x)^2 - 4*a^2*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(d*x)^2 + 4*a^2*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 + 16*a^2*tan(d*x)^2*tan(1/2*d*x) + 4*a^2*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*a^2*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*a^2*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(1/2*d*x)^2 + 16*a^2*tan(d*x)^2*tan(1/2*c) - 16*a^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*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*a^2*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*a^2*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(1/2*c)^2 - 16*a^2*tan(1/2*d*x)*tan(1/2*c)^2 + 4*a^2*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(c)^2 - 4*a^2*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(c)^2 + 4*a^2*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 + 16*a^2*tan(1/2*d*x)*tan(c)^2 + 16*a^2*tan(1/2*c)*tan(c)^2 + a^2*tan(d*x)^2 - a^2*tan(1/2*d*x)^2 - a^2*tan(1/2*c)^2 + 4*a^2*tan(d*x)*tan(c) + a^2*tan(c)^2 + 4*a^2*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^2*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^2*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)) + 16*a^2*tan(1/2*d*x) + 16*a^2*tan(1/2*c) - a^2)/(d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + d*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + d*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^2 + d*tan(d*x)^2*tan(1/2*c)^2 + d*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(d*x)^2*tan(c)^2 + d*tan(1/2*d*x)^2*tan(c)^2 + d*tan(1/2*c)^2*tan(c)^2 + d*tan(d*x)^2 + d*tan(1/2*d*x)^2 + d*tan(1/2*c)^2 + d*tan(c)^2 + d)","B",0
17,1,47,0,0.389361," ","integrate(cot(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{a^{2} {\left(\frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right)\right)}^{2} + 4 \, a^{2} {\left(\frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right)\right)}}{2 \, d}"," ",0,"-1/2*(a^2*(1/sin(d*x + c) + sin(d*x + c))^2 + 4*a^2*(1/sin(d*x + c) + sin(d*x + c)))/d","A",0
18,1,121,0,0.957648," ","integrate(cot(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{15 \, a^{2} \sin\left(d x + c\right)^{2} - 60 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 60 \, a^{2} \sin\left(d x + c\right) + \frac{147 \, a^{2} \sin\left(d x + c\right)^{6} + 180 \, a^{2} \sin\left(d x + c\right)^{5} - 60 \, a^{2} \sin\left(d x + c\right)^{3} - 15 \, a^{2} \sin\left(d x + c\right)^{2} + 12 \, a^{2} \sin\left(d x + c\right) + 5 \, a^{2}}{\sin\left(d x + c\right)^{6}}}{30 \, d}"," ",0,"-1/30*(15*a^2*sin(d*x + c)^2 - 60*a^2*log(abs(sin(d*x + c))) + 60*a^2*sin(d*x + c) + (147*a^2*sin(d*x + c)^6 + 180*a^2*sin(d*x + c)^5 - 60*a^2*sin(d*x + c)^3 - 15*a^2*sin(d*x + c)^2 + 12*a^2*sin(d*x + c) + 5*a^2)/sin(d*x + c)^6)/d","A",0
19,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,1,5370,0,24.521731," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c)^2,x, algorithm=""giac"")","-\frac{5 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 5 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 5 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 20 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} + 5 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 5 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 5 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 5 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 20 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 5 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 20 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 5 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 5 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 20 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 20 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 20 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} + 32 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 5 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 4 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 20 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 2 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 20 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 20 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 5 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 5 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 20 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 20 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 20 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 32 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 5 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 5 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 20 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 20 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 20 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 32 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 5 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 5 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 20 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 20 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 32 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 96 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{3} - 20 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 32 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} + 32 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 5 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 16 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 5 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 5 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 5 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} - 20 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 20 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 5 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 5 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 20 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 20 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 5 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 5 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + 20 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 20 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 20 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 32 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 5 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 5 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 20 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 20 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 32 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 96 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 20 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 32 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 32 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 5 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 5 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 20 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 20 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 32 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 96 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 20 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 32 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 32 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 5 \, a^{2} d x \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 5 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 20 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} + 32 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 32 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 96 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{3} - 32 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 4 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} - 16 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 16 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 20 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 4 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 20 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 2 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} - 20 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 2 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 20 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 4 \, a^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 5 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} + 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + 20 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 20 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 32 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 96 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 20 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 32 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 32 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 5 \, a^{2} d x \tan\left(\frac{1}{2} \, c\right)^{4} + 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 5 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 20 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) + 32 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 32 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 96 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 32 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 5 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 20 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 32 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 32 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 96 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 32 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 8 \, a^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 5 \, a^{2} d x \tan\left(d x\right) \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 32 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 5 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} - 16 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 20 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 20 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 5 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 5 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 20 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 20 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 5 \, a^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 5 \, a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 5 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 5 \, a^{2} d x \tan\left(d x\right)^{2} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + 20 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 32 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 32 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 96 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 32 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 8 \, a^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 5 \, a^{2} d x \tan\left(d x\right) \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(c\right) + 32 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 5 \, a^{2} d x \tan\left(c\right)^{2} + 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 32 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right) \tan\left(c\right)^{3} + 4 \, a^{2} \tan\left(d x\right)^{3} - 20 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 20 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) + 2 \, a^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + 4 \, a^{2} \tan\left(c\right)^{3} - 5 \, a^{2} d x + 8 \, a^{2} \tan\left(d x\right)^{2} - 32 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 8 \, a^{2} \tan\left(d x\right) \tan\left(c\right) + 8 \, a^{2} \tan\left(c\right)^{2} + 5 \, a^{2} \tan\left(d x\right) + 5 \, a^{2} \tan\left(c\right) + 8 \, a^{2}}{2 \, {\left(d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} + d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 4 \, d \tan\left(d x\right)^{2} \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} \tan\left(\frac{1}{2} \, c\right)^{4} - d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 4 \, d \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 4 \, d \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 4 \, d \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 4 \, d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} + d \tan\left(\frac{1}{2} \, d x\right)^{4} + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 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} + d \tan\left(d x\right)^{3} \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 4 \, d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + d \tan\left(d x\right) \tan\left(c\right)^{3} - d \tan\left(d x\right)^{2} + 4 \, d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + d \tan\left(d x\right) \tan\left(c\right) - d \tan\left(c\right)^{2} - d\right)}}"," ",0,"-1/2*(5*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 5*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - 5*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 20*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 + 5*a^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 - 8*a^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 5*a^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 5*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 - 5*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 20*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + 5*a^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - 8*a^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 20*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 - 5*a^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 8*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 5*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^3 - 20*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 20*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 20*a^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 + 32*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - 5*a^2*d*x*tan(d*x)^3*tan(1/2*c)^4*tan(c)^3 - 8*a^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 4*a^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4 + 2*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - 20*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 + 2*a^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 20*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 + 4*a^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 20*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3 - 5*a^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4 + 8*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 5*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(c) - 20*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 20*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 20*a^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + 32*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 5*a^2*d*x*tan(d*x)^3*tan(1/2*c)^4*tan(c) - 8*a^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 5*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + 20*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 20*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + 20*a^2*d*x*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 - 32*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 + 5*a^2*d*x*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 8*a^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 5*a^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(c)^3 - 8*a^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^3 - 20*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 20*a^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 32*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 96*a^2*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^3 - 20*a^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 32*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 + 32*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - 5*a^2*d*x*tan(d*x)*tan(1/2*c)^4*tan(c)^3 - 8*a^2*tan(d*x)^3*tan(1/2*c)^4*tan(c)^3 - 16*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3 + 5*a^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4 - 8*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + 5*a^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - 5*a^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^2 - 20*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 - 20*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 - 8*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 - 5*a^2*tan(d*x)^3*tan(1/2*c)^4*tan(c)^2 - 5*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^3 - 20*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 20*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 16*a^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - 5*a^2*tan(d*x)^2*tan(1/2*c)^4*tan(c)^3 + 5*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4 + 20*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c) + 20*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3 + 20*a^2*d*x*tan(1/2*d*x)^3*tan(1/2*c)^3 - 32*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3 + 5*a^2*d*x*tan(d*x)^2*tan(1/2*c)^4 + 8*a^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 5*a^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 8*a^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(c) - 20*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 20*a^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 32*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 96*a^2*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - 20*a^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 32*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) + 32*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 5*a^2*d*x*tan(d*x)*tan(1/2*c)^4*tan(c) - 8*a^2*tan(d*x)^3*tan(1/2*c)^4*tan(c) + 5*a^2*d*x*tan(1/2*d*x)^4*tan(c)^2 + 8*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + 20*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + 20*a^2*d*x*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 32*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 96*a^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 20*a^2*d*x*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + 32*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 - 32*a^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 + 5*a^2*d*x*tan(1/2*c)^4*tan(c)^2 + 8*a^2*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 5*a^2*d*x*tan(d*x)^3*tan(c)^3 - 8*a^2*tan(d*x)*tan(1/2*d*x)^4*tan(c)^3 - 20*a^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 + 32*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 32*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 96*a^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^3 - 32*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 8*a^2*tan(d*x)*tan(1/2*c)^4*tan(c)^3 - 4*a^2*tan(d*x)^3*tan(1/2*d*x)^4 - 16*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c) - 16*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3 - 20*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3 - 4*a^2*tan(d*x)^3*tan(1/2*c)^4 - 2*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(c) - 8*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 8*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 20*a^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 2*a^2*tan(d*x)^2*tan(1/2*c)^4*tan(c) - 2*a^2*tan(d*x)*tan(1/2*d*x)^4*tan(c)^2 - 20*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 - 8*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 - 8*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 - 2*a^2*tan(d*x)*tan(1/2*c)^4*tan(c)^2 - 4*a^2*tan(1/2*d*x)^4*tan(c)^3 - 20*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 16*a^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 16*a^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 4*a^2*tan(1/2*c)^4*tan(c)^3 + 5*a^2*d*x*tan(1/2*d*x)^4 + 8*a^2*tan(d*x)^2*tan(1/2*d*x)^4 + 20*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c) + 20*a^2*d*x*tan(1/2*d*x)^3*tan(1/2*c) + 32*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c) + 96*a^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 20*a^2*d*x*tan(1/2*d*x)*tan(1/2*c)^3 + 32*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3 - 32*a^2*tan(1/2*d*x)^3*tan(1/2*c)^3 + 5*a^2*d*x*tan(1/2*c)^4 + 8*a^2*tan(d*x)^2*tan(1/2*c)^4 + 5*a^2*d*x*tan(d*x)^3*tan(c) - 8*a^2*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 20*a^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) + 32*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 32*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 96*a^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - 32*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 8*a^2*tan(d*x)*tan(1/2*c)^4*tan(c) - 5*a^2*d*x*tan(d*x)^2*tan(c)^2 + 8*a^2*tan(1/2*d*x)^4*tan(c)^2 + 20*a^2*d*x*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 - 32*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + 32*a^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 96*a^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 32*a^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + 8*a^2*tan(1/2*c)^4*tan(c)^2 + 5*a^2*d*x*tan(d*x)*tan(c)^3 - 8*a^2*tan(d*x)^3*tan(c)^3 + 32*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 5*a^2*tan(d*x)*tan(1/2*d*x)^4 - 16*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c) - 20*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c) - 20*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3 - 5*a^2*tan(d*x)*tan(1/2*c)^4 - 5*a^2*tan(1/2*d*x)^4*tan(c) - 8*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 20*a^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 20*a^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 5*a^2*tan(1/2*c)^4*tan(c) + 5*a^2*tan(d*x)^3*tan(c)^2 - 8*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + 5*a^2*tan(d*x)^2*tan(c)^3 - 16*a^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 5*a^2*d*x*tan(d*x)^2 + 8*a^2*tan(1/2*d*x)^4 + 20*a^2*d*x*tan(1/2*d*x)*tan(1/2*c) - 32*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c) + 32*a^2*tan(1/2*d*x)^3*tan(1/2*c) + 96*a^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 32*a^2*tan(1/2*d*x)*tan(1/2*c)^3 + 8*a^2*tan(1/2*c)^4 + 5*a^2*d*x*tan(d*x)*tan(c) - 8*a^2*tan(d*x)^3*tan(c) + 32*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 5*a^2*d*x*tan(c)^2 + 8*a^2*tan(d*x)^2*tan(c)^2 - 32*a^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 - 8*a^2*tan(d*x)*tan(c)^3 + 4*a^2*tan(d*x)^3 - 20*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c) + 2*a^2*tan(d*x)^2*tan(c) - 20*a^2*tan(1/2*d*x)*tan(1/2*c)*tan(c) + 2*a^2*tan(d*x)*tan(c)^2 + 4*a^2*tan(c)^3 - 5*a^2*d*x + 8*a^2*tan(d*x)^2 - 32*a^2*tan(1/2*d*x)*tan(1/2*c) - 8*a^2*tan(d*x)*tan(c) + 8*a^2*tan(c)^2 + 5*a^2*tan(d*x) + 5*a^2*tan(c) + 8*a^2)/(d*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + d*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 4*d*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 + d*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 - d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 4*d*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + d*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 4*d*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 - d*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - d*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^3 - 4*d*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 4*d*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - d*tan(d*x)^3*tan(1/2*c)^4*tan(c)^3 + 4*d*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3 - d*tan(1/2*d*x)^4*tan(1/2*c)^4 - d*tan(d*x)^3*tan(1/2*d*x)^4*tan(c) - 4*d*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 4*d*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - d*tan(d*x)^3*tan(1/2*c)^4*tan(c) + d*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + 4*d*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 4*d*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + 4*d*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 + d*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 - d*tan(d*x)*tan(1/2*d*x)^4*tan(c)^3 - 4*d*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 4*d*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - d*tan(d*x)*tan(1/2*c)^4*tan(c)^3 + d*tan(d*x)^2*tan(1/2*d*x)^4 + 4*d*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c) + 4*d*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3 + 4*d*tan(1/2*d*x)^3*tan(1/2*c)^3 + d*tan(d*x)^2*tan(1/2*c)^4 - d*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 4*d*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - d*tan(d*x)*tan(1/2*c)^4*tan(c) + d*tan(1/2*d*x)^4*tan(c)^2 + 4*d*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + 4*d*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 4*d*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + d*tan(1/2*c)^4*tan(c)^2 + d*tan(d*x)^3*tan(c)^3 - 4*d*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 + d*tan(1/2*d*x)^4 + 4*d*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c) + 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 + d*tan(d*x)^3*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) - d*tan(d*x)^2*tan(c)^2 + 4*d*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + d*tan(d*x)*tan(c)^3 - d*tan(d*x)^2 + 4*d*tan(1/2*d*x)*tan(1/2*c) + d*tan(d*x)*tan(c) - d*tan(c)^2 - d)","B",0
