1,1,1017,0,3.958242," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{6 \, B a d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 6 \, C b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, C 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(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, B b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 18 \, B a d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 18 \, C b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 3 \, C a \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, B b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 9 \, C 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(d x\right)^{2} \tan\left(c\right)^{2} + 9 \, B b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 6 \, B a \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 6 \, C b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 6 \, B a \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 6 \, C b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 18 \, B a d x \tan\left(d x\right) \tan\left(c\right) - 18 \, C b d x \tan\left(d x\right) \tan\left(c\right) - 3 \, C a \tan\left(d x\right)^{3} \tan\left(c\right) - 3 \, B b \tan\left(d x\right)^{3} \tan\left(c\right) + 3 \, C a \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, B b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 3 \, C a \tan\left(d x\right) \tan\left(c\right)^{3} - 3 \, B b \tan\left(d x\right) \tan\left(c\right)^{3} + 2 \, C b \tan\left(d x\right)^{3} - 9 \, C 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(d x\right) \tan\left(c\right) - 9 \, B b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) - 12 \, B a \tan\left(d x\right)^{2} \tan\left(c\right) + 18 \, C b \tan\left(d x\right)^{2} \tan\left(c\right) - 12 \, B a \tan\left(d x\right) \tan\left(c\right)^{2} + 18 \, C b \tan\left(d x\right) \tan\left(c\right)^{2} + 2 \, C b \tan\left(c\right)^{3} - 6 \, B a d x + 6 \, C b d x + 3 \, C a \tan\left(d x\right)^{2} + 3 \, B b \tan\left(d x\right)^{2} - 3 \, C a \tan\left(d x\right) \tan\left(c\right) - 3 \, B b \tan\left(d x\right) \tan\left(c\right) + 3 \, C a \tan\left(c\right)^{2} + 3 \, B b \tan\left(c\right)^{2} + 3 \, C 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) + 3 \, B b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) + 6 \, B a \tan\left(d x\right) - 6 \, C b \tan\left(d x\right) + 6 \, B a \tan\left(c\right) - 6 \, C b \tan\left(c\right) + 3 \, C a + 3 \, B b}{6 \, {\left(d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"-1/6*(6*B*a*d*x*tan(d*x)^3*tan(c)^3 - 6*C*b*d*x*tan(d*x)^3*tan(c)^3 - 3*C*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(d*x)^3*tan(c)^3 - 3*B*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 - 18*B*a*d*x*tan(d*x)^2*tan(c)^2 + 18*C*b*d*x*tan(d*x)^2*tan(c)^2 - 3*C*a*tan(d*x)^3*tan(c)^3 - 3*B*b*tan(d*x)^3*tan(c)^3 + 9*C*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(d*x)^2*tan(c)^2 + 9*B*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 + 6*B*a*tan(d*x)^3*tan(c)^2 - 6*C*b*tan(d*x)^3*tan(c)^2 + 6*B*a*tan(d*x)^2*tan(c)^3 - 6*C*b*tan(d*x)^2*tan(c)^3 + 18*B*a*d*x*tan(d*x)*tan(c) - 18*C*b*d*x*tan(d*x)*tan(c) - 3*C*a*tan(d*x)^3*tan(c) - 3*B*b*tan(d*x)^3*tan(c) + 3*C*a*tan(d*x)^2*tan(c)^2 + 3*B*b*tan(d*x)^2*tan(c)^2 - 3*C*a*tan(d*x)*tan(c)^3 - 3*B*b*tan(d*x)*tan(c)^3 + 2*C*b*tan(d*x)^3 - 9*C*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(d*x)*tan(c) - 9*B*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) - 12*B*a*tan(d*x)^2*tan(c) + 18*C*b*tan(d*x)^2*tan(c) - 12*B*a*tan(d*x)*tan(c)^2 + 18*C*b*tan(d*x)*tan(c)^2 + 2*C*b*tan(c)^3 - 6*B*a*d*x + 6*C*b*d*x + 3*C*a*tan(d*x)^2 + 3*B*b*tan(d*x)^2 - 3*C*a*tan(d*x)*tan(c) - 3*B*b*tan(d*x)*tan(c) + 3*C*a*tan(c)^2 + 3*B*b*tan(c)^2 + 3*C*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)) + 3*B*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) + 6*B*a*tan(d*x) - 6*C*b*tan(d*x) + 6*B*a*tan(c) - 6*C*b*tan(c) + 3*C*a + 3*B*b)/(d*tan(d*x)^3*tan(c)^3 - 3*d*tan(d*x)^2*tan(c)^2 + 3*d*tan(d*x)*tan(c) - d)","B",0
2,1,616,0,2.921798," ","integrate((a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{2 \, C a d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 2 \, B b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + B 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(d x\right)^{2} \tan\left(c\right)^{2} - C b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 4 \, C a d x \tan\left(d x\right) \tan\left(c\right) - 4 \, B b d x \tan\left(d x\right) \tan\left(c\right) - C b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, B 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(d x\right) \tan\left(c\right) + 2 \, C b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) + 2 \, C a \tan\left(d x\right)^{2} \tan\left(c\right) + 2 \, B b \tan\left(d x\right)^{2} \tan\left(c\right) + 2 \, C a \tan\left(d x\right) \tan\left(c\right)^{2} + 2 \, B b \tan\left(d x\right) \tan\left(c\right)^{2} + 2 \, C a d x + 2 \, B b d x - C b \tan\left(d x\right)^{2} - C b \tan\left(c\right)^{2} + B 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) - C b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) - 2 \, C a \tan\left(d x\right) - 2 \, B b \tan\left(d x\right) - 2 \, C a \tan\left(c\right) - 2 \, B b \tan\left(c\right) - C b}{2 \, {\left(d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"-1/2*(2*C*a*d*x*tan(d*x)^2*tan(c)^2 + 2*B*b*d*x*tan(d*x)^2*tan(c)^2 + B*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(d*x)^2*tan(c)^2 - C*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 - 4*C*a*d*x*tan(d*x)*tan(c) - 4*B*b*d*x*tan(d*x)*tan(c) - C*b*tan(d*x)^2*tan(c)^2 - 2*B*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(d*x)*tan(c) + 2*C*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) + 2*C*a*tan(d*x)^2*tan(c) + 2*B*b*tan(d*x)^2*tan(c) + 2*C*a*tan(d*x)*tan(c)^2 + 2*B*b*tan(d*x)*tan(c)^2 + 2*C*a*d*x + 2*B*b*d*x - C*b*tan(d*x)^2 - C*b*tan(c)^2 + B*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)) - C*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) - 2*C*a*tan(d*x) - 2*B*b*tan(d*x) - 2*C*a*tan(c) - 2*B*b*tan(c) - C*b)/(d*tan(d*x)^2*tan(c)^2 - 2*d*tan(d*x)*tan(c) + d)","B",0
3,1,50,0,2.266593," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, C b \tan\left(d x + c\right) + 2 \, {\left(B a - C b\right)} {\left(d x + c\right)} + {\left(C a + B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*C*b*tan(d*x + c) + 2*(B*a - C*b)*(d*x + c) + (C*a + B*b)*log(tan(d*x + c)^2 + 1))/d","A",0
4,1,53,0,3.667891," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, B a \log\left({\left| \tan\left(d x + c\right) \right|}\right) + 2 \, {\left(C a + B b\right)} {\left(d x + c\right)} - {\left(B a - C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*B*a*log(abs(tan(d*x + c))) + 2*(C*a + B*b)*(d*x + c) - (B*a - C*b)*log(tan(d*x + c)^2 + 1))/d","A",0
5,1,119,0,4.313942," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(B a - C b\right)} {\left(d x + c\right)} - 2 \, {\left(C a + B b\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 2 \, {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"1/2*(B*a*tan(1/2*d*x + 1/2*c) - 2*(B*a - C*b)*(d*x + c) - 2*(C*a + B*b)*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c))) - (2*C*a*tan(1/2*d*x + 1/2*c) + 2*B*b*tan(1/2*d*x + 1/2*c) + B*a)/tan(1/2*d*x + 1/2*c))/d","B",0
6,1,179,0,5.636550," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, {\left(C a + B b\right)} {\left(d x + c\right)} - 8 \, {\left(B a - C b\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 8 \, {\left(B a - C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(B*a*tan(1/2*d*x + 1/2*c)^2 - 4*C*a*tan(1/2*d*x + 1/2*c) - 4*B*b*tan(1/2*d*x + 1/2*c) + 8*(C*a + B*b)*(d*x + c) - 8*(B*a - C*b)*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 8*(B*a - C*b)*log(abs(tan(1/2*d*x + 1/2*c))) - (12*B*a*tan(1/2*d*x + 1/2*c)^2 - 12*C*b*tan(1/2*d*x + 1/2*c)^2 - 4*C*a*tan(1/2*d*x + 1/2*c) - 4*B*b*tan(1/2*d*x + 1/2*c) - B*a)/tan(1/2*d*x + 1/2*c)^2)/d","B",0
7,1,237,0,7.624704," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, {\left(B a - C b\right)} {\left(d x + c\right)} + 24 \, {\left(C a + B b\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 24 \, {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{44 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 44 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(B*a*tan(1/2*d*x + 1/2*c)^3 - 3*C*a*tan(1/2*d*x + 1/2*c)^2 - 3*B*b*tan(1/2*d*x + 1/2*c)^2 - 15*B*a*tan(1/2*d*x + 1/2*c) + 12*C*b*tan(1/2*d*x + 1/2*c) + 24*(B*a - C*b)*(d*x + c) + 24*(C*a + B*b)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 24*(C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c))) + (44*C*a*tan(1/2*d*x + 1/2*c)^3 + 44*B*b*tan(1/2*d*x + 1/2*c)^3 + 15*B*a*tan(1/2*d*x + 1/2*c)^2 - 12*C*b*tan(1/2*d*x + 1/2*c)^2 - 3*C*a*tan(1/2*d*x + 1/2*c) - 3*B*b*tan(1/2*d*x + 1/2*c) - B*a)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
8,1,299,0,9.316833," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 192 \, {\left(C a + B b\right)} {\left(d x + c\right)} + 192 \, {\left(B a - C b\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 192 \, {\left(B a - C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{400 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 400 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*B*a*tan(1/2*d*x + 1/2*c)^4 - 8*C*a*tan(1/2*d*x + 1/2*c)^3 - 8*B*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*tan(1/2*d*x + 1/2*c)^2 + 24*C*b*tan(1/2*d*x + 1/2*c)^2 + 120*C*a*tan(1/2*d*x + 1/2*c) + 120*B*b*tan(1/2*d*x + 1/2*c) - 192*(C*a + B*b)*(d*x + c) + 192*(B*a - C*b)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 192*(B*a - C*b)*log(abs(tan(1/2*d*x + 1/2*c))) + (400*B*a*tan(1/2*d*x + 1/2*c)^4 - 400*C*b*tan(1/2*d*x + 1/2*c)^4 - 120*C*a*tan(1/2*d*x + 1/2*c)^3 - 120*B*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*tan(1/2*d*x + 1/2*c)^2 + 24*C*b*tan(1/2*d*x + 1/2*c)^2 + 8*C*a*tan(1/2*d*x + 1/2*c) + 8*B*b*tan(1/2*d*x + 1/2*c) + 3*B*a)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
9,1,2228,0,14.820304," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{12 \, B a^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 24 \, C a b d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 12 \, B b^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 6 \, C 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)^{4} \tan\left(c\right)^{4} - 12 \, B a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 6 \, C 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)^{4} \tan\left(c\right)^{4} - 48 \, B a^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 96 \, C a b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 48 \, B b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 6 \, C a^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 12 \, B a b \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 9 \, C b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 24 \, C 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)^{3} \tan\left(c\right)^{3} + 48 \, B a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 24 \, C 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)^{3} \tan\left(c\right)^{3} + 12 \, B a^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 24 \, C a b \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 12 \, B b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 12 \, B a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 24 \, C a b \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 12 \, B b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 72 \, B a^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 144 \, C a b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 72 \, B b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 6 \, C a^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 12 \, B a b \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 6 \, C b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 12 \, C a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 24 \, B a b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 24 \, C b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 6 \, C a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 12 \, B a b \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 6 \, C b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 8 \, C a b \tan\left(d x\right)^{4} \tan\left(c\right) + 4 \, B b^{2} \tan\left(d x\right)^{4} \tan\left(c\right) - 36 \, C 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} - 72 \, B a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 36 \, C 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} - 36 \, B a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 96 \, C a b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 48 \, B b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 36 \, B a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 96 \, C a b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 48 \, B b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 8 \, C a b \tan\left(d x\right) \tan\left(c\right)^{4} + 4 \, B b^{2} \tan\left(d x\right) \tan\left(c\right)^{4} - 3 \, C b^{2} \tan\left(d x\right)^{4} - 48 \, B a^{2} d x \tan\left(d x\right) \tan\left(c\right) + 96 \, C a b d x \tan\left(d x\right) \tan\left(c\right) + 48 \, B b^{2} d x \tan\left(d x\right) \tan\left(c\right) + 12 \, C a^{2} \tan\left(d x\right)^{3} \tan\left(c\right) + 24 \, B a b \tan\left(d x\right)^{3} \tan\left(c\right) - 24 \, C b^{2} \tan\left(d x\right)^{3} \tan\left(c\right) - 12 \, C a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 24 \, B a b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 12 \, C b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 12 \, C a^{2} \tan\left(d x\right) \tan\left(c\right)^{3} + 24 \, B a b \tan\left(d x\right) \tan\left(c\right)^{3} - 24 \, C b^{2} \tan\left(d x\right) \tan\left(c\right)^{3} - 3 \, C b^{2} \tan\left(c\right)^{4} - 8 \, C a b \tan\left(d x\right)^{3} - 4 \, B b^{2} \tan\left(d x\right)^{3} + 24 \, C 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) \tan\left(c\right) + 48 \, B a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) - 24 \, C 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) \tan\left(c\right) + 36 \, B a^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 96 \, C a b \tan\left(d x\right)^{2} \tan\left(c\right) - 48 \, B b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) + 36 \, B a^{2} \tan\left(d x\right) \tan\left(c\right)^{2} - 96 \, C a b \tan\left(d x\right) \tan\left(c\right)^{2} - 48 \, B b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} - 8 \, C a b \tan\left(c\right)^{3} - 4 \, B b^{2} \tan\left(c\right)^{3} + 12 \, B a^{2} d x - 24 \, C a b d x - 12 \, B b^{2} d x - 6 \, C a^{2} \tan\left(d x\right)^{2} - 12 \, B a b \tan\left(d x\right)^{2} + 6 \, C b^{2} \tan\left(d x\right)^{2} + 12 \, C a^{2} \tan\left(d x\right) \tan\left(c\right) + 24 \, B a b \tan\left(d x\right) \tan\left(c\right) - 24 \, C b^{2} \tan\left(d x\right) \tan\left(c\right) - 6 \, C a^{2} \tan\left(c\right)^{2} - 12 \, B a b \tan\left(c\right)^{2} + 6 \, C b^{2} \tan\left(c\right)^{2} - 6 \, C 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) - 12 \, B a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) + 6 \, C 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) - 12 \, B a^{2} \tan\left(d x\right) + 24 \, C a b \tan\left(d x\right) + 12 \, B b^{2} \tan\left(d x\right) - 12 \, B a^{2} \tan\left(c\right) + 24 \, C a b \tan\left(c\right) + 12 \, B b^{2} \tan\left(c\right) - 6 \, C a^{2} - 12 \, B a b + 9 \, C b^{2}}{12 \, {\left(d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 4 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 6 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 4 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"-1/12*(12*B*a^2*d*x*tan(d*x)^4*tan(c)^4 - 24*C*a*b*d*x*tan(d*x)^4*tan(c)^4 - 12*B*b^2*d*x*tan(d*x)^4*tan(c)^4 - 6*C*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)^4*tan(c)^4 - 12*B*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^4 + 6*C*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)^4*tan(c)^4 - 48*B*a^2*d*x*tan(d*x)^3*tan(c)^3 + 96*C*a*b*d*x*tan(d*x)^3*tan(c)^3 + 48*B*b^2*d*x*tan(d*x)^3*tan(c)^3 - 6*C*a^2*tan(d*x)^4*tan(c)^4 - 12*B*a*b*tan(d*x)^4*tan(c)^4 + 9*C*b^2*tan(d*x)^4*tan(c)^4 + 24*C*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)^3*tan(c)^3 + 48*B*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 - 24*C*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)^3*tan(c)^3 + 12*B*a^2*tan(d*x)^4*tan(c)^3 - 24*C*a*b*tan(d*x)^4*tan(c)^3 - 12*B*b^2*tan(d*x)^4*tan(c)^3 + 12*B*a^2*tan(d*x)^3*tan(c)^4 - 24*C*a*b*tan(d*x)^3*tan(c)^4 - 12*B*b^2*tan(d*x)^3*tan(c)^4 + 72*B*a^2*d*x*tan(d*x)^2*tan(c)^2 - 144*C*a*b*d*x*tan(d*x)^2*tan(c)^2 - 72*B*b^2*d*x*tan(d*x)^2*tan(c)^2 - 6*C*a^2*tan(d*x)^4*tan(c)^2 - 12*B*a*b*tan(d*x)^4*tan(c)^2 + 6*C*b^2*tan(d*x)^4*tan(c)^2 + 12*C*a^2*tan(d*x)^3*tan(c)^3 + 24*B*a*b*tan(d*x)^3*tan(c)^3 - 24*C*b^2*tan(d*x)^3*tan(c)^3 - 6*C*a^2*tan(d*x)^2*tan(c)^4 - 12*B*a*b*tan(d*x)^2*tan(c)^4 + 6*C*b^2*tan(d*x)^2*tan(c)^4 + 8*C*a*b*tan(d*x)^4*tan(c) + 4*B*b^2*tan(d*x)^4*tan(c) - 36*C*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 - 72*B*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 + 36*C*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 - 36*B*a^2*tan(d*x)^3*tan(c)^2 + 96*C*a*b*tan(d*x)^3*tan(c)^2 + 48*B*b^2*tan(d*x)^3*tan(c)^2 - 36*B*a^2*tan(d*x)^2*tan(c)^3 + 96*C*a*b*tan(d*x)^2*tan(c)^3 + 48*B*b^2*tan(d*x)^2*tan(c)^3 + 8*C*a*b*tan(d*x)*tan(c)^4 + 4*B*b^2*tan(d*x)*tan(c)^4 - 3*C*b^2*tan(d*x)^4 - 48*B*a^2*d*x*tan(d*x)*tan(c) + 96*C*a*b*d*x*tan(d*x)*tan(c) + 48*B*b^2*d*x*tan(d*x)*tan(c) + 12*C*a^2*tan(d*x)^3*tan(c) + 24*B*a*b*tan(d*x)^3*tan(c) - 24*C*b^2*tan(d*x)^3*tan(c) - 12*C*a^2*tan(d*x)^2*tan(c)^2 - 24*B*a*b*tan(d*x)^2*tan(c)^2 + 12*C*b^2*tan(d*x)^2*tan(c)^2 + 12*C*a^2*tan(d*x)*tan(c)^3 + 24*B*a*b*tan(d*x)*tan(c)^3 - 24*C*b^2*tan(d*x)*tan(c)^3 - 3*C*b^2*tan(c)^4 - 8*C*a*b*tan(d*x)^3 - 4*B*b^2*tan(d*x)^3 + 24*C*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)*tan(c) + 48*B*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) - 24*C*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)*tan(c) + 36*B*a^2*tan(d*x)^2*tan(c) - 96*C*a*b*tan(d*x)^2*tan(c) - 48*B*b^2*tan(d*x)^2*tan(c) + 36*B*a^2*tan(d*x)*tan(c)^2 - 96*C*a*b*tan(d*x)*tan(c)^2 - 48*B*b^2*tan(d*x)*tan(c)^2 - 8*C*a*b*tan(c)^3 - 4*B*b^2*tan(c)^3 + 12*B*a^2*d*x - 24*C*a*b*d*x - 12*B*b^2*d*x - 6*C*a^2*tan(d*x)^2 - 12*B*a*b*tan(d*x)^2 + 6*C*b^2*tan(d*x)^2 + 12*C*a^2*tan(d*x)*tan(c) + 24*B*a*b*tan(d*x)*tan(c) - 24*C*b^2*tan(d*x)*tan(c) - 6*C*a^2*tan(c)^2 - 12*B*a*b*tan(c)^2 + 6*C*b^2*tan(c)^2 - 6*C*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)) - 12*B*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) + 6*C*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)) - 12*B*a^2*tan(d*x) + 24*C*a*b*tan(d*x) + 12*B*b^2*tan(d*x) - 12*B*a^2*tan(c) + 24*C*a*b*tan(c) + 12*B*b^2*tan(c) - 6*C*a^2 - 12*B*a*b + 9*C*b^2)/(d*tan(d*x)^4*tan(c)^4 - 4*d*tan(d*x)^3*tan(c)^3 + 6*d*tan(d*x)^2*tan(c)^2 - 4*d*tan(d*x)*tan(c) + d)","B",0