22,1,38,0,0.324282," ","integrate((a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3}{2} \, a^{2} x - \frac{2 \, a^{2} \cos\left(d x + c\right)}{d} - \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"3/2*a^2*x - 2*a^2*cos(d*x + c)/d - 1/4*a^2*sin(2*d*x + 2*c)/d","A",0
23,1,143,0,0.255007," ","integrate(cot(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a^{2} - 4 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{4 \, a^{2} \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)} + \frac{2 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*((d*x + c)*a^2 - 4*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - a^2*tan(1/2*d*x + 1/2*c) + (4*a^2*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c) + 2*(a^2*tan(1/2*d*x + 1/2*c)^3 - 4*a^2*tan(1/2*d*x + 1/2*c)^2 - a^2*tan(1/2*d*x + 1/2*c) - 4*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
24,1,209,0,0.552317," ","integrate(cot(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, {\left(d x + c\right)} a^{2} - 72 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{24 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{132 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a^{2} \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)^{3}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*(d*x + c)*a^2 - 72*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a^2*tan(1/2*d*x + 1/2*c) + 24*(a^2*tan(1/2*d*x + 1/2*c)^3 - 4*a^2*tan(1/2*d*x + 1/2*c)^2 - a^2*tan(1/2*d*x + 1/2*c) - 4*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + (132*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*a^2*tan(1/2*d*x + 1/2*c)^2 - 6*a^2*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
25,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c)^7,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,1,94,0,1.430737," ","integrate(cot(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, a^{3} \sin\left(d x + c\right)^{3} + 9 \, a^{3} \sin\left(d x + c\right)^{2} - 12 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 12 \, a^{3} \sin\left(d x + c\right) + \frac{3 \, {\left(6 \, a^{3} \sin\left(d x + c\right)^{2} + 6 \, a^{3} \sin\left(d x + c\right) + a^{3}\right)}}{\sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"-1/6*(2*a^3*sin(d*x + c)^3 + 9*a^3*sin(d*x + c)^2 - 12*a^3*log(abs(sin(d*x + c))) + 12*a^3*sin(d*x + c) + 3*(6*a^3*sin(d*x + c)^2 + 6*a^3*sin(d*x + c) + a^3)/sin(d*x + c)^2)/d","A",0
29,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,1,55,0,0.368374," ","integrate((a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5}{2} \, a^{3} x + \frac{a^{3} \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{15 \, a^{3} \cos\left(d x + c\right)}{4 \, d} - \frac{3 \, a^{3} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"5/2*a^3*x + 1/12*a^3*cos(3*d*x + 3*c)/d - 15/4*a^3*cos(d*x + c)/d - 3/4*a^3*sin(2*d*x + 2*c)/d","A",0
33,1,162,0,1.394631," ","integrate(cot(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{3} + 18 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3 \, {\left(6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*a^3 + 18*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 3*a^3*tan(1/2*d*x + 1/2*c) - 3*(6*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c) - 2*(9*a^3*tan(1/2*d*x + 1/2*c)^5 - 12*a^3*tan(1/2*d*x + 1/2*c)^4 - 36*a^3*tan(1/2*d*x + 1/2*c)^2 - 9*a^3*tan(1/2*d*x + 1/2*c) - 16*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
34,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4*tan(d*x+c)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4*tan(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4*tan(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
37,1,96,0,0.548101," ","integrate(cot(d*x+c)^3*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{3 \, a^{4} \sin\left(d x + c\right)^{4} + 16 \, a^{4} \sin\left(d x + c\right)^{3} + 30 \, a^{4} \sin\left(d x + c\right)^{2} - 60 \, a^{4} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + \frac{6 \, {\left(15 \, a^{4} \sin\left(d x + c\right)^{2} + 8 \, a^{4} \sin\left(d x + c\right) + a^{4}\right)}}{\sin\left(d x + c\right)^{2}}}{12 \, d}"," ",0,"-1/12*(3*a^4*sin(d*x + c)^4 + 16*a^4*sin(d*x + c)^3 + 30*a^4*sin(d*x + c)^2 - 60*a^4*log(abs(sin(d*x + c))) + 6*(15*a^4*sin(d*x + c)^2 + 8*a^4*sin(d*x + c) + a^4)/sin(d*x + c)^2)/d","A",0
38,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4*tan(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4*tan(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,1,72,0,1.530896," ","integrate((a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{35}{8} \, a^{4} x + \frac{a^{4} \cos\left(3 \, d x + 3 \, c\right)}{3 \, d} - \frac{7 \, a^{4} \cos\left(d x + c\right)}{d} + \frac{a^{4} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{7 \, a^{4} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"35/8*a^4*x + 1/3*a^4*cos(3*d*x + 3*c)/d - 7*a^4*cos(d*x + c)/d + 1/32*a^4*sin(4*d*x + 4*c)/d - 7/4*a^4*sin(2*d*x + 2*c)/d","A",0
41,1,194,0,0.713938," ","integrate(cot(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{51 \, {\left(d x + c\right)} a^{4} + 96 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 12 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{12 \, {\left(8 \, a^{4} \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)} - \frac{2 \, {\left(69 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 93 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 192 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 93 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 256 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 69 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 64 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(51*(d*x + c)*a^4 + 96*a^4*log(abs(tan(1/2*d*x + 1/2*c))) + 12*a^4*tan(1/2*d*x + 1/2*c) - 12*(8*a^4*tan(1/2*d*x + 1/2*c) + a^4)/tan(1/2*d*x + 1/2*c) - 2*(69*a^4*tan(1/2*d*x + 1/2*c)^7 + 93*a^4*tan(1/2*d*x + 1/2*c)^5 - 192*a^4*tan(1/2*d*x + 1/2*c)^4 - 93*a^4*tan(1/2*d*x + 1/2*c)^3 - 256*a^4*tan(1/2*d*x + 1/2*c)^2 - 69*a^4*tan(1/2*d*x + 1/2*c) - 64*a^4)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
42,1,274,0,1.291736," ","integrate(cot(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 183 \, {\left(d x + c\right)} a^{4} - 48 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 57 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{88 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 57 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} + \frac{2 \, {\left(57 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 81 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 96 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 81 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 57 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 32 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(a^4*tan(1/2*d*x + 1/2*c)^3 + 12*a^4*tan(1/2*d*x + 1/2*c)^2 - 183*(d*x + c)*a^4 - 48*a^4*log(abs(tan(1/2*d*x + 1/2*c))) + 57*a^4*tan(1/2*d*x + 1/2*c) + (88*a^4*tan(1/2*d*x + 1/2*c)^3 - 57*a^4*tan(1/2*d*x + 1/2*c)^2 - 12*a^4*tan(1/2*d*x + 1/2*c) - a^4)/tan(1/2*d*x + 1/2*c)^3 + 2*(57*a^4*tan(1/2*d*x + 1/2*c)^7 + 96*a^4*tan(1/2*d*x + 1/2*c)^6 + 81*a^4*tan(1/2*d*x + 1/2*c)^5 + 96*a^4*tan(1/2*d*x + 1/2*c)^4 - 81*a^4*tan(1/2*d*x + 1/2*c)^3 + 32*a^4*tan(1/2*d*x + 1/2*c)^2 - 57*a^4*tan(1/2*d*x + 1/2*c) + 32*a^4)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
43,1,339,0,1.392146," ","integrate(cot(d*x+c)^6*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 85 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5820 \, {\left(d x + c\right)} a^{4} - 1200 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 2670 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{40 \, {\left(45 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 192 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 69 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 384 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 69 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 128 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}} + \frac{2740 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2670 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 85 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 30 \, a^{4} \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)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^4*tan(1/2*d*x + 1/2*c)^5 + 30*a^4*tan(1/2*d*x + 1/2*c)^4 + 85*a^4*tan(1/2*d*x + 1/2*c)^3 - 240*a^4*tan(1/2*d*x + 1/2*c)^2 + 5820*(d*x + c)*a^4 - 1200*a^4*log(abs(tan(1/2*d*x + 1/2*c))) - 2670*a^4*tan(1/2*d*x + 1/2*c) - 40*(45*a^4*tan(1/2*d*x + 1/2*c)^7 + 192*a^4*tan(1/2*d*x + 1/2*c)^6 + 69*a^4*tan(1/2*d*x + 1/2*c)^5 + 384*a^4*tan(1/2*d*x + 1/2*c)^4 - 69*a^4*tan(1/2*d*x + 1/2*c)^3 + 320*a^4*tan(1/2*d*x + 1/2*c)^2 - 45*a^4*tan(1/2*d*x + 1/2*c) + 128*a^4)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4 + (2740*a^4*tan(1/2*d*x + 1/2*c)^5 + 2670*a^4*tan(1/2*d*x + 1/2*c)^4 + 240*a^4*tan(1/2*d*x + 1/2*c)^3 - 85*a^4*tan(1/2*d*x + 1/2*c)^2 - 30*a^4*tan(1/2*d*x + 1/2*c) - 3*a^4)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
44,1,136,0,9.205990," ","integrate(tan(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{420 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{420 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(385 \, \sin\left(d x + c\right)^{3} - 807 \, \sin\left(d x + c\right)^{2} + 567 \, \sin\left(d x + c\right) - 129\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{875 \, \sin\left(d x + c\right)^{4} + 1964 \, \sin\left(d x + c\right)^{3} + 1554 \, \sin\left(d x + c\right)^{2} + 396 \, \sin\left(d x + c\right) - 21}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"-1/3072*(420*log(abs(sin(d*x + c) + 1))/a - 420*log(abs(sin(d*x + c) - 1))/a + 2*(385*sin(d*x + c)^3 - 807*sin(d*x + c)^2 + 567*sin(d*x + c) - 129)/(a*(sin(d*x + c) - 1)^3) - (875*sin(d*x + c)^4 + 1964*sin(d*x + c)^3 + 1554*sin(d*x + c)^2 + 396*sin(d*x + c) - 21)/(a*(sin(d*x + c) + 1)^4))/d","A",0
45,1,116,0,3.137278," ","integrate(tan(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{30 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{30 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{3 \, {\left(15 \, \sin\left(d x + c\right)^{2} - 18 \, \sin\left(d x + c\right) + 5\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{55 \, \sin\left(d x + c\right)^{3} + 69 \, \sin\left(d x + c\right)^{2} + 15 \, \sin\left(d x + c\right) - 7}{a {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{192 \, d}"," ",0,"1/192*(30*log(abs(sin(d*x + c) + 1))/a - 30*log(abs(sin(d*x + c) - 1))/a + 3*(15*sin(d*x + c)^2 - 18*sin(d*x + c) + 5)/(a*(sin(d*x + c) - 1)^2) - (55*sin(d*x + c)^3 + 69*sin(d*x + c)^2 + 15*sin(d*x + c) - 7)/(a*(sin(d*x + c) + 1)^3))/d","A",0
46,1,96,0,0.774938," ","integrate(tan(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{6 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(3 \, \sin\left(d x + c\right) - 1\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}} - \frac{9 \, \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) - 3}{a {\left(\sin\left(d x + c\right) + 1\right)}^{2}}}{32 \, d}"," ",0,"-1/32*(6*log(abs(sin(d*x + c) + 1))/a - 6*log(abs(sin(d*x + c) - 1))/a + 2*(3*sin(d*x + c) - 1)/(a*(sin(d*x + c) - 1)) - (9*sin(d*x + c)^2 + 2*sin(d*x + c) - 3)/(a*(sin(d*x + c) + 1)^2))/d","A",0
47,1,58,0,0.294956," ","integrate(tan(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{\sin\left(d x + c\right) - 1}{a {\left(\sin\left(d x + c\right) + 1\right)}}}{4 \, d}"," ",0,"1/4*(log(abs(sin(d*x + c) + 1))/a - log(abs(sin(d*x + c) - 1))/a - (sin(d*x + c) - 1)/(a*(sin(d*x + c) + 1)))/d","A",0
48,1,33,0,1.100741," ","integrate(cot(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{\log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a}}{d}"," ",0,"-(log(abs(sin(d*x + c) + 1))/a - log(abs(sin(d*x + c)))/a)/d","A",0
49,1,26,0,1.123679," ","integrate(cot(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, \sin\left(d x + c\right) - 1}{2 \, a d \sin\left(d x + c\right)^{2}}"," ",0,"1/2*(2*sin(d*x + c) - 1)/(a*d*sin(d*x + c)^2)","A",0
50,1,46,0,0.270886," ","integrate(cot(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{12 \, \sin\left(d x + c\right)^{3} - 6 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) + 3}{12 \, a d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(12*sin(d*x + c)^3 - 6*sin(d*x + c)^2 - 4*sin(d*x + c) + 3)/(a*d*sin(d*x + c)^4)","A",0
51,1,66,0,0.971647," ","integrate(cot(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{30 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} - 20 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)^{2} + 6 \, \sin\left(d x + c\right) - 5}{30 \, a d \sin\left(d x + c\right)^{6}}"," ",0,"1/30*(30*sin(d*x + c)^5 - 15*sin(d*x + c)^4 - 20*sin(d*x + c)^3 + 15*sin(d*x + c)^2 + 6*sin(d*x + c) - 5)/(a*d*sin(d*x + c)^6)","A",0
52,1,86,0,0.374428," ","integrate(cot(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{280 \, \sin\left(d x + c\right)^{7} - 140 \, \sin\left(d x + c\right)^{6} - 280 \, \sin\left(d x + c\right)^{5} + 210 \, \sin\left(d x + c\right)^{4} + 168 \, \sin\left(d x + c\right)^{3} - 140 \, \sin\left(d x + c\right)^{2} - 40 \, \sin\left(d x + c\right) + 35}{280 \, a d \sin\left(d x + c\right)^{8}}"," ",0,"-1/280*(280*sin(d*x + c)^7 - 140*sin(d*x + c)^6 - 280*sin(d*x + c)^5 + 210*sin(d*x + c)^4 + 168*sin(d*x + c)^3 - 140*sin(d*x + c)^2 - 40*sin(d*x + c) + 35)/(a*d*sin(d*x + c)^8)","A",0
53,1,172,0,4.391102," ","integrate(tan(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{7 \, {\left(25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 140 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{5}} - \frac{175 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1260 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3815 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6020 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4641 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1792 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 281}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{560 \, d}"," ",0,"-1/560*(7*(25*tan(1/2*d*x + 1/2*c)^4 - 120*tan(1/2*d*x + 1/2*c)^3 + 210*tan(1/2*d*x + 1/2*c)^2 - 140*tan(1/2*d*x + 1/2*c) + 33)/(a*(tan(1/2*d*x + 1/2*c) - 1)^5) - (175*tan(1/2*d*x + 1/2*c)^6 + 1260*tan(1/2*d*x + 1/2*c)^5 + 3815*tan(1/2*d*x + 1/2*c)^4 + 6020*tan(1/2*d*x + 1/2*c)^3 + 4641*tan(1/2*d*x + 1/2*c)^2 + 1792*tan(1/2*d*x + 1/2*c) + 281)/(a*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","B",0
54,1,120,0,6.775988," ","integrate(tan(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{5 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 490 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 320 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 73}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(5*(9*tan(1/2*d*x + 1/2*c)^2 - 24*tan(1/2*d*x + 1/2*c) + 11)/(a*(tan(1/2*d*x + 1/2*c) - 1)^3) - (45*tan(1/2*d*x + 1/2*c)^4 + 240*tan(1/2*d*x + 1/2*c)^3 + 490*tan(1/2*d*x + 1/2*c)^2 + 320*tan(1/2*d*x + 1/2*c) + 73)/(a*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
55,1,68,0,0.659723," ","integrate(tan(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3/(a*(tan(1/2*d*x + 1/2*c) - 1)) - (3*tan(1/2*d*x + 1/2*c)^2 + 12*tan(1/2*d*x + 1/2*c) + 5)/(a*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
56,1,21,0,0.340689," ","integrate(1/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2}{a d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}"," ",0,"-2/(a*d*(tan(1/2*d*x + 1/2*c) + 1))","A",0
57,1,65,0,4.004185," ","integrate(cot(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(2*log(abs(tan(1/2*d*x + 1/2*c)))/a - tan(1/2*d*x + 1/2*c)/a - (2*tan(1/2*d*x + 1/2*c) - 1)/(a*tan(1/2*d*x + 1/2*c)))/d","B",0
58,1,127,0,0.227798," ","integrate(cot(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{22 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(12*log(abs(tan(1/2*d*x + 1/2*c)))/a + (a^2*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*tan(1/2*d*x + 1/2*c))/a^3 - (22*tan(1/2*d*x + 1/2*c)^3 - 3*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 1)/(a*tan(1/2*d*x + 1/2*c)^3))/d","B",0
59,1,187,0,1.963374," ","integrate(cot(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{5}} - \frac{274 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{320 \, d}"," ",0,"-1/320*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a - (2*a^4*tan(1/2*d*x + 1/2*c)^5 - 5*a^4*tan(1/2*d*x + 1/2*c)^4 - 10*a^4*tan(1/2*d*x + 1/2*c)^3 + 40*a^4*tan(1/2*d*x + 1/2*c)^2 + 20*a^4*tan(1/2*d*x + 1/2*c))/a^5 - (274*tan(1/2*d*x + 1/2*c)^5 - 20*tan(1/2*d*x + 1/2*c)^4 - 40*tan(1/2*d*x + 1/2*c)^3 + 10*tan(1/2*d*x + 1/2*c)^2 + 5*tan(1/2*d*x + 1/2*c) - 2)/(a*tan(1/2*d*x + 1/2*c)^5))/d","B",0
60,1,244,0,0.316974," ","integrate(cot(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{840 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{3 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 63 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 315 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{7}} - \frac{2178 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, \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)^{7}}}{2688 \, d}"," ",0,"1/2688*(840*log(abs(tan(1/2*d*x + 1/2*c)))/a + (3*a^6*tan(1/2*d*x + 1/2*c)^7 - 7*a^6*tan(1/2*d*x + 1/2*c)^6 - 21*a^6*tan(1/2*d*x + 1/2*c)^5 + 63*a^6*tan(1/2*d*x + 1/2*c)^4 + 63*a^6*tan(1/2*d*x + 1/2*c)^3 - 315*a^6*tan(1/2*d*x + 1/2*c)^2 - 105*a^6*tan(1/2*d*x + 1/2*c))/a^7 - (2178*tan(1/2*d*x + 1/2*c)^7 - 105*tan(1/2*d*x + 1/2*c)^6 - 315*tan(1/2*d*x + 1/2*c)^5 + 63*tan(1/2*d*x + 1/2*c)^4 + 63*tan(1/2*d*x + 1/2*c)^3 - 21*tan(1/2*d*x + 1/2*c)^2 - 7*tan(1/2*d*x + 1/2*c) + 3)/(a*tan(1/2*d*x + 1/2*c)^7))/d","B",0
61,1,146,0,71.382045," ","integrate(tan(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{420 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2}} - \frac{420 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2}} + \frac{10 \, {\left(77 \, \sin\left(d x + c\right)^{3} - 105 \, \sin\left(d x + c\right)^{2} + 27 \, \sin\left(d x + c\right) + 9\right)}}{a^{2} {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{959 \, \sin\left(d x + c\right)^{5} + 6895 \, \sin\left(d x + c\right)^{4} + 14150 \, \sin\left(d x + c\right)^{3} + 13710 \, \sin\left(d x + c\right)^{2} + 6555 \, \sin\left(d x + c\right) + 1251}{a^{2} {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{15360 \, d}"," ",0,"-1/15360*(420*log(abs(sin(d*x + c) + 1))/a^2 - 420*log(abs(sin(d*x + c) - 1))/a^2 + 10*(77*sin(d*x + c)^3 - 105*sin(d*x + c)^2 + 27*sin(d*x + c) + 9)/(a^2*(sin(d*x + c) - 1)^3) - (959*sin(d*x + c)^5 + 6895*sin(d*x + c)^4 + 14150*sin(d*x + c)^3 + 13710*sin(d*x + c)^2 + 6555*sin(d*x + c) + 1251)/(a^2*(sin(d*x + c) + 1)^5))/d","A",0
62,1,126,0,19.848601," ","integrate(tan(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2}} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(15 \, \sin\left(d x + c\right)^{2} - 10 \, \sin\left(d x + c\right) - 1\right)}}{a^{2} {\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{125 \, \sin\left(d x + c\right)^{4} + 740 \, \sin\left(d x + c\right)^{3} + 1086 \, \sin\left(d x + c\right)^{2} + 676 \, \sin\left(d x + c\right) + 157}{a^{2} {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{1536 \, d}"," ",0,"1/1536*(60*log(abs(sin(d*x + c) + 1))/a^2 - 60*log(abs(sin(d*x + c) - 1))/a^2 + 6*(15*sin(d*x + c)^2 - 10*sin(d*x + c) - 1)/(a^2*(sin(d*x + c) - 1)^2) - (125*sin(d*x + c)^4 + 740*sin(d*x + c)^3 + 1086*sin(d*x + c)^2 + 676*sin(d*x + c) + 157)/(a^2*(sin(d*x + c) + 1)^4))/d","A",0
63,1,102,0,2.055544," ","integrate(tan(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, \sin\left(d x + c\right)}{a^{2} {\left(\sin\left(d x + c\right) - 1\right)}} - \frac{11 \, \sin\left(d x + c\right)^{3} + 51 \, \sin\left(d x + c\right)^{2} + 45 \, \sin\left(d x + c\right) + 13}{a^{2} {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{96 \, d}"," ",0,"-1/96*(6*log(abs(sin(d*x + c) + 1))/a^2 - 6*log(abs(sin(d*x + c) - 1))/a^2 + 6*sin(d*x + c)/(a^2*(sin(d*x + c) - 1)) - (11*sin(d*x + c)^3 + 51*sin(d*x + c)^2 + 45*sin(d*x + c) + 13)/(a^2*(sin(d*x + c) + 1)^3))/d","A",0
64,1,90,0,0.997063," ","integrate(tan(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{\log\left({\left| \frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) + 2 \right|}\right)}{a^{2}} - \frac{\log\left({\left| \frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) - 2 \right|}\right)}{a^{2}} - \frac{\frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) + 6}{a^{2} {\left(\frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) + 2\right)}}}{16 \, d}"," ",0,"1/16*(log(abs(1/sin(d*x + c) + sin(d*x + c) + 2))/a^2 - log(abs(1/sin(d*x + c) + sin(d*x + c) - 2))/a^2 - (1/sin(d*x + c) + sin(d*x + c) + 6)/(a^2*(1/sin(d*x + c) + sin(d*x + c) + 2)))/d","A",0
65,1,45,0,0.394895," ","integrate(cot(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a {\left(\frac{\log\left({\left| -\frac{a}{a \sin\left(d x + c\right) + a} + 1 \right|}\right)}{a^{3}} + \frac{1}{{\left(a \sin\left(d x + c\right) + a\right)} a^{2}}\right)}}{d}"," ",0,"a*(log(abs(-a/(a*sin(d*x + c) + a) + 1))/a^3 + 1/((a*sin(d*x + c) + a)*a^2))/d","A",0
66,1,115,0,0.489214," ","integrate(cot(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{32 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{16 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} + \frac{24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(32*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 16*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + (a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^2*tan(1/2*d*x + 1/2*c))/a^4 + (24*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 1)/(a^2*tan(1/2*d*x + 1/2*c)^2))/d","A",0
67,1,36,0,0.603775," ","integrate(cot(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{6 \, \sin\left(d x + c\right)^{2} - 8 \, \sin\left(d x + c\right) + 3}{12 \, a^{2} d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(6*sin(d*x + c)^2 - 8*sin(d*x + c) + 3)/(a^2*d*sin(d*x + c)^4)","A",0
68,1,46,0,0.605144," ","integrate(cot(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, \sin\left(d x + c\right)^{4} - 20 \, \sin\left(d x + c\right)^{3} + 12 \, \sin\left(d x + c\right) - 5}{30 \, a^{2} d \sin\left(d x + c\right)^{6}}"," ",0,"1/30*(15*sin(d*x + c)^4 - 20*sin(d*x + c)^3 + 12*sin(d*x + c) - 5)/(a^2*d*sin(d*x + c)^6)","A",0
69,1,76,0,0.770046," ","integrate(cot(d*x+c)^9/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{420 \, \sin\left(d x + c\right)^{6} - 560 \, \sin\left(d x + c\right)^{5} - 210 \, \sin\left(d x + c\right)^{4} + 672 \, \sin\left(d x + c\right)^{3} - 140 \, \sin\left(d x + c\right)^{2} - 240 \, \sin\left(d x + c\right) + 105}{840 \, a^{2} d \sin\left(d x + c\right)^{8}}"," ",0,"-1/840*(420*sin(d*x + c)^6 - 560*sin(d*x + c)^5 - 210*sin(d*x + c)^4 + 672*sin(d*x + c)^3 - 140*sin(d*x + c)^2 - 240*sin(d*x + c) + 105)/(a^2*d*sin(d*x + c)^8)","A",0
70,1,86,0,1.753742," ","integrate(cot(d*x+c)^11/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{630 \, \sin\left(d x + c\right)^{8} - 840 \, \sin\left(d x + c\right)^{7} - 630 \, \sin\left(d x + c\right)^{6} + 1512 \, \sin\left(d x + c\right)^{5} - 1080 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)^{2} + 280 \, \sin\left(d x + c\right) - 126}{1260 \, a^{2} d \sin\left(d x + c\right)^{10}}"," ",0,"1/1260*(630*sin(d*x + c)^8 - 840*sin(d*x + c)^7 - 630*sin(d*x + c)^6 + 1512*sin(d*x + c)^5 - 1080*sin(d*x + c)^3 + 315*sin(d*x + c)^2 + 280*sin(d*x + c) - 126)/(a^2*d*sin(d*x + c)^10)","A",0