10,1,1509,0,5.940722," ","integrate((a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{6 \, C a^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 12 \, B a b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 6 \, C b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 3 \, B 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)^{3} \tan\left(c\right)^{3} - 6 \, C a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, B 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)^{3} \tan\left(c\right)^{3} - 18 \, C a^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 36 \, B a b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 18 \, C b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 6 \, C a b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, B b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 9 \, B 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} + 18 \, C a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 9 \, B 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} + 6 \, C a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 12 \, B a b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 6 \, C b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 6 \, C a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 12 \, B a b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 6 \, C b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 18 \, C a^{2} d x \tan\left(d x\right) \tan\left(c\right) + 36 \, B a b d x \tan\left(d x\right) \tan\left(c\right) - 18 \, C b^{2} d x \tan\left(d x\right) \tan\left(c\right) - 6 \, C a b \tan\left(d x\right)^{3} \tan\left(c\right) - 3 \, B b^{2} \tan\left(d x\right)^{3} \tan\left(c\right) + 6 \, C a b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, B b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 6 \, C a b \tan\left(d x\right) \tan\left(c\right)^{3} - 3 \, B b^{2} \tan\left(d x\right) \tan\left(c\right)^{3} + 2 \, C b^{2} \tan\left(d x\right)^{3} + 9 \, B 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) \tan\left(c\right) - 18 \, C a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) - 9 \, B 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) \tan\left(c\right) - 12 \, C a^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 24 \, B a b \tan\left(d x\right)^{2} \tan\left(c\right) + 18 \, C b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 12 \, C a^{2} \tan\left(d x\right) \tan\left(c\right)^{2} - 24 \, B a b \tan\left(d x\right) \tan\left(c\right)^{2} + 18 \, C b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + 2 \, C b^{2} \tan\left(c\right)^{3} - 6 \, C a^{2} d x - 12 \, B a b d x + 6 \, C b^{2} d x + 6 \, C a b \tan\left(d x\right)^{2} + 3 \, B b^{2} \tan\left(d x\right)^{2} - 6 \, C a b \tan\left(d x\right) \tan\left(c\right) - 3 \, B b^{2} \tan\left(d x\right) \tan\left(c\right) + 6 \, C a b \tan\left(c\right)^{2} + 3 \, B b^{2} \tan\left(c\right)^{2} - 3 \, B 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) + 6 \, C a b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) + 3 \, B 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) + 6 \, C a^{2} \tan\left(d x\right) + 12 \, B a b \tan\left(d x\right) - 6 \, C b^{2} \tan\left(d x\right) + 6 \, C a^{2} \tan\left(c\right) + 12 \, B a b \tan\left(c\right) - 6 \, C b^{2} \tan\left(c\right) + 6 \, C a b + 3 \, B b^{2}}{6 \, {\left(d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"-1/6*(6*C*a^2*d*x*tan(d*x)^3*tan(c)^3 + 12*B*a*b*d*x*tan(d*x)^3*tan(c)^3 - 6*C*b^2*d*x*tan(d*x)^3*tan(c)^3 + 3*B*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)^3*tan(c)^3 - 6*C*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 - 3*B*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)^3*tan(c)^3 - 18*C*a^2*d*x*tan(d*x)^2*tan(c)^2 - 36*B*a*b*d*x*tan(d*x)^2*tan(c)^2 + 18*C*b^2*d*x*tan(d*x)^2*tan(c)^2 - 6*C*a*b*tan(d*x)^3*tan(c)^3 - 3*B*b^2*tan(d*x)^3*tan(c)^3 - 9*B*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 + 18*C*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 + 9*B*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 + 6*C*a^2*tan(d*x)^3*tan(c)^2 + 12*B*a*b*tan(d*x)^3*tan(c)^2 - 6*C*b^2*tan(d*x)^3*tan(c)^2 + 6*C*a^2*tan(d*x)^2*tan(c)^3 + 12*B*a*b*tan(d*x)^2*tan(c)^3 - 6*C*b^2*tan(d*x)^2*tan(c)^3 + 18*C*a^2*d*x*tan(d*x)*tan(c) + 36*B*a*b*d*x*tan(d*x)*tan(c) - 18*C*b^2*d*x*tan(d*x)*tan(c) - 6*C*a*b*tan(d*x)^3*tan(c) - 3*B*b^2*tan(d*x)^3*tan(c) + 6*C*a*b*tan(d*x)^2*tan(c)^2 + 3*B*b^2*tan(d*x)^2*tan(c)^2 - 6*C*a*b*tan(d*x)*tan(c)^3 - 3*B*b^2*tan(d*x)*tan(c)^3 + 2*C*b^2*tan(d*x)^3 + 9*B*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)*tan(c) - 18*C*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) - 9*B*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)*tan(c) - 12*C*a^2*tan(d*x)^2*tan(c) - 24*B*a*b*tan(d*x)^2*tan(c) + 18*C*b^2*tan(d*x)^2*tan(c) - 12*C*a^2*tan(d*x)*tan(c)^2 - 24*B*a*b*tan(d*x)*tan(c)^2 + 18*C*b^2*tan(d*x)*tan(c)^2 + 2*C*b^2*tan(c)^3 - 6*C*a^2*d*x - 12*B*a*b*d*x + 6*C*b^2*d*x + 6*C*a*b*tan(d*x)^2 + 3*B*b^2*tan(d*x)^2 - 6*C*a*b*tan(d*x)*tan(c) - 3*B*b^2*tan(d*x)*tan(c) + 6*C*a*b*tan(c)^2 + 3*B*b^2*tan(c)^2 - 3*B*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)) + 6*C*a*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) + 3*B*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)) + 6*C*a^2*tan(d*x) + 12*B*a*b*tan(d*x) - 6*C*b^2*tan(d*x) + 6*C*a^2*tan(c) + 12*B*a*b*tan(c) - 6*C*b^2*tan(c) + 6*C*a*b + 3*B*b^2)/(d*tan(d*x)^3*tan(c)^3 - 3*d*tan(d*x)^2*tan(c)^2 + 3*d*tan(d*x)*tan(c) - d)","B",0
11,1,95,0,4.425717," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{2} \tan\left(d x + c\right)^{2} + 4 \, C a b \tan\left(d x + c\right) + 2 \, B b^{2} \tan\left(d x + c\right) + 2 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)} + {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(C*b^2*tan(d*x + c)^2 + 4*C*a*b*tan(d*x + c) + 2*B*b^2*tan(d*x + c) + 2*(B*a^2 - 2*C*a*b - B*b^2)*(d*x + c) + (C*a^2 + 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1))/d","A",0
12,1,86,0,7.505215," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, B a^{2} \log\left({\left| \tan\left(d x + c\right) \right|}\right) + 2 \, C b^{2} \tan\left(d x + c\right) + 2 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)} - {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*B*a^2*log(abs(tan(d*x + c))) + 2*C*b^2*tan(d*x + c) + 2*(C*a^2 + 2*B*a*b - C*b^2)*(d*x + c) - (B*a^2 - 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1))/d","A",0
13,1,118,0,6.393677," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{2 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)} + {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, {\left(C a^{2} + 2 \, B a b\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right) + \frac{2 \, {\left(C a^{2} \tan\left(d x + c\right) + 2 \, B a b \tan\left(d x + c\right) + B a^{2}\right)}}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(B*a^2 - 2*C*a*b - B*b^2)*(d*x + c) + (C*a^2 + 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1) - 2*(C*a^2 + 2*B*a*b)*log(abs(tan(d*x + c))) + 2*(C*a^2*tan(d*x + c) + 2*B*a*b*tan(d*x + c) + B*a^2)/tan(d*x + c))/d","A",0
14,1,237,0,8.116977," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)} - 8 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 8 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{12 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(B*a^2*tan(1/2*d*x + 1/2*c)^2 - 4*C*a^2*tan(1/2*d*x + 1/2*c) - 8*B*a*b*tan(1/2*d*x + 1/2*c) + 8*(C*a^2 + 2*B*a*b - C*b^2)*(d*x + c) - 8*(B*a^2 - 2*C*a*b - B*b^2)*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 8*(B*a^2 - 2*C*a*b - B*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - (12*B*a^2*tan(1/2*d*x + 1/2*c)^2 - 24*C*a*b*tan(1/2*d*x + 1/2*c)^2 - 12*B*b^2*tan(1/2*d*x + 1/2*c)^2 - 4*C*a^2*tan(1/2*d*x + 1/2*c) - 8*B*a*b*tan(1/2*d*x + 1/2*c) - B*a^2)/tan(1/2*d*x + 1/2*c)^2)/d","B",0
15,1,334,0,11.085321," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)} + 24 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 24 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{44 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 88 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(B*a^2*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^2*tan(1/2*d*x + 1/2*c)^2 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^2 - 15*B*a^2*tan(1/2*d*x + 1/2*c) + 24*C*a*b*tan(1/2*d*x + 1/2*c) + 12*B*b^2*tan(1/2*d*x + 1/2*c) + 24*(B*a^2 - 2*C*a*b - B*b^2)*(d*x + c) + 24*(C*a^2 + 2*B*a*b - C*b^2)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 24*(C*a^2 + 2*B*a*b - C*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (44*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 88*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 44*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^2*tan(1/2*d*x + 1/2*c)^2 - 24*C*a*b*tan(1/2*d*x + 1/2*c)^2 - 12*B*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*C*a^2*tan(1/2*d*x + 1/2*c) - 6*B*a*b*tan(1/2*d*x + 1/2*c) - B*a^2)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
16,1,435,0,21.201179," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 192 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)} + 192 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 192 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{400 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 800 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 400 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 96 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*B*a^2*tan(1/2*d*x + 1/2*c)^4 - 8*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 16*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^2*tan(1/2*d*x + 1/2*c)^2 + 48*C*a*b*tan(1/2*d*x + 1/2*c)^2 + 24*B*b^2*tan(1/2*d*x + 1/2*c)^2 + 120*C*a^2*tan(1/2*d*x + 1/2*c) + 240*B*a*b*tan(1/2*d*x + 1/2*c) - 96*C*b^2*tan(1/2*d*x + 1/2*c) - 192*(C*a^2 + 2*B*a*b - C*b^2)*(d*x + c) + 192*(B*a^2 - 2*C*a*b - B*b^2)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 192*(B*a^2 - 2*C*a*b - B*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (400*B*a^2*tan(1/2*d*x + 1/2*c)^4 - 800*C*a*b*tan(1/2*d*x + 1/2*c)^4 - 400*B*b^2*tan(1/2*d*x + 1/2*c)^4 - 120*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 240*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 96*C*b^2*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^2*tan(1/2*d*x + 1/2*c)^2 + 48*C*a*b*tan(1/2*d*x + 1/2*c)^2 + 24*B*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*C*a^2*tan(1/2*d*x + 1/2*c) + 16*B*a*b*tan(1/2*d*x + 1/2*c) + 3*B*a^2)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
17,1,2870,0,12.647673," ","integrate((a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{12 \, C a^{3} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 36 \, B a^{2} b d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 36 \, C a b^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 12 \, B b^{3} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 6 \, B a^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 18 \, C a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 18 \, B a 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)^{4} \tan\left(c\right)^{4} + 6 \, C b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 48 \, C a^{3} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 144 \, B a^{2} b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 144 \, C a b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 48 \, B b^{3} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 18 \, C a^{2} b \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 18 \, B a b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 9 \, C b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 24 \, B a^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 72 \, C a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 72 \, B a 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)^{3} \tan\left(c\right)^{3} - 24 \, C b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 12 \, C a^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 36 \, B a^{2} b \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 36 \, C a b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 12 \, B b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 12 \, C a^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 36 \, B a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 36 \, C a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 12 \, B b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 72 \, C a^{3} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 216 \, B a^{2} b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 216 \, C a b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 72 \, B b^{3} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 18 \, C a^{2} b \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 18 \, B a b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 6 \, C b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 36 \, C a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 36 \, B a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 24 \, C b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 18 \, C a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 18 \, B a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 6 \, C b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 12 \, C a b^{2} \tan\left(d x\right)^{4} \tan\left(c\right) + 4 \, B b^{3} \tan\left(d x\right)^{4} \tan\left(c\right) + 36 \, B a^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 108 \, C a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 108 \, B a 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} + 36 \, C b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 36 \, C a^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 108 \, B a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 144 \, C a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 48 \, B b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 36 \, C a^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 108 \, B a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 144 \, C a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 48 \, B b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 12 \, C a b^{2} \tan\left(d x\right) \tan\left(c\right)^{4} + 4 \, B b^{3} \tan\left(d x\right) \tan\left(c\right)^{4} - 3 \, C b^{3} \tan\left(d x\right)^{4} - 48 \, C a^{3} d x \tan\left(d x\right) \tan\left(c\right) - 144 \, B a^{2} b d x \tan\left(d x\right) \tan\left(c\right) + 144 \, C a b^{2} d x \tan\left(d x\right) \tan\left(c\right) + 48 \, B b^{3} d x \tan\left(d x\right) \tan\left(c\right) + 36 \, C a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right) + 36 \, B a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right) - 24 \, C b^{3} \tan\left(d x\right)^{3} \tan\left(c\right) - 36 \, C a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 36 \, B a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 12 \, C b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 36 \, C a^{2} b \tan\left(d x\right) \tan\left(c\right)^{3} + 36 \, B a b^{2} \tan\left(d x\right) \tan\left(c\right)^{3} - 24 \, C b^{3} \tan\left(d x\right) \tan\left(c\right)^{3} - 3 \, C b^{3} \tan\left(c\right)^{4} - 12 \, C a b^{2} \tan\left(d x\right)^{3} - 4 \, B b^{3} \tan\left(d x\right)^{3} - 24 \, B a^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) + 72 \, C a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) + 72 \, B a 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) \tan\left(c\right) - 24 \, C b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) + 36 \, C a^{3} \tan\left(d x\right)^{2} \tan\left(c\right) + 108 \, B a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right) - 144 \, C a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 48 \, B b^{3} \tan\left(d x\right)^{2} \tan\left(c\right) + 36 \, C a^{3} \tan\left(d x\right) \tan\left(c\right)^{2} + 108 \, B a^{2} b \tan\left(d x\right) \tan\left(c\right)^{2} - 144 \, C a b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} - 48 \, B b^{3} \tan\left(d x\right) \tan\left(c\right)^{2} - 12 \, C a b^{2} \tan\left(c\right)^{3} - 4 \, B b^{3} \tan\left(c\right)^{3} + 12 \, C a^{3} d x + 36 \, B a^{2} b d x - 36 \, C a b^{2} d x - 12 \, B b^{3} d x - 18 \, C a^{2} b \tan\left(d x\right)^{2} - 18 \, B a b^{2} \tan\left(d x\right)^{2} + 6 \, C b^{3} \tan\left(d x\right)^{2} + 36 \, C a^{2} b \tan\left(d x\right) \tan\left(c\right) + 36 \, B a b^{2} \tan\left(d x\right) \tan\left(c\right) - 24 \, C b^{3} \tan\left(d x\right) \tan\left(c\right) - 18 \, C a^{2} b \tan\left(c\right)^{2} - 18 \, B a b^{2} \tan\left(c\right)^{2} + 6 \, C b^{3} \tan\left(c\right)^{2} + 6 \, B a^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) - 18 \, C a^{2} b \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) - 18 \, B a 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) + 6 \, C b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) - 12 \, C a^{3} \tan\left(d x\right) - 36 \, B a^{2} b \tan\left(d x\right) + 36 \, C a b^{2} \tan\left(d x\right) + 12 \, B b^{3} \tan\left(d x\right) - 12 \, C a^{3} \tan\left(c\right) - 36 \, B a^{2} b \tan\left(c\right) + 36 \, C a b^{2} \tan\left(c\right) + 12 \, B b^{3} \tan\left(c\right) - 18 \, C a^{2} b - 18 \, B a b^{2} + 9 \, C b^{3}}{12 \, {\left(d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 4 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 6 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 4 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"-1/12*(12*C*a^3*d*x*tan(d*x)^4*tan(c)^4 + 36*B*a^2*b*d*x*tan(d*x)^4*tan(c)^4 - 36*C*a*b^2*d*x*tan(d*x)^4*tan(c)^4 - 12*B*b^3*d*x*tan(d*x)^4*tan(c)^4 + 6*B*a^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^4 - 18*C*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^4 - 18*B*a*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)^4*tan(c)^4 + 6*C*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^4*tan(c)^4 - 48*C*a^3*d*x*tan(d*x)^3*tan(c)^3 - 144*B*a^2*b*d*x*tan(d*x)^3*tan(c)^3 + 144*C*a*b^2*d*x*tan(d*x)^3*tan(c)^3 + 48*B*b^3*d*x*tan(d*x)^3*tan(c)^3 - 18*C*a^2*b*tan(d*x)^4*tan(c)^4 - 18*B*a*b^2*tan(d*x)^4*tan(c)^4 + 9*C*b^3*tan(d*x)^4*tan(c)^4 - 24*B*a^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 + 72*C*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 + 72*B*a*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)^3*tan(c)^3 - 24*C*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^3*tan(c)^3 + 12*C*a^3*tan(d*x)^4*tan(c)^3 + 36*B*a^2*b*tan(d*x)^4*tan(c)^3 - 36*C*a*b^2*tan(d*x)^4*tan(c)^3 - 12*B*b^3*tan(d*x)^4*tan(c)^3 + 12*C*a^3*tan(d*x)^3*tan(c)^4 + 36*B*a^2*b*tan(d*x)^3*tan(c)^4 - 36*C*a*b^2*tan(d*x)^3*tan(c)^4 - 12*B*b^3*tan(d*x)^3*tan(c)^4 + 72*C*a^3*d*x*tan(d*x)^2*tan(c)^2 + 216*B*a^2*b*d*x*tan(d*x)^2*tan(c)^2 - 216*C*a*b^2*d*x*tan(d*x)^2*tan(c)^2 - 72*B*b^3*d*x*tan(d*x)^2*tan(c)^2 - 18*C*a^2*b*tan(d*x)^4*tan(c)^2 - 18*B*a*b^2*tan(d*x)^4*tan(c)^2 + 6*C*b^3*tan(d*x)^4*tan(c)^2 + 36*C*a^2*b*tan(d*x)^3*tan(c)^3 + 36*B*a*b^2*tan(d*x)^3*tan(c)^3 - 24*C*b^3*tan(d*x)^3*tan(c)^3 - 18*C*a^2*b*tan(d*x)^2*tan(c)^4 - 18*B*a*b^2*tan(d*x)^2*tan(c)^4 + 6*C*b^3*tan(d*x)^2*tan(c)^4 + 12*C*a*b^2*tan(d*x)^4*tan(c) + 4*B*b^3*tan(d*x)^4*tan(c) + 36*B*a^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 - 108*C*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 - 108*B*a*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 + 36*C*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 - 36*C*a^3*tan(d*x)^3*tan(c)^2 - 108*B*a^2*b*tan(d*x)^3*tan(c)^2 + 144*C*a*b^2*tan(d*x)^3*tan(c)^2 + 48*B*b^3*tan(d*x)^3*tan(c)^2 - 36*C*a^3*tan(d*x)^2*tan(c)^3 - 108*B*a^2*b*tan(d*x)^2*tan(c)^3 + 144*C*a*b^2*tan(d*x)^2*tan(c)^3 + 48*B*b^3*tan(d*x)^2*tan(c)^3 + 12*C*a*b^2*tan(d*x)*tan(c)^4 + 4*B*b^3*tan(d*x)*tan(c)^4 - 3*C*b^3*tan(d*x)^4 - 48*C*a^3*d*x*tan(d*x)*tan(c) - 144*B*a^2*b*d*x*tan(d*x)*tan(c) + 144*C*a*b^2*d*x*tan(d*x)*tan(c) + 48*B*b^3*d*x*tan(d*x)*tan(c) + 36*C*a^2*b*tan(d*x)^3*tan(c) + 36*B*a*b^2*tan(d*x)^3*tan(c) - 24*C*b^3*tan(d*x)^3*tan(c) - 36*C*a^2*b*tan(d*x)^2*tan(c)^2 - 36*B*a*b^2*tan(d*x)^2*tan(c)^2 + 12*C*b^3*tan(d*x)^2*tan(c)^2 + 36*C*a^2*b*tan(d*x)*tan(c)^3 + 36*B*a*b^2*tan(d*x)*tan(c)^3 - 24*C*b^3*tan(d*x)*tan(c)^3 - 3*C*b^3*tan(c)^4 - 12*C*a*b^2*tan(d*x)^3 - 4*B*b^3*tan(d*x)^3 - 24*B*a^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) + 72*C*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) + 72*B*a*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)*tan(c) - 24*C*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)*tan(c) + 36*C*a^3*tan(d*x)^2*tan(c) + 108*B*a^2*b*tan(d*x)^2*tan(c) - 144*C*a*b^2*tan(d*x)^2*tan(c) - 48*B*b^3*tan(d*x)^2*tan(c) + 36*C*a^3*tan(d*x)*tan(c)^2 + 108*B*a^2*b*tan(d*x)*tan(c)^2 - 144*C*a*b^2*tan(d*x)*tan(c)^2 - 48*B*b^3*tan(d*x)*tan(c)^2 - 12*C*a*b^2*tan(c)^3 - 4*B*b^3*tan(c)^3 + 12*C*a^3*d*x + 36*B*a^2*b*d*x - 36*C*a*b^2*d*x - 12*B*b^3*d*x - 18*C*a^2*b*tan(d*x)^2 - 18*B*a*b^2*tan(d*x)^2 + 6*C*b^3*tan(d*x)^2 + 36*C*a^2*b*tan(d*x)*tan(c) + 36*B*a*b^2*tan(d*x)*tan(c) - 24*C*b^3*tan(d*x)*tan(c) - 18*C*a^2*b*tan(c)^2 - 18*B*a*b^2*tan(c)^2 + 6*C*b^3*tan(c)^2 + 6*B*a^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) - 18*C*a^2*b*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) - 18*B*a*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)) + 6*C*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) - 12*C*a^3*tan(d*x) - 36*B*a^2*b*tan(d*x) + 36*C*a*b^2*tan(d*x) + 12*B*b^3*tan(d*x) - 12*C*a^3*tan(c) - 36*B*a^2*b*tan(c) + 36*C*a*b^2*tan(c) + 12*B*b^3*tan(c) - 18*C*a^2*b - 18*B*a*b^2 + 9*C*b^3)/(d*tan(d*x)^4*tan(c)^4 - 4*d*tan(d*x)^3*tan(c)^3 + 6*d*tan(d*x)^2*tan(c)^2 - 4*d*tan(d*x)*tan(c) + d)","B",0
18,1,158,0,5.957876," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, C b^{3} \tan\left(d x + c\right)^{3} + 9 \, C a b^{2} \tan\left(d x + c\right)^{2} + 3 \, B b^{3} \tan\left(d x + c\right)^{2} + 18 \, C a^{2} b \tan\left(d x + c\right) + 18 \, B a b^{2} \tan\left(d x + c\right) - 6 \, C b^{3} \tan\left(d x + c\right) + 6 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{6 \, d}"," ",0,"1/6*(2*C*b^3*tan(d*x + c)^3 + 9*C*a*b^2*tan(d*x + c)^2 + 3*B*b^3*tan(d*x + c)^2 + 18*C*a^2*b*tan(d*x + c) + 18*B*a*b^2*tan(d*x + c) - 6*C*b^3*tan(d*x + c) + 6*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*(d*x + c) + 3*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(d*x + c)^2 + 1))/d","A",0
19,1,129,0,8.844398," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{3} \tan\left(d x + c\right)^{2} + 2 \, B a^{3} \log\left({\left| \tan\left(d x + c\right) \right|}\right) + 6 \, C a b^{2} \tan\left(d x + c\right) + 2 \, B b^{3} \tan\left(d x + c\right) + 2 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} {\left(d x + c\right)} - {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(C*b^3*tan(d*x + c)^2 + 2*B*a^3*log(abs(tan(d*x + c))) + 6*C*a*b^2*tan(d*x + c) + 2*B*b^3*tan(d*x + c) + 2*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*(d*x + c) - (B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(tan(d*x + c)^2 + 1))/d","A",0