71,1,116,0,1.327281," ","integrate(cot(d*x+c)^13/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{6930 \, \sin\left(d x + c\right)^{10} - 9240 \, \sin\left(d x + c\right)^{9} - 10395 \, \sin\left(d x + c\right)^{8} + 22176 \, \sin\left(d x + c\right)^{7} + 4620 \, \sin\left(d x + c\right)^{6} - 23760 \, \sin\left(d x + c\right)^{5} + 3465 \, \sin\left(d x + c\right)^{4} + 12320 \, \sin\left(d x + c\right)^{3} - 4158 \, \sin\left(d x + c\right)^{2} - 2520 \, \sin\left(d x + c\right) + 1155}{13860 \, a^{2} d \sin\left(d x + c\right)^{12}}"," ",0,"-1/13860*(6930*sin(d*x + c)^10 - 9240*sin(d*x + c)^9 - 10395*sin(d*x + c)^8 + 22176*sin(d*x + c)^7 + 4620*sin(d*x + c)^6 - 23760*sin(d*x + c)^5 + 3465*sin(d*x + c)^4 + 12320*sin(d*x + c)^3 - 4158*sin(d*x + c)^2 - 2520*sin(d*x + c) + 1155)/(a^2*d*sin(d*x + c)^12)","A",0
72,1,136,0,24.624687," ","integrate(tan(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3}} + \frac{30 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 10 \, \sin\left(d x + c\right) - 9\right)}}{a^{3} {\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{137 \, \sin\left(d x + c\right)^{5} + 1285 \, \sin\left(d x + c\right)^{4} + 4970 \, \sin\left(d x + c\right)^{3} + 6010 \, \sin\left(d x + c\right)^{2} + 3245 \, \sin\left(d x + c\right) + 673}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{15360 \, d}"," ",0,"1/15360*(60*log(abs(sin(d*x + c) + 1))/a^3 - 60*log(abs(sin(d*x + c) - 1))/a^3 + 30*(3*sin(d*x + c)^2 + 10*sin(d*x + c) - 9)/(a^3*(sin(d*x + c) - 1)^2) - (137*sin(d*x + c)^5 + 1285*sin(d*x + c)^4 + 4970*sin(d*x + c)^3 + 6010*sin(d*x + c)^2 + 3245*sin(d*x + c) + 673)/(a^3*(sin(d*x + c) + 1)^5))/d","A",0
73,1,114,0,1.911874," ","integrate(tan(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{12 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3}} + \frac{12 \, {\left(\sin\left(d x + c\right) + 1\right)}}{a^{3} {\left(\sin\left(d x + c\right) - 1\right)}} - \frac{25 \, \sin\left(d x + c\right)^{4} + 148 \, \sin\left(d x + c\right)^{3} + 366 \, \sin\left(d x + c\right)^{2} + 260 \, \sin\left(d x + c\right) + 65}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{768 \, d}"," ",0,"-1/768*(12*log(abs(sin(d*x + c) + 1))/a^3 - 12*log(abs(sin(d*x + c) - 1))/a^3 + 12*(sin(d*x + c) + 1)/(a^3*(sin(d*x + c) - 1)) - (25*sin(d*x + c)^4 + 148*sin(d*x + c)^3 + 366*sin(d*x + c)^2 + 260*sin(d*x + c) + 65)/(a^3*(sin(d*x + c) + 1)^4))/d","A",0
74,1,81,0,0.790147," ","integrate(tan(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{6 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3}} - \frac{11 \, \sin\left(d x + c\right)^{3} + 45 \, \sin\left(d x + c\right)^{2} + 69 \, \sin\left(d x + c\right) + 19}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{96 \, d}"," ",0,"1/96*(6*log(abs(sin(d*x + c) + 1))/a^3 - 6*log(abs(sin(d*x + c) - 1))/a^3 - (11*sin(d*x + c)^3 + 45*sin(d*x + c)^2 + 69*sin(d*x + c) + 19)/(a^3*(sin(d*x + c) + 1)^3))/d","A",0
75,1,59,0,0.640708," ","integrate(cot(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{2 \, \sin\left(d x + c\right) + 3}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*log(abs(sin(d*x + c) + 1))/a^3 - 2*log(abs(sin(d*x + c)))/a^3 - (2*sin(d*x + c) + 3)/(a^3*(sin(d*x + c) + 1)^2))/d","A",0
76,1,154,0,0.483888," ","integrate(cot(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{80 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{40 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 53 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2} a^{3}} + \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{8 \, d}"," ",0,"-1/8*(80*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 40*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (30*tan(1/2*d*x + 1/2*c)^4 + 40*tan(1/2*d*x + 1/2*c)^3 + 53*tan(1/2*d*x + 1/2*c)^2 + 10*tan(1/2*d*x + 1/2*c) - 1)/((tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c))^2*a^3) + (a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^3*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
77,1,174,0,0.962584," ","integrate(cot(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{1536 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{768 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{1600 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 456 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 108 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{3 \, {\left(a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 152 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{12}}}{192 \, d}"," ",0,"-1/192*(1536*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 768*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + (1600*tan(1/2*d*x + 1/2*c)^4 - 456*tan(1/2*d*x + 1/2*c)^3 + 108*tan(1/2*d*x + 1/2*c)^2 - 24*tan(1/2*d*x + 1/2*c) + 3)/(a^3*tan(1/2*d*x + 1/2*c)^4) + 3*(a^9*tan(1/2*d*x + 1/2*c)^4 - 8*a^9*tan(1/2*d*x + 1/2*c)^3 + 36*a^9*tan(1/2*d*x + 1/2*c)^2 - 152*a^9*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
78,1,46,0,0.813129," ","integrate(cot(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{20 \, \sin\left(d x + c\right)^{3} - 45 \, \sin\left(d x + c\right)^{2} + 36 \, \sin\left(d x + c\right) - 10}{60 \, a^{3} d \sin\left(d x + c\right)^{6}}"," ",0,"1/60*(20*sin(d*x + c)^3 - 45*sin(d*x + c)^2 + 36*sin(d*x + c) - 10)/(a^3*d*sin(d*x + c)^6)","A",0
79,1,66,0,2.038951," ","integrate(cot(d*x+c)^9/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{280 \, \sin\left(d x + c\right)^{5} - 630 \, \sin\left(d x + c\right)^{4} + 336 \, \sin\left(d x + c\right)^{3} + 280 \, \sin\left(d x + c\right)^{2} - 360 \, \sin\left(d x + c\right) + 105}{840 \, a^{3} d \sin\left(d x + c\right)^{8}}"," ",0,"-1/840*(280*sin(d*x + c)^5 - 630*sin(d*x + c)^4 + 336*sin(d*x + c)^3 + 280*sin(d*x + c)^2 - 360*sin(d*x + c) + 105)/(a^3*d*sin(d*x + c)^8)","A",0
80,1,86,0,2.482531," ","integrate(cot(d*x+c)^11/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{280 \, \sin\left(d x + c\right)^{7} - 630 \, \sin\left(d x + c\right)^{6} + 168 \, \sin\left(d x + c\right)^{5} + 700 \, \sin\left(d x + c\right)^{4} - 600 \, \sin\left(d x + c\right)^{3} - 105 \, \sin\left(d x + c\right)^{2} + 280 \, \sin\left(d x + c\right) - 84}{840 \, a^{3} d \sin\left(d x + c\right)^{10}}"," ",0,"1/840*(280*sin(d*x + c)^7 - 630*sin(d*x + c)^6 + 168*sin(d*x + c)^5 + 700*sin(d*x + c)^4 - 600*sin(d*x + c)^3 - 105*sin(d*x + c)^2 + 280*sin(d*x + c) - 84)/(a^3*d*sin(d*x + c)^10)","A",0
81,1,86,0,6.359269," ","integrate(cot(d*x+c)^13/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{924 \, \sin\left(d x + c\right)^{9} - 2079 \, \sin\left(d x + c\right)^{8} + 3696 \, \sin\left(d x + c\right)^{6} - 2376 \, \sin\left(d x + c\right)^{5} - 2079 \, \sin\left(d x + c\right)^{4} + 2464 \, \sin\left(d x + c\right)^{3} - 756 \, \sin\left(d x + c\right) + 231}{2772 \, a^{3} d \sin\left(d x + c\right)^{12}}"," ",0,"-1/2772*(924*sin(d*x + c)^9 - 2079*sin(d*x + c)^8 + 3696*sin(d*x + c)^6 - 2376*sin(d*x + c)^5 - 2079*sin(d*x + c)^4 + 2464*sin(d*x + c)^3 - 756*sin(d*x + c) + 231)/(a^3*d*sin(d*x + c)^12)","A",0
82,1,146,0,7.590608," ","integrate(tan(d*x+c)^5/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4}} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{4}} + \frac{30 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 12 \, \sin\left(d x + c\right) + 7\right)}}{a^{4} {\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{147 \, \sin\left(d x + c\right)^{6} + 822 \, \sin\left(d x + c\right)^{5} + 1605 \, \sin\left(d x + c\right)^{4} + 340 \, \sin\left(d x + c\right)^{3} - 675 \, \sin\left(d x + c\right)^{2} - 522 \, \sin\left(d x + c\right) - 117}{a^{4} {\left(\sin\left(d x + c\right) + 1\right)}^{6}}}{15360 \, d}"," ",0,"-1/15360*(60*log(abs(sin(d*x + c) + 1))/a^4 - 60*log(abs(sin(d*x + c) - 1))/a^4 + 30*(3*sin(d*x + c)^2 - 12*sin(d*x + c) + 7)/(a^4*(sin(d*x + c) - 1)^2) - (147*sin(d*x + c)^6 + 822*sin(d*x + c)^5 + 1605*sin(d*x + c)^4 + 340*sin(d*x + c)^3 - 675*sin(d*x + c)^2 - 522*sin(d*x + c) - 117)/(a^4*(sin(d*x + c) + 1)^6))/d","A",0
83,1,76,0,2.337448," ","integrate(tan(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{5}{a^{4} {\left(\sin\left(d x + c\right) - 1\right)}} - \frac{5 \, \sin\left(d x + c\right)^{4} + 30 \, \sin\left(d x + c\right)^{3} + 80 \, \sin\left(d x + c\right)^{2} + 50 \, \sin\left(d x + c\right) + 11}{a^{4} {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{320 \, d}"," ",0,"-1/320*(5/(a^4*(sin(d*x + c) - 1)) - (5*sin(d*x + c)^4 + 30*sin(d*x + c)^3 + 80*sin(d*x + c)^2 + 50*sin(d*x + c) + 11)/(a^4*(sin(d*x + c) + 1)^5))/d","A",0
84,1,91,0,0.717787," ","integrate(tan(d*x+c)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4}} - \frac{12 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{4}} - \frac{25 \, \sin\left(d x + c\right)^{4} + 124 \, \sin\left(d x + c\right)^{3} + 246 \, \sin\left(d x + c\right)^{2} + 252 \, \sin\left(d x + c\right) + 57}{a^{4} {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{384 \, d}"," ",0,"1/384*(12*log(abs(sin(d*x + c) + 1))/a^4 - 12*log(abs(sin(d*x + c) - 1))/a^4 - (25*sin(d*x + c)^4 + 124*sin(d*x + c)^3 + 246*sin(d*x + c)^2 + 252*sin(d*x + c) + 57)/(a^4*(sin(d*x + c) + 1)^4))/d","A",0
85,1,185,0,1.178364," ","integrate(cot(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{144 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{72 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} + \frac{108 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{8}} - \frac{4 \, {\left(75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 272 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 402 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 272 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{4}}}{8 \, d}"," ",0,"-1/8*(144*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 72*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 + (108*tan(1/2*d*x + 1/2*c)^2 - 16*tan(1/2*d*x + 1/2*c) + 1)/(a^4*tan(1/2*d*x + 1/2*c)^2) + (a^4*tan(1/2*d*x + 1/2*c)^2 - 16*a^4*tan(1/2*d*x + 1/2*c))/a^8 - 4*(75*tan(1/2*d*x + 1/2*c)^4 + 272*tan(1/2*d*x + 1/2*c)^3 + 402*tan(1/2*d*x + 1/2*c)^2 + 272*tan(1/2*d*x + 1/2*c) + 75)/(a^4*(tan(1/2*d*x + 1/2*c) + 1)^4))/d","A",0
86,1,232,0,1.122206," ","integrate(cot(d*x+c)^7/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{30720 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{15360 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} + \frac{37632 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 10080 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2835 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, \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}} + \frac{5 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 48 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 880 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2835 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10080 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{24}}}{1920 \, d}"," ",0,"-1/1920*(30720*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 15360*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 + (37632*tan(1/2*d*x + 1/2*c)^6 - 10080*tan(1/2*d*x + 1/2*c)^5 + 2835*tan(1/2*d*x + 1/2*c)^4 - 880*tan(1/2*d*x + 1/2*c)^3 + 240*tan(1/2*d*x + 1/2*c)^2 - 48*tan(1/2*d*x + 1/2*c) + 5)/(a^4*tan(1/2*d*x + 1/2*c)^6) + (5*a^20*tan(1/2*d*x + 1/2*c)^6 - 48*a^20*tan(1/2*d*x + 1/2*c)^5 + 240*a^20*tan(1/2*d*x + 1/2*c)^4 - 880*a^20*tan(1/2*d*x + 1/2*c)^3 + 2835*a^20*tan(1/2*d*x + 1/2*c)^2 - 10080*a^20*tan(1/2*d*x + 1/2*c))/a^24)/d","A",0
87,1,146,0,1.808298," ","integrate(tan(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{315}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 3150 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1050 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 630 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8064 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6006 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5274 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 846 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 59}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{5040 \, d}"," ",0,"-1/5040*(315/(a^4*(tan(1/2*d*x + 1/2*c) - 1)) - (315*tan(1/2*d*x + 1/2*c)^8 + 3150*tan(1/2*d*x + 1/2*c)^7 + 1050*tan(1/2*d*x + 1/2*c)^6 + 630*tan(1/2*d*x + 1/2*c)^5 - 8064*tan(1/2*d*x + 1/2*c)^4 - 6006*tan(1/2*d*x + 1/2*c)^3 - 5274*tan(1/2*d*x + 1/2*c)^2 - 846*tan(1/2*d*x + 1/2*c) - 59)/(a^4*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
88,1,135,0,0.702191," ","integrate(cot(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} - \frac{15 \, {\left(8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{4 \, {\left(135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 435 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 605 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 385 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 104\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{30 \, d}"," ",0,"-1/30*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - 15*tan(1/2*d*x + 1/2*c)/a^4 - 15*(8*tan(1/2*d*x + 1/2*c) - 1)/(a^4*tan(1/2*d*x + 1/2*c)) + 4*(135*tan(1/2*d*x + 1/2*c)^4 + 435*tan(1/2*d*x + 1/2*c)^3 + 605*tan(1/2*d*x + 1/2*c)^2 + 385*tan(1/2*d*x + 1/2*c) + 104)/(a^4*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
89,1,179,0,0.417747," ","integrate(cot(d*x+c)^4/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{336 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{308 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 51 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 723 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 676 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{3} a^{4}} - \frac{a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 105 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{12}}}{24 \, d}"," ",0,"-1/24*(336*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - (308*tan(1/2*d*x + 1/2*c)^6 + 51*tan(1/2*d*x + 1/2*c)^5 - 723*tan(1/2*d*x + 1/2*c)^4 - 676*tan(1/2*d*x + 1/2*c)^3 - 72*tan(1/2*d*x + 1/2*c)^2 + 9*tan(1/2*d*x + 1/2*c) - 1)/((tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c))^3*a^4) - (a^8*tan(1/2*d*x + 1/2*c)^3 - 12*a^8*tan(1/2*d*x + 1/2*c)^2 + 105*a^8*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
90,1,204,0,1.287735," ","integrate(cot(d*x+c)^6/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{2160 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} + \frac{2560}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}} - \frac{4932 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 55 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} - \frac{a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 55 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1110 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{20}}}{160 \, d}"," ",0,"-1/160*(2160*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 + 2560/(a^4*(tan(1/2*d*x + 1/2*c) + 1)) - (4932*tan(1/2*d*x + 1/2*c)^5 - 1110*tan(1/2*d*x + 1/2*c)^4 + 240*tan(1/2*d*x + 1/2*c)^3 - 55*tan(1/2*d*x + 1/2*c)^2 + 10*tan(1/2*d*x + 1/2*c) - 1)/(a^4*tan(1/2*d*x + 1/2*c)^5) - (a^16*tan(1/2*d*x + 1/2*c)^5 - 10*a^16*tan(1/2*d*x + 1/2*c)^4 + 55*a^16*tan(1/2*d*x + 1/2*c)^3 - 240*a^16*tan(1/2*d*x + 1/2*c)^2 + 1110*a^16*tan(1/2*d*x + 1/2*c))/a^20)/d","A",0
91,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*tan(f*x+e)^4,x, algorithm=""giac"")","\int \sqrt{a \sin\left(f x + e\right) + a} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*tan(f*x + e)^4, x)","F",0
92,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*tan(f*x+e)^2,x, algorithm=""giac"")","\int \sqrt{a \sin\left(f x + e\right) + a} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*tan(f*x + e)^2, x)","F",0
93,-1,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*tan(f*x+e)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*tan(f*x+e)^2,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)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)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)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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(8448*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+21504*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^2-12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^3+75264*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^4+12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^5+21504*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^6+12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^7+8448*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^8+21504*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*f*x)^2-12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*f*x)^3+75264*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*f*x)^4+12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*f*x)^5+21504*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*f*x)^6+12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*f*x)^7+8448*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*f*x)^8-12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))-12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*f*x)+430080*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^2*tan(1/4*f*x)^2+49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^2*tan(1/4*f*x)^3-559104*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^2*tan(1/4*f*x)^4-49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^2*tan(1/4*f*x)^5+430080*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^2*tan(1/4*f*x)^6-49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^2*tan(1/4*f*x)^7+21504*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^2*tan(1/4*f*x)^8+49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^2*tan(1/4*f*x)+49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^3*tan(1/4*f*x)^2-1204224*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^3*tan(1/4*f*x)^3+122880*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^3*tan(1/4*f*x)^4+1204224*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^3*tan(1/4*f*x)^5+49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^3*tan(1/4*f*x)^6-172032*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^3*tan(1/4*f*x)^7-12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^3*tan(1/4*f*x)^8+172032*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^3*tan(1/4*f*x)-559104*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^4*tan(1/4*f*x)^2+122880*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^4*tan(1/4*f*x)^3+2171904*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^4*tan(1/4*f*x)^4-122880*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^4*tan(1/4*f*x)^5-559104*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^4*tan(1/4*f*x)^6-122880*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^4*tan(1/4*f*x)^7+75264*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^4*tan(1/4*f*x)^8+122880*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^4*tan(1/4*f*x)-49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^5*tan(1/4*f*x)^2+1204224*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^5*tan(1/4*f*x)^3-122880*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^5*tan(1/4*f*x)^4-1204224*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^5*tan(1/4*f*x)^5-49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^5*tan(1/4*f*x)^6+172032*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^5*tan(1/4*f*x)^7+12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^5*tan(1/4*f*x)^8-172032*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^5*tan(1/4*f*x)+430080*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^6*tan(1/4*f*x)^2+49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^6*tan(1/4*f*x)^3-559104*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^6*tan(1/4*f*x)^4-49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^6*tan(1/4*f*x)^5+430080*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^6*tan(1/4*f*x)^6-49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^6*tan(1/4*f*x)^7+21504*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^6*tan(1/4*f*x)^8+49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^6*tan(1/4*f*x)-49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^7*tan(1/4*f*x)^2-172032*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^7*tan(1/4*f*x)^3-122880*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^7*tan(1/4*f*x)^4+172032*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^7*tan(1/4*f*x)^5-49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^7*tan(1/4*f*x)^6-24576*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^7*tan(1/4*f*x)^7+12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^7*tan(1/4*f*x)^8+24576*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^7*tan(1/4*f*x)+21504*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^8*tan(1/4*f*x)^2-12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^8*tan(1/4*f*x)^3+75264*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^8*tan(1/4*f*x)^4+12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^8*tan(1/4*f*x)^5+21504*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^8*tan(1/4*f*x)^6+12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^8*tan(1/4*f*x)^7+8448*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^8*tan(1/4*f*x)^8-12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^8*tan(1/4*f*x)+49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))*tan(1/4*f*x)^2+172032*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))*tan(1/4*f*x)^3+122880*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))*tan(1/4*f*x)^4-172032*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))*tan(1/4*f*x)^5+49152*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))*tan(1/4*f*x)^6+24576*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))*tan(1/4*f*x)^7-12288*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))*tan(1/4*f*x)^8-24576*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))*tan(1/4*f*x))/(-2304*sqrt(2)*f*tan(1/4*exp(1))-2304*sqrt(2)*f*tan(1/4*f*x)-4608*sqrt(2)*f*tan(1/4*exp(1))^2*tan(1/4*f*x)+1152*sqrt(2)*f*tan(1/4*exp(1))^8*tan(1/4*f*x)^8+2304*sqrt(2)*f*tan(1/4*exp(1))^7*tan(1/4*f*x)^8+2304*sqrt(2)*f*tan(1/4*exp(1))^8*tan(1/4*f*x)^7+2304*sqrt(2)*f*tan(1/4*exp(1))^6*tan(1/4*f*x)^8-4608*sqrt(2)*f*tan(1/4*exp(1))^7*tan(1/4*f*x)^7+2304*sqrt(2)*f*tan(1/4*exp(1))^8*tan(1/4*f*x)^6+6912*sqrt(2)*f*tan(1/4*exp(1))^5*tan(1/4*f*x)^8+4608*sqrt(2)*f*tan(1/4*exp(1))^6*tan(1/4*f*x)^7+4608*sqrt(2)*f*tan(1/4*exp(1))^7*tan(1/4*f*x)^6+6912*sqrt(2)*f*tan(1/4*exp(1))^8*tan(1/4*f*x)^5-13824*sqrt(2)*f*tan(1/4*exp(1))^5*tan(1/4*f*x)^7+4608*sqrt(2)*f*tan(1/4*exp(1))^6*tan(1/4*f*x)^6-13824*sqrt(2)*f*tan(1/4*exp(1))^7*tan(1/4*f*x)^5+6912*sqrt(2)*f*tan(1/4*exp(1))^3*tan(1/4*f*x)^8+13824*sqrt(2)*f*tan(1/4*exp(1))^5*tan(1/4*f*x)^6+13824*sqrt(2)*f*tan(1/4*exp(1))^6*tan(1/4*f*x)^5+6912*sqrt(2)*f*tan(1/4*exp(1))^8*tan(1/4*f*x)^3-2304*sqrt(2)*f*tan(1/4*exp(1))^2*tan(1/4*f*x)^8-13824*sqrt(2)*f*tan(1/4*exp(1))^3*tan(1/4*f*x)^7-41472*sqrt(2)*f*tan(1/4*exp(1))^5*tan(1/4*f*x)^5-13824*sqrt(2)*f*tan(1/4*exp(1))^7*tan(1/4*f*x)^3-2304*sqrt(2)*f*tan(1/4*exp(1))^8*tan(1/4*f*x)^2-4608*sqrt(2)*f*tan(1/4*exp(1))^2*tan(1/4*f*x)^7+13824*sqrt(2)*f*tan(1/4*exp(1))^3*tan(1/4*f*x)^6+13824*sqrt(2)*f*tan(1/4*exp(1))^6*tan(1/4*f*x)^3-4608*sqrt(2)*f*tan(1/4*exp(1))^7*tan(1/4*f*x)^2-1152*sqrt(2)*f*tan(1/4*exp(1))^8-1152*sqrt(2)*f*tan(1/4*f*x)^8-4608*sqrt(2)*f*tan(1/4*exp(1))^2*tan(1/4*f*x)^6-41472*sqrt(2)*f*tan(1/4*exp(1))^3*tan(1/4*f*x)^5-41472*sqrt(2)*f*tan(1/4*exp(1))^5*tan(1/4*f*x)^3-4608*sqrt(2)*f*tan(1/4*exp(1))^6*tan(1/4*f*x)^2-2304*sqrt(2)*f*tan(1/4*exp(1))^7-2304*sqrt(2)*f*tan(1/4*f*x)^7-13824*sqrt(2)*f*tan(1/4*exp(1))^2*tan(1/4*f*x)^5-13824*sqrt(2)*f*tan(1/4*exp(1))^5*tan(1/4*f*x)^2-2304*sqrt(2)*f*tan(1/4*exp(1))^6-2304*sqrt(2)*f*tan(1/4*f*x)^6-41472*sqrt(2)*f*tan(1/4*exp(1))^3*tan(1/4*f*x)^3-6912*sqrt(2)*f*tan(1/4*exp(1))^5-6912*sqrt(2)*f*tan(1/4*f*x)^5-13824*sqrt(2)*f*tan(1/4*exp(1))^2*tan(1/4*f*x)^3-13824*sqrt(2)*f*tan(1/4*exp(1))^3*tan(1/4*f*x)^2+4608*sqrt(2)*f*tan(1/4*exp(1))^2*tan(1/4*f*x)^2-6912*sqrt(2)*f*tan(1/4*exp(1))^3-6912*sqrt(2)*f*tan(1/4*f*x)^3+2304*sqrt(2)*f*tan(1/4*exp(1))^2+2304*sqrt(2)*f*tan(1/4*f*x)^2+1152*sqrt(2)*f-13824*sqrt(2)*f*tan(1/4*exp(1))^3*tan(1/4*f*x)-13824*sqrt(2)*f*tan(1/4*exp(1))^5*tan(1/4*f*x)+4608*sqrt(2)*f*tan(1/4*exp(1))^6*tan(1/4*f*x)-4608*sqrt(2)*f*tan(1/4*exp(1))^7*tan(1/4*f*x)+2304*sqrt(2)*f*tan(1/4*exp(1))^8*tan(1/4*f*x)-4608*sqrt(2)*f*tan(1/4*exp(1))*tan(1/4*f*x)^2-13824*sqrt(2)*f*tan(1/4*exp(1))*tan(1/4*f*x)^3-13824*sqrt(2)*f*tan(1/4*exp(1))*tan(1/4*f*x)^5+4608*sqrt(2)*f*tan(1/4*exp(1))*tan(1/4*f*x)^6-4608*sqrt(2)*f*tan(1/4*exp(1))*tan(1/4*f*x)^7+2304*sqrt(2)*f*tan(1/4*exp(1))*tan(1/4*f*x)^8-4608*sqrt(2)*f*tan(1/4*exp(1))*tan(1/4*f*x))","F(-2)",0