20,1,152,0,12.043757," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, C b^{3} \tan\left(d x + c\right) - 2 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} {\left(d x + c\right)} - {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right) - \frac{2 \, {\left(C a^{3} \tan\left(d x + c\right) + 3 \, B a^{2} b \tan\left(d x + c\right) + B a^{3}\right)}}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*C*b^3*tan(d*x + c) - 2*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*(d*x + c) - (C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(d*x + c)^2 + 1) + 2*(C*a^3 + 3*B*a^2*b)*log(abs(tan(d*x + c))) - 2*(C*a^3*tan(d*x + c) + 3*B*a^2*b*tan(d*x + c) + B*a^3)/tan(d*x + c))/d","A",0
21,1,193,0,22.948316," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{2 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} {\left(d x + c\right)} - {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right) - \frac{3 \, B a^{3} \tan\left(d x + c\right)^{2} - 9 \, C a^{2} b \tan\left(d x + c\right)^{2} - 9 \, B a b^{2} \tan\left(d x + c\right)^{2} - 2 \, C a^{3} \tan\left(d x + c\right) - 6 \, B a^{2} b \tan\left(d x + c\right) - B a^{3}}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*(d*x + c) - (B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(tan(d*x + c)^2 + 1) + 2*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2)*log(abs(tan(d*x + c))) - (3*B*a^3*tan(d*x + c)^2 - 9*C*a^2*b*tan(d*x + c)^2 - 9*B*a*b^2*tan(d*x + c)^2 - 2*C*a^3*tan(d*x + c) - 6*B*a^2*b*tan(d*x + c) - B*a^3)/tan(d*x + c)^2)/d","A",0
22,1,390,0,27.330145," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} {\left(d x + c\right)} + 24 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 24 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{44 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 132 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 132 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(B*a^3*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^3*tan(1/2*d*x + 1/2*c)^2 - 9*B*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 15*B*a^3*tan(1/2*d*x + 1/2*c) + 36*C*a^2*b*tan(1/2*d*x + 1/2*c) + 36*B*a*b^2*tan(1/2*d*x + 1/2*c) + 24*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*(d*x + c) + 24*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 24*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) + (44*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 132*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 132*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 44*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^3*tan(1/2*d*x + 1/2*c)^2 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*C*a^3*tan(1/2*d*x + 1/2*c) - 9*B*a^2*b*tan(1/2*d*x + 1/2*c) - B*a^3)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
23,1,528,0,90.464988," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","-\frac{3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 288 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 192 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} {\left(d x + c\right)} + 192 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 192 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{400 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1200 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1200 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 400 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 288 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 96 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*B*a^3*tan(1/2*d*x + 1/2*c)^4 - 8*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 24*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^3*tan(1/2*d*x + 1/2*c)^2 + 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 120*C*a^3*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b*tan(1/2*d*x + 1/2*c) - 288*C*a*b^2*tan(1/2*d*x + 1/2*c) - 96*B*b^3*tan(1/2*d*x + 1/2*c) - 192*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*(d*x + c) + 192*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 192*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) + (400*B*a^3*tan(1/2*d*x + 1/2*c)^4 - 1200*C*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 1200*B*a*b^2*tan(1/2*d*x + 1/2*c)^4 + 400*C*b^3*tan(1/2*d*x + 1/2*c)^4 - 120*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 360*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 288*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 96*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^3*tan(1/2*d*x + 1/2*c)^2 + 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*C*a^3*tan(1/2*d*x + 1/2*c) + 24*B*a^2*b*tan(1/2*d*x + 1/2*c) + 3*B*a^3)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
24,1,670,0,61.537793," ","integrate(cot(d*x+c)^7*(a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{6 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 45 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 540 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 660 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1800 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1800 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} {\left(d x + c\right)} - 960 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 960 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2192 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6576 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6576 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2192 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 660 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1800 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1800 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 480 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 180 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 540 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 70 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^3*tan(1/2*d*x + 1/2*c)^4 - 45*B*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 70*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 120*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 120*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 180*C*a^3*tan(1/2*d*x + 1/2*c)^2 + 540*B*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 120*B*b^3*tan(1/2*d*x + 1/2*c)^2 + 660*B*a^3*tan(1/2*d*x + 1/2*c) - 1800*C*a^2*b*tan(1/2*d*x + 1/2*c) - 1800*B*a*b^2*tan(1/2*d*x + 1/2*c) + 480*C*b^3*tan(1/2*d*x + 1/2*c) - 960*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*(d*x + c) - 960*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 960*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) - (2192*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 6576*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 6576*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 2192*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 660*B*a^3*tan(1/2*d*x + 1/2*c)^4 - 1800*C*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 1800*B*a*b^2*tan(1/2*d*x + 1/2*c)^4 + 480*C*b^3*tan(1/2*d*x + 1/2*c)^4 - 180*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 540*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 70*B*a^3*tan(1/2*d*x + 1/2*c)^2 + 120*C*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 120*B*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*C*a^3*tan(1/2*d*x + 1/2*c) + 45*B*a^2*b*tan(1/2*d*x + 1/2*c) + 6*B*a^3)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
25,1,135,0,2.110910," ","integrate(tan(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a - B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{{\left(B a + C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(C a^{4} - B a^{3} b\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b^{3} + b^{5}} + \frac{C b \tan\left(d x + c\right)^{2} - 2 \, C a \tan\left(d x + c\right) + 2 \, B b \tan\left(d x + c\right)}{b^{2}}}{2 \, d}"," ",0,"1/2*(2*(C*a - B*b)*(d*x + c)/(a^2 + b^2) - (B*a + C*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 2*(C*a^4 - B*a^3*b)*log(abs(b*tan(d*x + c) + a))/(a^2*b^3 + b^5) + (C*b*tan(d*x + c)^2 - 2*C*a*tan(d*x + c) + 2*B*b*tan(d*x + c))/b^2)/d","A",0
26,1,110,0,1.809378," ","integrate(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(B a + C b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{{\left(C a - B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(C a^{3} - B a^{2} b\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b^{2} + b^{4}} - \frac{2 \, C \tan\left(d x + c\right)}{b}}{2 \, d}"," ",0,"-1/2*(2*(B*a + C*b)*(d*x + c)/(a^2 + b^2) + (C*a - B*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 2*(C*a^3 - B*a^2*b)*log(abs(b*tan(d*x + c) + a))/(a^2*b^2 + b^4) - 2*C*tan(d*x + c)/b)/d","A",0
27,1,95,0,1.523412," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(C a - B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{{\left(B a + C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, {\left(C a^{2} - B a b\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b + b^{3}}}{2 \, d}"," ",0,"-1/2*(2*(C*a - B*b)*(d*x + c)/(a^2 + b^2) - (B*a + C*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*(C*a^2 - B*a*b)*log(abs(b*tan(d*x + c) + a))/(a^2*b + b^3))/d","A",0
28,1,94,0,2.152811," ","integrate(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a + C b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{{\left(C a - B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, {\left(C a b - B b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b + b^{3}}}{2 \, d}"," ",0,"1/2*(2*(B*a + C*b)*(d*x + c)/(a^2 + b^2) + (C*a - B*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*(C*a*b - B*b^2)*log(abs(b*tan(d*x + c) + a))/(a^2*b + b^3))/d","A",0
29,1,113,0,4.110839," ","integrate(cot(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a - B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{{\left(B a + C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(C a b^{2} - B b^{3}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{3} b + a b^{3}} + \frac{2 \, B \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a}}{2 \, d}"," ",0,"1/2*(2*(C*a - B*b)*(d*x + c)/(a^2 + b^2) - (B*a + C*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 2*(C*a*b^2 - B*b^3)*log(abs(b*tan(d*x + c) + a))/(a^3*b + a*b^3) + 2*B*log(abs(tan(d*x + c)))/a)/d","A",0
30,1,157,0,4.810194," ","integrate(cot(d*x+c)^3*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(B a + C b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{{\left(C a - B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(C a b^{3} - B b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b + a^{2} b^{3}} - \frac{2 \, {\left(C a - B b\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{2}} + \frac{2 \, {\left(C a \tan\left(d x + c\right) - B b \tan\left(d x + c\right) + B a\right)}}{a^{2} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(B*a + C*b)*(d*x + c)/(a^2 + b^2) + (C*a - B*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 2*(C*a*b^3 - B*b^4)*log(abs(b*tan(d*x + c) + a))/(a^4*b + a^2*b^3) - 2*(C*a - B*b)*log(abs(tan(d*x + c)))/a^2 + 2*(C*a*tan(d*x + c) - B*b*tan(d*x + c) + B*a)/(a^2*tan(d*x + c)))/d","A",0
31,1,214,0,5.475493," ","integrate(cot(d*x+c)^4*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(C a - B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{{\left(B a + C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, {\left(C a b^{4} - B b^{5}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{5} b + a^{3} b^{3}} + \frac{2 \, {\left(B a^{2} + C a b - B b^{2}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{3 \, B a^{2} \tan\left(d x + c\right)^{2} + 3 \, C a b \tan\left(d x + c\right)^{2} - 3 \, B b^{2} \tan\left(d x + c\right)^{2} - 2 \, C a^{2} \tan\left(d x + c\right) + 2 \, B a b \tan\left(d x + c\right) - B a^{2}}{a^{3} \tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(C*a - B*b)*(d*x + c)/(a^2 + b^2) - (B*a + C*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*(C*a*b^4 - B*b^5)*log(abs(b*tan(d*x + c) + a))/(a^5*b + a^3*b^3) + 2*(B*a^2 + C*a*b - B*b^2)*log(abs(tan(d*x + c)))/a^3 - (3*B*a^2*tan(d*x + c)^2 + 3*C*a*b*tan(d*x + c)^2 - 3*B*b^2*tan(d*x + c)^2 - 2*C*a^2*tan(d*x + c) + 2*B*a*b*tan(d*x + c) - B*a^2)/(a^3*tan(d*x + c)^2))/d","A",0
32,1,290,0,2.935873," ","integrate(tan(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{2} - 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(B a^{2} + 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(2 \, C a^{5} - B a^{4} b + 4 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}} + \frac{2 \, C \tan\left(d x + c\right)}{b^{2}} + \frac{2 \, {\left(2 \, C a^{5} b \tan\left(d x + c\right) - B a^{4} b^{2} \tan\left(d x + c\right) + 4 \, C a^{3} b^{3} \tan\left(d x + c\right) - 3 \, B a^{2} b^{4} \tan\left(d x + c\right) + C a^{6} + 3 \, C a^{4} b^{2} - 2 \, B a^{3} b^{3}\right)}}{{\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} {\left(b \tan\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"1/2*(2*(C*a^2 - 2*B*a*b - C*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - (B*a^2 + 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(2*C*a^5 - B*a^4*b + 4*C*a^3*b^2 - 3*B*a^2*b^3)*log(abs(b*tan(d*x + c) + a))/(a^4*b^3 + 2*a^2*b^5 + b^7) + 2*C*tan(d*x + c)/b^2 + 2*(2*C*a^5*b*tan(d*x + c) - B*a^4*b^2*tan(d*x + c) + 4*C*a^3*b^3*tan(d*x + c) - 3*B*a^2*b^4*tan(d*x + c) + C*a^6 + 3*C*a^4*b^2 - 2*B*a^3*b^3)/((a^4*b^3 + 2*a^2*b^5 + b^7)*(b*tan(d*x + c) + a)))/d","A",0
33,1,244,0,2.015311," ","integrate(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(B a^{2} + 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(C a^{2} - 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(C a^{4} + 3 \, C a^{2} b^{2} - 2 \, B a b^{3}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(C a^{4} \tan\left(d x + c\right) + 3 \, C a^{2} b^{2} \tan\left(d x + c\right) - 2 \, B a b^{3} \tan\left(d x + c\right) + B a^{4} + 2 \, C a^{3} b - B a^{2} b^{2}\right)}}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} {\left(b \tan\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"-1/2*(2*(B*a^2 + 2*C*a*b - B*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + (C*a^2 - 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3)*log(abs(b*tan(d*x + c) + a))/(a^4*b^2 + 2*a^2*b^4 + b^6) + 2*(C*a^4*tan(d*x + c) + 3*C*a^2*b^2*tan(d*x + c) - 2*B*a*b^3*tan(d*x + c) + B*a^4 + 2*C*a^3*b - B*a^2*b^2)/((a^4*b + 2*a^2*b^3 + b^5)*(b*tan(d*x + c) + a)))/d","A",0
34,1,241,0,1.985468," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(C a^{2} - 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(B a^{2} + 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(B a^{2} b + 2 \, C a b^{2} - B b^{3}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} - \frac{2 \, {\left(B a^{2} b^{2} \tan\left(d x + c\right) + 2 \, C a b^{3} \tan\left(d x + c\right) - B b^{4} \tan\left(d x + c\right) - C a^{4} + 2 \, B a^{3} b + C a^{2} b^{2}\right)}}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} {\left(b \tan\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"-1/2*(2*(C*a^2 - 2*B*a*b - C*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - (B*a^2 + 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(B*a^2*b + 2*C*a*b^2 - B*b^3)*log(abs(b*tan(d*x + c) + a))/(a^4*b + 2*a^2*b^3 + b^5) - 2*(B*a^2*b^2*tan(d*x + c) + 2*C*a*b^3*tan(d*x + c) - B*b^4*tan(d*x + c) - C*a^4 + 2*B*a^3*b + C*a^2*b^2)/((a^4*b + 2*a^2*b^3 + b^5)*(b*tan(d*x + c) + a)))/d","B",0
35,1,234,0,2.613157," ","integrate(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a^{2} + 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(C a^{2} - 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(C a^{2} b - 2 \, B a b^{2} - C b^{3}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} + \frac{2 \, {\left(C a^{2} b \tan\left(d x + c\right) - 2 \, B a b^{2} \tan\left(d x + c\right) - C b^{3} \tan\left(d x + c\right) + 2 \, C a^{3} - 3 \, B a^{2} b - B b^{3}\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"1/2*(2*(B*a^2 + 2*C*a*b - B*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + (C*a^2 - 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(C*a^2*b - 2*B*a*b^2 - C*b^3)*log(abs(b*tan(d*x + c) + a))/(a^4*b + 2*a^2*b^3 + b^5) + 2*(C*a^2*b*tan(d*x + c) - 2*B*a*b^2*tan(d*x + c) - C*b^3*tan(d*x + c) + 2*C*a^3 - 3*B*a^2*b - B*b^3)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(d*x + c) + a)))/d","B",0
36,1,279,0,5.291991," ","integrate(cot(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{2} - 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(B a^{2} + 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(2 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - B b^{5}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}} + \frac{2 \, B \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{2}} - \frac{2 \, {\left(2 \, C a^{3} b^{2} \tan\left(d x + c\right) - 3 \, B a^{2} b^{3} \tan\left(d x + c\right) - B b^{5} \tan\left(d x + c\right) + 3 \, C a^{4} b - 4 \, B a^{3} b^{2} + C a^{2} b^{3} - 2 \, B a b^{4}\right)}}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(b \tan\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"1/2*(2*(C*a^2 - 2*B*a*b - C*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - (B*a^2 + 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(2*C*a^3*b^2 - 3*B*a^2*b^3 - B*b^5)*log(abs(b*tan(d*x + c) + a))/(a^6*b + 2*a^4*b^3 + a^2*b^5) + 2*B*log(abs(tan(d*x + c)))/a^2 - 2*(2*C*a^3*b^2*tan(d*x + c) - 3*B*a^2*b^3*tan(d*x + c) - B*b^5*tan(d*x + c) + 3*C*a^4*b - 4*B*a^3*b^2 + C*a^2*b^3 - 2*B*a*b^4)/((a^6 + 2*a^4*b^2 + a^2*b^4)*(b*tan(d*x + c) + a)))/d","B",0
37,1,362,0,6.711792," ","integrate(cot(d*x+c)^3*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(B a^{2} + 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(C a^{2} - 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(3 \, C a^{3} b^{3} - 4 \, B a^{2} b^{4} + C a b^{5} - 2 \, B b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}} + \frac{C a^{4} b \tan\left(d x + c\right)^{2} - 2 \, B a^{3} b^{2} \tan\left(d x + c\right)^{2} - C a^{2} b^{3} \tan\left(d x + c\right)^{2} + C a^{5} \tan\left(d x + c\right) - 3 \, C a^{3} b^{2} \tan\left(d x + c\right) + 6 \, B a^{2} b^{3} \tan\left(d x + c\right) - 2 \, C a b^{4} \tan\left(d x + c\right) + 4 \, B b^{5} \tan\left(d x + c\right) + 2 \, B a^{5} + 4 \, B a^{3} b^{2} + 2 \, B a b^{4}}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(b \tan\left(d x + c\right)^{2} + a \tan\left(d x + c\right)\right)}} - \frac{2 \, {\left(C a - 2 \, B b\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{3}}}{2 \, d}"," ",0,"-1/2*(2*(B*a^2 + 2*C*a*b - B*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + (C*a^2 - 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(3*C*a^3*b^3 - 4*B*a^2*b^4 + C*a*b^5 - 2*B*b^6)*log(abs(b*tan(d*x + c) + a))/(a^7*b + 2*a^5*b^3 + a^3*b^5) + (C*a^4*b*tan(d*x + c)^2 - 2*B*a^3*b^2*tan(d*x + c)^2 - C*a^2*b^3*tan(d*x + c)^2 + C*a^5*tan(d*x + c) - 3*C*a^3*b^2*tan(d*x + c) + 6*B*a^2*b^3*tan(d*x + c) - 2*C*a*b^4*tan(d*x + c) + 4*B*b^5*tan(d*x + c) + 2*B*a^5 + 4*B*a^3*b^2 + 2*B*a*b^4)/((a^6 + 2*a^4*b^2 + a^2*b^4)*(b*tan(d*x + c)^2 + a*tan(d*x + c))) - 2*(C*a - 2*B*b)*log(abs(tan(d*x + c)))/a^3)/d","A",0
38,1,505,0,4.343286," ","integrate(tan(d*x+c)^3*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(3 \, C a^{7} - B a^{6} b + 9 \, C a^{5} b^{2} - 3 \, B a^{4} b^{3} + 10 \, C a^{3} b^{4} - 6 \, B a^{2} b^{5}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}} + \frac{2 \, C \tan\left(d x + c\right)}{b^{3}} + \frac{9 \, C a^{7} b^{2} \tan\left(d x + c\right)^{2} - 3 \, B a^{6} b^{3} \tan\left(d x + c\right)^{2} + 27 \, C a^{5} b^{4} \tan\left(d x + c\right)^{2} - 9 \, B a^{4} b^{5} \tan\left(d x + c\right)^{2} + 30 \, C a^{3} b^{6} \tan\left(d x + c\right)^{2} - 18 \, B a^{2} b^{7} \tan\left(d x + c\right)^{2} + 12 \, C a^{8} b \tan\left(d x + c\right) - 2 \, B a^{7} b^{2} \tan\left(d x + c\right) + 38 \, C a^{6} b^{3} \tan\left(d x + c\right) - 6 \, B a^{5} b^{4} \tan\left(d x + c\right) + 50 \, C a^{4} b^{5} \tan\left(d x + c\right) - 28 \, B a^{3} b^{6} \tan\left(d x + c\right) + 4 \, C a^{9} + 13 \, C a^{7} b^{2} + B a^{6} b^{3} + 21 \, C a^{5} b^{4} - 11 \, B a^{4} b^{5}}{{\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(3*C*a^7 - B*a^6*b + 9*C*a^5*b^2 - 3*B*a^4*b^3 + 10*C*a^3*b^4 - 6*B*a^2*b^5)*log(abs(b*tan(d*x + c) + a))/(a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10) + 2*C*tan(d*x + c)/b^3 + (9*C*a^7*b^2*tan(d*x + c)^2 - 3*B*a^6*b^3*tan(d*x + c)^2 + 27*C*a^5*b^4*tan(d*x + c)^2 - 9*B*a^4*b^5*tan(d*x + c)^2 + 30*C*a^3*b^6*tan(d*x + c)^2 - 18*B*a^2*b^7*tan(d*x + c)^2 + 12*C*a^8*b*tan(d*x + c) - 2*B*a^7*b^2*tan(d*x + c) + 38*C*a^6*b^3*tan(d*x + c) - 6*B*a^5*b^4*tan(d*x + c) + 50*C*a^4*b^5*tan(d*x + c) - 28*B*a^3*b^6*tan(d*x + c) + 4*C*a^9 + 13*C*a^7*b^2 + B*a^6*b^3 + 21*C*a^5*b^4 - 11*B*a^4*b^5)/((a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10)*(b*tan(d*x + c) + a)^2))/d","A",0