97,-1,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*tan(f*x+e)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*tan(f*x+e)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-2,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+a*sin(f*x+e))^(1/2),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)2/f*2*(-1/48*(9*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+39*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-26*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+69*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-78*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-13*sqrt(a)*a^2)/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^3/sign(tan((f*x+exp(1))/2)+1)+1/128*(43*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7-237*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6+161*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+221*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4+25*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3-93*a^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-103*sqrt(a)*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-17*sqrt(a)*a^3)/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^4/sign(tan((f*x+exp(1))/2)+1)+67/128*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
104,-2,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+a*sin(f*x+e))^(1/2),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)2/f*2*(-1/4*(sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a)-sqrt(a*tan((f*x+exp(1))/2)^2+a))/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)/sign(tan((f*x+exp(1))/2)+1)+1/8*(-3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+sqrt(a)*a)/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^2/sign(tan((f*x+exp(1))/2)+1)-5/8*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
105,-2,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+a*sin(f*x+e))^(1/2),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)2/f*(1/4*sqrt(a*tan((f*x+exp(1))/2)^2+a)/sign(tan((f*x+exp(1))/2)+1)/a+2*(1/4*sqrt(a)/((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-a)/sign(tan((f*x+exp(1))/2)+1)-1/4*atan((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(-a))/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1)+1/8*sqrt(a)*ln(abs(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a)))/a/sign(tan((f*x+exp(1))/2)+1))+(-sqrt(-a)*sqrt(2)*ln(sqrt(2)*sqrt(a)+sqrt(a))-sqrt(-a)*sqrt(2)-sqrt(-a)*ln(sqrt(2)*sqrt(a)+sqrt(a))-3*sqrt(-a)+2*sqrt(2)*sqrt(a)*atan((sqrt(2)*sqrt(a)+sqrt(a))/sqrt(-a))+2*sqrt(a)*atan((sqrt(2)*sqrt(a)+sqrt(a))/sqrt(-a)))/(4*sqrt(-a)*sqrt(2)*sqrt(a)+4*sqrt(-a)*sqrt(a))*sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
106,-2,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+a*sin(f*x+e))^(1/2),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)2/f*(2*sqrt(a*tan((f*x+exp(1))/2)^2+a)*(tan((f*x+exp(1))/2)*(1/96*tan((f*x+exp(1))/2)/a/sign(tan((f*x+exp(1))/2)+1)-1/64/a/sign(tan((f*x+exp(1))/2)+1))-11/96/a/sign(tan((f*x+exp(1))/2)+1))+2*(1/96*(3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5-18*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-3*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+48*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-22*sqrt(a)*a^2)/((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-a)^3/sign(tan((f*x+exp(1))/2)+1)+7/32*atan((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(-a))/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1)-7/64*ln(abs(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a)))/sqrt(a)/sign(tan((f*x+exp(1))/2)+1))+(105*sqrt(-a)*sqrt(2)*ln(sqrt(2)*sqrt(a)+sqrt(a))+128*sqrt(-a)*sqrt(2)+147*sqrt(-a)*ln(sqrt(2)*sqrt(a)+sqrt(a))+186*sqrt(-a)-210*sqrt(2)*sqrt(a)*atan((sqrt(2)*sqrt(a)+sqrt(a))/sqrt(-a))-294*sqrt(a)*atan((sqrt(2)*sqrt(a)+sqrt(a))/sqrt(-a)))/(480*sqrt(-a)*sqrt(2)*sqrt(a)+672*sqrt(-a)*sqrt(a))*sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
107,-2,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+a*sin(f*x+e))^(3/2),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)2/f*2*(-1/48*(3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+15*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-10*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+27*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-30*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-5*sqrt(a)*a^2)/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^3/a/sign(tan((f*x+exp(1))/2)+1)+1/1536*(-117*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^11+1479*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^10-6645*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^9+4875*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^8+7710*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7-3002*sqrt(a)*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6-5562*a^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5-3690*sqrt(a)*a^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4+1255*a^4*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+831*a^5*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+2787*sqrt(a)*a^4*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+79*sqrt(a)*a^5)/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^6/a/sign(tan((f*x+exp(1))/2)+1)-7/512*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/sqrt(-a)/a/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
108,-2,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+a*sin(f*x+e))^(3/2),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)2/f*2*(-1/8*(sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a)-sqrt(a*tan((f*x+exp(1))/2)^2+a))/a/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)/sign(tan((f*x+exp(1))/2)+1)+1/64*(7*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7-81*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6+53*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+65*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4+13*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3-33*a^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-19*sqrt(a)*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-5*sqrt(a)*a^3)/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^4/a/sign(tan((f*x+exp(1))/2)+1)-1/64*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/sqrt(-a)/a/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
109,-2,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+a*sin(f*x+e))^(3/2),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)2/f*(1/4*sqrt(a*tan((f*x+exp(1))/2)^2+a)/a^2/sign(tan((f*x+exp(1))/2)+1)+2*(-3/4*atan((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(-a))/sqrt(-a)/a/sign(tan((f*x+exp(1))/2)+1)+3/8*ln(abs(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a)))/sqrt(a)/a/sign(tan((f*x+exp(1))/2)+1)+sqrt(2)*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(-a)/a/sign(tan((f*x+exp(1))/2)+1)+1/4/sqrt(a)/((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-a)/sign(tan((f*x+exp(1))/2)+1))+(-3*sqrt(-a)*sqrt(2)*ln(sqrt(2)*sqrt(a)+sqrt(a))-sqrt(-a)*sqrt(2)-3*sqrt(-a)*ln(sqrt(2)*sqrt(a)+sqrt(a))-3*sqrt(-a)+6*sqrt(2)*sqrt(a)*atan((sqrt(2)*sqrt(a)+sqrt(a))/sqrt(-a))-8*sqrt(2)*sqrt(a)*atan(sqrt(a)/sqrt(-a))+6*sqrt(a)*atan((sqrt(2)*sqrt(a)+sqrt(a))/sqrt(-a))-16*sqrt(a)*atan(sqrt(a)/sqrt(-a)))/(4*a*sqrt(-a)*sqrt(2)*sqrt(a)+4*a*sqrt(-a)*sqrt(a))*sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
110,-2,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+a*sin(f*x+e))^(3/2),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)2/f*(2*sqrt(a*tan((f*x+exp(1))/2)^2+a)*(tan((f*x+exp(1))/2)*(1/96*tan((f*x+exp(1))/2)/a^2/sign(tan((f*x+exp(1))/2)+1)-3/64/a^2/sign(tan((f*x+exp(1))/2)+1))+7/96/a^2/sign(tan((f*x+exp(1))/2)+1))+2*(1/96*(9*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+18*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-9*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-24*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+14*sqrt(a)*a^2)/((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-a)^3/a/sign(tan((f*x+exp(1))/2)+1)+1/32*atan((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(-a))/sqrt(-a)/a/sign(tan((f*x+exp(1))/2)+1)-1/64*ln(abs(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a)))/sqrt(a)/a/sign(tan((f*x+exp(1))/2)+1))+(15*sqrt(-a)*sqrt(2)*ln(sqrt(2)*sqrt(a)+sqrt(a))-280*sqrt(-a)*sqrt(2)+21*sqrt(-a)*ln(sqrt(2)*sqrt(a)+sqrt(a))-402*sqrt(-a)-30*sqrt(2)*sqrt(a)*atan((sqrt(2)*sqrt(a)+sqrt(a))/sqrt(-a))-42*sqrt(a)*atan((sqrt(2)*sqrt(a)+sqrt(a))/sqrt(-a)))/(480*a*sqrt(-a)*sqrt(2)*sqrt(a)+672*a*sqrt(-a)*sqrt(a))*sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
111,-2,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+a*sin(f*x+e))^(5/2),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)2/f*2*(-1/192*(3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+21*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-14*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+39*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-42*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-7*sqrt(a)*a^2)/a^2/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^3/sign(tan((f*x+exp(1))/2)+1)+1/24576*(-1335*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^15+20025*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^14-111513*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^13+173379*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^12-26091*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^11-247283*sqrt(a)*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^10+157019*a^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^9+345215*sqrt(a)*a^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^8-87061*a^4*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7-353877*sqrt(a)*a^4*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6-89371*a^5*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+95561*sqrt(a)*a^5*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4+78327*a^6*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+7705*a^7*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+38735*sqrt(a)*a^6*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+565*sqrt(a)*a^7)/a^2/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^8/sign(tan((f*x+exp(1))/2)+1)-317/8192*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/a^2/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
112,-2,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+a*sin(f*x+e))^(5/2),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)2/f*2*(-1/16*(sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a)-sqrt(a*tan((f*x+exp(1))/2)^2+a))/a^2/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)/sign(tan((f*x+exp(1))/2)+1)+1/768*(81*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^11-1083*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^10+2001*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^9-1071*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^8-2502*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7+1330*sqrt(a)*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6+3378*a^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+546*sqrt(a)*a^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-1499*a^4*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3-339*a^5*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-807*sqrt(a)*a^4*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-35*sqrt(a)*a^5)/a^2/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^6/sign(tan((f*x+exp(1))/2)+1)+11/256*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/a^2/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
113,-2,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+a*sin(f*x+e))^(5/2),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)2/f*(1/4*sqrt(a*tan((f*x+exp(1))/2)^2+a)/a^3/sign(tan((f*x+exp(1))/2)+1)+2*(1/2*(-3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+sqrt(a)*a)/a^2/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^2/sign(tan((f*x+exp(1))/2)+1)-5/4*atan((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(-a))/a^2/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1)+7/2*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/a^2/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1)+5/8/sqrt(a)/a^2*ln(abs(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a)))/sign(tan((f*x+exp(1))/2)+1)-1/4/sqrt(a)/a/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+a)/sign(tan((f*x+exp(1))/2)+1)))","F(-2)",0
114,-2,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+a*sin(f*x+e))^(5/2),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)2/f*(2*sqrt(a*tan((f*x+exp(1))/2)^2+a)*(tan((f*x+exp(1))/2)*(1/96*tan((f*x+exp(1))/2)/a^3/sign(tan((f*x+exp(1))/2)+1)-5/64/a^3/sign(tan((f*x+exp(1))/2)+1))+37/96/a^3/sign(tan((f*x+exp(1))/2)+1))+2*(1/96*(15*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+78*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-15*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-144*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+74*sqrt(a)*a^2)/a^2/((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-a)^3/sign(tan((f*x+exp(1))/2)+1)-45/32*atan((-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(-a))/a^2/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1)+4*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/a^2/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1)+45/64/sqrt(a)/a^2*ln(abs(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a)))/sign(tan((f*x+exp(1))/2)+1))+(-945*sqrt(-a)*sqrt(2)*ln(sqrt(2)*sqrt(a)+sqrt(a))-1302*sqrt(-a)*sqrt(2)-1350*sqrt(-a)*ln(sqrt(2)*sqrt(a)+sqrt(a))-1808*sqrt(-a)+1890*sqrt(2)*sqrt(a)*atan((sqrt(2)*sqrt(a)+sqrt(a))/sqrt(-a))-3840*sqrt(2)*sqrt(a)*atan(sqrt(a)/sqrt(-a))+2700*sqrt(a)*atan((sqrt(2)*sqrt(a)+sqrt(a))/sqrt(-a))-5376*sqrt(a)*atan(sqrt(a)/sqrt(-a)))/(672*a^2*sqrt(-a)*sqrt(2)*sqrt(a)+960*a^2*sqrt(-a)*sqrt(a))*sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
115,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/3)*tan(f*x+e)^4,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(1/3)*tan(f*x + e)^4, x)","F",0
116,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/3)*tan(f*x+e)^2,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(1/3)*tan(f*x + e)^2, x)","F",0
117,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+a*sin(f*x+e))^(1/3),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(1/3)*cot(f*x + e)^2, x)","F",0
118,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+a*sin(f*x+e))^(1/3),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(1/3)*cot(f*x + e)^4, x)","F",0
119,0,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+a*sin(f*x+e))^(1/3),x, algorithm=""giac"")","\int \frac{\tan\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(f*x + e)^4/(a*sin(f*x + e) + a)^(1/3), x)","F",0
120,0,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+a*sin(f*x+e))^(1/3),x, algorithm=""giac"")","\int \frac{\tan\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(f*x + e)^2/(a*sin(f*x + e) + a)^(1/3), x)","F",0
121,0,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+a*sin(f*x+e))^(1/3),x, algorithm=""giac"")","\int \frac{\cot\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cot(f*x + e)^2/(a*sin(f*x + e) + a)^(1/3), x)","F",0
122,0,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+a*sin(f*x+e))^(1/3),x, algorithm=""giac"")","\int \frac{\cot\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cot(f*x + e)^4/(a*sin(f*x + e) + a)^(1/3), x)","F",0
123,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(g*tan(f*x+e))^p,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(g*tan(f*x + e))^p, x)","F",0
124,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(g*tan(f*x+e))^p,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(g*tan(f*x + e))^p, x)","F",0
125,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(g*tan(f*x+e))^p,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(g*tan(f*x + e))^p, x)","F",0
126,0,0,0,0.000000," ","integrate((g*tan(f*x+e))^p/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \tan\left(f x + e\right)\right)^{p}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*tan(f*x + e))^p/(a*sin(f*x + e) + a), x)","F",0
127,0,0,0,0.000000," ","integrate((g*tan(f*x+e))^p/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(g \tan\left(f x + e\right)\right)^{p}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((g*tan(f*x + e))^p/(a*sin(f*x + e) + a)^2, x)","F",0
128,0,0,0,0.000000," ","integrate((g*tan(f*x+e))^p/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\left(g \tan\left(f x + e\right)\right)^{p}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((g*tan(f*x + e))^p/(a*sin(f*x + e) + a)^3, x)","F",0
129,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(g*tan(f*x+e))^p,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(g*tan(f*x + e))^p, x)","F",0
130,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*tan(f*x+e)^3,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*tan(f*x + e)^3, x)","F",0
131,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*tan(f*x+e),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*tan(f*x + e), x)","F",0
132,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cot(f*x + e), x)","F",0
133,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cot(f*x + e)^3, x)","F",0
134,0,0,0,0.000000," ","integrate(cot(f*x+e)^5*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cot\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cot(f*x + e)^5, x)","F",0
135,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*tan(f*x+e)^4,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*tan(f*x + e)^4, x)","F",0
136,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*tan(f*x+e)^2,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*tan(f*x + e)^2, x)","F",0
137,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m, x)","F",0
138,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cot(f*x + e)^2, x)","F",0
139,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cot(f*x + e)^4, x)","F",0
140,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))*tan(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,1,1456,0,4.249422," ","integrate((a+b*sin(d*x+c))*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} + a \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(\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} + a \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(\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} + a \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(\frac{1}{2} \, c\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x\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) - 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 \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 \tan\left(\frac{1}{2} \, d x\right) + 4 \, b \tan\left(\frac{1}{2} \, c\right)}{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 + a*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(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 + a*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(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 + a*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(1/2*c)^2 - 4*b*tan(1/2*d*x)*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)) + a*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*tan(1/2*d*x) + 4*b*tan(1/2*c))/(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
142,1,23,0,1.273595," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + b \sin\left(d x + c\right)}{d}"," ",0,"(a*log(abs(sin(d*x + c))) + b*sin(d*x + c))/d","A",0
143,1,60,0,1.790055," ","integrate(cot(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 2 \, b \sin\left(d x + c\right) - \frac{3 \, a \sin\left(d x + c\right)^{2} - 2 \, b \sin\left(d x + c\right) - a}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*a*log(abs(sin(d*x + c))) + 2*b*sin(d*x + c) - (3*a*sin(d*x + c)^2 - 2*b*sin(d*x + c) - a)/sin(d*x + c)^2)/d","A",0
144,1,82,0,1.843788," ","integrate(cot(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{12 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 12 \, b \sin\left(d x + c\right) - \frac{25 \, a \sin\left(d x + c\right)^{4} - 24 \, b \sin\left(d x + c\right)^{3} - 12 \, a \sin\left(d x + c\right)^{2} + 4 \, b \sin\left(d x + c\right) + 3 \, a}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*a*log(abs(sin(d*x + c))) + 12*b*sin(d*x + c) - (25*a*sin(d*x + c)^4 - 24*b*sin(d*x + c)^3 - 12*a*sin(d*x + c)^2 + 4*b*sin(d*x + c) + 3*a)/sin(d*x + c)^4)/d","A",0
145,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))*tan(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,1,1008,0,35.577737," ","integrate((a+b*sin(d*x+c))*tan(d*x+c)^2,x, algorithm=""giac"")","-\frac{a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - a d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 2 \, b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + a \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 4 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 8 \, b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 4 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + a d x \tan\left(\frac{1}{2} \, d x\right)^{4} + 4 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 8 \, b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + a d x \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, a d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 8 \, b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 24 \, b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 8 \, b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 2 \, b \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} - 4 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 4 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - a \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} - a \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - a \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 2 \, b \tan\left(\frac{1}{2} \, d x\right)^{4} + 4 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 8 \, b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 24 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, c\right)^{4} + a d x \tan\left(d x\right) \tan\left(c\right) + 8 \, b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, a \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - a d x - 8 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b \tan\left(d x\right) \tan\left(c\right) + a \tan\left(d x\right) + a \tan\left(c\right) + 2 \, b}{d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 4 \, d \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 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(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) + 4 \, d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + d \tan\left(d x\right) \tan\left(c\right) - d}"," ",0,"-(a*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - a*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4 - 4*a*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 2*b*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + a*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4 + a*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 4*a*d*x*tan(1/2*d*x)^3*tan(1/2*c)^3 + 2*b*tan(1/2*d*x)^4*tan(1/2*c)^4 - a*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 4*a*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 4*a*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) + 8*b*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - a*d*x*tan(d*x)*tan(1/2*c)^4*tan(c) - 4*a*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3 - 4*a*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + a*d*x*tan(1/2*d*x)^4 + 4*a*d*x*tan(1/2*d*x)^3*tan(1/2*c) + 4*a*d*x*tan(1/2*d*x)*tan(1/2*c)^3 - 8*b*tan(1/2*d*x)^3*tan(1/2*c)^3 + a*d*x*tan(1/2*c)^4 - 2*b*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 4*a*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 8*b*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 24*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - 8*b*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 2*b*tan(d*x)*tan(1/2*c)^4*tan(c) - a*tan(d*x)*tan(1/2*d*x)^4 - 4*a*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c) - 4*a*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3 - a*tan(d*x)*tan(1/2*c)^4 - a*tan(1/2*d*x)^4*tan(c) - 4*a*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 4*a*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - a*tan(1/2*c)^4*tan(c) + 2*b*tan(1/2*d*x)^4 + 4*a*d*x*tan(1/2*d*x)*tan(1/2*c) + 8*b*tan(1/2*d*x)^3*tan(1/2*c) + 24*b*tan(1/2*d*x)^2*tan(1/2*c)^2 + 8*b*tan(1/2*d*x)*tan(1/2*c)^3 + 2*b*tan(1/2*c)^4 + a*d*x*tan(d*x)*tan(c) + 8*b*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 4*a*tan(d*x)*tan(1/2*d*x)*tan(1/2*c) - 4*a*tan(1/2*d*x)*tan(1/2*c)*tan(c) - a*d*x - 8*b*tan(1/2*d*x)*tan(1/2*c) - 2*b*tan(d*x)*tan(c) + a*tan(d*x) + a*tan(c) + 2*b)/(d*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - d*tan(1/2*d*x)^4*tan(1/2*c)^4 - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + 4*d*tan(1/2*d*x)^3*tan(1/2*c)^3 - d*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - d*tan(d*x)*tan(1/2*c)^4*tan(c) + 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(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) + 4*d*tan(1/2*d*x)*tan(1/2*c) + d*tan(d*x)*tan(c) - d)","B",0