39,1,458,0,3.009151," ","integrate(tan(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(C a^{6} + 3 \, C a^{4} b^{2} + B a^{3} b^{3} + 6 \, C a^{2} b^{4} - 3 \, B a b^{5}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}} - \frac{3 \, C a^{6} b \tan\left(d x + c\right)^{2} + 9 \, C a^{4} b^{3} \tan\left(d x + c\right)^{2} + 3 \, B a^{3} b^{4} \tan\left(d x + c\right)^{2} + 18 \, C a^{2} b^{5} \tan\left(d x + c\right)^{2} - 9 \, B a b^{6} \tan\left(d x + c\right)^{2} + 2 \, C a^{7} \tan\left(d x + c\right) + 2 \, B a^{6} b \tan\left(d x + c\right) + 6 \, C a^{5} b^{2} \tan\left(d x + c\right) + 14 \, B a^{4} b^{3} \tan\left(d x + c\right) + 28 \, C a^{3} b^{4} \tan\left(d x + c\right) - 12 \, B a^{2} b^{5} \tan\left(d x + c\right) + B a^{7} - C a^{6} b + 9 \, B a^{5} b^{2} + 11 \, C a^{4} b^{3} - 4 \, B a^{3} b^{4}}{{\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(C*a^6 + 3*C*a^4*b^2 + B*a^3*b^3 + 6*C*a^2*b^4 - 3*B*a*b^5)*log(abs(b*tan(d*x + c) + a))/(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9) - (3*C*a^6*b*tan(d*x + c)^2 + 9*C*a^4*b^3*tan(d*x + c)^2 + 3*B*a^3*b^4*tan(d*x + c)^2 + 18*C*a^2*b^5*tan(d*x + c)^2 - 9*B*a*b^6*tan(d*x + c)^2 + 2*C*a^7*tan(d*x + c) + 2*B*a^6*b*tan(d*x + c) + 6*C*a^5*b^2*tan(d*x + c) + 14*B*a^4*b^3*tan(d*x + c) + 28*C*a^3*b^4*tan(d*x + c) - 12*B*a^2*b^5*tan(d*x + c) + B*a^7 - C*a^6*b + 9*B*a^5*b^2 + 11*C*a^4*b^3 - 4*B*a^3*b^4)/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*(b*tan(d*x + c) + a)^2))/d","A",0
40,1,410,0,2.268795," ","integrate(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(C a^{3} b - 3 \, B a^{2} b^{2} - 3 \, C a b^{3} + B b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} + \frac{3 \, C a^{3} b^{4} \tan\left(d x + c\right)^{2} - 9 \, B a^{2} b^{5} \tan\left(d x + c\right)^{2} - 9 \, C a b^{6} \tan\left(d x + c\right)^{2} + 3 \, B b^{7} \tan\left(d x + c\right)^{2} + 2 \, C a^{6} b \tan\left(d x + c\right) + 14 \, C a^{4} b^{3} \tan\left(d x + c\right) - 22 \, B a^{3} b^{4} \tan\left(d x + c\right) - 12 \, C a^{2} b^{5} \tan\left(d x + c\right) + 2 \, B a b^{6} \tan\left(d x + c\right) + C a^{7} + B a^{6} b + 9 \, C a^{5} b^{2} - 11 \, B a^{4} b^{3} - 4 \, C a^{3} b^{4}}{{\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*(B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(C*a^3*b - 3*B*a^2*b^2 - 3*C*a*b^3 + B*b^4)*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) + (3*C*a^3*b^4*tan(d*x + c)^2 - 9*B*a^2*b^5*tan(d*x + c)^2 - 9*C*a*b^6*tan(d*x + c)^2 + 3*B*b^7*tan(d*x + c)^2 + 2*C*a^6*b*tan(d*x + c) + 14*C*a^4*b^3*tan(d*x + c) - 22*B*a^3*b^4*tan(d*x + c) - 12*C*a^2*b^5*tan(d*x + c) + 2*B*a*b^6*tan(d*x + c) + C*a^7 + B*a^6*b + 9*C*a^5*b^2 - 11*B*a^4*b^3 - 4*C*a^3*b^4)/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*(b*tan(d*x + c) + a)^2))/d","B",0
41,1,410,0,2.646767," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(B a^{3} b + 3 \, C a^{2} b^{2} - 3 \, B a b^{3} - C b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{3 \, B a^{3} b^{3} \tan\left(d x + c\right)^{2} + 9 \, C a^{2} b^{4} \tan\left(d x + c\right)^{2} - 9 \, B a b^{5} \tan\left(d x + c\right)^{2} - 3 \, C b^{6} \tan\left(d x + c\right)^{2} + 8 \, B a^{4} b^{2} \tan\left(d x + c\right) + 22 \, C a^{3} b^{3} \tan\left(d x + c\right) - 18 \, B a^{2} b^{4} \tan\left(d x + c\right) - 2 \, C a b^{5} \tan\left(d x + c\right) - 2 \, B b^{6} \tan\left(d x + c\right) - C a^{6} + 6 \, B a^{5} b + 11 \, C a^{4} b^{2} - 7 \, B a^{3} b^{3} - B a b^{5}}{{\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*(C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(B*a^3*b + 3*C*a^2*b^2 - 3*B*a*b^3 - C*b^4)*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - (3*B*a^3*b^3*tan(d*x + c)^2 + 9*C*a^2*b^4*tan(d*x + c)^2 - 9*B*a*b^5*tan(d*x + c)^2 - 3*C*b^6*tan(d*x + c)^2 + 8*B*a^4*b^2*tan(d*x + c) + 22*C*a^3*b^3*tan(d*x + c) - 18*B*a^2*b^4*tan(d*x + c) - 2*C*a*b^5*tan(d*x + c) - 2*B*b^6*tan(d*x + c) - C*a^6 + 6*B*a^5*b + 11*C*a^4*b^2 - 7*B*a^3*b^3 - B*a*b^5)/((a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*(b*tan(d*x + c) + a)^2))/d","B",0
42,1,409,0,4.716698," ","integrate(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(C a^{3} b - 3 \, B a^{2} b^{2} - 3 \, C a b^{3} + B b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} + \frac{3 \, C a^{3} b^{2} \tan\left(d x + c\right)^{2} - 9 \, B a^{2} b^{3} \tan\left(d x + c\right)^{2} - 9 \, C a b^{4} \tan\left(d x + c\right)^{2} + 3 \, B b^{5} \tan\left(d x + c\right)^{2} + 8 \, C a^{4} b \tan\left(d x + c\right) - 22 \, B a^{3} b^{2} \tan\left(d x + c\right) - 18 \, C a^{2} b^{3} \tan\left(d x + c\right) + 2 \, B a b^{4} \tan\left(d x + c\right) - 2 \, C b^{5} \tan\left(d x + c\right) + 6 \, C a^{5} - 14 \, B a^{4} b - 7 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - C a b^{4} - B b^{5}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(C*a^3*b - 3*B*a^2*b^2 - 3*C*a*b^3 + B*b^4)*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) + (3*C*a^3*b^2*tan(d*x + c)^2 - 9*B*a^2*b^3*tan(d*x + c)^2 - 9*C*a*b^4*tan(d*x + c)^2 + 3*B*b^5*tan(d*x + c)^2 + 8*C*a^4*b*tan(d*x + c) - 22*B*a^3*b^2*tan(d*x + c) - 18*C*a^2*b^3*tan(d*x + c) + 2*B*a*b^4*tan(d*x + c) - 2*C*b^5*tan(d*x + c) + 6*C*a^5 - 14*B*a^4*b - 7*C*a^3*b^2 - 3*B*a^2*b^3 - C*a*b^4 - B*b^5)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(b*tan(d*x + c) + a)^2))/d","B",0
43,1,479,0,8.669208," ","integrate(cot(d*x+c)^2*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(3 \, C a^{5} b^{2} - 6 \, B a^{4} b^{3} - C a^{3} b^{4} - 3 \, B a^{2} b^{5} - B b^{7}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{9} b + 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} + a^{3} b^{7}} + \frac{2 \, B \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{9 \, C a^{5} b^{3} \tan\left(d x + c\right)^{2} - 18 \, B a^{4} b^{4} \tan\left(d x + c\right)^{2} - 3 \, C a^{3} b^{5} \tan\left(d x + c\right)^{2} - 9 \, B a^{2} b^{6} \tan\left(d x + c\right)^{2} - 3 \, B b^{8} \tan\left(d x + c\right)^{2} + 22 \, C a^{6} b^{2} \tan\left(d x + c\right) - 42 \, B a^{5} b^{3} \tan\left(d x + c\right) - 2 \, C a^{4} b^{4} \tan\left(d x + c\right) - 26 \, B a^{3} b^{5} \tan\left(d x + c\right) - 8 \, B a b^{7} \tan\left(d x + c\right) + 14 \, C a^{7} b - 25 \, B a^{6} b^{2} + 3 \, C a^{5} b^{3} - 19 \, B a^{4} b^{4} + C a^{3} b^{5} - 6 \, B a^{2} b^{6}}{{\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(3*C*a^5*b^2 - 6*B*a^4*b^3 - C*a^3*b^4 - 3*B*a^2*b^5 - B*b^7)*log(abs(b*tan(d*x + c) + a))/(a^9*b + 3*a^7*b^3 + 3*a^5*b^5 + a^3*b^7) + 2*B*log(abs(tan(d*x + c)))/a^3 - (9*C*a^5*b^3*tan(d*x + c)^2 - 18*B*a^4*b^4*tan(d*x + c)^2 - 3*C*a^3*b^5*tan(d*x + c)^2 - 9*B*a^2*b^6*tan(d*x + c)^2 - 3*B*b^8*tan(d*x + c)^2 + 22*C*a^6*b^2*tan(d*x + c) - 42*B*a^5*b^3*tan(d*x + c) - 2*C*a^4*b^4*tan(d*x + c) - 26*B*a^3*b^5*tan(d*x + c) - 8*B*a*b^7*tan(d*x + c) + 14*C*a^7*b - 25*B*a^6*b^2 + 3*C*a^5*b^3 - 19*B*a^4*b^4 + C*a^3*b^5 - 6*B*a^2*b^6)/((a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*(b*tan(d*x + c) + a)^2))/d","B",0
44,1,560,0,9.824621," ","integrate(cot(d*x+c)^3*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(6 \, C a^{5} b^{3} - 10 \, B a^{4} b^{4} + 3 \, C a^{3} b^{5} - 9 \, B a^{2} b^{6} + C a b^{7} - 3 \, B b^{8}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{10} b + 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} + a^{4} b^{7}} - \frac{18 \, C a^{5} b^{4} \tan\left(d x + c\right)^{2} - 30 \, B a^{4} b^{5} \tan\left(d x + c\right)^{2} + 9 \, C a^{3} b^{6} \tan\left(d x + c\right)^{2} - 27 \, B a^{2} b^{7} \tan\left(d x + c\right)^{2} + 3 \, C a b^{8} \tan\left(d x + c\right)^{2} - 9 \, B b^{9} \tan\left(d x + c\right)^{2} + 42 \, C a^{6} b^{3} \tan\left(d x + c\right) - 68 \, B a^{5} b^{4} \tan\left(d x + c\right) + 26 \, C a^{4} b^{5} \tan\left(d x + c\right) - 66 \, B a^{3} b^{6} \tan\left(d x + c\right) + 8 \, C a^{2} b^{7} \tan\left(d x + c\right) - 22 \, B a b^{8} \tan\left(d x + c\right) + 25 \, C a^{7} b^{2} - 39 \, B a^{6} b^{3} + 19 \, C a^{5} b^{4} - 41 \, B a^{4} b^{5} + 6 \, C a^{3} b^{6} - 14 \, B a^{2} b^{7}}{{\left(a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}} - \frac{2 \, {\left(C a - 3 \, B b\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{4}} + \frac{2 \, {\left(C a \tan\left(d x + c\right) - 3 \, B b \tan\left(d x + c\right) + B a\right)}}{a^{4} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(6*C*a^5*b^3 - 10*B*a^4*b^4 + 3*C*a^3*b^5 - 9*B*a^2*b^6 + C*a*b^7 - 3*B*b^8)*log(abs(b*tan(d*x + c) + a))/(a^10*b + 3*a^8*b^3 + 3*a^6*b^5 + a^4*b^7) - (18*C*a^5*b^4*tan(d*x + c)^2 - 30*B*a^4*b^5*tan(d*x + c)^2 + 9*C*a^3*b^6*tan(d*x + c)^2 - 27*B*a^2*b^7*tan(d*x + c)^2 + 3*C*a*b^8*tan(d*x + c)^2 - 9*B*b^9*tan(d*x + c)^2 + 42*C*a^6*b^3*tan(d*x + c) - 68*B*a^5*b^4*tan(d*x + c) + 26*C*a^4*b^5*tan(d*x + c) - 66*B*a^3*b^6*tan(d*x + c) + 8*C*a^2*b^7*tan(d*x + c) - 22*B*a*b^8*tan(d*x + c) + 25*C*a^7*b^2 - 39*B*a^6*b^3 + 19*C*a^5*b^4 - 41*B*a^4*b^5 + 6*C*a^3*b^6 - 14*B*a^2*b^7)/((a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6)*(b*tan(d*x + c) + a)^2) - 2*(C*a - 3*B*b)*log(abs(tan(d*x + c)))/a^4 + 2*(C*a*tan(d*x + c) - 3*B*b*tan(d*x + c) + B*a)/(a^4*tan(d*x + c)))/d","A",0
45,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(b*tan(d*x+c))^n*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \tan\left(d x + c\right)^{2} + B \tan\left(d x + c\right) + A\right)} \left(b \tan\left(d x + c\right)\right)^{n} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*tan(d*x + c)^2 + B*tan(d*x + c) + A)*(b*tan(d*x + c))^n*tan(d*x + c)^2, x)","F",0
46,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(b*tan(d*x+c))^n*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \tan\left(d x + c\right)^{2} + B \tan\left(d x + c\right) + A\right)} \left(b \tan\left(d x + c\right)\right)^{n} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*tan(d*x + c)^2 + B*tan(d*x + c) + A)*(b*tan(d*x + c))^n*tan(d*x + c)^m, x)","F",0
47,-1,0,0,0.000000," ","integrate(tan(d*x+c)^m*(b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c)+C*tan(d*x+c)^2)/(b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \tan\left(d x + c\right)^{2} + B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{\sqrt{b \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*tan(d*x + c)^2 + B*tan(d*x + c) + A)*tan(d*x + c)^m/sqrt(b*tan(d*x + c)), x)","F",0
49,-1,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,1,6502,0,23.117548," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\frac{12 \, A a^{2} c f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, C a^{2} c f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 24 \, B a b c f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, A b^{2} c f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, C b^{2} c f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, B a^{2} d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 24 \, A a b d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 24 \, C a b d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, B b^{2} d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 6 \, B a^{2} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, A a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, C a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, B b^{2} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 6 \, A a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, C a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, B a b d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, A b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 6 \, C b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 48 \, A a^{2} c f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, C a^{2} c f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 96 \, B a b c f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, A b^{2} c f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 48 \, C b^{2} c f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, B a^{2} d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 96 \, A a b d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 96 \, C a b d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 48 \, B b^{2} d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 12 \, C a b c \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, B b^{2} c \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, C a^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, B a b d \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, A b^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 9 \, C b^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 24 \, B a^{2} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, A a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 48 \, C a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, B b^{2} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, A a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, C a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 48 \, B a b d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, A b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, C b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, C a^{2} c \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 24 \, B a b c \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 12 \, A b^{2} c \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 12 \, C b^{2} c \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 12 \, B a^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 24 \, A a b d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 24 \, C a b d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 12 \, B b^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 12 \, C a^{2} c \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 24 \, B a b c \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 12 \, A b^{2} c \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 12 \, C b^{2} c \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 12 \, B a^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 24 \, A a b d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 24 \, C a b d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 12 \, B b^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 72 \, A a^{2} c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, C a^{2} c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 144 \, B a b c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, A b^{2} c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, C b^{2} c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, B a^{2} d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 144 \, A a b d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 144 \, C a b d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, B b^{2} d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 12 \, C a b c \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 6 \, B b^{2} c \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 6 \, C a^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 12 \, B a b d \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 6 \, A b^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 6 \, C b^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 24 \, C a b c \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, B b^{2} c \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, C a^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, B a b d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, A b^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, C b^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 12 \, C a b c \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 6 \, B b^{2} c \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 6 \, C a^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 12 \, B a b d \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 6 \, A b^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 6 \, C b^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 4 \, C b^{2} c \tan\left(f x\right)^{4} \tan\left(e\right) - 8 \, C a b d \tan\left(f x\right)^{4} \tan\left(e\right) - 4 \, B b^{2} d \tan\left(f x\right)^{4} \tan\left(e\right) - 36 \, B a^{2} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, A a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, C a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, B b^{2} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 36 \, A a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, C a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, B a b d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, A b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 36 \, C b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, C a^{2} c \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 72 \, B a b c \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 36 \, A b^{2} c \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 48 \, C b^{2} c \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 36 \, B a^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 72 \, A a b d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 96 \, C a b d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 48 \, B b^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 36 \, C a^{2} c \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 72 \, B a b c \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 36 \, A b^{2} c \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 48 \, C b^{2} c \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 36 \, B a^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 72 \, A a b d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 96 \, C a b d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 48 \, B b^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 4 \, C b^{2} c \tan\left(f x\right) \tan\left(e\right)^{4} - 8 \, C a b d \tan\left(f x\right) \tan\left(e\right)^{4} - 4 \, B b^{2} d \tan\left(f x\right) \tan\left(e\right)^{4} + 3 \, C b^{2} d \tan\left(f x\right)^{4} - 48 \, A a^{2} c f x \tan\left(f x\right) \tan\left(e\right) + 48 \, C a^{2} c f x \tan\left(f x\right) \tan\left(e\right) + 96 \, B a b c f x \tan\left(f x\right) \tan\left(e\right) + 48 \, A b^{2} c f x \tan\left(f x\right) \tan\left(e\right) - 48 \, C b^{2} c f x \tan\left(f x\right) \tan\left(e\right) + 48 \, B a^{2} d f x \tan\left(f x\right) \tan\left(e\right) + 96 \, A a b d f x \tan\left(f x\right) \tan\left(e\right) - 96 \, C a b d f x \tan\left(f x\right) \tan\left(e\right) - 48 \, B b^{2} d f x \tan\left(f x\right) \tan\left(e\right) - 24 \, C a b c \tan\left(f x\right)^{3} \tan\left(e\right) - 12 \, B b^{2} c \tan\left(f x\right)^{3} \tan\left(e\right) - 12 \, C a^{2} d \tan\left(f x\right)^{3} \tan\left(e\right) - 24 \, B a b d \tan\left(f x\right)^{3} \tan\left(e\right) - 12 \, A b^{2} d \tan\left(f x\right)^{3} \tan\left(e\right) + 24 \, C b^{2} d \tan\left(f x\right)^{3} \tan\left(e\right) + 24 \, C a b c \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 12 \, B b^{2} c \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 12 \, C a^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 24 \, B a b d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 12 \, A b^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 12 \, C b^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 24 \, C a b c \tan\left(f x\right) \tan\left(e\right)^{3} - 12 \, B b^{2} c \tan\left(f x\right) \tan\left(e\right)^{3} - 12 \, C a^{2} d \tan\left(f x\right) \tan\left(e\right)^{3} - 24 \, B a b d \tan\left(f x\right) \tan\left(e\right)^{3} - 12 \, A b^{2} d \tan\left(f x\right) \tan\left(e\right)^{3} + 24 \, C b^{2} d \tan\left(f x\right) \tan\left(e\right)^{3} + 3 \, C b^{2} d \tan\left(e\right)^{4} + 4 \, C b^{2} c \tan\left(f x\right)^{3} + 8 \, C a b d \tan\left(f x\right)^{3} + 4 \, B b^{2} d \tan\left(f x\right)^{3} + 24 \, B a^{2} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 48 \, A a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 48 \, C a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 24 \, B b^{2} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 24 \, A a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 24 \, C a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 48 \, B a b d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 24 \, A b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 24 \, C b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 36 \, C a^{2} c \tan\left(f x\right)^{2} \tan\left(e\right) - 72 \, B a b c \tan\left(f x\right)^{2} \tan\left(e\right) - 36 \, A b^{2} c \tan\left(f x\right)^{2} \tan\left(e\right) + 48 \, C b^{2} c \tan\left(f x\right)^{2} \tan\left(e\right) - 36 \, B a^{2} d \tan\left(f x\right)^{2} \tan\left(e\right) - 72 \, A a b d \tan\left(f x\right)^{2} \tan\left(e\right) + 96 \, C a b d \tan\left(f x\right)^{2} \tan\left(e\right) + 48 \, B b^{2} d \tan\left(f x\right)^{2} \tan\left(e\right) - 36 \, C a^{2} c \tan\left(f x\right) \tan\left(e\right)^{2} - 72 \, B a b c \tan\left(f x\right) \tan\left(e\right)^{2} - 36 \, A b^{2} c \tan\left(f x\right) \tan\left(e\right)^{2} + 48 \, C b^{2} c \tan\left(f x\right) \tan\left(e\right)^{2} - 36 \, B a^{2} d \tan\left(f x\right) \tan\left(e\right)^{2} - 72 \, A a b d \tan\left(f x\right) \tan\left(e\right)^{2} + 96 \, C a b d \tan\left(f x\right) \tan\left(e\right)^{2} + 48 \, B b^{2} d \tan\left(f x\right) \tan\left(e\right)^{2} + 4 \, C b^{2} c \tan\left(e\right)^{3} + 8 \, C a b d \tan\left(e\right)^{3} + 4 \, B b^{2} d \tan\left(e\right)^{3} + 12 \, A a^{2} c f x - 12 \, C a^{2} c f x - 24 \, B a b c f x - 12 \, A b^{2} c f x + 12 \, C b^{2} c f x - 12 \, B a^{2} d f x - 24 \, A a b d f x + 24 \, C a b d f x + 12 \, B b^{2} d f x + 12 \, C a b c \tan\left(f x\right)^{2} + 6 \, B b^{2} c \tan\left(f x\right)^{2} + 6 \, C a^{2} d \tan\left(f x\right)^{2} + 12 \, B a b d \tan\left(f x\right)^{2} + 6 \, A b^{2} d \tan\left(f x\right)^{2} - 6 \, C b^{2} d \tan\left(f x\right)^{2} - 24 \, C a b c \tan\left(f x\right) \tan\left(e\right) - 12 \, B b^{2} c \tan\left(f x\right) \tan\left(e\right) - 12 \, C a^{2} d \tan\left(f x\right) \tan\left(e\right) - 24 \, B a b d \tan\left(f x\right) \tan\left(e\right) - 12 \, A b^{2} d \tan\left(f x\right) \tan\left(e\right) + 24 \, C b^{2} d \tan\left(f x\right) \tan\left(e\right) + 12 \, C a b c \tan\left(e\right)^{2} + 6 \, B b^{2} c \tan\left(e\right)^{2} + 6 \, C a^{2} d \tan\left(e\right)^{2} + 12 \, B a b d \tan\left(e\right)^{2} + 6 \, A b^{2} d \tan\left(e\right)^{2} - 6 \, C b^{2} d \tan\left(e\right)^{2} - 6 \, B a^{2} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 12 \, A a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 12 \, C a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 6 \, B b^{2} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 6 \, A a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 6 \, C a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 12 \, B a b d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 6 \, A b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 6 \, C b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 12 \, C a^{2} c \tan\left(f x\right) + 24 \, B a b c \tan\left(f x\right) + 12 \, A b^{2} c \tan\left(f x\right) - 12 \, C b^{2} c \tan\left(f x\right) + 12 \, B a^{2} d \tan\left(f x\right) + 24 \, A a b d \tan\left(f x\right) - 24 \, C a b d \tan\left(f x\right) - 12 \, B b^{2} d \tan\left(f x\right) + 12 \, C a^{2} c \tan\left(e\right) + 24 \, B a b c \tan\left(e\right) + 12 \, A b^{2} c \tan\left(e\right) - 12 \, C b^{2} c \tan\left(e\right) + 12 \, B a^{2} d \tan\left(e\right) + 24 \, A a b d \tan\left(e\right) - 24 \, C a b d \tan\left(e\right) - 12 \, B b^{2} d \tan\left(e\right) + 12 \, C a b c + 6 \, B b^{2} c + 6 \, C a^{2} d + 12 \, B a b d + 6 \, A b^{2} d - 9 \, C b^{2} d}{12 \, {\left(f \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 4 \, f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 4 \, f \tan\left(f x\right) \tan\left(e\right) + f\right)}}"," ",0,"1/12*(12*A*a^2*c*f*x*tan(f*x)^4*tan(e)^4 - 12*C*a^2*c*f*x*tan(f*x)^4*tan(e)^4 - 24*B*a*b*c*f*x*tan(f*x)^4*tan(e)^4 - 12*A*b^2*c*f*x*tan(f*x)^4*tan(e)^4 + 12*C*b^2*c*f*x*tan(f*x)^4*tan(e)^4 - 12*B*a^2*d*f*x*tan(f*x)^4*tan(e)^4 - 24*A*a*b*d*f*x*tan(f*x)^4*tan(e)^4 + 24*C*a*b*d*f*x*tan(f*x)^4*tan(e)^4 + 12*B*b^2*d*f*x*tan(f*x)^4*tan(e)^4 - 6*B*a^2*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 12*A*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 12*C*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 6*B*b^2*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 6*A*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 6*C*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 12*B*a*b*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 6*A*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 6*C*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 48*A*a^2*c*f*x*tan(f*x)^3*tan(e)^3 + 48*C*a^2*c*f*x*tan(f*x)^3*tan(e)^3 + 96*B*a*b*c*f*x*tan(f*x)^3*tan(e)^3 + 48*A*b^2*c*f*x*tan(f*x)^3*tan(e)^3 - 48*C*b^2*c*f*x*tan(f*x)^3*tan(e)^3 + 48*B*a^2*d*f*x*tan(f*x)^3*tan(e)^3 + 96*A*a*b*d*f*x*tan(f*x)^3*tan(e)^3 - 96*C*a*b*d*f*x*tan(f*x)^3*tan(e)^3 - 48*B*b^2*d*f*x*tan(f*x)^3*tan(e)^3 + 12*C*a*b*c*tan(f*x)^4*tan(e)^4 + 6*B*b^2*c*tan(f*x)^4*tan(e)^4 + 6*C*a^2*d*tan(f*x)^4*tan(e)^4 + 12*B*a*b*d*tan(f*x)^4*tan(e)^4 + 6*A*b^2*d*tan(f*x)^4*tan(e)^4 - 9*C*b^2*d*tan(f*x)^4*tan(e)^4 + 24*B*a^2*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 48*A*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 48*C*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 24*B*b^2*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 24*A*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 24*C*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 48*B*a*b*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 24*A*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 24*C*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 12*C*a^2*c*tan(f*x)^4*tan(e)^3 - 24*B*a*b*c*tan(f*x)^4*tan(e)^3 - 12*A*b^2*c*tan(f*x)^4*tan(e)^3 + 12*C*b^2*c*tan(f*x)^4*tan(e)^3 - 12*B*a^2*d*tan(f*x)^4*tan(e)^3 - 24*A*a*b*d*tan(f*x)^4*tan(e)^3 + 24*C*a*b*d*tan(f*x)^4*tan(e)^3 + 12*B*b^2*d*tan(f*x)^4*tan(e)^3 - 12*C*a^2*c*tan(f*x)^3*tan(e)^4 - 24*B*a*b*c*tan(f*x)^3*tan(e)^4 - 12*A*b^2*c*tan(f*x)^3*tan(e)^4 + 12*C*b^2*c*tan(f*x)^3*tan(e)^4 - 12*B*a^2*d*tan(f*x)^3*tan(e)^4 - 24*A*a*b*d*tan(f*x)^3*tan(e)^4 + 24*C*a*b*d*tan(f*x)^3*tan(e)^4 + 12*B*b^2*d*tan(f*x)^3*tan(e)^4 + 72*A*a^2*c*f*x*tan(f*x)^2*tan(e)^2 - 72*C*a^2*c*f*x*tan(f*x)^2*tan(e)^2 - 144*B*a*b*c*f*x*tan(f*x)^2*tan(e)^2 - 72*A*b^2*c*f*x*tan(f*x)^2*tan(e)^2 + 72*C*b^2*c*f*x*tan(f*x)^2*tan(e)^2 - 72*B*a^2*d*f*x*tan(f*x)^2*tan(e)^2 - 144*A*a*b*d*f*x*tan(f*x)^2*tan(e)^2 + 144*C*a*b*d*f*x*tan(f*x)^2*tan(e)^2 + 72*B*b^2*d*f*x*tan(f*x)^2*tan(e)^2 + 12*C*a*b*c*tan(f*x)^4*tan(e)^2 + 6*B*b^2*c*tan(f*x)^4*tan(e)^2 + 6*C*a^2*d*tan(f*x)^4*tan(e)^2 + 12*B*a*b*d*tan(f*x)^4*tan(e)^2 + 6*A*b^2*d*tan(f*x)^4*tan(e)^2 - 6*C*b^2*d*tan(f*x)^4*tan(e)^2 - 24*C*a*b*c*tan(f*x)^3*tan(e)^3 - 12*B*b^2*c*tan(f*x)^3*tan(e)^3 - 12*C*a^2*d*tan(f*x)^3*tan(e)^3 - 24*B*a*b*d*tan(f*x)^3*tan(e)^3 - 12*A*b^2*d*tan(f*x)^3*tan(e)^3 + 24*C*b^2*d*tan(f*x)^3*tan(e)^3 + 12*C*a*b*c*tan(f*x)^2*tan(e)^4 + 6*B*b^2*c*tan(f*x)^2*tan(e)^4 + 6*C*a^2*d*tan(f*x)^2*tan(e)^4 + 12*B*a*b*d*tan(f*x)^2*tan(e)^4 + 6*A*b^2*d*tan(f*x)^2*tan(e)^4 - 6*C*b^2*d*tan(f*x)^2*tan(e)^4 - 4*C*b^2*c*tan(f*x)^4*tan(e) - 8*C*a*b*d*tan(f*x)^4*tan(e) - 4*B*b^2*d*tan(f*x)^4*tan(e) - 36*B*a^2*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 72*A*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 72*C*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*B*b^2*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 36*A*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*C*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 72*B*a*b*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*A*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 36*C*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*C*a^2*c*tan(f*x)^3*tan(e)^2 + 72*B*a*b*c*tan(f*x)^3*tan(e)^2 + 36*A*b^2*c*tan(f*x)^3*tan(e)^2 - 48*C*b^2*c*tan(f*x)^3*tan(e)^2 + 36*B*a^2*d*tan(f*x)^3*tan(e)^2 + 72*A*a*b*d*tan(f*x)^3*tan(e)^2 - 96*C*a*b*d*tan(f*x)^3*tan(e)^2 - 48*B*b^2*d*tan(f*x)^3*tan(e)^2 + 36*C*a^2*c*tan(f*x)^2*tan(e)^3 + 72*B*a*b*c*tan(f*x)^2*tan(e)^3 + 36*A*b^2*c*tan(f*x)^2*tan(e)^3 - 48*C*b^2*c*tan(f*x)^2*tan(e)^3 + 36*B*a^2*d*tan(f*x)^2*tan(e)^3 + 72*A*a*b*d*tan(f*x)^2*tan(e)^3 - 96*C*a*b*d*tan(f*x)^2*tan(e)^3 - 48*B*b^2*d*tan(f*x)^2*tan(e)^3 - 4*C*b^2*c*tan(f*x)*tan(e)^4 - 8*C*a*b*d*tan(f*x)*tan(e)^4 - 4*B*b^2*d*tan(f*x)*tan(e)^4 + 3*C*b^2*d*tan(f*x)^4 - 48*A*a^2*c*f*x*tan(f*x)*tan(e) + 48*C*a^2*c*f*x*tan(f*x)*tan(e) + 96*B*a*b*c*f*x*tan(f*x)*tan(e) + 48*A*b^2*c*f*x*tan(f*x)*tan(e) - 48*C*b^2*c*f*x*tan(f*x)*tan(e) + 48*B*a^2*d*f*x*tan(f*x)*tan(e) + 96*A*a*b*d*f*x*tan(f*x)*tan(e) - 96*C*a*b*d*f*x*tan(f*x)*tan(e) - 48*B*b^2*d*f*x*tan(f*x)*tan(e) - 24*C*a*b*c*tan(f*x)^3*tan(e) - 12*B*b^2*c*tan(f*x)^3*tan(e) - 12*C*a^2*d*tan(f*x)^3*tan(e) - 24*B*a*b*d*tan(f*x)^3*tan(e) - 12*A*b^2*d*tan(f*x)^3*tan(e) + 24*C*b^2*d*tan(f*x)^3*tan(e) + 24*C*a*b*c*tan(f*x)^2*tan(e)^2 + 12*B*b^2*c*tan(f*x)^2*tan(e)^2 + 12*C*a^2*d*tan(f*x)^2*tan(e)^2 + 24*B*a*b*d*tan(f*x)^2*tan(e)^2 + 12*A*b^2*d*tan(f*x)^2*tan(e)^2 - 12*C*b^2*d*tan(f*x)^2*tan(e)^2 - 24*C*a*b*c*tan(f*x)*tan(e)^3 - 12*B*b^2*c*tan(f*x)*tan(e)^3 - 12*C*a^2*d*tan(f*x)*tan(e)^3 - 24*B*a*b*d*tan(f*x)*tan(e)^3 - 12*A*b^2*d*tan(f*x)*tan(e)^3 + 24*C*b^2*d*tan(f*x)*tan(e)^3 + 3*C*b^2*d*tan(e)^4 + 4*C*b^2*c*tan(f*x)^3 + 8*C*a*b*d*tan(f*x)^3 + 4*B*b^2*d*tan(f*x)^3 + 24*B*a^2*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 48*A*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 48*C*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 24*B*b^2*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 24*A*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 24*C*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 48*B*a*b*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 24*A*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 24*C*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 36*C*a^2*c*tan(f*x)^2*tan(e) - 72*B*a*b*c*tan(f*x)^2*tan(e) - 36*A*b^2*c*tan(f*x)^2*tan(e) + 48*C*b^2*c*tan(f*x)^2*tan(e) - 36*B*a^2*d*tan(f*x)^2*tan(e) - 72*A*a*b*d*tan(f*x)^2*tan(e) + 96*C*a*b*d*tan(f*x)^2*tan(e) + 48*B*b^2*d*tan(f*x)^2*tan(e) - 36*C*a^2*c*tan(f*x)*tan(e)^2 - 72*B*a*b*c*tan(f*x)*tan(e)^2 - 36*A*b^2*c*tan(f*x)*tan(e)^2 + 48*C*b^2*c*tan(f*x)*tan(e)^2 - 36*B*a^2*d*tan(f*x)*tan(e)^2 - 72*A*a*b*d*tan(f*x)*tan(e)^2 + 96*C*a*b*d*tan(f*x)*tan(e)^2 + 48*B*b^2*d*tan(f*x)*tan(e)^2 + 4*C*b^2*c*tan(e)^3 + 8*C*a*b*d*tan(e)^3 + 4*B*b^2*d*tan(e)^3 + 12*A*a^2*c*f*x - 12*C*a^2*c*f*x - 24*B*a*b*c*f*x - 12*A*b^2*c*f*x + 12*C*b^2*c*f*x - 12*B*a^2*d*f*x - 24*A*a*b*d*f*x + 24*C*a*b*d*f*x + 12*B*b^2*d*f*x + 12*C*a*b*c*tan(f*x)^2 + 6*B*b^2*c*tan(f*x)^2 + 6*C*a^2*d*tan(f*x)^2 + 12*B*a*b*d*tan(f*x)^2 + 6*A*b^2*d*tan(f*x)^2 - 6*C*b^2*d*tan(f*x)^2 - 24*C*a*b*c*tan(f*x)*tan(e) - 12*B*b^2*c*tan(f*x)*tan(e) - 12*C*a^2*d*tan(f*x)*tan(e) - 24*B*a*b*d*tan(f*x)*tan(e) - 12*A*b^2*d*tan(f*x)*tan(e) + 24*C*b^2*d*tan(f*x)*tan(e) + 12*C*a*b*c*tan(e)^2 + 6*B*b^2*c*tan(e)^2 + 6*C*a^2*d*tan(e)^2 + 12*B*a*b*d*tan(e)^2 + 6*A*b^2*d*tan(e)^2 - 6*C*b^2*d*tan(e)^2 - 6*B*a^2*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 12*A*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 12*C*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 6*B*b^2*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 6*A*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 6*C*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 12*B*a*b*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 6*A*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 6*C*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 12*C*a^2*c*tan(f*x) + 24*B*a*b*c*tan(f*x) + 12*A*b^2*c*tan(f*x) - 12*C*b^2*c*tan(f*x) + 12*B*a^2*d*tan(f*x) + 24*A*a*b*d*tan(f*x) - 24*C*a*b*d*tan(f*x) - 12*B*b^2*d*tan(f*x) + 12*C*a^2*c*tan(e) + 24*B*a*b*c*tan(e) + 12*A*b^2*c*tan(e) - 12*C*b^2*c*tan(e) + 12*B*a^2*d*tan(e) + 24*A*a*b*d*tan(e) - 24*C*a*b*d*tan(e) - 12*B*b^2*d*tan(e) + 12*C*a*b*c + 6*B*b^2*c + 6*C*a^2*d + 12*B*a*b*d + 6*A*b^2*d - 9*C*b^2*d)/(f*tan(f*x)^4*tan(e)^4 - 4*f*tan(f*x)^3*tan(e)^3 + 6*f*tan(f*x)^2*tan(e)^2 - 4*f*tan(f*x)*tan(e) + f)","B",0
52,1,2918,0,7.335998," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\frac{6 \, A a c f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 6 \, C a c f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 6 \, B b c f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 6 \, B a d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 6 \, A b d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, C b d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, B a c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, A b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, C b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, A a d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, C a d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, B b d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 18 \, A a c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 18 \, C a c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 18 \, B b c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 18 \, B a d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 18 \, A b d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 18 \, C b d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, C b c \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, C a d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, B b d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 9 \, B a c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 9 \, A b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 9 \, C b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 9 \, A a d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 9 \, C a d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 9 \, B b d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 6 \, C a c \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 6 \, B b c \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 6 \, B a d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 6 \, A b d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 6 \, C b d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 6 \, C a c \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 6 \, B b c \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 6 \, B a d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 6 \, A b d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 6 \, C b d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 18 \, A a c f x \tan\left(f x\right) \tan\left(e\right) - 18 \, C a c f x \tan\left(f x\right) \tan\left(e\right) - 18 \, B b c f x \tan\left(f x\right) \tan\left(e\right) - 18 \, B a d f x \tan\left(f x\right) \tan\left(e\right) - 18 \, A b d f x \tan\left(f x\right) \tan\left(e\right) + 18 \, C b d f x \tan\left(f x\right) \tan\left(e\right) + 3 \, C b c \tan\left(f x\right)^{3} \tan\left(e\right) + 3 \, C a d \tan\left(f x\right)^{3} \tan\left(e\right) + 3 \, B b d \tan\left(f x\right)^{3} \tan\left(e\right) - 3 \, C b c \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 3 \, C a d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 3 \, B b d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, C b c \tan\left(f x\right) \tan\left(e\right)^{3} + 3 \, C a d \tan\left(f x\right) \tan\left(e\right)^{3} + 3 \, B b d \tan\left(f x\right) \tan\left(e\right)^{3} - 2 \, C b d \tan\left(f x\right)^{3} - 9 \, B a c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 9 \, A b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 9 \, C b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 9 \, A a d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 9 \, C a d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 9 \, B b d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 12 \, C a c \tan\left(f x\right)^{2} \tan\left(e\right) + 12 \, B b c \tan\left(f x\right)^{2} \tan\left(e\right) + 12 \, B a d \tan\left(f x\right)^{2} \tan\left(e\right) + 12 \, A b d \tan\left(f x\right)^{2} \tan\left(e\right) - 18 \, C b d \tan\left(f x\right)^{2} \tan\left(e\right) + 12 \, C a c \tan\left(f x\right) \tan\left(e\right)^{2} + 12 \, B b c \tan\left(f x\right) \tan\left(e\right)^{2} + 12 \, B a d \tan\left(f x\right) \tan\left(e\right)^{2} + 12 \, A b d \tan\left(f x\right) \tan\left(e\right)^{2} - 18 \, C b d \tan\left(f x\right) \tan\left(e\right)^{2} - 2 \, C b d \tan\left(e\right)^{3} - 6 \, A a c f x + 6 \, C a c f x + 6 \, B b c f x + 6 \, B a d f x + 6 \, A b d f x - 6 \, C b d f x - 3 \, C b c \tan\left(f x\right)^{2} - 3 \, C a d \tan\left(f x\right)^{2} - 3 \, B b d \tan\left(f x\right)^{2} + 3 \, C b c \tan\left(f x\right) \tan\left(e\right) + 3 \, C a d \tan\left(f x\right) \tan\left(e\right) + 3 \, B b d \tan\left(f x\right) \tan\left(e\right) - 3 \, C b c \tan\left(e\right)^{2} - 3 \, C a d \tan\left(e\right)^{2} - 3 \, B b d \tan\left(e\right)^{2} + 3 \, B a c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 3 \, A b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 3 \, C b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 3 \, A a d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 3 \, C a d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 3 \, B b d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 6 \, C a c \tan\left(f x\right) - 6 \, B b c \tan\left(f x\right) - 6 \, B a d \tan\left(f x\right) - 6 \, A b d \tan\left(f x\right) + 6 \, C b d \tan\left(f x\right) - 6 \, C a c \tan\left(e\right) - 6 \, B b c \tan\left(e\right) - 6 \, B a d \tan\left(e\right) - 6 \, A b d \tan\left(e\right) + 6 \, C b d \tan\left(e\right) - 3 \, C b c - 3 \, C a d - 3 \, B b d}{6 \, {\left(f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, f \tan\left(f x\right) \tan\left(e\right) - f\right)}}"," ",0,"1/6*(6*A*a*c*f*x*tan(f*x)^3*tan(e)^3 - 6*C*a*c*f*x*tan(f*x)^3*tan(e)^3 - 6*B*b*c*f*x*tan(f*x)^3*tan(e)^3 - 6*B*a*d*f*x*tan(f*x)^3*tan(e)^3 - 6*A*b*d*f*x*tan(f*x)^3*tan(e)^3 + 6*C*b*d*f*x*tan(f*x)^3*tan(e)^3 - 3*B*a*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 3*A*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 3*C*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 3*A*a*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 3*C*a*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 3*B*b*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 18*A*a*c*f*x*tan(f*x)^2*tan(e)^2 + 18*C*a*c*f*x*tan(f*x)^2*tan(e)^2 + 18*B*b*c*f*x*tan(f*x)^2*tan(e)^2 + 18*B*a*d*f*x*tan(f*x)^2*tan(e)^2 + 18*A*b*d*f*x*tan(f*x)^2*tan(e)^2 - 18*C*b*d*f*x*tan(f*x)^2*tan(e)^2 + 3*C*b*c*tan(f*x)^3*tan(e)^3 + 3*C*a*d*tan(f*x)^3*tan(e)^3 + 3*B*b*d*tan(f*x)^3*tan(e)^3 + 9*B*a*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 9*A*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 9*C*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 9*A*a*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 9*C*a*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 9*B*b*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 6*C*a*c*tan(f*x)^3*tan(e)^2 - 6*B*b*c*tan(f*x)^3*tan(e)^2 - 6*B*a*d*tan(f*x)^3*tan(e)^2 - 6*A*b*d*tan(f*x)^3*tan(e)^2 + 6*C*b*d*tan(f*x)^3*tan(e)^2 - 6*C*a*c*tan(f*x)^2*tan(e)^3 - 6*B*b*c*tan(f*x)^2*tan(e)^3 - 6*B*a*d*tan(f*x)^2*tan(e)^3 - 6*A*b*d*tan(f*x)^2*tan(e)^3 + 6*C*b*d*tan(f*x)^2*tan(e)^3 + 18*A*a*c*f*x*tan(f*x)*tan(e) - 18*C*a*c*f*x*tan(f*x)*tan(e) - 18*B*b*c*f*x*tan(f*x)*tan(e) - 18*B*a*d*f*x*tan(f*x)*tan(e) - 18*A*b*d*f*x*tan(f*x)*tan(e) + 18*C*b*d*f*x*tan(f*x)*tan(e) + 3*C*b*c*tan(f*x)^3*tan(e) + 3*C*a*d*tan(f*x)^3*tan(e) + 3*B*b*d*tan(f*x)^3*tan(e) - 3*C*b*c*tan(f*x)^2*tan(e)^2 - 3*C*a*d*tan(f*x)^2*tan(e)^2 - 3*B*b*d*tan(f*x)^2*tan(e)^2 + 3*C*b*c*tan(f*x)*tan(e)^3 + 3*C*a*d*tan(f*x)*tan(e)^3 + 3*B*b*d*tan(f*x)*tan(e)^3 - 2*C*b*d*tan(f*x)^3 - 9*B*a*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 9*A*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 9*C*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 9*A*a*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 9*C*a*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 9*B*b*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 12*C*a*c*tan(f*x)^2*tan(e) + 12*B*b*c*tan(f*x)^2*tan(e) + 12*B*a*d*tan(f*x)^2*tan(e) + 12*A*b*d*tan(f*x)^2*tan(e) - 18*C*b*d*tan(f*x)^2*tan(e) + 12*C*a*c*tan(f*x)*tan(e)^2 + 12*B*b*c*tan(f*x)*tan(e)^2 + 12*B*a*d*tan(f*x)*tan(e)^2 + 12*A*b*d*tan(f*x)*tan(e)^2 - 18*C*b*d*tan(f*x)*tan(e)^2 - 2*C*b*d*tan(e)^3 - 6*A*a*c*f*x + 6*C*a*c*f*x + 6*B*b*c*f*x + 6*B*a*d*f*x + 6*A*b*d*f*x - 6*C*b*d*f*x - 3*C*b*c*tan(f*x)^2 - 3*C*a*d*tan(f*x)^2 - 3*B*b*d*tan(f*x)^2 + 3*C*b*c*tan(f*x)*tan(e) + 3*C*a*d*tan(f*x)*tan(e) + 3*B*b*d*tan(f*x)*tan(e) - 3*C*b*c*tan(e)^2 - 3*C*a*d*tan(e)^2 - 3*B*b*d*tan(e)^2 + 3*B*a*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 3*A*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 3*C*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 3*A*a*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 3*C*a*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 3*B*b*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 6*C*a*c*tan(f*x) - 6*B*b*c*tan(f*x) - 6*B*a*d*tan(f*x) - 6*A*b*d*tan(f*x) + 6*C*b*d*tan(f*x) - 6*C*a*c*tan(e) - 6*B*b*c*tan(e) - 6*B*a*d*tan(e) - 6*A*b*d*tan(e) + 6*C*b*d*tan(e) - 3*C*b*c - 3*C*a*d - 3*B*b*d)/(f*tan(f*x)^3*tan(e)^3 - 3*f*tan(f*x)^2*tan(e)^2 + 3*f*tan(f*x)*tan(e) - f)","B",0