147,1,108,0,0.284567," ","integrate(cot(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{6 \, {\left(d x + c\right)} a - 6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, 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)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*a - 6*b*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a*tan(1/2*d*x + 1/2*c) + (2*b*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c)^2 - 10*b*tan(1/2*d*x + 1/2*c) + 3*a)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c)))/d","B",0
148,1,141,0,0.575192," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, {\left(d x + c\right)} a - 36 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{48 \, b}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{66 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, 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)^{3}}}{24 \, d}"," ",0,"1/24*(a*tan(1/2*d*x + 1/2*c)^3 + 3*b*tan(1/2*d*x + 1/2*c)^2 + 24*(d*x + c)*a - 36*b*log(abs(tan(1/2*d*x + 1/2*c))) - 15*a*tan(1/2*d*x + 1/2*c) - 48*b/(tan(1/2*d*x + 1/2*c)^2 + 1) + (66*b*tan(1/2*d*x + 1/2*c)^3 + 15*a*tan(1/2*d*x + 1/2*c)^2 - 3*b*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
149,1,199,0,0.682607," ","integrate(cot(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 960 \, {\left(d x + c\right)} a + 1800 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 660 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1920 \, b}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - \frac{4110 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 660 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 70 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a*tan(1/2*d*x + 1/2*c)^5 + 15*b*tan(1/2*d*x + 1/2*c)^4 - 70*a*tan(1/2*d*x + 1/2*c)^3 - 240*b*tan(1/2*d*x + 1/2*c)^2 - 960*(d*x + c)*a + 1800*b*log(abs(tan(1/2*d*x + 1/2*c))) + 660*a*tan(1/2*d*x + 1/2*c) + 1920*b/(tan(1/2*d*x + 1/2*c)^2 + 1) - (4110*b*tan(1/2*d*x + 1/2*c)^5 + 660*a*tan(1/2*d*x + 1/2*c)^4 - 240*b*tan(1/2*d*x + 1/2*c)^3 - 70*a*tan(1/2*d*x + 1/2*c)^2 + 15*b*tan(1/2*d*x + 1/2*c) + 6*a)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
150,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2*tan(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,1,7855,0,12.160335," ","integrate((a+b*sin(d*x+c))^2*tan(d*x+c),x, algorithm=""giac"")","-\frac{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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, d x\right)^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} - 16 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(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(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(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(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - 16 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(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)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(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)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} - b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\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(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, d x\right)^{2} - 16 \, a b \tan\left(d x\right)^{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(d x\right)^{2} \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(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, c\right)^{2} - 16 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \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)^{2} \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)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, d x\right)^{2} \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(d x\right)^{2} \tan\left(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(d x\right)^{2} \tan\left(c\right)^{2} + 2 \, a^{2} \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 \, b^{2} \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} + 16 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(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)^{2} \tan\left(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)^{2} \tan\left(c\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 16 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 16 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(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} \, c\right)^{2} \tan\left(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} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - 16 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) + 4 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + b^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(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(d x\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(d x\right)^{2} + 2 \, a^{2} \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} \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} + 16 \, a b \tan\left(d x\right)^{2} \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)^{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)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, d x\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, d x\right)^{2} + 16 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 16 \, a b \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} \, 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} \, c\right)^{2} + 2 \, a^{2} \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(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} \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(\frac{1}{2} \, c\right)^{2} - 16 \, a b \tan\left(\frac{1}{2} \, d x\right) \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(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(c\right)^{2} + 2 \, a^{2} \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 \, b^{2} \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} + 16 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(c\right)^{2} + 16 \, a b \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + b^{2} \tan\left(d x\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} \tan\left(d x\right) \tan\left(c\right) + b^{2} \tan\left(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) - 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) + 2 \, a^{2} \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 \, b^{2} \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) + 16 \, a b \tan\left(\frac{1}{2} \, d x\right) + 16 \, a b \tan\left(\frac{1}{2} \, c\right) - b^{2}}{4 \, {\left(d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(c\right)^{2} + d\right)}}"," ",0,"-1/4*(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(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(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(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 2*a^2*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(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 2*b^2*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(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 - b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(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(d*x)^2*tan(1/2*d*x)^2*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(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*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(1/2*d*x)^2*tan(1/2*c)^2 + 2*b^2*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(1/2*d*x)^2*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(d*x)^2*tan(1/2*d*x)^2*tan(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(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + 2*a^2*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(1/2*d*x)^2*tan(c)^2 + 2*b^2*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(1/2*d*x)^2*tan(c)^2 - 16*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(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(d*x)^2*tan(1/2*c)^2*tan(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(d*x)^2*tan(1/2*c)^2*tan(c)^2 + 2*a^2*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(1/2*c)^2*tan(c)^2 + 2*b^2*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(1/2*c)^2*tan(c)^2 - 16*a*b*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(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)^2*tan(1/2*c)^2*tan(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)^2*tan(1/2*c)^2*tan(c)^2 + 2*a^2*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(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 2*b^2*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(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*b^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 - b^2*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + b^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(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(d*x)^2*tan(1/2*d*x)^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(d*x)^2*tan(1/2*d*x)^2 + 2*a^2*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(1/2*d*x)^2 + 2*b^2*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(1/2*d*x)^2 - 16*a*b*tan(d*x)^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(d*x)^2*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(d*x)^2*tan(1/2*c)^2 + 2*a^2*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(1/2*c)^2 + 2*b^2*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(1/2*c)^2 - 16*a*b*tan(d*x)^2*tan(1/2*d*x)*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)^2*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)^2*tan(1/2*c)^2 + 2*a^2*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(1/2*d*x)^2*tan(1/2*c)^2 + 2*b^2*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(1/2*d*x)^2*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(d*x)^2*tan(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(d*x)^2*tan(c)^2 + 2*a^2*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*b^2*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 + 16*a*b*tan(d*x)^2*tan(1/2*d*x)*tan(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)^2*tan(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)^2*tan(c)^2 + 2*a^2*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(1/2*d*x)^2*tan(c)^2 + 2*b^2*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(1/2*d*x)^2*tan(c)^2 + 16*a*b*tan(d*x)^2*tan(1/2*c)*tan(c)^2 - 16*a*b*tan(1/2*d*x)^2*tan(1/2*c)*tan(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*c)^2*tan(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*c)^2*tan(c)^2 + 2*a^2*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(1/2*c)^2*tan(c)^2 + 2*b^2*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(1/2*c)^2*tan(c)^2 - 16*a*b*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^2 + b^2*tan(d*x)^2*tan(1/2*d*x)^2 + b^2*tan(d*x)^2*tan(1/2*c)^2 - b^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*b^2*tan(d*x)*tan(1/2*d*x)^2*tan(c) + 4*b^2*tan(d*x)*tan(1/2*c)^2*tan(c) - b^2*tan(d*x)^2*tan(c)^2 + b^2*tan(1/2*d*x)^2*tan(c)^2 + b^2*tan(1/2*c)^2*tan(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(d*x)^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(d*x)^2 + 2*a^2*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*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 + 16*a*b*tan(d*x)^2*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)^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)^2 + 2*a^2*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(1/2*d*x)^2 + 2*b^2*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(1/2*d*x)^2 + 16*a*b*tan(d*x)^2*tan(1/2*c) - 16*a*b*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*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*c)^2 + 2*a^2*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(1/2*c)^2 + 2*b^2*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(1/2*c)^2 - 16*a*b*tan(1/2*d*x)*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(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(c)^2 + 2*a^2*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*b^2*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 + 16*a*b*tan(1/2*d*x)*tan(c)^2 + 16*a*b*tan(1/2*c)*tan(c)^2 + b^2*tan(d*x)^2 - b^2*tan(1/2*d*x)^2 - b^2*tan(1/2*c)^2 + 4*b^2*tan(d*x)*tan(c) + b^2*tan(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)) - 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)) + 2*a^2*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*b^2*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)) + 16*a*b*tan(1/2*d*x) + 16*a*b*tan(1/2*c) - b^2)/(d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + d*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + d*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^2 + d*tan(d*x)^2*tan(1/2*c)^2 + d*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(d*x)^2*tan(c)^2 + d*tan(1/2*d*x)^2*tan(c)^2 + d*tan(1/2*c)^2*tan(c)^2 + d*tan(d*x)^2 + d*tan(1/2*d*x)^2 + d*tan(1/2*c)^2 + d*tan(c)^2 + d)","B",0
152,1,41,0,0.417167," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{b^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 4 \, a b \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b^2*sin(d*x + c)^2 + 2*a^2*log(abs(sin(d*x + c))) + 4*a*b*sin(d*x + c))/d","A",0
153,1,99,0,0.745473," ","integrate(cot(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{b^{2} \sin\left(d x + c\right)^{2} + 4 \, a b \sin\left(d x + c\right) + 2 \, {\left(a^{2} - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{3 \, a^{2} \sin\left(d x + c\right)^{2} - 3 \, b^{2} \sin\left(d x + c\right)^{2} - 4 \, a b \sin\left(d x + c\right) - a^{2}}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(b^2*sin(d*x + c)^2 + 4*a*b*sin(d*x + c) + 2*(a^2 - b^2)*log(abs(sin(d*x + c))) - (3*a^2*sin(d*x + c)^2 - 3*b^2*sin(d*x + c)^2 - 4*a*b*sin(d*x + c) - a^2)/sin(d*x + c)^2)/d","A",0
154,1,138,0,0.872982," ","integrate(cot(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, b^{2} \sin\left(d x + c\right)^{2} + 24 \, a b \sin\left(d x + c\right) + 12 \, {\left(a^{2} - 2 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{25 \, a^{2} \sin\left(d x + c\right)^{4} - 50 \, b^{2} \sin\left(d x + c\right)^{4} - 48 \, a b \sin\left(d x + c\right)^{3} - 12 \, a^{2} \sin\left(d x + c\right)^{2} + 6 \, b^{2} \sin\left(d x + c\right)^{2} + 8 \, a b \sin\left(d x + c\right) + 3 \, a^{2}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(6*b^2*sin(d*x + c)^2 + 24*a*b*sin(d*x + c) + 12*(a^2 - 2*b^2)*log(abs(sin(d*x + c))) - (25*a^2*sin(d*x + c)^4 - 50*b^2*sin(d*x + c)^4 - 48*a*b*sin(d*x + c)^3 - 12*a^2*sin(d*x + c)^2 + 6*b^2*sin(d*x + c)^2 + 8*a*b*sin(d*x + c) + 3*a^2)/sin(d*x + c)^4)/d","A",0
155,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2*tan(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,1,7670,0,45.198920," ","integrate((a+b*sin(d*x+c))^2*tan(d*x+c)^2,x, algorithm=""giac"")","-\frac{2 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 3 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 2 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 3 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 2 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 8 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 12 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} + 2 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 3 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 8 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 2 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 3 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 3 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 2 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 8 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 12 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 2 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 3 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 8 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 8 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 12 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 3 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 8 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 2 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 3 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 8 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 12 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 8 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 12 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 8 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 12 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} + 32 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 2 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 3 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 8 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 2 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 2 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 12 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 2 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 12 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} + 2 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 2 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 8 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 12 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 3 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 8 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 3 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 8 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 12 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 8 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 12 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 8 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 12 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 32 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 2 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 3 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 8 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 2 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 8 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 12 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 8 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 12 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 12 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 2 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 8 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 2 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 3 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 8 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 8 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 12 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 8 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 12 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 32 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 96 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{3} - 8 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 12 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 32 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} + 32 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 2 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 3 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 8 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 8 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 2 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 3 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 2 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} - 3 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 12 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 12 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 2 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 3 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 3 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 12 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 12 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 8 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 3 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 2 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + 8 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 12 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 12 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 12 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 8 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 3 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 8 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 8 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 12 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 8 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 12 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 32 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 96 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 8 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 12 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 32 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + 32 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 2 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 3 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 8 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 8 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 8 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 12 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 12 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 12 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 32 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 8 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 2 \, 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} - 8 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 8 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 12 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} + 32 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 32 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 96 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{3} - 32 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 8 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 2 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} - 2 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 8 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 8 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 12 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 2 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 12 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 2 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 2 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 2 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 12 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 8 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 8 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 2 \, a^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - 2 \, b^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} + 3 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} + 8 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + 8 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 12 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 12 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 12 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 32 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{4} + 8 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 2 \, 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) - 8 