53,1,918,0,2.929224," ","integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\frac{2 \, A c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2 \, C c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2 \, B d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - B c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - A d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + C d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 4 \, A c f x \tan\left(f x\right) \tan\left(e\right) + 4 \, C c f x \tan\left(f x\right) \tan\left(e\right) + 4 \, B d f x \tan\left(f x\right) \tan\left(e\right) + C d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 2 \, B c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 2 \, A d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 2 \, C d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 2 \, C c \tan\left(f x\right)^{2} \tan\left(e\right) - 2 \, B d \tan\left(f x\right)^{2} \tan\left(e\right) - 2 \, C c \tan\left(f x\right) \tan\left(e\right)^{2} - 2 \, B d \tan\left(f x\right) \tan\left(e\right)^{2} + 2 \, A c f x - 2 \, C c f x - 2 \, B d f x + C d \tan\left(f x\right)^{2} + C d \tan\left(e\right)^{2} - B c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - A d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + C d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 2 \, C c \tan\left(f x\right) + 2 \, B d \tan\left(f x\right) + 2 \, C c \tan\left(e\right) + 2 \, B d \tan\left(e\right) + C d}{2 \, {\left(f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2 \, f \tan\left(f x\right) \tan\left(e\right) + f\right)}}"," ",0,"1/2*(2*A*c*f*x*tan(f*x)^2*tan(e)^2 - 2*C*c*f*x*tan(f*x)^2*tan(e)^2 - 2*B*d*f*x*tan(f*x)^2*tan(e)^2 - B*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - A*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + C*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 4*A*c*f*x*tan(f*x)*tan(e) + 4*C*c*f*x*tan(f*x)*tan(e) + 4*B*d*f*x*tan(f*x)*tan(e) + C*d*tan(f*x)^2*tan(e)^2 + 2*B*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 2*A*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 2*C*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 2*C*c*tan(f*x)^2*tan(e) - 2*B*d*tan(f*x)^2*tan(e) - 2*C*c*tan(f*x)*tan(e)^2 - 2*B*d*tan(f*x)*tan(e)^2 + 2*A*c*f*x - 2*C*c*f*x - 2*B*d*f*x + C*d*tan(f*x)^2 + C*d*tan(e)^2 - B*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - A*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + C*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 2*C*c*tan(f*x) + 2*B*d*tan(f*x) + 2*C*c*tan(e) + 2*B*d*tan(e) + C*d)/(f*tan(f*x)^2*tan(e)^2 - 2*f*tan(f*x)*tan(e) + f)","B",0
54,1,186,0,1.792850," ","integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, C d \tan\left(f x + e\right)}{b} + \frac{2 \, {\left(A a c - C a c + B b c - B a d + A b d - C b d\right)} {\left(f x + e\right)}}{a^{2} + b^{2}} + \frac{{\left(B a c - A b c + C b c + A a d - C a d + B b d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(C a^{2} b c - B a b^{2} c + A b^{3} c - C a^{3} d + B a^{2} b d - A a b^{2} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b^{2} + b^{4}}}{2 \, f}"," ",0,"1/2*(2*C*d*tan(f*x + e)/b + 2*(A*a*c - C*a*c + B*b*c - B*a*d + A*b*d - C*b*d)*(f*x + e)/(a^2 + b^2) + (B*a*c - A*b*c + C*b*c + A*a*d - C*a*d + B*b*d)*log(tan(f*x + e)^2 + 1)/(a^2 + b^2) + 2*(C*a^2*b*c - B*a*b^2*c + A*b^3*c - C*a^3*d + B*a^2*b*d - A*a*b^2*d)*log(abs(b*tan(f*x + e) + a))/(a^2*b^2 + b^4))/f","A",0
55,1,531,0,2.354609," ","integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{2} c - C a^{2} c + 2 \, B a b c - A b^{2} c + C b^{2} c - B a^{2} d + 2 \, A a b d - 2 \, C a b d + B b^{2} d\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(B a^{2} c - 2 \, A a b c + 2 \, C a b c - B b^{2} c + A a^{2} d - C a^{2} d + 2 \, B a b d - A b^{2} d + C b^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(B a^{2} b^{2} c - 2 \, A a b^{3} c + 2 \, C a b^{3} c - B b^{4} c - C a^{4} d + A a^{2} b^{2} d - 3 \, C a^{2} b^{2} d + 2 \, B a b^{3} d - A b^{4} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(B a^{2} b^{2} c \tan\left(f x + e\right) - 2 \, A a b^{3} c \tan\left(f x + e\right) + 2 \, C a b^{3} c \tan\left(f x + e\right) - B b^{4} c \tan\left(f x + e\right) - C a^{4} d \tan\left(f x + e\right) + A a^{2} b^{2} d \tan\left(f x + e\right) - 3 \, C a^{2} b^{2} d \tan\left(f x + e\right) + 2 \, B a b^{3} d \tan\left(f x + e\right) - A b^{4} d \tan\left(f x + e\right) - C a^{4} c + 2 \, B a^{3} b c - 3 \, A a^{2} b^{2} c + C a^{2} b^{2} c - A b^{4} c - B a^{4} d + 2 \, A a^{3} b d - 2 \, C a^{3} b d + B a^{2} b^{2} d\right)}}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} {\left(b \tan\left(f x + e\right) + a\right)}}}{2 \, f}"," ",0,"1/2*(2*(A*a^2*c - C*a^2*c + 2*B*a*b*c - A*b^2*c + C*b^2*c - B*a^2*d + 2*A*a*b*d - 2*C*a*b*d + B*b^2*d)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) + (B*a^2*c - 2*A*a*b*c + 2*C*a*b*c - B*b^2*c + A*a^2*d - C*a^2*d + 2*B*a*b*d - A*b^2*d + C*b^2*d)*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(B*a^2*b^2*c - 2*A*a*b^3*c + 2*C*a*b^3*c - B*b^4*c - C*a^4*d + A*a^2*b^2*d - 3*C*a^2*b^2*d + 2*B*a*b^3*d - A*b^4*d)*log(abs(b*tan(f*x + e) + a))/(a^4*b^2 + 2*a^2*b^4 + b^6) + 2*(B*a^2*b^2*c*tan(f*x + e) - 2*A*a*b^3*c*tan(f*x + e) + 2*C*a*b^3*c*tan(f*x + e) - B*b^4*c*tan(f*x + e) - C*a^4*d*tan(f*x + e) + A*a^2*b^2*d*tan(f*x + e) - 3*C*a^2*b^2*d*tan(f*x + e) + 2*B*a*b^3*d*tan(f*x + e) - A*b^4*d*tan(f*x + e) - C*a^4*c + 2*B*a^3*b*c - 3*A*a^2*b^2*c + C*a^2*b^2*c - A*b^4*c - B*a^4*d + 2*A*a^3*b*d - 2*C*a^3*b*d + B*a^2*b^2*d)/((a^4*b + 2*a^2*b^3 + b^5)*(b*tan(f*x + e) + a)))/f","B",0
56,1,1037,0,3.169101," ","integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{3} c - C a^{3} c + 3 \, B a^{2} b c - 3 \, A a b^{2} c + 3 \, C a b^{2} c - B b^{3} c - B a^{3} d + 3 \, A a^{2} b d - 3 \, C a^{2} b d + 3 \, B a b^{2} d - A b^{3} d + C b^{3} d\right)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(B a^{3} c - 3 \, A a^{2} b c + 3 \, C a^{2} b c - 3 \, B a b^{2} c + A b^{3} c - C b^{3} c + A a^{3} d - C a^{3} d + 3 \, B a^{2} b d - 3 \, A a b^{2} d + 3 \, C a b^{2} d - B b^{3} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(B a^{3} b c - 3 \, A a^{2} b^{2} c + 3 \, C a^{2} b^{2} c - 3 \, B a b^{3} c + A b^{4} c - C b^{4} c + A a^{3} b d - C a^{3} b d + 3 \, B a^{2} b^{2} d - 3 \, A a b^{3} d + 3 \, C a b^{3} d - B b^{4} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} + \frac{3 \, B a^{3} b^{4} c \tan\left(f x + e\right)^{2} - 9 \, A a^{2} b^{5} c \tan\left(f x + e\right)^{2} + 9 \, C a^{2} b^{5} c \tan\left(f x + e\right)^{2} - 9 \, B a b^{6} c \tan\left(f x + e\right)^{2} + 3 \, A b^{7} c \tan\left(f x + e\right)^{2} - 3 \, C b^{7} c \tan\left(f x + e\right)^{2} + 3 \, A a^{3} b^{4} d \tan\left(f x + e\right)^{2} - 3 \, C a^{3} b^{4} d \tan\left(f x + e\right)^{2} + 9 \, B a^{2} b^{5} d \tan\left(f x + e\right)^{2} - 9 \, A a b^{6} d \tan\left(f x + e\right)^{2} + 9 \, C a b^{6} d \tan\left(f x + e\right)^{2} - 3 \, B b^{7} d \tan\left(f x + e\right)^{2} + 8 \, B a^{4} b^{3} c \tan\left(f x + e\right) - 22 \, A a^{3} b^{4} c \tan\left(f x + e\right) + 22 \, C a^{3} b^{4} c \tan\left(f x + e\right) - 18 \, B a^{2} b^{5} c \tan\left(f x + e\right) + 2 \, A a b^{6} c \tan\left(f x + e\right) - 2 \, C a b^{6} c \tan\left(f x + e\right) - 2 \, B b^{7} c \tan\left(f x + e\right) - 2 \, C a^{6} b d \tan\left(f x + e\right) + 8 \, A a^{4} b^{3} d \tan\left(f x + e\right) - 14 \, C a^{4} b^{3} d \tan\left(f x + e\right) + 22 \, B a^{3} b^{4} d \tan\left(f x + e\right) - 18 \, A a^{2} b^{5} d \tan\left(f x + e\right) + 12 \, C a^{2} b^{5} d \tan\left(f x + e\right) - 2 \, B a b^{6} d \tan\left(f x + e\right) - 2 \, A b^{7} d \tan\left(f x + e\right) - C a^{6} b c + 6 \, B a^{5} b^{2} c - 14 \, A a^{4} b^{3} c + 11 \, C a^{4} b^{3} c - 7 \, B a^{3} b^{4} c - 3 \, A a^{2} b^{5} c - B a b^{6} c - A b^{7} c - C a^{7} d - B a^{6} b d + 6 \, A a^{5} b^{2} d - 9 \, C a^{5} b^{2} d + 11 \, B a^{4} b^{3} d - 7 \, A a^{3} b^{4} d + 4 \, C a^{3} b^{4} d - A a b^{6} d}{{\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*a^3*c - C*a^3*c + 3*B*a^2*b*c - 3*A*a*b^2*c + 3*C*a*b^2*c - B*b^3*c - B*a^3*d + 3*A*a^2*b*d - 3*C*a^2*b*d + 3*B*a*b^2*d - A*b^3*d + C*b^3*d)*(f*x + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (B*a^3*c - 3*A*a^2*b*c + 3*C*a^2*b*c - 3*B*a*b^2*c + A*b^3*c - C*b^3*c + A*a^3*d - C*a^3*d + 3*B*a^2*b*d - 3*A*a*b^2*d + 3*C*a*b^2*d - B*b^3*d)*log(tan(f*x + e)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(B*a^3*b*c - 3*A*a^2*b^2*c + 3*C*a^2*b^2*c - 3*B*a*b^3*c + A*b^4*c - C*b^4*c + A*a^3*b*d - C*a^3*b*d + 3*B*a^2*b^2*d - 3*A*a*b^3*d + 3*C*a*b^3*d - B*b^4*d)*log(abs(b*tan(f*x + e) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) + (3*B*a^3*b^4*c*tan(f*x + e)^2 - 9*A*a^2*b^5*c*tan(f*x + e)^2 + 9*C*a^2*b^5*c*tan(f*x + e)^2 - 9*B*a*b^6*c*tan(f*x + e)^2 + 3*A*b^7*c*tan(f*x + e)^2 - 3*C*b^7*c*tan(f*x + e)^2 + 3*A*a^3*b^4*d*tan(f*x + e)^2 - 3*C*a^3*b^4*d*tan(f*x + e)^2 + 9*B*a^2*b^5*d*tan(f*x + e)^2 - 9*A*a*b^6*d*tan(f*x + e)^2 + 9*C*a*b^6*d*tan(f*x + e)^2 - 3*B*b^7*d*tan(f*x + e)^2 + 8*B*a^4*b^3*c*tan(f*x + e) - 22*A*a^3*b^4*c*tan(f*x + e) + 22*C*a^3*b^4*c*tan(f*x + e) - 18*B*a^2*b^5*c*tan(f*x + e) + 2*A*a*b^6*c*tan(f*x + e) - 2*C*a*b^6*c*tan(f*x + e) - 2*B*b^7*c*tan(f*x + e) - 2*C*a^6*b*d*tan(f*x + e) + 8*A*a^4*b^3*d*tan(f*x + e) - 14*C*a^4*b^3*d*tan(f*x + e) + 22*B*a^3*b^4*d*tan(f*x + e) - 18*A*a^2*b^5*d*tan(f*x + e) + 12*C*a^2*b^5*d*tan(f*x + e) - 2*B*a*b^6*d*tan(f*x + e) - 2*A*b^7*d*tan(f*x + e) - C*a^6*b*c + 6*B*a^5*b^2*c - 14*A*a^4*b^3*c + 11*C*a^4*b^3*c - 7*B*a^3*b^4*c - 3*A*a^2*b^5*c - B*a*b^6*c - A*b^7*c - C*a^7*d - B*a^6*b*d + 6*A*a^5*b^2*d - 9*C*a^5*b^2*d + 11*B*a^4*b^3*d - 7*A*a^3*b^4*d + 4*C*a^3*b^4*d - A*a*b^6*d)/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*(b*tan(f*x + e) + a)^2))/f","B",0
57,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,1,6502,0,33.119014," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\frac{12 \, A a c^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, C a c^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, B b c^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 24 \, B a c d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 24 \, A b c d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 24 \, C b c d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, A a d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, C a d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, B b d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 6 \, B a c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 6 \, A b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, C b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, A a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, C a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, B b c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, B a d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, A b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 6 \, C b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 48 \, A a c^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, C a c^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, B b c^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 96 \, B a c d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 96 \, A b c d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 96 \, C b c d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, A a d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 48 \, C a d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 48 \, B b d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, C b c^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, C a c d \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, B b c d \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, B a d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, A b d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 9 \, C b d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 24 \, B a c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, A b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, C b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, A a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 48 \, C a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 48 \, B b c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, B a d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, A b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, C b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, C a c^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 12 \, B b c^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 24 \, B a c d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 24 \, A b c d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 24 \, C b c d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 12 \, A a d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 12 \, C a d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 12 \, B b d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 12 \, C a c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 12 \, B b c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 24 \, B a c d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 24 \, A b c d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 24 \, C b c d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 12 \, A a d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 12 \, C a d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 12 \, B b d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 72 \, A a c^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, C a c^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, B b c^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 144 \, B a c d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 144 \, A b c d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 144 \, C b c d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, A a d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, C a d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, B b d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 6 \, C b c^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 12 \, C a c d \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 12 \, B b c d \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 6 \, B a d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 6 \, A b d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 6 \, C b d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 12 \, C b c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, C a c d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, B b c d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, B a d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, A b d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, C b d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, C b c^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 12 \, C a c d \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 12 \, B b c d \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 6 \, B a d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 6 \, A b d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 6 \, C b d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 8 \, C b c d \tan\left(f x\right)^{4} \tan\left(e\right) - 4 \, C a d^{2} \tan\left(f x\right)^{4} \tan\left(e\right) - 4 \, B b d^{2} \tan\left(f x\right)^{4} \tan\left(e\right) - 36 \, B a c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 36 \, A b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, C b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, A a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, C a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, B b c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, B a d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, A b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 36 \, C b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, C a c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 36 \, B b c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 72 \, B a c d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 72 \, A b c d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 96 \, C b c d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 36 \, A a d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 48 \, C a d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 48 \, B b d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 36 \, C a c^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 36 \, B b c^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 72 \, B a c d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 72 \, A b c d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 96 \, C b c d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 36 \, A a d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 48 \, C a d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 48 \, B b d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 8 \, C b c d \tan\left(f x\right) \tan\left(e\right)^{4} - 4 \, C a d^{2} \tan\left(f x\right) \tan\left(e\right)^{4} - 4 \, B b d^{2} \tan\left(f x\right) \tan\left(e\right)^{4} + 3 \, C b d^{2} \tan\left(f x\right)^{4} - 48 \, A a c^{2} f x \tan\left(f x\right) \tan\left(e\right) + 48 \, C a c^{2} f x \tan\left(f x\right) \tan\left(e\right) + 48 \, B b c^{2} f x \tan\left(f x\right) \tan\left(e\right) + 96 \, B a c d f x \tan\left(f x\right) \tan\left(e\right) + 96 \, A b c d f x \tan\left(f x\right) \tan\left(e\right) - 96 \, C b c d f x \tan\left(f x\right) \tan\left(e\right) + 48 \, A a d^{2} f x \tan\left(f x\right) \tan\left(e\right) - 48 \, C a d^{2} f x \tan\left(f x\right) \tan\left(e\right) - 48 \, B b d^{2} f x \tan\left(f x\right) \tan\left(e\right) - 12 \, C b c^{2} \tan\left(f x\right)^{3} \tan\left(e\right) - 24 \, C a c d \tan\left(f x\right)^{3} \tan\left(e\right) - 24 \, B b c d \tan\left(f x\right)^{3} \tan\left(e\right) - 12 \, B a d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) - 12 \, A b d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) + 24 \, C b d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) + 12 \, C b c^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 24 \, C a c d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 24 \, B b c d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 12 \, B a d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 12 \, A b d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 12 \, C b d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 12 \, C b c^{2} \tan\left(f x\right) \tan\left(e\right)^{3} - 24 \, C a c d \tan\left(f x\right) \tan\left(e\right)^{3} - 24 \, B b c d \tan\left(f x\right) \tan\left(e\right)^{3} - 12 \, B a d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} - 12 \, A b d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} + 24 \, C b d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} + 3 \, C b d^{2} \tan\left(e\right)^{4} + 8 \, C b c d \tan\left(f x\right)^{3} + 4 \, C a d^{2} \tan\left(f x\right)^{3} + 4 \, B b d^{2} \tan\left(f x\right)^{3} + 24 \, B a c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 24 \, A b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 24 \, C b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 48 \, A a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 48 \, C a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 48 \, B b c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 24 \, B a d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 24 \, A b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 24 \, C b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 36 \, C a c^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 36 \, B b c^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 72 \, B a c d \tan\left(f x\right)^{2} \tan\left(e\right) - 72 \, A b c d \tan\left(f x\right)^{2} \tan\left(e\right) + 96 \, C b c d \tan\left(f x\right)^{2} \tan\left(e\right) - 36 \, A a d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 48 \, C a d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 48 \, B b d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 36 \, C a c^{2} \tan\left(f x\right) \tan\left(e\right)^{2} - 36 \, B b c^{2} \tan\left(f x\right) \tan\left(e\right)^{2} - 72 \, B a c d \tan\left(f x\right) \tan\left(e\right)^{2} - 72 \, A b c d \tan\left(f x\right) \tan\left(e\right)^{2} + 96 \, C b c d \tan\left(f x\right) \tan\left(e\right)^{2} - 36 \, A a d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 48 \, C a d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 48 \, B b d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 8 \, C b c d \tan\left(e\right)^{3} + 4 \, C a d^{2} \tan\left(e\right)^{3} + 4 \, B b d^{2} \tan\left(e\right)^{3} + 12 \, A a c^{2} f x - 12 \, C a c^{2} f x - 12 \, B b c^{2} f x - 24 \, B a c d f x - 24 \, A b c d f x + 24 \, C b c d f x - 12 \, A a d^{2} f x + 12 \, C a d^{2} f x + 12 \, B b d^{2} f x + 6 \, C b c^{2} \tan\left(f x\right)^{2} + 12 \, C a c d \tan\left(f x\right)^{2} + 12 \, B b c d \tan\left(f x\right)^{2} + 6 \, B a d^{2} \tan\left(f x\right)^{2} + 6 \, A b d^{2} \tan\left(f x\right)^{2} - 6 \, C b d^{2} \tan\left(f x\right)^{2} - 12 \, C b c^{2} \tan\left(f x\right) \tan\left(e\right) - 24 \, C a c d \tan\left(f x\right) \tan\left(e\right) - 24 \, B b c d \tan\left(f x\right) \tan\left(e\right) - 12 \, B a d^{2} \tan\left(f x\right) \tan\left(e\right) - 12 \, A b d^{2} \tan\left(f x\right) \tan\left(e\right) + 24 \, C b d^{2} \tan\left(f x\right) \tan\left(e\right) + 6 \, C b c^{2} \tan\left(e\right)^{2} + 12 \, C a c d \tan\left(e\right)^{2} + 12 \, B b c d \tan\left(e\right)^{2} + 6 \, B a d^{2} \tan\left(e\right)^{2} + 6 \, A b d^{2} \tan\left(e\right)^{2} - 6 \, C b d^{2} \tan\left(e\right)^{2} - 6 \, B a c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 6 \, A b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 6 \, C b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 12 \, A a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 12 \, C a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 12 \, B b c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 6 \, B a d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 6 \, A b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 6 \, C b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 12 \, C a c^{2} \tan\left(f x\right) + 12 \, B b c^{2} \tan\left(f x\right) + 24 \, B a c d \tan\left(f x\right) + 24 \, A b c d \tan\left(f x\right) - 24 \, C b c d \tan\left(f x\right) + 12 \, A a d^{2} \tan\left(f x\right) - 12 \, C a d^{2} \tan\left(f x\right) - 12 \, B b d^{2} \tan\left(f x\right) + 12 \, C a c^{2} \tan\left(e\right) + 12 \, B b c^{2} \tan\left(e\right) + 24 \, B a c d \tan\left(e\right) + 24 \, A b c d \tan\left(e\right) - 24 \, C b c d \tan\left(e\right) + 12 \, A a d^{2} \tan\left(e\right) - 12 \, C a d^{2} \tan\left(e\right) - 12 \, B b d^{2} \tan\left(e\right) + 6 \, C b c^{2} + 12 \, C a c d + 12 \, B b c d + 6 \, B a d^{2} + 6 \, A b d^{2} - 9 \, C b d^{2}}{12 \, {\left(f \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 4 \, f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 4 \, f \tan\left(f x\right) \tan\left(e\right) + f\right)}}"," ",0,"1/12*(12*A*a*c^2*f*x*tan(f*x)^4*tan(e)^4 - 12*C*a*c^2*f*x*tan(f*x)^4*tan(e)^4 - 12*B*b*c^2*f*x*tan(f*x)^4*tan(e)^4 - 24*B*a*c*d*f*x*tan(f*x)^4*tan(e)^4 - 24*A*b*c*d*f*x*tan(f*x)^4*tan(e)^4 + 24*C*b*c*d*f*x*tan(f*x)^4*tan(e)^4 - 12*A*a*d^2*f*x*tan(f*x)^4*tan(e)^4 + 12*C*a*d^2*f*x*tan(f*x)^4*tan(e)^4 + 12*B*b*d^2*f*x*tan(f*x)^4*tan(e)^4 - 6*B*a*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 6*A*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 6*C*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 12*A*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 12*C*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 12*B*b*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 6*B*a*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 6*A*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 6*C*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 48*A*a*c^2*f*x*tan(f*x)^3*tan(e)^3 + 48*C*a*c^2*f*x*tan(f*x)^3*tan(e)^3 + 48*B*b*c^2*f*x*tan(f*x)^3*tan(e)^3 + 96*B*a*c*d*f*x*tan(f*x)^3*tan(e)^3 + 96*A*b*c*d*f*x*tan(f*x)^3*tan(e)^3 - 96*C*b*c*d*f*x*tan(f*x)^3*tan(e)^3 + 48*A*a*d^2*f*x*tan(f*x)^3*tan(e)^3 - 48*C*a*d^2*f*x*tan(f*x)^3*tan(e)^3 - 48*B*b*d^2*f*x*tan(f*x)^3*tan(e)^3 + 6*C*b*c^2*tan(f*x)^4*tan(e)^4 + 12*C*a*c*d*tan(f*x)^4*tan(e)^4 + 12*B*b*c*d*tan(f*x)^4*tan(e)^4 + 6*B*a*d^2*tan(f*x)^4*tan(e)^4 + 6*A*b*d^2*tan(f*x)^4*tan(e)^4 - 9*C*b*d^2*tan(f*x)^4*tan(e)^4 + 24*B*a*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 24*A*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 24*C*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 48*A*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 48*C*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 48*B*b*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 24*B*a*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 24*A*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 24*C*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 12*C*a*c^2*tan(f*x)^4*tan(e)^3 - 12*B*b*c^2*tan(f*x)^4*tan(e)^3 - 24*B*a*c*d*tan(f*x)^4*tan(e)^3 - 24*A*b*c*d*tan(f*x)^4*tan(e)^3 + 24*C*b*c*d*tan(f*x)^4*tan(e)^3 - 12*A*a*d^2*tan(f*x)^4*tan(e)^3 + 12*C*a*d^2*tan(f*x)^4*tan(e)^3 + 12*B*b*d^2*tan(f*x)^4*tan(e)^3 - 12*C*a*c^2*tan(f*x)^3*tan(e)^4 - 12*B*b*c^2*tan(f*x)^3*tan(e)^4 - 24*B*a*c*d*tan(f*x)^3*tan(e)^4 - 24*A*b*c*d*tan(f*x)^3*tan(e)^4 + 24*C*b*c*d*tan(f*x)^3*tan(e)^4 - 12*A*a*d^2*tan(f*x)^3*tan(e)^4 + 12*C*a*d^2*tan(f*x)^3*tan(e)^4 + 12*B*b*d^2*tan(f*x)^3*tan(e)^4 + 72*A*a*c^2*f*x*tan(f*x)^2*tan(e)^2 - 72*C*a*c^2*f*x*tan(f*x)^2*tan(e)^2 - 72*B*b*c^2*f*x*tan(f*x)^2*tan(e)^2 - 144*B*a*c*d*f*x*tan(f*x)^2*tan(e)^2 - 144*A*b*c*d*f*x*tan(f*x)^2*tan(e)^2 + 144*C*b*c*d*f*x*tan(f*x)^2*tan(e)^2 - 72*A*a*d^2*f*x*tan(f*x)^2*tan(e)^2 + 72*C*a*d^2*f*x*tan(f*x)^2*tan(e)^2 + 72*B*b*d^2*f*x*tan(f*x)^2*tan(e)^2 + 6*C*b*c^2*tan(f*x)^4*tan(e)^2 + 12*C*a*c*d*tan(f*x)^4*tan(e)^2 + 12*B*b*c*d*tan(f*x)^4*tan(e)^2 + 6*B*a*d^2*tan(f*x)^4*tan(e)^2 + 6*A*b*d^2*tan(f*x)^4*tan(e)^2 - 6*C*b*d^2*tan(f*x)^4*tan(e)^2 - 12*C*b*c^2*tan(f*x)^3*tan(e)^3 - 24*C*a*c*d*tan(f*x)^3*tan(e)^3 - 24*B*b*c*d*tan(f*x)^3*tan(e)^3 - 12*B*a*d^2*tan(f*x)^3*tan(e)^3 - 12*A*b*d^2*tan(f*x)^3*tan(e)^3 + 24*C*b*d^2*tan(f*x)^3*tan(e)^3 + 6*C*b*c^2*tan(f*x)^2*tan(e)^4 + 12*C*a*c*d*tan(f*x)^2*tan(e)^4 + 12*B*b*c*d*tan(f*x)^2*tan(e)^4 + 6*B*a*d^2*tan(f*x)^2*tan(e)^4 + 6*A*b*d^2*tan(f*x)^2*tan(e)^4 - 6*C*b*d^2*tan(f*x)^2*tan(e)^4 - 8*C*b*c*d*tan(f*x)^4*tan(e) - 4*C*a*d^2*tan(f*x)^4*tan(e) - 4*B*b*d^2*tan(f*x)^4*tan(e) - 36*B*a*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 36*A*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*C*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 72*A*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 72*C*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 72*B*b*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*B*a*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*A*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 36*C*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*C*a*c^2*tan(f*x)^3*tan(e)^2 + 36*B*b*c^2*tan(f*x)^3*tan(e)^2 + 72*B*a*c*d*tan(f*x)^3*tan(e)^2 + 72*A*b*c*d*tan(f*x)^3*tan(e)^2 - 96*C*b*c*d*tan(f*x)^3*tan(e)^2 + 36*A*a*d^2*tan(f*x)^3*tan(e)^2 - 48*C*a*d^2*tan(f*x)^3*tan(e)^2 - 48*B*b*d^2*tan(f*x)^3*tan(e)^2 + 36*C*a*c^2*tan(f*x)^2*tan(e)^3 + 36*B*b*c^2*tan(f*x)^2*tan(e)^3 + 72*B*a*c*d*tan(f*x)^2*tan(e)^3 + 72*A*b*c*d*tan(f*x)^2*tan(e)^3 - 96*C*b*c*d*tan(f*x)^2*tan(e)^3 + 36*A*a*d^2*tan(f*x)^2*tan(e)^3 - 48*C*a*d^2*tan(f*x)^2*tan(e)^3 - 48*B*b*d^2*tan(f*x)^2*tan(e)^3 - 8*C*b*c*d*tan(f*x)*tan(e)^4 - 4*C*a*d^2*tan(f*x)*tan(e)^4 - 4*B*b*d^2*tan(f*x)*tan(e)^4 + 3*C*b*d^2*tan(f*x)^4 - 48*A*a*c^2*f*x*tan(f*x)*tan(e) + 48*C*a*c^2*f*x*tan(f*x)*tan(e) + 48*B*b*c^2*f*x*tan(f*x)*tan(e) + 96*B*a*c*d*f*x*tan(f*x)*tan(e) + 96*A*b*c*d*f*x*tan(f*x)*tan(e) - 96*C*b*c*d*f*x*tan(f*x)*tan(e) + 48*A*a*d^2*f*x*tan(f*x)*tan(e) - 48*C*a*d^2*f*x*tan(f*x)*tan(e) - 48*B*b*d^2*f*x*tan(f*x)*tan(e) - 12*C*b*c^2*tan(f*x)^3*tan(e) - 24*C*a*c*d*tan(f*x)^3*tan(e) - 24*B*b*c*d*tan(f*x)^3*tan(e) - 12*B*a*d^2*tan(f*x)^3*tan(e) - 12*A*b*d^2*tan(f*x)^3*tan(e) + 24*C*b*d^2*tan(f*x)^3*tan(e) + 12*C*b*c^2*tan(f*x)^2*tan(e)^2 + 24*C*a*c*d*tan(f*x)^2*tan(e)^2 + 24*B*b*c*d*tan(f*x)^2*tan(e)^2 + 12*B*a*d^2*tan(f*x)^2*tan(e)^2 + 12*A*b*d^2*tan(f*x)^2*tan(e)^2 - 12*C*b*d^2*tan(f*x)^2*tan(e)^2 - 12*C*b*c^2*tan(f*x)*tan(e)^3 - 24*C*a*c*d*tan(f*x)*tan(e)^3 - 24*B*b*c*d*tan(f*x)*tan(e)^3 - 12*B*a*d^2*tan(f*x)*tan(e)^3 - 12*A*b*d^2*tan(f*x)*tan(e)^3 + 24*C*b*d^2*tan(f*x)*tan(e)^3 + 3*C*b*d^2*tan(e)^4 + 8*C*b*c*d*tan(f*x)^3 + 4*C*a*d^2*tan(f*x)^3 + 4*B*b*d^2*tan(f*x)^3 + 24*B*a*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 24*A*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 24*C*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 48*A*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 48*C*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 48*B*b*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 24*B*a*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 24*A*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 24*C*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 36*C*a*c^2*tan(f*x)^2*tan(e) - 36*B*b*c^2*tan(f*x)^2*tan(e) - 72*B*a*c*d*tan(f*x)^2*tan(e) - 72*A*b*c*d*tan(f*x)^2*tan(e) + 96*C*b*c*d*tan(f*x)^2*tan(e) - 36*A*a*d^2*tan(f*x)^2*tan(e) + 48*C*a*d^2*tan(f*x)^2*tan(e) + 48*B*b*d^2*tan(f*x)^2*tan(e) - 36*C*a*c^2*tan(f*x)*tan(e)^2 - 36*B*b*c^2*tan(f*x)*tan(e)^2 - 72*B*a*c*d*tan(f*x)*tan(e)^2 - 72*A*b*c*d*tan(f*x)*tan(e)^2 + 96*C*b*c*d*tan(f*x)*tan(e)^2 - 36*A*a*d^2*tan(f*x)*tan(e)^2 + 48*C*a*d^2*tan(f*x)*tan(e)^2 + 48*B*b*d^2*tan(f*x)*tan(e)^2 + 8*C*b*c*d*tan(e)^3 + 4*C*a*d^2*tan(e)^3 + 4*B*b*d^2*tan(e)^3 + 12*A*a*c^2*f*x - 12*C*a*c^2*f*x - 12*B*b*c^2*f*x - 24*B*a*c*d*f*x - 24*A*b*c*d*f*x + 24*C*b*c*d*f*x - 12*A*a*d^2*f*x + 12*C*a*d^2*f*x + 12*B*b*d^2*f*x + 6*C*b*c^2*tan(f*x)^2 + 12*C*a*c*d*tan(f*x)^2 + 12*B*b*c*d*tan(f*x)^2 + 6*B*a*d^2*tan(f*x)^2 + 6*A*b*d^2*tan(f*x)^2 - 6*C*b*d^2*tan(f*x)^2 - 12*C*b*c^2*tan(f*x)*tan(e) - 24*C*a*c*d*tan(f*x)*tan(e) - 24*B*b*c*d*tan(f*x)*tan(e) - 12*B*a*d^2*tan(f*x)*tan(e) - 12*A*b*d^2*tan(f*x)*tan(e) + 24*C*b*d^2*tan(f*x)*tan(e) + 6*C*b*c^2*tan(e)^2 + 12*C*a*c*d*tan(e)^2 + 12*B*b*c*d*tan(e)^2 + 6*B*a*d^2*tan(e)^2 + 6*A*b*d^2*tan(e)^2 - 6*C*b*d^2*tan(e)^2 - 6*B*a*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 6*A*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 6*C*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 12*A*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 12*C*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 12*B*b*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 6*B*a*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 6*A*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 6*C*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 12*C*a*c^2*tan(f*x) + 12*B*b*c^2*tan(f*x) + 24*B*a*c*d*tan(f*x) + 24*A*b*c*d*tan(f*x) - 24*C*b*c*d*tan(f*x) + 12*A*a*d^2*tan(f*x) - 12*C*a*d^2*tan(f*x) - 12*B*b*d^2*tan(f*x) + 12*C*a*c^2*tan(e) + 12*B*b*c^2*tan(e) + 24*B*a*c*d*tan(e) + 24*A*b*c*d*tan(e) - 24*C*b*c*d*tan(e) + 12*A*a*d^2*tan(e) - 12*C*a*d^2*tan(e) - 12*B*b*d^2*tan(e) + 6*C*b*c^2 + 12*C*a*c*d + 12*B*b*c*d + 6*B*a*d^2 + 6*A*b*d^2 - 9*C*b*d^2)/(f*tan(f*x)^4*tan(e)^4 - 4*f*tan(f*x)^3*tan(e)^3 + 6*f*tan(f*x)^2*tan(e)^2 - 4*f*tan(f*x)*tan(e) + f)","B",0
60,1,2128,0,5.569912," ","integrate((c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\frac{6 \, A c^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 6 \, C c^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, B c d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 6 \, A d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, C d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, B c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 6 \, A c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, C c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, B d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 18 \, A c^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 18 \, C c^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, B c d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 18 \, A d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 18 \, C d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 6 \, C c d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, B d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 9 \, B c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 18 \, A c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 18 \, C c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 9 \, B d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 6 \, C c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 12 \, B c d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 6 \, A d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 6 \, C d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 6 \, C c^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 12 \, B c d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 6 \, A d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 6 \, C d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 18 \, A c^{2} f x \tan\left(f x\right) \tan\left(e\right) - 18 \, C c^{2} f x \tan\left(f x\right) \tan\left(e\right) - 36 \, B c d f x \tan\left(f x\right) \tan\left(e\right) - 18 \, A d^{2} f x \tan\left(f x\right) \tan\left(e\right) + 18 \, C d^{2} f x \tan\left(f x\right) \tan\left(e\right) + 6 \, C c d \tan\left(f x\right)^{3} \tan\left(e\right) + 3 \, B d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) - 6 \, C c d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 3 \, B d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 6 \, C c d \tan\left(f x\right) \tan\left(e\right)^{3} + 3 \, B d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} - 2 \, C d^{2} \tan\left(f x\right)^{3} - 9 \, B c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 18 \, A c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 18 \, C c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 9 \, B d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 12 \, C c^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 24 \, B c d \tan\left(f x\right)^{2} \tan\left(e\right) + 12 \, A d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 18 \, C d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 12 \, C c^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 24 \, B c d \tan\left(f x\right) \tan\left(e\right)^{2} + 12 \, A d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} - 18 \, C d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} - 2 \, C d^{2} \tan\left(e\right)^{3} - 6 \, A c^{2} f x + 6 \, C c^{2} f x + 12 \, B c d f x + 6 \, A d^{2} f x - 6 \, C d^{2} f x - 6 \, C c d \tan\left(f x\right)^{2} - 3 \, B d^{2} \tan\left(f x\right)^{2} + 6 \, C c d \tan\left(f x\right) \tan\left(e\right) + 3 \, B d^{2} \tan\left(f x\right) \tan\left(e\right) - 6 \, C c d \tan\left(e\right)^{2} - 3 \, B d^{2} \tan\left(e\right)^{2} + 3 \, B c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 6 \, A c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 6 \, C c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 3 \, B d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 6 \, C c^{2} \tan\left(f x\right) - 12 \, B c d \tan\left(f x\right) - 6 \, A d^{2} \tan\left(f x\right) + 6 \, C d^{2} \tan\left(f x\right) - 6 \, C c^{2} \tan\left(e\right) - 12 \, B c d \tan\left(e\right) - 6 \, A d^{2} \tan\left(e\right) + 6 \, C d^{2} \tan\left(e\right) - 6 \, C c d - 3 \, B d^{2}}{6 \, {\left(f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, f \tan\left(f x\right) \tan\left(e\right) - f\right)}}"," ",0,"1/6*(6*A*c^2*f*x*tan(f*x)^3*tan(e)^3 - 6*C*c^2*f*x*tan(f*x)^3*tan(e)^3 - 12*B*c*d*f*x*tan(f*x)^3*tan(e)^3 - 6*A*d^2*f*x*tan(f*x)^3*tan(e)^3 + 6*C*d^2*f*x*tan(f*x)^3*tan(e)^3 - 3*B*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 6*A*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 6*C*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 3*B*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 18*A*c^2*f*x*tan(f*x)^2*tan(e)^2 + 18*C*c^2*f*x*tan(f*x)^2*tan(e)^2 + 36*B*c*d*f*x*tan(f*x)^2*tan(e)^2 + 18*A*d^2*f*x*tan(f*x)^2*tan(e)^2 - 18*C*d^2*f*x*tan(f*x)^2*tan(e)^2 + 6*C*c*d*tan(f*x)^3*tan(e)^3 + 3*B*d^2*tan(f*x)^3*tan(e)^3 + 9*B*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 18*A*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 18*C*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 9*B*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 6*C*c^2*tan(f*x)^3*tan(e)^2 - 12*B*c*d*tan(f*x)^3*tan(e)^2 - 6*A*d^2*tan(f*x)^3*tan(e)^2 + 6*C*d^2*tan(f*x)^3*tan(e)^2 - 6*C*c^2*tan(f*x)^2*tan(e)^3 - 12*B*c*d*tan(f*x)^2*tan(e)^3 - 6*A*d^2*tan(f*x)^2*tan(e)^3 + 6*C*d^2*tan(f*x)^2*tan(e)^3 + 18*A*c^2*f*x*tan(f*x)*tan(e) - 18*C*c^2*f*x*tan(f*x)*tan(e) - 36*B*c*d*f*x*tan(f*x)*tan(e) - 18*A*d^2*f*x*tan(f*x)*tan(e) + 18*C*d^2*f*x*tan(f*x)*tan(e) + 6*C*c*d*tan(f*x)^3*tan(e) + 3*B*d^2*tan(f*x)^3*tan(e) - 6*C*c*d*tan(f*x)^2*tan(e)^2 - 3*B*d^2*tan(f*x)^2*tan(e)^2 + 6*C*c*d*tan(f*x)*tan(e)^3 + 3*B*d^2*tan(f*x)*tan(e)^3 - 2*C*d^2*tan(f*x)^3 - 9*B*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 18*A*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 18*C*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 9*B*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 12*C*c^2*tan(f*x)^2*tan(e) + 24*B*c*d*tan(f*x)^2*tan(e) + 12*A*d^2*tan(f*x)^2*tan(e) - 18*C*d^2*tan(f*x)^2*tan(e) + 12*C*c^2*tan(f*x)*tan(e)^2 + 24*B*c*d*tan(f*x)*tan(e)^2 + 12*A*d^2*tan(f*x)*tan(e)^2 - 18*C*d^2*tan(f*x)*tan(e)^2 - 2*C*d^2*tan(e)^3 - 6*A*c^2*f*x + 6*C*c^2*f*x + 12*B*c*d*f*x + 6*A*d^2*f*x - 6*C*d^2*f*x - 6*C*c*d*tan(f*x)^2 - 3*B*d^2*tan(f*x)^2 + 6*C*c*d*tan(f*x)*tan(e) + 3*B*d^2*tan(f*x)*tan(e) - 6*C*c*d*tan(e)^2 - 3*B*d^2*tan(e)^2 + 3*B*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 6*A*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 6*C*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 3*B*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 6*C*c^2*tan(f*x) - 12*B*c*d*tan(f*x) - 6*A*d^2*tan(f*x) + 6*C*d^2*tan(f*x) - 6*C*c^2*tan(e) - 12*B*c*d*tan(e) - 6*A*d^2*tan(e) + 6*C*d^2*tan(e) - 6*C*c*d - 3*B*d^2)/(f*tan(f*x)^3*tan(e)^3 - 3*f*tan(f*x)^2*tan(e)^2 + 3*f*tan(f*x)*tan(e) - f)","B",0
61,1,338,0,3.656560," ","integrate((c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a c^{2} - C a c^{2} + B b c^{2} - 2 \, B a c d + 2 \, A b c d - 2 \, C b c d - A a d^{2} + C a d^{2} - B b d^{2}\right)} {\left(f x + e\right)}}{a^{2} + b^{2}} + \frac{{\left(B a c^{2} - A b c^{2} + C b c^{2} + 2 \, A a c d - 2 \, C a c d + 2 \, B b c d - B a d^{2} + A b d^{2} - C b d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(C a^{2} b^{2} c^{2} - B a b^{3} c^{2} + A b^{4} c^{2} - 2 \, C a^{3} b c d + 2 \, B a^{2} b^{2} c d - 2 \, A a b^{3} c d + C a^{4} d^{2} - B a^{3} b d^{2} + A a^{2} b^{2} d^{2}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b^{3} + b^{5}} + \frac{C b d^{2} \tan\left(f x + e\right)^{2} + 4 \, C b c d \tan\left(f x + e\right) - 2 \, C a d^{2} \tan\left(f x + e\right) + 2 \, B b d^{2} \tan\left(f x + e\right)}{b^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*a*c^2 - C*a*c^2 + B*b*c^2 - 2*B*a*c*d + 2*A*b*c*d - 2*C*b*c*d - A*a*d^2 + C*a*d^2 - B*b*d^2)*(f*x + e)/(a^2 + b^2) + (B*a*c^2 - A*b*c^2 + C*b*c^2 + 2*A*a*c*d - 2*C*a*c*d + 2*B*b*c*d - B*a*d^2 + A*b*d^2 - C*b*d^2)*log(tan(f*x + e)^2 + 1)/(a^2 + b^2) + 2*(C*a^2*b^2*c^2 - B*a*b^3*c^2 + A*b^4*c^2 - 2*C*a^3*b*c*d + 2*B*a^2*b^2*c*d - 2*A*a*b^3*c*d + C*a^4*d^2 - B*a^3*b*d^2 + A*a^2*b^2*d^2)*log(abs(b*tan(f*x + e) + a))/(a^2*b^3 + b^5) + (C*b*d^2*tan(f*x + e)^2 + 4*C*b*c*d*tan(f*x + e) - 2*C*a*d^2*tan(f*x + e) + 2*B*b*d^2*tan(f*x + e))/b^2)/f","A",0
62,1,912,0,3.064784," ","integrate((c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, C d^{2} \tan\left(f x + e\right)}{b^{2}} + \frac{2 \, {\left(A a^{2} c^{2} - C a^{2} c^{2} + 2 \, B a b c^{2} - A b^{2} c^{2} + C b^{2} c^{2} - 2 \, B a^{2} c d + 4 \, A a b c d - 4 \, C a b c d + 2 \, B b^{2} c d - A a^{2} d^{2} + C a^{2} d^{2} - 2 \, B a b d^{2} + A b^{2} d^{2} - C b^{2} d^{2}\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(B a^{2} c^{2} - 2 \, A a b c^{2} + 2 \, C a b c^{2} - B b^{2} c^{2} + 2 \, A a^{2} c d - 2 \, C a^{2} c d + 4 \, B a b c d - 2 \, A b^{2} c d + 2 \, C b^{2} c d - B a^{2} d^{2} + 2 \, A a b d^{2} - 2 \, C a b d^{2} + B b^{2} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(B a^{2} b^{3} c^{2} - 2 \, A a b^{4} c^{2} + 2 \, C a b^{4} c^{2} - B b^{5} c^{2} - 2 \, C a^{4} b c d + 2 \, A a^{2} b^{3} c d - 6 \, C a^{2} b^{3} c d + 4 \, B a b^{4} c d - 2 \, A b^{5} c d + 2 \, C a^{5} d^{2} - B a^{4} b d^{2} + 4 \, C a^{3} b^{2} d^{2} - 3 \, B a^{2} b^{3} d^{2} + 2 \, A a b^{4} d^{2}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}} + \frac{2 \, {\left(B a^{2} b^{4} c^{2} \tan\left(f x + e\right) - 2 \, A a b^{5} c^{2} \tan\left(f x + e\right) + 2 \, C a b^{5} c^{2} \tan\left(f x + e\right) - B b^{6} c^{2} \tan\left(f x + e\right) - 2 \, C a^{4} b^{2} c d \tan\left(f x + e\right) + 2 \, A a^{2} b^{4} c d \tan\left(f x + e\right) - 6 \, C a^{2} b^{4} c d \tan\left(f x + e\right) + 4 \, B a b^{5} c d \tan\left(f x + e\right) - 2 \, A b^{6} c d \tan\left(f x + e\right) + 2 \, C a^{5} b d^{2} \tan\left(f x + e\right) - B a^{4} b^{2} d^{2} \tan\left(f x + e\right) + 4 \, C a^{3} b^{3} d^{2} \tan\left(f x + e\right) - 3 \, B a^{2} b^{4} d^{2} \tan\left(f x + e\right) + 2 \, A a b^{5} d^{2} \tan\left(f x + e\right) - C a^{4} b^{2} c^{2} + 2 \, B a^{3} b^{3} c^{2} - 3 \, A a^{2} b^{4} c^{2} + C a^{2} b^{4} c^{2} - A b^{6} c^{2} - 2 \, B a^{4} b^{2} c d + 4 \, A a^{3} b^{3} c d - 4 \, C a^{3} b^{3} c d + 2 \, B a^{2} b^{4} c d + C a^{6} d^{2} - A a^{4} b^{2} d^{2} + 3 \, C a^{4} b^{2} d^{2} - 2 \, B a^{3} b^{3} d^{2} + A a^{2} b^{4} d^{2}\right)}}{{\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} {\left(b \tan\left(f x + e\right) + a\right)}}}{2 \, f}"," ",0,"1/2*(2*C*d^2*tan(f*x + e)/b^2 + 2*(A*a^2*c^2 - C*a^2*c^2 + 2*B*a*b*c^2 - A*b^2*c^2 + C*b^2*c^2 - 2*B*a^2*c*d + 4*A*a*b*c*d - 4*C*a*b*c*d + 2*B*b^2*c*d - A*a^2*d^2 + C*a^2*d^2 - 2*B*a*b*d^2 + A*b^2*d^2 - C*b^2*d^2)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) + (B*a^2*c^2 - 2*A*a*b*c^2 + 2*C*a*b*c^2 - B*b^2*c^2 + 2*A*a^2*c*d - 2*C*a^2*c*d + 4*B*a*b*c*d - 2*A*b^2*c*d + 2*C*b^2*c*d - B*a^2*d^2 + 2*A*a*b*d^2 - 2*C*a*b*d^2 + B*b^2*d^2)*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(B*a^2*b^3*c^2 - 2*A*a*b^4*c^2 + 2*C*a*b^4*c^2 - B*b^5*c^2 - 2*C*a^4*b*c*d + 2*A*a^2*b^3*c*d - 6*C*a^2*b^3*c*d + 4*B*a*b^4*c*d - 2*A*b^5*c*d + 2*C*a^5*d^2 - B*a^4*b*d^2 + 4*C*a^3*b^2*d^2 - 3*B*a^2*b^3*d^2 + 2*A*a*b^4*d^2)*log(abs(b*tan(f*x + e) + a))/(a^4*b^3 + 2*a^2*b^5 + b^7) + 2*(B*a^2*b^4*c^2*tan(f*x + e) - 2*A*a*b^5*c^2*tan(f*x + e) + 2*C*a*b^5*c^2*tan(f*x + e) - B*b^6*c^2*tan(f*x + e) - 2*C*a^4*b^2*c*d*tan(f*x + e) + 2*A*a^2*b^4*c*d*tan(f*x + e) - 6*C*a^2*b^4*c*d*tan(f*x + e) + 4*B*a*b^5*c*d*tan(f*x + e) - 2*A*b^6*c*d*tan(f*x + e) + 2*C*a^5*b*d^2*tan(f*x + e) - B*a^4*b^2*d^2*tan(f*x + e) + 4*C*a^3*b^3*d^2*tan(f*x + e) - 3*B*a^2*b^4*d^2*tan(f*x + e) + 2*A*a*b^5*d^2*tan(f*x + e) - C*a^4*b^2*c^2 + 2*B*a^3*b^3*c^2 - 3*A*a^2*b^4*c^2 + C*a^2*b^4*c^2 - A*b^6*c^2 - 2*B*a^4*b^2*c*d + 4*A*a^3*b^3*c*d - 4*C*a^3*b^3*c*d + 2*B*a^2*b^4*c*d + C*a^6*d^2 - A*a^4*b^2*d^2 + 3*C*a^4*b^2*d^2 - 2*B*a^3*b^3*d^2 + A*a^2*b^4*d^2)/((a^4*b^3 + 2*a^2*b^5 + b^7)*(b*tan(f*x + e) + a)))/f","B",0