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 8 \, a^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 12 \, b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) + 32 \, a b \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 32 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 96 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 32 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 8 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 2 \, 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} + 8 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 12 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 32 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 32 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 8 \, a b \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 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} - 8 \, a b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 32 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 2 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} - 3 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} - 8 \, a^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 8 \, b^{2} \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 12 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 12 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 3 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 3 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 8 \, a^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 2 \, a^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 3 \, b^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \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} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 2 \, 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} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 8 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 2 \, a^{2} d x \tan\left(d x\right)^{2} - 3 \, b^{2} d x \tan\left(d x\right)^{2} + 8 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 12 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 32 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 32 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 8 \, a b \tan\left(\frac{1}{2} \, c\right)^{4} + 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) - 8 \, a b \tan\left(d x\right)^{3} \tan\left(c\right) + 32 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 2 \, a^{2} d x \tan\left(c\right)^{2} - 3 \, b^{2} d x \tan\left(c\right)^{2} + 8 \, a b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 32 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 8 \, a b \tan\left(d x\right) \tan\left(c\right)^{3} + 2 \, a^{2} \tan\left(d x\right)^{3} + 2 \, b^{2} \tan\left(d x\right)^{3} - 8 \, a^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 12 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) + 2 \, a^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + 2 \, a^{2} \tan\left(c\right)^{3} + 2 \, b^{2} \tan\left(c\right)^{3} - 2 \, a^{2} d x - 3 \, b^{2} d x + 8 \, a b \tan\left(d x\right)^{2} - 32 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 8 \, a b \tan\left(d x\right) \tan\left(c\right) + 8 \, a b \tan\left(c\right)^{2} + 2 \, a^{2} \tan\left(d x\right) + 3 \, b^{2} \tan\left(d x\right) + 2 \, a^{2} \tan\left(c\right) + 3 \, b^{2} \tan\left(c\right) + 8 \, a b}{2 \, {\left(d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} + d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} - d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) + d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + 4 \, d \tan\left(d x\right)^{2} \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} \tan\left(\frac{1}{2} \, c\right)^{4} - d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 4 \, d \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{3} - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{3} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 4 \, d \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 4 \, d \tan\left(d x\right)^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right) - d \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 4 \, d \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 4 \, d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{3} + d \tan\left(\frac{1}{2} \, d x\right)^{4} + 4 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 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} + d \tan\left(d x\right)^{3} \tan\left(c\right) - 4 \, d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) - d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 4 \, d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + d \tan\left(d x\right) \tan\left(c\right)^{3} - d \tan\left(d x\right)^{2} + 4 \, d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + d \tan\left(d x\right) \tan\left(c\right) - d \tan\left(c\right)^{2} - d\right)}}"," ",0,"-1/2*(2*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 3*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 2*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 3*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - 2*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 3*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 8*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - 12*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 + 2*a^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 3*b^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 - 8*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 2*a^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 3*b^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 2*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 3*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 - 2*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 3*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 8*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 12*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + 2*a^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 3*b^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - 8*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 8*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 + 12*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 - 2*a^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 3*b^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 8*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 2*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^3 - 3*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^3 - 8*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 12*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 8*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 12*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 8*a^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - 12*b^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 + 32*a*b*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - 2*a^2*d*x*tan(d*x)^3*tan(1/2*c)^4*tan(c)^3 - 3*b^2*d*x*tan(d*x)^3*tan(1/2*c)^4*tan(c)^3 - 8*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 2*a^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4 + 2*b^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4 + 2*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - 8*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 - 12*b^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 + 2*a^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 8*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - 12*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 + 2*a^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 2*b^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 8*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3 + 12*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3 - 2*a^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4 - 3*b^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4 + 8*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 2*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(c) - 3*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)^4*tan(c) - 8*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 12*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 8*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 12*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 8*a^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 12*b^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + 32*a*b*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 2*a^2*d*x*tan(d*x)^3*tan(1/2*c)^4*tan(c) - 3*b^2*d*x*tan(d*x)^3*tan(1/2*c)^4*tan(c) - 8*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 2*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + 3*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + 8*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 12*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 8*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + 12*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + 8*a^2*d*x*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 + 12*b^2*d*x*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 - 32*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 + 2*a^2*d*x*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 3*b^2*d*x*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 8*a*b*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 2*a^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(c)^3 - 3*b^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(c)^3 - 8*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^3 - 8*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 12*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 8*a^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 12*b^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 32*a*b*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 96*a*b*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^3 - 8*a^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 12*b^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 32*a*b*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 + 32*a*b*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - 2*a^2*d*x*tan(d*x)*tan(1/2*c)^4*tan(c)^3 - 3*b^2*d*x*tan(d*x)*tan(1/2*c)^4*tan(c)^3 - 8*a*b*tan(d*x)^3*tan(1/2*c)^4*tan(c)^3 - 8*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3 - 8*b^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3 + 2*a^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4 + 3*b^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4 - 8*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + 2*a^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 3*b^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - 2*a^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^2 - 3*b^2*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^2 - 8*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 - 12*b^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 - 8*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 - 12*b^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 - 8*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 - 2*a^2*tan(d*x)^3*tan(1/2*c)^4*tan(c)^2 - 3*b^2*tan(d*x)^3*tan(1/2*c)^4*tan(c)^2 - 2*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^3 - 3*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^3 - 8*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 12*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 8*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 12*b^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 8*a^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - 8*b^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - 2*a^2*tan(d*x)^2*tan(1/2*c)^4*tan(c)^3 - 3*b^2*tan(d*x)^2*tan(1/2*c)^4*tan(c)^3 + 2*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4 + 3*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4 + 8*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c) + 12*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c) + 8*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3 + 12*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3 + 8*a^2*d*x*tan(1/2*d*x)^3*tan(1/2*c)^3 + 12*b^2*d*x*tan(1/2*d*x)^3*tan(1/2*c)^3 - 32*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3 + 2*a^2*d*x*tan(d*x)^2*tan(1/2*c)^4 + 3*b^2*d*x*tan(d*x)^2*tan(1/2*c)^4 + 8*a*b*tan(1/2*d*x)^4*tan(1/2*c)^4 - 2*a^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 3*b^2*d*x*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 8*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(c) - 8*a^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 12*b^2*d*x*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 8*a^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 12*b^2*d*x*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 32*a*b*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 96*a*b*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - 8*a^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 12*b^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 32*a*b*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) + 32*a*b*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 2*a^2*d*x*tan(d*x)*tan(1/2*c)^4*tan(c) - 3*b^2*d*x*tan(d*x)*tan(1/2*c)^4*tan(c) - 8*a*b*tan(d*x)^3*tan(1/2*c)^4*tan(c) + 2*a^2*d*x*tan(1/2*d*x)^4*tan(c)^2 + 3*b^2*d*x*tan(1/2*d*x)^4*tan(c)^2 + 8*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + 8*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + 12*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + 8*a^2*d*x*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 12*b^2*d*x*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 32*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 96*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 8*a^2*d*x*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + 12*b^2*d*x*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + 32*a*b*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 - 32*a*b*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 + 2*a^2*d*x*tan(1/2*c)^4*tan(c)^2 + 3*b^2*d*x*tan(1/2*c)^4*tan(c)^2 + 8*a*b*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 2*a^2*d*x*tan(d*x)^3*tan(c)^3 + 3*b^2*d*x*tan(d*x)^3*tan(c)^3 - 8*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(c)^3 - 8*a^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 12*b^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 + 32*a*b*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 32*a*b*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 96*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^3 - 32*a*b*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 8*a*b*tan(d*x)*tan(1/2*c)^4*tan(c)^3 - 2*a^2*tan(d*x)^3*tan(1/2*d*x)^4 - 2*b^2*tan(d*x)^3*tan(1/2*d*x)^4 - 8*a^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c) - 8*b^2*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c) - 8*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3 - 8*b^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3 - 8*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3 - 12*b^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3 - 2*a^2*tan(d*x)^3*tan(1/2*c)^4 - 2*b^2*tan(d*x)^3*tan(1/2*c)^4 - 2*a^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(c) - 8*a^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 8*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 8*a^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 12*b^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - 2*a^2*tan(d*x)^2*tan(1/2*c)^4*tan(c) - 2*a^2*tan(d*x)*tan(1/2*d*x)^4*tan(c)^2 - 8*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 - 12*b^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 - 8*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 - 8*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 - 2*a^2*tan(d*x)*tan(1/2*c)^4*tan(c)^2 - 2*a^2*tan(1/2*d*x)^4*tan(c)^3 - 2*b^2*tan(1/2*d*x)^4*tan(c)^3 - 8*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 12*b^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 8*a^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 8*b^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 8*a^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 8*b^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 2*a^2*tan(1/2*c)^4*tan(c)^3 - 2*b^2*tan(1/2*c)^4*tan(c)^3 + 2*a^2*d*x*tan(1/2*d*x)^4 + 3*b^2*d*x*tan(1/2*d*x)^4 + 8*a*b*tan(d*x)^2*tan(1/2*d*x)^4 + 8*a^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c) + 12*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c) + 8*a^2*d*x*tan(1/2*d*x)^3*tan(1/2*c) + 12*b^2*d*x*tan(1/2*d*x)^3*tan(1/2*c) + 32*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c) + 96*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 8*a^2*d*x*tan(1/2*d*x)*tan(1/2*c)^3 + 12*b^2*d*x*tan(1/2*d*x)*tan(1/2*c)^3 + 32*a*b*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3 - 32*a*b*tan(1/2*d*x)^3*tan(1/2*c)^3 + 2*a^2*d*x*tan(1/2*c)^4 + 3*b^2*d*x*tan(1/2*c)^4 + 8*a*b*tan(d*x)^2*tan(1/2*c)^4 + 2*a^2*d*x*tan(d*x)^3*tan(c) + 3*b^2*d*x*tan(d*x)^3*tan(c) - 8*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 8*a^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 12*b^2*d*x*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) + 32*a*b*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 32*a*b*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 96*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - 32*a*b*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 8*a*b*tan(d*x)*tan(1/2*c)^4*tan(c) - 2*a^2*d*x*tan(d*x)^2*tan(c)^2 - 3*b^2*d*x*tan(d*x)^2*tan(c)^2 + 8*a*b*tan(1/2*d*x)^4*tan(c)^2 + 8*a^2*d*x*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + 12*b^2*d*x*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 - 32*a*b*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + 32*a*b*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 96*a*b*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 32*a*b*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + 8*a*b*tan(1/2*c)^4*tan(c)^2 + 2*a^2*d*x*tan(d*x)*tan(c)^3 + 3*b^2*d*x*tan(d*x)*tan(c)^3 - 8*a*b*tan(d*x)^3*tan(c)^3 + 32*a*b*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 2*a^2*tan(d*x)*tan(1/2*d*x)^4 - 3*b^2*tan(d*x)*tan(1/2*d*x)^4 - 8*a^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c) - 8*b^2*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c) - 8*a^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c) - 12*b^2*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c) - 8*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3 - 12*b^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3 - 2*a^2*tan(d*x)*tan(1/2*c)^4 - 3*b^2*tan(d*x)*tan(1/2*c)^4 - 2*a^2*tan(1/2*d*x)^4*tan(c) - 3*b^2*tan(1/2*d*x)^4*tan(c) - 8*a^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 8*a^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 12*b^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 8*a^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 12*b^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 2*a^2*tan(1/2*c)^4*tan(c) - 3*b^2*tan(1/2*c)^4*tan(c) + 2*a^2*tan(d*x)^3*tan(c)^2 + 3*b^2*tan(d*x)^3*tan(c)^2 - 8*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + 2*a^2*tan(d*x)^2*tan(c)^3 + 3*b^2*tan(d*x)^2*tan(c)^3 - 8*a^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 8*b^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 2*a^2*d*x*tan(d*x)^2 - 3*b^2*d*x*tan(d*x)^2 + 8*a*b*tan(1/2*d*x)^4 + 8*a^2*d*x*tan(1/2*d*x)*tan(1/2*c) + 12*b^2*d*x*tan(1/2*d*x)*tan(1/2*c) - 32*a*b*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c) + 32*a*b*tan(1/2*d*x)^3*tan(1/2*c) + 96*a*b*tan(1/2*d*x)^2*tan(1/2*c)^2 + 32*a*b*tan(1/2*d*x)*tan(1/2*c)^3 + 8*a*b*tan(1/2*c)^4 + 2*a^2*d*x*tan(d*x)*tan(c) + 3*b^2*d*x*tan(d*x)*tan(c) - 8*a*b*tan(d*x)^3*tan(c) + 32*a*b*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 2*a^2*d*x*tan(c)^2 - 3*b^2*d*x*tan(c)^2 + 8*a*b*tan(d*x)^2*tan(c)^2 - 32*a*b*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 - 8*a*b*tan(d*x)*tan(c)^3 + 2*a^2*tan(d*x)^3 + 2*b^2*tan(d*x)^3 - 8*a^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c) - 12*b^2*tan(d*x)*tan(1/2*d*x)*tan(1/2*c) + 2*a^2*tan(d*x)^2*tan(c) - 8*a^2*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 12*b^2*tan(1/2*d*x)*tan(1/2*c)*tan(c) + 2*a^2*tan(d*x)*tan(c)^2 + 2*a^2*tan(c)^3 + 2*b^2*tan(c)^3 - 2*a^2*d*x - 3*b^2*d*x + 8*a*b*tan(d*x)^2 - 32*a*b*tan(1/2*d*x)*tan(1/2*c) - 8*a*b*tan(d*x)*tan(c) + 8*a*b*tan(c)^2 + 2*a^2*tan(d*x) + 3*b^2*tan(d*x) + 2*a^2*tan(c) + 3*b^2*tan(c) + 8*a*b)/(d*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + d*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 4*d*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 + d*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 - d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 4*d*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) + d*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 4*d*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 - d*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - d*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^3 - 4*d*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 4*d*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^3 - d*tan(d*x)^3*tan(1/2*c)^4*tan(c)^3 + 4*d*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^3 - d*tan(1/2*d*x)^4*tan(1/2*c)^4 - d*tan(d*x)^3*tan(1/2*d*x)^4*tan(c) - 4*d*tan(d*x)^3*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 4*d*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c) - d*tan(d*x)^3*tan(1/2*c)^4*tan(c) + d*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + 4*d*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 4*d*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + 4*d*tan(1/2*d*x)^3*tan(1/2*c)^3*tan(c)^2 + d*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 - d*tan(d*x)*tan(1/2*d*x)^4*tan(c)^3 - 4*d*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^3 - 4*d*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^3 - d*tan(d*x)*tan(1/2*c)^4*tan(c)^3 + d*tan(d*x)^2*tan(1/2*d*x)^4 + 4*d*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c) + 4*d*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^3 + 4*d*tan(1/2*d*x)^3*tan(1/2*c)^3 + d*tan(d*x)^2*tan(1/2*c)^4 - d*tan(d*x)*tan(1/2*d*x)^4*tan(c) - 4*d*tan(d*x)^3*tan(1/2*d*x)*tan(1/2*c)*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)^3*tan(1/2*c)*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^3*tan(c) - d*tan(d*x)*tan(1/2*c)^4*tan(c) + d*tan(1/2*d*x)^4*tan(c)^2 + 4*d*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + 4*d*tan(1/2*d*x)^3*tan(1/2*c)*tan(c)^2 + 4*d*tan(1/2*d*x)*tan(1/2*c)^3*tan(c)^2 + d*tan(1/2*c)^4*tan(c)^2 + d*tan(d*x)^3*tan(c)^3 - 4*d*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c)^3 + d*tan(1/2*d*x)^4 + 4*d*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c) + 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 + d*tan(d*x)^3*tan(c) - 4*d*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)*tan(c) - d*tan(d*x)^2*tan(c)^2 + 4*d*tan(1/2*d*x)*tan(1/2*c)*tan(c)^2 + d*tan(d*x)*tan(c)^3 - d*tan(d*x)^2 + 4*d*tan(1/2*d*x)*tan(1/2*c) + d*tan(d*x)*tan(c) - d*tan(c)^2 - d)","B",0
157,1,148,0,0.198581," ","integrate(cot(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{4 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - {\left(2 \, a^{2} - b^{2}\right)} {\left(d x + c\right)} - \frac{4 \, 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)} - \frac{2 \, {\left(b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + a^2*tan(1/2*d*x + 1/2*c) - (2*a^2 - b^2)*(d*x + c) - (4*a*b*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c) - 2*(b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^2 - b^2*tan(1/2*d*x + 1/2*c) - 4*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
158,1,241,0,0.352692," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 72 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} {\left(d x + c\right)} + \frac{24 \, {\left(b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{132 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, 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} - 6 \, 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)^{3}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 + 6*a*b*tan(1/2*d*x + 1/2*c)^2 - 72*a*b*log(abs(tan(1/2*d*x + 1/2*c))) - 15*a^2*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c) + 12*(2*a^2 - 3*b^2)*(d*x + c) + 24*(b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^2 - b^2*tan(1/2*d*x + 1/2*c) - 4*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + (132*a*b*tan(1/2*d*x + 1/2*c)^3 + 15*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*a*b*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
159,1,337,0,0.504771," ","integrate(cot(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1800 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 540 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, {\left(2 \, a^{2} - 5 \, b^{2}\right)} {\left(d x + c\right)} - \frac{480 \, {\left(b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{4110 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 540 \, 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} - 35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, 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)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^2*tan(1/2*d*x + 1/2*c)^5 + 15*a*b*tan(1/2*d*x + 1/2*c)^4 - 35*a^2*tan(1/2*d*x + 1/2*c)^3 + 20*b^2*tan(1/2*d*x + 1/2*c)^3 - 240*a*b*tan(1/2*d*x + 1/2*c)^2 + 1800*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + 330*a^2*tan(1/2*d*x + 1/2*c) - 540*b^2*tan(1/2*d*x + 1/2*c) - 240*(2*a^2 - 5*b^2)*(d*x + c) - 480*(b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^2 - b^2*tan(1/2*d*x + 1/2*c) - 4*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - (4110*a*b*tan(1/2*d*x + 1/2*c)^5 + 330*a^2*tan(1/2*d*x + 1/2*c)^4 - 540*b^2*tan(1/2*d*x + 1/2*c)^4 - 240*a*b*tan(1/2*d*x + 1/2*c)^3 - 35*a^2*tan(1/2*d*x + 1/2*c)^2 + 20*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*a*b*tan(1/2*d*x + 1/2*c) + 3*a^2)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
160,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3*tan(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3*tan(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,1,58,0,0.921723," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, b^{3} \sin\left(d x + c\right)^{3} + 9 \, a b^{2} \sin\left(d x + c\right)^{2} + 6 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 18 \, a^{2} b \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*b^3*sin(d*x + c)^3 + 9*a*b^2*sin(d*x + c)^2 + 6*a^3*log(abs(sin(d*x + c))) + 18*a^2*b*sin(d*x + c))/d","A",0
163,1,131,0,0.940070," ","integrate(cot(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, b^{3} \sin\left(d x + c\right)^{3} + 9 \, a b^{2} \sin\left(d x + c\right)^{2} + 18 \, a^{2} b \sin\left(d x + c\right) - 6 \, b^{3} \sin\left(d x + c\right) + 6 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{3 \, {\left(3 \, a^{3} \sin\left(d x + c\right)^{2} - 9 \, a b^{2} \sin\left(d x + c\right)^{2} - 6 \, a^{2} b \sin\left(d x + c\right) - a^{3}\right)}}{\sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"-1/6*(2*b^3*sin(d*x + c)^3 + 9*a*b^2*sin(d*x + c)^2 + 18*a^2*b*sin(d*x + c) - 6*b^3*sin(d*x + c) + 6*(a^3 - 3*a*b^2)*log(abs(sin(d*x + c))) - 3*(3*a^3*sin(d*x + c)^2 - 9*a*b^2*sin(d*x + c)^2 - 6*a^2*b*sin(d*x + c) - a^3)/sin(d*x + c)^2)/d","A",0
164,1,185,0,2.447388," ","integrate(cot(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{4 \, b^{3} \sin\left(d x + c\right)^{3} + 18 \, a b^{2} \sin\left(d x + c\right)^{2} + 36 \, a^{2} b \sin\left(d x + c\right) - 24 \, b^{3} \sin\left(d x + c\right) + 12 \, {\left(a^{3} - 6 \, a b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{25 \, a^{3} \sin\left(d x + c\right)^{4} - 150 \, a b^{2} \sin\left(d x + c\right)^{4} - 72 \, a^{2} b \sin\left(d x + c\right)^{3} + 12 \, b^{3} \sin\left(d x + c\right)^{3} - 12 \, a^{3} \sin\left(d x + c\right)^{2} + 18 \, a b^{2} \sin\left(d x + c\right)^{2} + 12 \, a^{2} b \sin\left(d x + c\right) + 3 \, a^{3}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(4*b^3*sin(d*x + c)^3 + 18*a*b^2*sin(d*x + c)^2 + 36*a^2*b*sin(d*x + c) - 24*b^3*sin(d*x + c) + 12*(a^3 - 6*a*b^2)*log(abs(sin(d*x + c))) - (25*a^3*sin(d*x + c)^4 - 150*a*b^2*sin(d*x + c)^4 - 72*a^2*b*sin(d*x + c)^3 + 12*b^3*sin(d*x + c)^3 - 12*a^3*sin(d*x + c)^2 + 18*a*b^2*sin(d*x + c)^2 + 12*a^2*b*sin(d*x + c) + 3*a^3)/sin(d*x + c)^4)/d","A",0
165,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3*tan(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3*tan(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,1,199,0,1.620953," ","integrate(cot(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{18 \, a^{2} b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)} - \frac{3 \, {\left(6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a^{2} b + 2 \, b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*a^2*b*log(abs(tan(1/2*d*x + 1/2*c))) + 3*a^3*tan(1/2*d*x + 1/2*c) - 3*(2*a^3 - 3*a*b^2)*(d*x + c) - 3*(6*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c) - 2*(9*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 18*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 6*b^3*tan(1/2*d*x + 1/2*c)^4 - 36*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 9*a*b^2*tan(1/2*d*x + 1/2*c) - 18*a^2*b + 2*b^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
168,1,421,0,0.689317," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 108 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, {\left(2 \, a^{3} - 9 \, a b^{2}\right)} {\left(d x + c\right)} - 36 \, {\left(9 \, a^{2} b - 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{198 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 44 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 108 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 135 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 156 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 132 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 324 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 351 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 156 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 126 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 540 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 315 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 148 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 108 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, 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)}^{3}}}{72 \, d}"," ",0,"1/72*(3*a^3*tan(1/2*d*x + 1/2*c)^3 + 27*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 45*a^3*tan(1/2*d*x + 1/2*c) + 108*a*b^2*tan(1/2*d*x + 1/2*c) + 36*(2*a^3 - 9*a*b^2)*(d*x + c) - 36*(9*a^2*b - 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) + (198*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 44*b^3*tan(1/2*d*x + 1/2*c)^9 + 45*a^3*tan(1/2*d*x + 1/2*c)^8 + 108*a*b^2*tan(1/2*d*x + 1/2*c)^8 + 135*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 156*b^3*tan(1/2*d*x + 1/2*c)^7 + 132*a^3*tan(1/2*d*x + 1/2*c)^6 - 324*a*b^2*tan(1/2*d*x + 1/2*c)^6 - 351*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 156*b^3*tan(1/2*d*x + 1/2*c)^5 + 126*a^3*tan(1/2*d*x + 1/2*c)^4 - 540*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 315*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 148*b^3*tan(1/2*d*x + 1/2*c)^3 + 36*a^3*tan(1/2*d*x + 1/2*c)^2 - 108*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 27*a^2*b*tan(1/2*d*x + 1/2*c) - 3*a^3)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^3)/d","B",0
169,1,471,0,1.050721," ","integrate(cot(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 660 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3240 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 480 \, {\left(2 \, a^{3} - 15 \, a b^{2}\right)} {\left(d x + c\right)} + 600 \, {\left(9 \, a^{2} b - 4 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{320 \, {\left(9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a^{2} b + 14 \, b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}} - \frac{12330 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5480 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 660 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3240 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 70 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a^3*tan(1/2*d*x + 1/2*c)^5 + 45*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 70*a^3*tan(1/2*d*x + 1/2*c)^3 + 120*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 720*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 120*b^3*tan(1/2*d*x + 1/2*c)^2 + 660*a^3*tan(1/2*d*x + 1/2*c) - 3240*a*b^2*tan(1/2*d*x + 1/2*c) - 480*(2*a^3 - 15*a*b^2)*(d*x + c) + 600*(9*a^2*b - 4*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) - 320*(9*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 18*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 18*b^3*tan(1/2*d*x + 1/2*c)^4 - 36*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 24*b^3*tan(1/2*d*x + 1/2*c)^2 - 9*a*b^2*tan(1/2*d*x + 1/2*c) - 18*a^2*b + 14*b^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3 - (12330*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 5480*b^3*tan(1/2*d*x + 1/2*c)^5 + 660*a^3*tan(1/2*d*x + 1/2*c)^4 - 3240*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 720*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 120*b^3*tan(1/2*d*x + 1/2*c)^3 - 70*a^3*tan(1/2*d*x + 1/2*c)^2 + 120*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 45*a^2*b*tan(1/2*d*x + 1/2*c) + 6*a^3)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
170,1,343,0,10.463698," ","integrate(tan(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{16 \, a^{5} b \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{{\left(8 \, a^{2} - 9 \, a b + 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(8 \, a^{2} + 9 \, a b + 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(6 \, a^{5} \sin\left(d x + c\right)^{4} - 9 \, a^{4} b \sin\left(d x + c\right)^{3} + 14 \, a^{2} b^{3} \sin\left(d x + c\right)^{3} - 5 \, b^{5} \sin\left(d x + c\right)^{3} - 4 \, a^{5} \sin\left(d x + c\right)^{2} - 12 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} + 4 \, a b^{4} \sin\left(d x + c\right)^{2} + 7 \, a^{4} b \sin\left(d x + c\right) - 10 \, a^{2} b^{3} \sin\left(d x + c\right) + 3 \, b^{5} \sin\left(d x + c\right) + 8 \, 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(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*a^5*b*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - (8*a^2 - 9*a*b + 3*b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (8*a^2 + 9*a*b + 3*b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(6*a^5*sin(d*x + c)^4 - 9*a^4*b*sin(d*x + c)^3 + 14*a^2*b^3*sin(d*x + c)^3 - 5*b^5*sin(d*x + c)^3 - 4*a^5*sin(d*x + c)^2 - 12*a^3*b^2*sin(d*x + c)^2 + 4*a*b^4*sin(d*x + c)^2 + 7*a^4*b*sin(d*x + c) - 10*a^2*b^3*sin(d*x + c) + 3*b^5*sin(d*x + c) + 8*a^3*b^2 - 2*a*b^4)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
171,1,177,0,2.103773," ","integrate(tan(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, a^{3} b \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b - 2 \, a^{2} b^{3} + b^{5}} - \frac{{\left(2 \, a - b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(2 \, a + b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(a^{3} \sin\left(d x + c\right)^{2} - a^{2} b \sin\left(d x + c\right) + b^{3} \sin\left(d x + c\right) - a b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}}}{4 \, d}"," ",0,"-1/4*(4*a^3*b*log(abs(b*sin(d*x + c) + a))/(a^4*b - 2*a^2*b^3 + b^5) - (2*a - b)*log(abs(sin(d*x + c) + 1))/(a^2 - 2*a*b + b^2) - (2*a + b)*log(abs(sin(d*x + c) - 1))/(a^2 + 2*a*b + b^2) + 2*(a^3*sin(d*x + c)^2 - a^2*b*sin(d*x + c) + b^3*sin(d*x + c) - a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(sin(d*x + c)^2 - 1)))/d","A",0
172,1,71,0,0.405415," ","integrate(tan(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, a b \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{2} b - b^{3}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a - b} - \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a + b}}{2 \, d}"," ",0,"1/2*(2*a*b*log(abs(b*sin(d*x + c) + a))/(a^2*b - b^3) - log(abs(sin(d*x + c) + 1))/(a - b) - log(abs(sin(d*x + c) - 1))/(a + b))/d","A",0
173,1,35,0,0.717542," ","integrate(cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{\log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a} - \frac{\log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a}}{d}"," ",0,"-(log(abs(b*sin(d*x + c) + a))/a - log(abs(sin(d*x + c)))/a)/d","A",0
174,1,114,0,0.381193," ","integrate(cot(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{2 \, {\left(a^{2} b - b^{3}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{3} b} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{2} - 3 \, b^{2} \sin\left(d x + c\right)^{2} + 2 \, a b \sin\left(d x + c\right) - a^{2}}{a^{3} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(a^2 - b^2)*log(abs(sin(d*x + c)))/a^3 - 2*(a^2*b - b^3)*log(abs(b*sin(d*x + c) + a))/(a^3*b) - (3*a^2*sin(d*x + c)^2 - 3*b^2*sin(d*x + c)^2 + 2*a*b*sin(d*x + c) - a^2)/(a^3*sin(d*x + c)^2))/d","A",0
175,1,201,0,0.454599," ","integrate(cot(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{5}} - \frac{12 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{5} b} - \frac{25 \, a^{4} \sin\left(d x + c\right)^{4} - 50 \, a^{2} b^{2} \sin\left(d x + c\right)^{4} + 25 \, b^{4} \sin\left(d x + c\right)^{4} + 24 \, a^{3} b \sin\left(d x + c\right)^{3} - 12 \, a b^{3} \sin\left(d x + c\right)^{3} - 12 \, a^{4} \sin\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} \sin\left(d x + c\right)^{2} - 4 \, a^{3} b \sin\left(d x + c\right) + 3 \, a^{4}}{a^{5} \sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(a^4 - 2*a^2*b^2 + b^4)*log(abs(sin(d*x + c)))/a^5 - 12*(a^4*b - 2*a^2*b^3 + b^5)*log(abs(b*sin(d*x + c) + a))/(a^5*b) - (25*a^4*sin(d*x + c)^4 - 50*a^2*b^2*sin(d*x + c)^4 + 25*b^4*sin(d*x + c)^4 + 24*a^3*b*sin(d*x + c)^3 - 12*a*b^3*sin(d*x + c)^3 - 12*a^4*sin(d*x + c)^2 + 6*a^2*b^2*sin(d*x + c)^2 - 4*a^3*b*sin(d*x + c) + 3*a^4)/(a^5*sin(d*x + c)^4))/d","A",0
176,1,241,0,3.698586," ","integrate(tan(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{4}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{2} b + 2 \, b^{3}}{{\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}}\right)}}{3 \, d}"," ",0,"2/3*(3*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a^4/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (3*a^3*tan(1/2*d*x + 1/2*c)^5 - 3*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 10*a^3*tan(1/2*d*x + 1/2*c)^3 + 4*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 6*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^3*tan(1/2*d*x + 1/2*c) - 5*a^2*b + 2*b^3)/((a^4 - 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","A",0
177,1,107,0,1.790452," ","integrate(tan(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{2}}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} + \frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b}{{\left(a^{2} - b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}\right)}}{d}"," ",0,"-2*((pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a^2/(a^2 - b^2)^(3/2) + (a*tan(1/2*d*x + 1/2*c) - b)/((a^2 - b^2)*(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
178,1,129,0,0.415953," ","integrate(cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{4 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} \sqrt{a^{2} - b^{2}}}{a^{2}} - \frac{2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(2*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - tan(1/2*d*x + 1/2*c)/a + 4*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*sqrt(a^2 - b^2)/a^2 - (2*b*tan(1/2*d*x + 1/2*c) - a)/(a^2*tan(1/2*d*x + 1/2*c)))/d","A",0
179,1,273,0,0.390092," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} + \frac{12 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} + \frac{48 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4}} - \frac{66 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a b^{2} \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) + a^{3}}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*((a^2*tan(1/2*d*x + 1/2*c)^3 - 3*a*b*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c))/a^3 + 12*(3*a^2*b - 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 + 48*(a^4 - 2*a^2*b^2 + b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4) - (66*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 44*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^4*tan(1/2*d*x + 1/2*c)^3))/d","A",0
180,1,490,0,0.596586," ","integrate(cot(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 660 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1080 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{5}} - \frac{120 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{6}} - \frac{1920 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{6}} + \frac{4110 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5480 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2192 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 660 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1080 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 480 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 70 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 40 \, a^{3} b^{2} \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) - 6 \, a^{5}}{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*((6*a^4*tan(1/2*d*x + 1/2*c)^5 - 15*a^3*b*tan(1/2*d*x + 1/2*c)^4 - 70*a^4*tan(1/2*d*x + 1/2*c)^3 + 40*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 240*a^3*b*tan(1/2*d*x + 1/2*c)^2 - 120*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 660*a^4*tan(1/2*d*x + 1/2*c) - 1080*a^2*b^2*tan(1/2*d*x + 1/2*c) + 480*b^4*tan(1/2*d*x + 1/2*c))/a^5 - 120*(15*a^4*b - 20*a^2*b^3 + 8*b^5)*log(abs(tan(1/2*d*x + 1/2*c)))/a^6 - 1920*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^6) + (4110*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 5480*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 2192*b^5*tan(1/2*d*x + 1/2*c)^5 - 660*a^5*tan(1/2*d*x + 1/2*c)^4 + 1080*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 - 480*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 240*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 120*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 70*a^5*tan(1/2*d*x + 1/2*c)^2 - 40*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*a^4*b*tan(1/2*d*x + 1/2*c) - 6*a^5)/(a^6*tan(1/2*d*x + 1/2*c)^5))/d","A",0
181,1,494,0,9.559698," ","integrate(tan(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{8 \, {\left(a^{6} b + 5 \, a^{4} b^{3}\right)} \log\left({\left| b \sin\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{{\left(4 \, a^{2} - a b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{{\left(4 \, a^{2} + a b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{8 \, {\left(a^{6} b \sin\left(d x + c\right) + 5 \, a^{4} b^{3} \sin\left(d x + c\right) + 2 \, a^{7} + 4 \, a^{5} b^{2}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \sin\left(d x + c\right) + a\right)}} + \frac{2 \, {\left(3 \, a^{6} \sin\left(d x + c\right)^{4} + 15 \, a^{4} b^{2} \sin\left(d x + c\right)^{4} - 9 \, a^{5} b \sin\left(d x + c\right)^{3} + 10 \, a^{3} b^{3} \sin\left(d x + c\right)^{3} - a b^{5} \sin\left(d x + c\right)^{3} - 2 \, a^{6} \sin\left(d x + c\right)^{2} - 28 \, a^{4} b^{2} \sin\left(d x + c\right)^{2} - 8 \, a^{2} b^{4} \sin\left(d x + c\right)^{2} + 2 \, b^{6} \sin\left(d x + c\right)^{2} + 7 \, a^{5} b \sin\left(d x + c\right) - 6 \, a^{3} b^{3} \sin\left(d x + c\right) - a b^{5} \sin\left(d x + c\right) + 12 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*(8*(a^6*b + 5*a^4*b^3)*log(abs(b*sin(d*x + c) + a))/(a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9) - (4*a^2 - a*b)*log(abs(sin(d*x + c) + 1))/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - (4*a^2 + a*b)*log(abs(sin(d*x + c) - 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 8*(a^6*b*sin(d*x + c) + 5*a^4*b^3*sin(d*x + c) + 2*a^7 + 4*a^5*b^2)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(b*sin(d*x + c) + a)) + 2*(3*a^6*sin(d*x + c)^4 + 15*a^4*b^2*sin(d*x + c)^4 - 9*a^5*b*sin(d*x + c)^3 + 10*a^3*b^3*sin(d*x + c)^3 - a*b^5*sin(d*x + c)^3 - 2*a^6*sin(d*x + c)^2 - 28*a^4*b^2*sin(d*x + c)^2 - 8*a^2*b^4*sin(d*x + c)^2 + 2*b^6*sin(d*x + c)^2 + 7*a^5*b*sin(d*x + c) - 6*a^3*b^3*sin(d*x + c) - a*b^5*sin(d*x + c) + 12*a^4*b^2 + 7*a^2*b^4 - b^6)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(sin(d*x + c)^2 - 1)^2))/d","B",0
182,1,248,0,1.981308," ","integrate(tan(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a^{4} b + 3 \, a^{2} b^{3}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{2} + 2 \, a b^{2} \sin\left(d x + c\right)^{2} + a^{2} b \sin\left(d x + c\right) - b^{3} \sin\left(d x + c\right) - 3 \, a^{3} - a b^{2}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - b \sin\left(d x + c\right) - a\right)}}}{2 \, d}"," ",0,"-1/2*(2*(a^4*b + 3*a^2*b^3)*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - a*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - a*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (2*a^3*sin(d*x + c)^2 + 2*a*b^2*sin(d*x + c)^2 + a^2*b*sin(d*x + c) - b^3*sin(d*x + c) - 3*a^3 - a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(b*sin(d*x + c)^3 + a*sin(d*x + c)^2 - b*sin(d*x + c) - a)))/d","A",0
183,1,156,0,0.459705," ","integrate(tan(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{2} b + b^{3}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b - 2 \, a^{2} b^{3} + b^{5}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(a^{2} b \sin\left(d x + c\right) + b^{3} \sin\left(d x + c\right) + 2 \, a^{3}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \sin\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"1/2*(2*(a^2*b + b^3)*log(abs(b*sin(d*x + c) + a))/(a^4*b - 2*a^2*b^3 + b^5) - log(abs(sin(d*x + c) + 1))/(a^2 - 2*a*b + b^2) - log(abs(sin(d*x + c) - 1))/(a^2 + 2*a*b + b^2) - 2*(a^2*b*sin(d*x + c) + b^3*sin(d*x + c) + 2*a^3)/((a^4 - 2*a^2*b^2 + b^4)*(b*sin(d*x + c) + a)))/d","A",0
184,1,51,0,0.416452," ","integrate(cot(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{b {\left(\frac{\log\left({\left| -\frac{a}{b \sin\left(d x + c\right) + a} + 1 \right|}\right)}{a^{2} b} + \frac{1}{{\left(b \sin\left(d x + c\right) + a\right)} a b}\right)}}{d}"," ",0,"b*(log(abs(-a/(b*sin(d*x + c) + a) + 1))/(a^2*b) + 1/((b*sin(d*x + c) + a)*a*b))/d","A",0
185,1,165,0,0.430583," ","integrate(cot(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a^{2} - 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{4}} - \frac{2 \, {\left(a^{2} b - 3 \, b^{3}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b} + \frac{2 \, {\left(a^{2} b \sin\left(d x + c\right) - 3 \, b^{3} \sin\left(d x + c\right) + 2 \, a^{3} - 4 \, a b^{2}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} a^{4}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{2} - 9 \, b^{2} \sin\left(d x + c\right)^{2} + 4 \, a b \sin\left(d x + c\right) - a^{2}}{a^{4} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(a^2 - 3*b^2)*log(abs(sin(d*x + c)))/a^4 - 2*(a^2*b - 3*b^3)*log(abs(b*sin(d*x + c) + a))/(a^4*b) + 2*(a^2*b*sin(d*x + c) - 3*b^3*sin(d*x + c) + 2*a^3 - 4*a*b^2)/((b*sin(d*x + c) + a)*a^4) - (3*a^2*sin(d*x + c)^2 - 9*b^2*sin(d*x + c)^2 + 4*a*b*sin(d*x + c) - a^2)/(a^4*sin(d*x + c)^2))/d","A",0
186,1,278,0,0.416442," ","integrate(cot(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 5 \, b^{4}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{6}} - \frac{12 \, {\left(a^{4} b - 6 \, a^{2} b^{3} + 5 \, b^{5}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b} + \frac{12 \, {\left(a^{4} b \sin\left(d x + c\right) - 6 \, a^{2} b^{3} \sin\left(d x + c\right) + 5 \, b^{5} \sin\left(d x + c\right) + 2 \, a^{5} - 8 \, a^{3} b^{2} + 6 \, a b^{4}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} a^{6}} - \frac{25 \, a^{4} \sin\left(d x + c\right)^{4} - 150 \, a^{2} b^{2} \sin\left(d x + c\right)^{4} + 125 \, b^{4} \sin\left(d x + c\right)^{4} + 48 \, a^{3} b \sin\left(d x + c\right)^{3} - 48 \, a b^{3} \sin\left(d x + c\right)^{3} - 12 \, a^{4} \sin\left(d x + c\right)^{2} + 18 \, a^{2} b^{2} \sin\left(d x + c\right)^{2} - 8 \, a^{3} b \sin\left(d x + c\right) + 3 \, a^{4}}{a^{6} \sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(a^4 - 6*a^2*b^2 + 5*b^4)*log(abs(sin(d*x + c)))/a^6 - 12*(a^4*b - 6*a^2*b^3 + 5*b^5)*log(abs(b*sin(d*x + c) + a))/(a^6*b) + 12*(a^4*b*sin(d*x + c) - 6*a^2*b^3*sin(d*x + c) + 5*b^5*sin(d*x + c) + 2*a^5 - 8*a^3*b^2 + 6*a*b^4)/((b*sin(d*x + c) + a)*a^6) - (25*a^4*sin(d*x + c)^4 - 150*a^2*b^2*sin(d*x + c)^4 + 125*b^4*sin(d*x + c)^4 + 48*a^3*b*sin(d*x + c)^3 - 48*a*b^3*sin(d*x + c)^3 - 12*a^4*sin(d*x + c)^2 + 18*a^2*b^2*sin(d*x + c)^2 - 8*a^3*b*sin(d*x + c) + 3*a^4)/(a^6*sin(d*x + c)^4))/d","A",0
187,1,406,0,2.980422," ","integrate(tan(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(a^{5} + 4 \, a^{3} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\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{3 \, {\left(a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{4} b\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}} + \frac{3 \, a^{4} \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)^{5} - 6 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 10 \, a^{3} b - 2 \, a b^{3}}{{\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)}^{3}}\right)}}{3 \, d}"," ",0,"2/3*(3*(a^5 + 4*a^3*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + 3*(a^3*b^2*tan(1/2*d*x + 1/2*c) + a^4*b)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)) + (3*a^4*tan(1/2*d*x + 1/2*c)^5 + 9*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*a^3*b*tan(1/2*d*x + 1/2*c)^4 - 6*a*b^3*tan(1/2*d*x + 1/2*c)^4 - 10*a^4*tan(1/2*d*x + 1/2*c)^3 - 18*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*b^4*tan(1/2*d*x + 1/2*c)^3 + 24*a^3*b*tan(1/2*d*x + 1/2*c)^2 + 3*a^4*tan(1/2*d*x + 1/2*c) + 9*a^2*b^2*tan(1/2*d*x + 1/2*c) - 10*a^3*b - 2*a*b^3)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","A",0
188,1,251,0,0.873588," ","integrate(tan(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(a^{3} + 2 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)} {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)}}\right)}}{d}"," ",0,"-2*((a^3 + 2*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (a^3*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^2*tan(1/2*d*x + 1/2*c)^3 + a^2*b*tan(1/2*d*x + 1/2*c)^2 + 2*b^3*tan(1/2*d*x + 1/2*c)^2 + a^3*tan(1/2*d*x + 1/2*c) - 4*a*b^2*tan(1/2*d*x + 1/2*c) - 3*a^2*b)/((a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c) - a)*(a^4 - 2*a^2*b^2 + b^4)))/d","A",0
189,1,218,0,0.395889," ","integrate(cot(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} + \frac{12 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(a^{2} - 2 \, b^{2}\right)}}{\sqrt{a^{2} - b^{2}} a^{3}} - \frac{4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 14 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{3}}}{6 \, d}"," ",0,"-1/6*(12*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 3*tan(1/2*d*x + 1/2*c)/a^2 + 12*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*(a^2 - 2*b^2)/(sqrt(a^2 - b^2)*a^3) - (4*a*b*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*tan(1/2*d*x + 1/2*c)^2 - 4*b^2*tan(1/2*d*x + 1/2*c)^2 - 14*a*b*tan(1/2*d*x + 1/2*c) - 3*a^2)/((a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^2 + a*tan(1/2*d*x + 1/2*c))*a^3))/d","A",0
190,1,356,0,0.541851," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(3 \, a^{2} b - 4 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} + \frac{48 \, {\left(a^{4} - 5 \, a^{2} b^{2} + 4 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{5}} + \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}} + \frac{48 \, {\left(a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} b - a b^{3}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{5}} - \frac{132 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 176 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(24*(3*a^2*b - 4*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 + 48*(a^4 - 5*a^2*b^2 + 4*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^5) + (a^4*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*b*tan(1/2*d*x + 1/2*c)^2 - 15*a^4*tan(1/2*d*x + 1/2*c) + 36*a^2*b^2*tan(1/2*d*x + 1/2*c))/a^6 + 48*(a^2*b^2*tan(1/2*d*x + 1/2*c) - b^4*tan(1/2*d*x + 1/2*c) + a^3*b - a*b^3)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^5) - (132*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 176*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 + 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^5*tan(1/2*d*x + 1/2*c)^3))/d","A",0
191,1,596,0,0.899079," ","integrate(cot(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{120 \, {\left(15 \, a^{4} b - 40 \, a^{2} b^{3} + 24 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{7}} + \frac{960 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 13 \, a^{2} b^{4} - 6 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{7}} + \frac{960 \, {\left(a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{7}} - \frac{3 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 35 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 240 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 330 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1620 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1200 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{10}} - \frac{4110 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10960 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6576 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 330 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1620 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1200 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, a^{3} b^{2} \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) - 3 \, a^{5}}{a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"-1/480*(120*(15*a^4*b - 40*a^2*b^3 + 24*b^5)*log(abs(tan(1/2*d*x + 1/2*c)))/a^7 + 960*(a^6 - 8*a^4*b^2 + 13*a^2*b^4 - 6*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^7) + 960*(a^4*b^2*tan(1/2*d*x + 1/2*c) - 2*a^2*b^4*tan(1/2*d*x + 1/2*c) + b^6*tan(1/2*d*x + 1/2*c) + a^5*b - 2*a^3*b^3 + a*b^5)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^7) - (3*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*a^7*b*tan(1/2*d*x + 1/2*c)^4 - 35*a^8*tan(1/2*d*x + 1/2*c)^3 + 60*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 240*a^7*b*tan(1/2*d*x + 1/2*c)^2 - 240*a^5*b^3*tan(1/2*d*x + 1/2*c)^2 + 330*a^8*tan(1/2*d*x + 1/2*c) - 1620*a^6*b^2*tan(1/2*d*x + 1/2*c) + 1200*a^4*b^4*tan(1/2*d*x + 1/2*c))/a^10 - (4110*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 10960*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 6576*b^5*tan(1/2*d*x + 1/2*c)^5 - 330*a^5*tan(1/2*d*x + 1/2*c)^4 + 1620*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 - 1200*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 240*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 240*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 35*a^5*tan(1/2*d*x + 1/2*c)^2 - 60*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*a^4*b*tan(1/2*d*x + 1/2*c) - 3*a^5)/(a^7*tan(1/2*d*x + 1/2*c)^5))/d","A",0
192,1,585,0,6.813813," ","integrate(tan(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{16 \, {\left(a^{7} b + 13 \, a^{5} b^{3} + 10 \, a^{3} b^{5}\right)} \log\left({\left| b \sin\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{{\left(8 \, a^{2} + 5 \, a b - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}} - \frac{{\left(8 \, a^{2} - 5 \, a b - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}} - \frac{2 \, {\left(8 \, a^{6} b \sin\left(d x + c\right)^{5} + 67 \, a^{4} b^{3} \sin\left(d x + c\right)^{5} + 22 \, a^{2} b^{5} \sin\left(d x + c\right)^{5} - b^{7} \sin\left(d x + c\right)^{5} + 12 \, a^{7} \sin\left(d x + c\right)^{4} + 82 \, a^{5} b^{2} \sin\left(d x + c\right)^{4} + 4 \, a^{3} b^{4} \sin\left(d x + c\right)^{4} - 2 \, a b^{6} \sin\left(d x + c\right)^{4} - 5 \, a^{6} b \sin\left(d x + c\right)^{3} - 159 \, a^{4} b^{3} \sin\left(d x + c\right)^{3} - 27 \, a^{2} b^{5} \sin\left(d x + c\right)^{3} - b^{7} \sin\left(d x + c\right)^{3} - 32 \, a^{7} \sin\left(d x + c\right)^{2} - 148 \, a^{5} b^{2} \sin\left(d x + c\right)^{2} - 16 \, a^{3} b^{4} \sin\left(d x + c\right)^{2} + 4 \, a b^{6} \sin\left(d x + c\right)^{2} - a^{6} b \sin\left(d x + c\right) + 86 \, a^{4} b^{3} \sin\left(d x + c\right) + 11 \, a^{2} b^{5} \sin\left(d x + c\right) + 18 \, a^{7} + 72 \, a^{5} b^{2} + 6 \, a^{3} b^{4}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - b \sin\left(d x + c\right) - a\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*(a^7*b + 13*a^5*b^3 + 10*a^3*b^5)*log(abs(b*sin(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) - (8*a^2 + 5*a*b - b^2)*log(abs(sin(d*x + c) + 1))/(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5) - (8*a^2 - 5*a*b - b^2)*log(abs(sin(d*x + c) - 1))/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) - 2*(8*a^6*b*sin(d*x + c)^5 + 67*a^4*b^3*sin(d*x + c)^5 + 22*a^2*b^5*sin(d*x + c)^5 - b^7*sin(d*x + c)^5 + 12*a^7*sin(d*x + c)^4 + 82*a^5*b^2*sin(d*x + c)^4 + 4*a^3*b^4*sin(d*x + c)^4 - 2*a*b^6*sin(d*x + c)^4 - 5*a^6*b*sin(d*x + c)^3 - 159*a^4*b^3*sin(d*x + c)^3 - 27*a^2*b^5*sin(d*x + c)^3 - b^7*sin(d*x + c)^3 - 32*a^7*sin(d*x + c)^2 - 148*a^5*b^2*sin(d*x + c)^2 - 16*a^3*b^4*sin(d*x + c)^2 + 4*a*b^6*sin(d*x + c)^2 - a^6*b*sin(d*x + c) + 86*a^4*b^3*sin(d*x + c) + 11*a^2*b^5*sin(d*x + c) + 18*a^7 + 72*a^5*b^2 + 6*a^3*b^4)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(b*sin(d*x + c)^3 + a*sin(d*x + c)^2 - b*sin(d*x + c) - a)^2))/d","A",0
193,1,464,0,2.389732," ","integrate(tan(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(a^{5} b + 8 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \log\left({\left| b \sin\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{{\left(2 \, a + b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{{\left(2 \, a - b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{2 \, {\left(a^{5} \sin\left(d x + c\right)^{2} + 8 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} + 3 \, a b^{4} \sin\left(d x + c\right)^{2} - 3 \, a^{4} b \sin\left(d x + c\right) + 2 \, a^{2} b^{3} \sin\left(d x + c\right) + b^{5} \sin\left(d x + c\right) - 6 \, a^{3} b^{2} - 6 \, a b^{4}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}} - \frac{2 \, {\left(3 \, a^{5} b^{2} \sin\left(d x + c\right)^{2} + 24 \, a^{3} b^{4} \sin\left(d x + c\right)^{2} + 9 \, a b^{6} \sin\left(d x + c\right)^{2} + 8 \, a^{6} b \sin\left(d x + c\right) + 52 \, a^{4} b^{3} \sin\left(d x + c\right) + 12 \, a^{2} b^{5} \sin\left(d x + c\right) + 6 \, a^{7} + 26 \, a^{5} b^{2} + 4 \, a^{3} b^{4}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}}{4 \, d}"," ",0,"-1/4*(4*(a^5*b + 8*a^3*b^3 + 3*a*b^5)*log(abs(b*sin(d*x + c) + a))/(a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9) - (2*a + b)*log(abs(sin(d*x + c) + 1))/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - (2*a - b)*log(abs(sin(d*x + c) - 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 2*(a^5*sin(d*x + c)^2 + 8*a^3*b^2*sin(d*x + c)^2 + 3*a*b^4*sin(d*x + c)^2 - 3*a^4*b*sin(d*x + c) + 2*a^2*b^3*sin(d*x + c) + b^5*sin(d*x + c) - 6*a^3*b^2 - 6*a*b^4)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(sin(d*x + c)^2 - 1)) - 2*(3*a^5*b^2*sin(d*x + c)^2 + 24*a^3*b^4*sin(d*x + c)^2 + 9*a*b^6*sin(d*x + c)^2 + 8*a^6*b*sin(d*x + c) + 52*a^4*b^3*sin(d*x + c) + 12*a^2*b^5*sin(d*x + c) + 6*a^7 + 26*a^5*b^2 + 4*a^3*b^4)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(b*sin(d*x + c) + a)^2))/d","B",0
194,1,257,0,0.530468," ","integrate(tan(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{3} b + 3 \, a b^{3}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{3 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} + 9 \, a b^{4} \sin\left(d x + c\right)^{2} + 8 \, a^{4} b \sin\left(d x + c\right) + 18 \, a^{2} b^{3} \sin\left(d x + c\right) - 2 \, b^{5} \sin\left(d x + c\right) + 6 \, a^{5} + 7 \, a^{3} b^{2} - a b^{4}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(a^3*b + 3*a*b^3)*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (3*a^3*b^2*sin(d*x + c)^2 + 9*a*b^4*sin(d*x + c)^2 + 8*a^4*b*sin(d*x + c) + 18*a^2*b^3*sin(d*x + c) - 2*b^5*sin(d*x + c) + 6*a^5 + 7*a^3*b^2 - a*b^4)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(b*sin(d*x + c) + a)^2))/d","A",0
195,1,69,0,1.082721," ","integrate(cot(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{3}} - \frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{2 \, a b \sin\left(d x + c\right) + 3 \, a^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2} a^{3}}}{2 \, d}"," ",0,"-1/2*(2*log(abs(b*sin(d*x + c) + a))/a^3 - 2*log(abs(sin(d*x + c)))/a^3 - (2*a*b*sin(d*x + c) + 3*a^2)/((b*sin(d*x + c) + a)^2*a^3))/d","A",0
196,1,154,0,0.536059," ","integrate(cot(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a^{2} - 6 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{5}} - \frac{2 \, {\left(a^{2} b - 6 \, b^{3}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{5} b} + \frac{2 \, a^{2} b \sin\left(d x + c\right)^{3} - 12 \, b^{3} \sin\left(d x + c\right)^{3} + 3 \, a^{3} \sin\left(d x + c\right)^{2} - 18 \, a b^{2} \sin\left(d x + c\right)^{2} - 4 \, a^{2} b \sin\left(d x + c\right) + a^{3}}{{\left(b \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right)\right)}^{2} a^{4}}}{2 \, d}"," ",0,"-1/2*(2*(a^2 - 6*b^2)*log(abs(sin(d*x + c)))/a^5 - 2*(a^2*b - 6*b^3)*log(abs(b*sin(d*x + c) + a))/(a^5*b) + (2*a^2*b*sin(d*x + c)^3 - 12*b^3*sin(d*x + c)^3 + 3*a^3*sin(d*x + c)^2 - 18*a*b^2*sin(d*x + c)^2 - 4*a^2*b*sin(d*x + c) + a^3)/((b*sin(d*x + c)^2 + a*sin(d*x + c))^2*a^4))/d","A",0
197,1,327,0,0.835048," ","integrate(cot(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(a^{4} - 12 \, a^{2} b^{2} + 15 \, b^{4}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{7}} - \frac{12 \, {\left(a^{4} b - 12 \, a^{2} b^{3} + 15 \, b^{5}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{7} b} + \frac{6 \, {\left(3 \, a^{4} b^{2} \sin\left(d x + c\right)^{2} - 36 \, a^{2} b^{4} \sin\left(d x + c\right)^{2} + 45 \, b^{6} \sin\left(d x + c\right)^{2} + 8 \, a^{5} b \sin\left(d x + c\right) - 84 \, a^{3} b^{3} \sin\left(d x + c\right) + 100 \, a b^{5} \sin\left(d x + c\right) + 6 \, a^{6} - 50 \, a^{4} b^{2} + 56 \, a^{2} b^{4}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2} a^{7}} - \frac{25 \, a^{4} \sin\left(d x + c\right)^{4} - 300 \, a^{2} b^{2} \sin\left(d x + c\right)^{4} + 375 \, b^{4} \sin\left(d x + c\right)^{4} + 72 \, a^{3} b \sin\left(d x + c\right)^{3} - 120 \, a b^{3} \sin\left(d x + c\right)^{3} - 12 \, a^{4} \sin\left(d x + c\right)^{2} + 36 \, a^{2} b^{2} \sin\left(d x + c\right)^{2} - 12 \, a^{3} b \sin\left(d x + c\right) + 3 \, a^{4}}{a^{7} \sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(a^4 - 12*a^2*b^2 + 15*b^4)*log(abs(sin(d*x + c)))/a^7 - 12*(a^4*b - 12*a^2*b^3 + 15*b^5)*log(abs(b*sin(d*x + c) + a))/(a^7*b) + 6*(3*a^4*b^2*sin(d*x + c)^2 - 36*a^2*b^4*sin(d*x + c)^2 + 45*b^6*sin(d*x + c)^2 + 8*a^5*b*sin(d*x + c) - 84*a^3*b^3*sin(d*x + c) + 100*a*b^5*sin(d*x + c) + 6*a^6 - 50*a^4*b^2 + 56*a^2*b^4)/((b*sin(d*x + c) + a)^2*a^7) - (25*a^4*sin(d*x + c)^4 - 300*a^2*b^2*sin(d*x + c)^4 + 375*b^4*sin(d*x + c)^4 + 72*a^3*b*sin(d*x + c)^3 - 120*a*b^3*sin(d*x + c)^3 - 12*a^4*sin(d*x + c)^2 + 36*a^2*b^2*sin(d*x + c)^2 - 12*a^3*b*sin(d*x + c) + 3*a^4)/(a^7*sin(d*x + c)^4))/d","A",0
198,1,632,0,2.415791," ","integrate(tan(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{6} + 21 \, a^{4} b^{2} + 12 \, a^{2} b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, {\left(5 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 14 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 22 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{6} b + 7 \, 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(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}} + \frac{2 \, {\left(3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, a^{4} b - 20 \, a^{2} b^{3} - b^{5}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(2*a^6 + 21*a^4*b^2 + 12*a^2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*sqrt(a^2 - b^2)) + 3*(5*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*a^6*b*tan(1/2*d*x + 1/2*c)^2 + 15*a^4*b^3*tan(1/2*d*x + 1/2*c)^2 + 14*a^2*b^5*tan(1/2*d*x + 1/2*c)^2 + 11*a^5*b^2*tan(1/2*d*x + 1/2*c) + 22*a^3*b^4*tan(1/2*d*x + 1/2*c) + 4*a^6*b + 7*a^4*b^3)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2) + 2*(3*a^5*tan(1/2*d*x + 1/2*c)^5 + 24*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 9*a^4*b*tan(1/2*d*x + 1/2*c)^4 - 24*a^2*b^3*tan(1/2*d*x + 1/2*c)^4 - 3*b^5*tan(1/2*d*x + 1/2*c)^4 - 10*a^5*tan(1/2*d*x + 1/2*c)^3 - 56*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 36*a^4*b*tan(1/2*d*x + 1/2*c)^2 + 36*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^5*tan(1/2*d*x + 1/2*c) + 24*a^3*b^2*tan(1/2*d*x + 1/2*c) + 9*a*b^4*tan(1/2*d*x + 1/2*c) - 15*a^4*b - 20*a^2*b^3 - b^5)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","A",0
199,1,384,0,1.820684," ","integrate(tan(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, a^{4} + 11 \, a^{2} b^{2} + 2 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\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(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b - b^{3}\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)}} + \frac{5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{4} b + 3 \, a^{2} b^{3}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}}}{d}"," ",0,"-((2*a^4 + 11*a^2*b^2 + 2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/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*(a^3*tan(1/2*d*x + 1/2*c) + 3*a*b^2*tan(1/2*d*x + 1/2*c) - 3*a^2*b - b^3)/((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*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^2 + 11*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 + 6*b^5*tan(1/2*d*x + 1/2*c)^2 + 11*a^3*b^2*tan(1/2*d*x + 1/2*c) + 10*a*b^4*tan(1/2*d*x + 1/2*c) + 4*a^4*b + 3*a^2*b^3)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2))/d","A",0
200,1,339,0,0.499900," ","integrate(cot(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(2 \, a^{4} - 9 \, a^{2} b^{2} + 6 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{4} b - 5 \, a^{2} b^{3}\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}} + \frac{6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{6 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(2*(2*a^4 - 9*a^2*b^2 + 6*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6 - a^4*b^2)*sqrt(a^2 - b^2)) + 2*(5*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^2 + 3*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 10*b^5*tan(1/2*d*x + 1/2*c)^2 + 11*a^3*b^2*tan(1/2*d*x + 1/2*c) - 14*a*b^4*tan(1/2*d*x + 1/2*c) + 4*a^4*b - 5*a^2*b^3)/((a^6 - a^4*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2) + 6*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - tan(1/2*d*x + 1/2*c)/a^3 - (6*b*tan(1/2*d*x + 1/2*c) - a)/(a^4*tan(1/2*d*x + 1/2*c)))/d","A",0
201,1,451,0,0.920429," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(9 \, a^{2} b - 20 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{6}} + \frac{24 \, {\left(2 \, a^{4} - 19 \, a^{2} b^{2} + 20 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{6}} + \frac{24 \, {\left(5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 18 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 26 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{4} b - 9 \, a^{2} b^{3}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{6}} + \frac{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{9}} - \frac{198 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 440 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(12*(9*a^2*b - 20*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^6 + 24*(2*a^4 - 19*a^2*b^2 + 20*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^6) + 24*(5*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 10*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^2 - a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 18*b^5*tan(1/2*d*x + 1/2*c)^2 + 11*a^3*b^2*tan(1/2*d*x + 1/2*c) - 26*a*b^4*tan(1/2*d*x + 1/2*c) + 4*a^4*b - 9*a^2*b^3)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^6) + (a^6*tan(1/2*d*x + 1/2*c)^3 - 9*a^5*b*tan(1/2*d*x + 1/2*c)^2 - 15*a^6*tan(1/2*d*x + 1/2*c) + 72*a^4*b^2*tan(1/2*d*x + 1/2*c))/a^9 - (198*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 440*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 + 72*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 9*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^6*tan(1/2*d*x + 1/2*c)^3))/d","A",0
202,1,731,0,1.517828," ","integrate(cot(d*x+c)^6/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{120 \, {\left(45 \, a^{4} b - 200 \, a^{2} b^{3} + 168 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{8}} + \frac{960 \, {\left(2 \, a^{6} - 31 \, a^{4} b^{2} + 71 \, a^{2} b^{4} - 42 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{8}} + \frac{960 \, {\left(5 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 19 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 21 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 26 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 49 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 38 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{6} b - 17 \, a^{4} b^{3} + 13 \, a^{2} b^{5}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{8}} - \frac{12330 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 54800 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 46032 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 660 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6480 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 7200 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 720 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1200 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 70 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 240 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{5}}{a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} - \frac{6 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{11} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{10} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 720 \, a^{11} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1200 \, a^{9} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 660 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6480 \, a^{10} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7200 \, a^{8} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{960 \, d}"," ",0,"-1/960*(120*(45*a^4*b - 200*a^2*b^3 + 168*b^5)*log(abs(tan(1/2*d*x + 1/2*c)))/a^8 + 960*(2*a^6 - 31*a^4*b^2 + 71*a^2*b^4 - 42*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^8) + 960*(5*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 19*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 14*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 4*a^6*b*tan(1/2*d*x + 1/2*c)^2 - 9*a^4*b^3*tan(1/2*d*x + 1/2*c)^2 - 21*a^2*b^5*tan(1/2*d*x + 1/2*c)^2 + 26*b^7*tan(1/2*d*x + 1/2*c)^2 + 11*a^5*b^2*tan(1/2*d*x + 1/2*c) - 49*a^3*b^4*tan(1/2*d*x + 1/2*c) + 38*a*b^6*tan(1/2*d*x + 1/2*c) + 4*a^6*b - 17*a^4*b^3 + 13*a^2*b^5)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^8) - (12330*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 54800*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 46032*b^5*tan(1/2*d*x + 1/2*c)^5 - 660*a^5*tan(1/2*d*x + 1/2*c)^4 + 6480*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 - 7200*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 720*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 1200*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 70*a^5*tan(1/2*d*x + 1/2*c)^2 - 240*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 45*a^4*b*tan(1/2*d*x + 1/2*c) - 6*a^5)/(a^8*tan(1/2*d*x + 1/2*c)^5) - (6*a^12*tan(1/2*d*x + 1/2*c)^5 - 45*a^11*b*tan(1/2*d*x + 1/2*c)^4 - 70*a^12*tan(1/2*d*x + 1/2*c)^3 + 240*a^10*b^2*tan(1/2*d*x + 1/2*c)^3 + 720*a^11*b*tan(1/2*d*x + 1/2*c)^2 - 1200*a^9*b^3*tan(1/2*d*x + 1/2*c)^2 + 660*a^12*tan(1/2*d*x + 1/2*c) - 6480*a^10*b^2*tan(1/2*d*x + 1/2*c) + 7200*a^8*b^4*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
203,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3*(g*tan(f*x+e))^p,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*(g*tan(f*x + e))^p, x)","F",0
204,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2*(g*tan(f*x+e))^p,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(g*tan(f*x + e))^p, x)","F",0
205,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(g*tan(f*x+e))^p,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(g*tan(f*x + e))^p, x)","F",0
206,0,0,0,0.000000," ","integrate((g*tan(f*x+e))^p/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \tan\left(f x + e\right)\right)^{p}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*tan(f*x + e))^p/(b*sin(f*x + e) + a), x)","F",0
207,0,0,0,0.000000," ","integrate((g*tan(f*x+e))^p/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(g \tan\left(f x + e\right)\right)^{p}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((g*tan(f*x + e))^p/(b*sin(f*x + e) + a)^2, x)","F",0
208,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(g*tan(f*x+e))^p,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{m} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m*(g*tan(f*x + e))^p, x)","F",0