63,1,1714,0,2.698092," ","integrate((c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{3} c^{2} - C a^{3} c^{2} + 3 \, B a^{2} b c^{2} - 3 \, A a b^{2} c^{2} + 3 \, C a b^{2} c^{2} - B b^{3} c^{2} - 2 \, B a^{3} c d + 6 \, A a^{2} b c d - 6 \, C a^{2} b c d + 6 \, B a b^{2} c d - 2 \, A b^{3} c d + 2 \, C b^{3} c d - A a^{3} d^{2} + C a^{3} d^{2} - 3 \, B a^{2} b d^{2} + 3 \, A a b^{2} d^{2} - 3 \, C a b^{2} d^{2} + B b^{3} d^{2}\right)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(B a^{3} c^{2} - 3 \, A a^{2} b c^{2} + 3 \, C a^{2} b c^{2} - 3 \, B a b^{2} c^{2} + A b^{3} c^{2} - C b^{3} c^{2} + 2 \, A a^{3} c d - 2 \, C a^{3} c d + 6 \, B a^{2} b c d - 6 \, A a b^{2} c d + 6 \, C a b^{2} c d - 2 \, B b^{3} c d - B a^{3} d^{2} + 3 \, A a^{2} b d^{2} - 3 \, C a^{2} b d^{2} + 3 \, B a b^{2} d^{2} - A b^{3} d^{2} + C b^{3} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(B a^{3} b^{3} c^{2} - 3 \, A a^{2} b^{4} c^{2} + 3 \, C a^{2} b^{4} c^{2} - 3 \, B a b^{5} c^{2} + A b^{6} c^{2} - C b^{6} c^{2} + 2 \, A a^{3} b^{3} c d - 2 \, C a^{3} b^{3} c d + 6 \, B a^{2} b^{4} c d - 6 \, A a b^{5} c d + 6 \, C a b^{5} c d - 2 \, B b^{6} c d - C a^{6} d^{2} - 3 \, C a^{4} b^{2} d^{2} - B a^{3} b^{3} d^{2} + 3 \, A a^{2} b^{4} d^{2} - 6 \, C a^{2} b^{4} d^{2} + 3 \, B a b^{5} d^{2} - A b^{6} d^{2}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}} + \frac{3 \, B a^{3} b^{4} c^{2} \tan\left(f x + e\right)^{2} - 9 \, A a^{2} b^{5} c^{2} \tan\left(f x + e\right)^{2} + 9 \, C a^{2} b^{5} c^{2} \tan\left(f x + e\right)^{2} - 9 \, B a b^{6} c^{2} \tan\left(f x + e\right)^{2} + 3 \, A b^{7} c^{2} \tan\left(f x + e\right)^{2} - 3 \, C b^{7} c^{2} \tan\left(f x + e\right)^{2} + 6 \, A a^{3} b^{4} c d \tan\left(f x + e\right)^{2} - 6 \, C a^{3} b^{4} c d \tan\left(f x + e\right)^{2} + 18 \, B a^{2} b^{5} c d \tan\left(f x + e\right)^{2} - 18 \, A a b^{6} c d \tan\left(f x + e\right)^{2} + 18 \, C a b^{6} c d \tan\left(f x + e\right)^{2} - 6 \, B b^{7} c d \tan\left(f x + e\right)^{2} - 3 \, C a^{6} b d^{2} \tan\left(f x + e\right)^{2} - 9 \, C a^{4} b^{3} d^{2} \tan\left(f x + e\right)^{2} - 3 \, B a^{3} b^{4} d^{2} \tan\left(f x + e\right)^{2} + 9 \, A a^{2} b^{5} d^{2} \tan\left(f x + e\right)^{2} - 18 \, C a^{2} b^{5} d^{2} \tan\left(f x + e\right)^{2} + 9 \, B a b^{6} d^{2} \tan\left(f x + e\right)^{2} - 3 \, A b^{7} d^{2} \tan\left(f x + e\right)^{2} + 8 \, B a^{4} b^{3} c^{2} \tan\left(f x + e\right) - 22 \, A a^{3} b^{4} c^{2} \tan\left(f x + e\right) + 22 \, C a^{3} b^{4} c^{2} \tan\left(f x + e\right) - 18 \, B a^{2} b^{5} c^{2} \tan\left(f x + e\right) + 2 \, A a b^{6} c^{2} \tan\left(f x + e\right) - 2 \, C a b^{6} c^{2} \tan\left(f x + e\right) - 2 \, B b^{7} c^{2} \tan\left(f x + e\right) - 4 \, C a^{6} b c d \tan\left(f x + e\right) + 16 \, A a^{4} b^{3} c d \tan\left(f x + e\right) - 28 \, C a^{4} b^{3} c d \tan\left(f x + e\right) + 44 \, B a^{3} b^{4} c d \tan\left(f x + e\right) - 36 \, A a^{2} b^{5} c d \tan\left(f x + e\right) + 24 \, C a^{2} b^{5} c d \tan\left(f x + e\right) - 4 \, B a b^{6} c d \tan\left(f x + e\right) - 4 \, A b^{7} c d \tan\left(f x + e\right) - 2 \, C a^{7} d^{2} \tan\left(f x + e\right) - 2 \, B a^{6} b d^{2} \tan\left(f x + e\right) - 6 \, C a^{5} b^{2} d^{2} \tan\left(f x + e\right) - 14 \, B a^{4} b^{3} d^{2} \tan\left(f x + e\right) + 22 \, A a^{3} b^{4} d^{2} \tan\left(f x + e\right) - 28 \, C a^{3} b^{4} d^{2} \tan\left(f x + e\right) + 12 \, B a^{2} b^{5} d^{2} \tan\left(f x + e\right) - 2 \, A a b^{6} d^{2} \tan\left(f x + e\right) - C a^{6} b c^{2} + 6 \, B a^{5} b^{2} c^{2} - 14 \, A a^{4} b^{3} c^{2} + 11 \, C a^{4} b^{3} c^{2} - 7 \, B a^{3} b^{4} c^{2} - 3 \, A a^{2} b^{5} c^{2} - B a b^{6} c^{2} - A b^{7} c^{2} - 2 \, C a^{7} c d - 2 \, B a^{6} b c d + 12 \, A a^{5} b^{2} c d - 18 \, C a^{5} b^{2} c d + 22 \, B a^{4} b^{3} c d - 14 \, A a^{3} b^{4} c d + 8 \, C a^{3} b^{4} c d - 2 \, A a b^{6} c d - B a^{7} d^{2} - A a^{6} b d^{2} + C a^{6} b d^{2} - 9 \, B a^{5} b^{2} d^{2} + 11 \, A a^{4} b^{3} d^{2} - 11 \, C a^{4} b^{3} d^{2} + 4 \, B a^{3} b^{4} d^{2}}{{\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*a^3*c^2 - C*a^3*c^2 + 3*B*a^2*b*c^2 - 3*A*a*b^2*c^2 + 3*C*a*b^2*c^2 - B*b^3*c^2 - 2*B*a^3*c*d + 6*A*a^2*b*c*d - 6*C*a^2*b*c*d + 6*B*a*b^2*c*d - 2*A*b^3*c*d + 2*C*b^3*c*d - A*a^3*d^2 + C*a^3*d^2 - 3*B*a^2*b*d^2 + 3*A*a*b^2*d^2 - 3*C*a*b^2*d^2 + B*b^3*d^2)*(f*x + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (B*a^3*c^2 - 3*A*a^2*b*c^2 + 3*C*a^2*b*c^2 - 3*B*a*b^2*c^2 + A*b^3*c^2 - C*b^3*c^2 + 2*A*a^3*c*d - 2*C*a^3*c*d + 6*B*a^2*b*c*d - 6*A*a*b^2*c*d + 6*C*a*b^2*c*d - 2*B*b^3*c*d - B*a^3*d^2 + 3*A*a^2*b*d^2 - 3*C*a^2*b*d^2 + 3*B*a*b^2*d^2 - A*b^3*d^2 + C*b^3*d^2)*log(tan(f*x + e)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(B*a^3*b^3*c^2 - 3*A*a^2*b^4*c^2 + 3*C*a^2*b^4*c^2 - 3*B*a*b^5*c^2 + A*b^6*c^2 - C*b^6*c^2 + 2*A*a^3*b^3*c*d - 2*C*a^3*b^3*c*d + 6*B*a^2*b^4*c*d - 6*A*a*b^5*c*d + 6*C*a*b^5*c*d - 2*B*b^6*c*d - C*a^6*d^2 - 3*C*a^4*b^2*d^2 - B*a^3*b^3*d^2 + 3*A*a^2*b^4*d^2 - 6*C*a^2*b^4*d^2 + 3*B*a*b^5*d^2 - A*b^6*d^2)*log(abs(b*tan(f*x + e) + a))/(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9) + (3*B*a^3*b^4*c^2*tan(f*x + e)^2 - 9*A*a^2*b^5*c^2*tan(f*x + e)^2 + 9*C*a^2*b^5*c^2*tan(f*x + e)^2 - 9*B*a*b^6*c^2*tan(f*x + e)^2 + 3*A*b^7*c^2*tan(f*x + e)^2 - 3*C*b^7*c^2*tan(f*x + e)^2 + 6*A*a^3*b^4*c*d*tan(f*x + e)^2 - 6*C*a^3*b^4*c*d*tan(f*x + e)^2 + 18*B*a^2*b^5*c*d*tan(f*x + e)^2 - 18*A*a*b^6*c*d*tan(f*x + e)^2 + 18*C*a*b^6*c*d*tan(f*x + e)^2 - 6*B*b^7*c*d*tan(f*x + e)^2 - 3*C*a^6*b*d^2*tan(f*x + e)^2 - 9*C*a^4*b^3*d^2*tan(f*x + e)^2 - 3*B*a^3*b^4*d^2*tan(f*x + e)^2 + 9*A*a^2*b^5*d^2*tan(f*x + e)^2 - 18*C*a^2*b^5*d^2*tan(f*x + e)^2 + 9*B*a*b^6*d^2*tan(f*x + e)^2 - 3*A*b^7*d^2*tan(f*x + e)^2 + 8*B*a^4*b^3*c^2*tan(f*x + e) - 22*A*a^3*b^4*c^2*tan(f*x + e) + 22*C*a^3*b^4*c^2*tan(f*x + e) - 18*B*a^2*b^5*c^2*tan(f*x + e) + 2*A*a*b^6*c^2*tan(f*x + e) - 2*C*a*b^6*c^2*tan(f*x + e) - 2*B*b^7*c^2*tan(f*x + e) - 4*C*a^6*b*c*d*tan(f*x + e) + 16*A*a^4*b^3*c*d*tan(f*x + e) - 28*C*a^4*b^3*c*d*tan(f*x + e) + 44*B*a^3*b^4*c*d*tan(f*x + e) - 36*A*a^2*b^5*c*d*tan(f*x + e) + 24*C*a^2*b^5*c*d*tan(f*x + e) - 4*B*a*b^6*c*d*tan(f*x + e) - 4*A*b^7*c*d*tan(f*x + e) - 2*C*a^7*d^2*tan(f*x + e) - 2*B*a^6*b*d^2*tan(f*x + e) - 6*C*a^5*b^2*d^2*tan(f*x + e) - 14*B*a^4*b^3*d^2*tan(f*x + e) + 22*A*a^3*b^4*d^2*tan(f*x + e) - 28*C*a^3*b^4*d^2*tan(f*x + e) + 12*B*a^2*b^5*d^2*tan(f*x + e) - 2*A*a*b^6*d^2*tan(f*x + e) - C*a^6*b*c^2 + 6*B*a^5*b^2*c^2 - 14*A*a^4*b^3*c^2 + 11*C*a^4*b^3*c^2 - 7*B*a^3*b^4*c^2 - 3*A*a^2*b^5*c^2 - B*a*b^6*c^2 - A*b^7*c^2 - 2*C*a^7*c*d - 2*B*a^6*b*c*d + 12*A*a^5*b^2*c*d - 18*C*a^5*b^2*c*d + 22*B*a^4*b^3*c*d - 14*A*a^3*b^4*c*d + 8*C*a^3*b^4*c*d - 2*A*a*b^6*c*d - B*a^7*d^2 - A*a^6*b*d^2 + C*a^6*b*d^2 - 9*B*a^5*b^2*d^2 + 11*A*a^4*b^3*d^2 - 11*C*a^4*b^3*d^2 + 4*B*a^3*b^4*d^2)/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*(b*tan(f*x + e) + a)^2))/f","B",0
64,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,1,4300,0,24.806863," ","integrate((c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\frac{12 \, A c^{3} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, C c^{3} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 36 \, B c^{2} d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 36 \, A c d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 36 \, C c d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 12 \, B d^{3} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 6 \, B c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 18 \, A c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 18 \, C c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 18 \, B c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, A d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 6 \, C d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 48 \, A c^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, C c^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 144 \, B c^{2} d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 144 \, A c d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 144 \, C c d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 48 \, B d^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 18 \, C c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 18 \, B c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, A d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 9 \, C d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 24 \, B c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 72 \, A c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 72 \, C c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 72 \, B c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, A d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, C d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, C c^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 36 \, B c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 36 \, A c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 36 \, C c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 12 \, B d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 12 \, C c^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 36 \, B c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 36 \, A c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 36 \, C c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 12 \, B d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 72 \, A c^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, C c^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 216 \, B c^{2} d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 216 \, A c d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 216 \, C c d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, B d^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 18 \, C c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 18 \, B c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 6 \, A d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 6 \, C d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 36 \, C c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 36 \, B c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, A d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, C d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 18 \, C c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 18 \, B c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 6 \, A d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 6 \, C d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 12 \, C c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right) - 4 \, B d^{3} \tan\left(f x\right)^{4} \tan\left(e\right) - 36 \, B c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 108 \, A c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 108 \, C c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 108 \, B c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, A d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 36 \, C d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, C c^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 108 \, B c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 108 \, A c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 144 \, C c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 48 \, B d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 36 \, C c^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 108 \, B c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 108 \, A c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 144 \, C c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 48 \, B d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 12 \, C c d^{2} \tan\left(f x\right) \tan\left(e\right)^{4} - 4 \, B d^{3} \tan\left(f x\right) \tan\left(e\right)^{4} + 3 \, C d^{3} \tan\left(f x\right)^{4} - 48 \, A c^{3} f x \tan\left(f x\right) \tan\left(e\right) + 48 \, C c^{3} f x \tan\left(f x\right) \tan\left(e\right) + 144 \, B c^{2} d f x \tan\left(f x\right) \tan\left(e\right) + 144 \, A c d^{2} f x \tan\left(f x\right) \tan\left(e\right) - 144 \, C c d^{2} f x \tan\left(f x\right) \tan\left(e\right) - 48 \, B d^{3} f x \tan\left(f x\right) \tan\left(e\right) - 36 \, C c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right) - 36 \, B c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) - 12 \, A d^{3} \tan\left(f x\right)^{3} \tan\left(e\right) + 24 \, C d^{3} \tan\left(f x\right)^{3} \tan\left(e\right) + 36 \, C c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, B c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 12 \, A d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 12 \, C d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 36 \, C c^{2} d \tan\left(f x\right) \tan\left(e\right)^{3} - 36 \, B c d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} - 12 \, A d^{3} \tan\left(f x\right) \tan\left(e\right)^{3} + 24 \, C d^{3} \tan\left(f x\right) \tan\left(e\right)^{3} + 3 \, C d^{3} \tan\left(e\right)^{4} + 12 \, C c d^{2} \tan\left(f x\right)^{3} + 4 \, B d^{3} \tan\left(f x\right)^{3} + 24 \, B c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 72 \, A c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 72 \, C c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 72 \, B c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 24 \, A d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 24 \, C d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 36 \, C c^{3} \tan\left(f x\right)^{2} \tan\left(e\right) - 108 \, B c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right) - 108 \, A c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 144 \, C c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 48 \, B d^{3} \tan\left(f x\right)^{2} \tan\left(e\right) - 36 \, C c^{3} \tan\left(f x\right) \tan\left(e\right)^{2} - 108 \, B c^{2} d \tan\left(f x\right) \tan\left(e\right)^{2} - 108 \, A c d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 144 \, C c d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 48 \, B d^{3} \tan\left(f x\right) \tan\left(e\right)^{2} + 12 \, C c d^{2} \tan\left(e\right)^{3} + 4 \, B d^{3} \tan\left(e\right)^{3} + 12 \, A c^{3} f x - 12 \, C c^{3} f x - 36 \, B c^{2} d f x - 36 \, A c d^{2} f x + 36 \, C c d^{2} f x + 12 \, B d^{3} f x + 18 \, C c^{2} d \tan\left(f x\right)^{2} + 18 \, B c d^{2} \tan\left(f x\right)^{2} + 6 \, A d^{3} \tan\left(f x\right)^{2} - 6 \, C d^{3} \tan\left(f x\right)^{2} - 36 \, C c^{2} d \tan\left(f x\right) \tan\left(e\right) - 36 \, B c d^{2} \tan\left(f x\right) \tan\left(e\right) - 12 \, A d^{3} \tan\left(f x\right) \tan\left(e\right) + 24 \, C d^{3} \tan\left(f x\right) \tan\left(e\right) + 18 \, C c^{2} d \tan\left(e\right)^{2} + 18 \, B c d^{2} \tan\left(e\right)^{2} + 6 \, A d^{3} \tan\left(e\right)^{2} - 6 \, C d^{3} \tan\left(e\right)^{2} - 6 \, B c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 18 \, A c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 18 \, C c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 18 \, B c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 6 \, A d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 6 \, C d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 12 \, C c^{3} \tan\left(f x\right) + 36 \, B c^{2} d \tan\left(f x\right) + 36 \, A c d^{2} \tan\left(f x\right) - 36 \, C c d^{2} \tan\left(f x\right) - 12 \, B d^{3} \tan\left(f x\right) + 12 \, C c^{3} \tan\left(e\right) + 36 \, B c^{2} d \tan\left(e\right) + 36 \, A c d^{2} \tan\left(e\right) - 36 \, C c d^{2} \tan\left(e\right) - 12 \, B d^{3} \tan\left(e\right) + 18 \, C c^{2} d + 18 \, B c d^{2} + 6 \, A d^{3} - 9 \, C d^{3}}{12 \, {\left(f \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 4 \, f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 4 \, f \tan\left(f x\right) \tan\left(e\right) + f\right)}}"," ",0,"1/12*(12*A*c^3*f*x*tan(f*x)^4*tan(e)^4 - 12*C*c^3*f*x*tan(f*x)^4*tan(e)^4 - 36*B*c^2*d*f*x*tan(f*x)^4*tan(e)^4 - 36*A*c*d^2*f*x*tan(f*x)^4*tan(e)^4 + 36*C*c*d^2*f*x*tan(f*x)^4*tan(e)^4 + 12*B*d^3*f*x*tan(f*x)^4*tan(e)^4 - 6*B*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 18*A*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 18*C*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 18*B*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 6*A*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 6*C*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 48*A*c^3*f*x*tan(f*x)^3*tan(e)^3 + 48*C*c^3*f*x*tan(f*x)^3*tan(e)^3 + 144*B*c^2*d*f*x*tan(f*x)^3*tan(e)^3 + 144*A*c*d^2*f*x*tan(f*x)^3*tan(e)^3 - 144*C*c*d^2*f*x*tan(f*x)^3*tan(e)^3 - 48*B*d^3*f*x*tan(f*x)^3*tan(e)^3 + 18*C*c^2*d*tan(f*x)^4*tan(e)^4 + 18*B*c*d^2*tan(f*x)^4*tan(e)^4 + 6*A*d^3*tan(f*x)^4*tan(e)^4 - 9*C*d^3*tan(f*x)^4*tan(e)^4 + 24*B*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 72*A*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 72*C*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 72*B*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 24*A*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 24*C*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 12*C*c^3*tan(f*x)^4*tan(e)^3 - 36*B*c^2*d*tan(f*x)^4*tan(e)^3 - 36*A*c*d^2*tan(f*x)^4*tan(e)^3 + 36*C*c*d^2*tan(f*x)^4*tan(e)^3 + 12*B*d^3*tan(f*x)^4*tan(e)^3 - 12*C*c^3*tan(f*x)^3*tan(e)^4 - 36*B*c^2*d*tan(f*x)^3*tan(e)^4 - 36*A*c*d^2*tan(f*x)^3*tan(e)^4 + 36*C*c*d^2*tan(f*x)^3*tan(e)^4 + 12*B*d^3*tan(f*x)^3*tan(e)^4 + 72*A*c^3*f*x*tan(f*x)^2*tan(e)^2 - 72*C*c^3*f*x*tan(f*x)^2*tan(e)^2 - 216*B*c^2*d*f*x*tan(f*x)^2*tan(e)^2 - 216*A*c*d^2*f*x*tan(f*x)^2*tan(e)^2 + 216*C*c*d^2*f*x*tan(f*x)^2*tan(e)^2 + 72*B*d^3*f*x*tan(f*x)^2*tan(e)^2 + 18*C*c^2*d*tan(f*x)^4*tan(e)^2 + 18*B*c*d^2*tan(f*x)^4*tan(e)^2 + 6*A*d^3*tan(f*x)^4*tan(e)^2 - 6*C*d^3*tan(f*x)^4*tan(e)^2 - 36*C*c^2*d*tan(f*x)^3*tan(e)^3 - 36*B*c*d^2*tan(f*x)^3*tan(e)^3 - 12*A*d^3*tan(f*x)^3*tan(e)^3 + 24*C*d^3*tan(f*x)^3*tan(e)^3 + 18*C*c^2*d*tan(f*x)^2*tan(e)^4 + 18*B*c*d^2*tan(f*x)^2*tan(e)^4 + 6*A*d^3*tan(f*x)^2*tan(e)^4 - 6*C*d^3*tan(f*x)^2*tan(e)^4 - 12*C*c*d^2*tan(f*x)^4*tan(e) - 4*B*d^3*tan(f*x)^4*tan(e) - 36*B*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 108*A*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 108*C*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 108*B*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*A*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 36*C*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*C*c^3*tan(f*x)^3*tan(e)^2 + 108*B*c^2*d*tan(f*x)^3*tan(e)^2 + 108*A*c*d^2*tan(f*x)^3*tan(e)^2 - 144*C*c*d^2*tan(f*x)^3*tan(e)^2 - 48*B*d^3*tan(f*x)^3*tan(e)^2 + 36*C*c^3*tan(f*x)^2*tan(e)^3 + 108*B*c^2*d*tan(f*x)^2*tan(e)^3 + 108*A*c*d^2*tan(f*x)^2*tan(e)^3 - 144*C*c*d^2*tan(f*x)^2*tan(e)^3 - 48*B*d^3*tan(f*x)^2*tan(e)^3 - 12*C*c*d^2*tan(f*x)*tan(e)^4 - 4*B*d^3*tan(f*x)*tan(e)^4 + 3*C*d^3*tan(f*x)^4 - 48*A*c^3*f*x*tan(f*x)*tan(e) + 48*C*c^3*f*x*tan(f*x)*tan(e) + 144*B*c^2*d*f*x*tan(f*x)*tan(e) + 144*A*c*d^2*f*x*tan(f*x)*tan(e) - 144*C*c*d^2*f*x*tan(f*x)*tan(e) - 48*B*d^3*f*x*tan(f*x)*tan(e) - 36*C*c^2*d*tan(f*x)^3*tan(e) - 36*B*c*d^2*tan(f*x)^3*tan(e) - 12*A*d^3*tan(f*x)^3*tan(e) + 24*C*d^3*tan(f*x)^3*tan(e) + 36*C*c^2*d*tan(f*x)^2*tan(e)^2 + 36*B*c*d^2*tan(f*x)^2*tan(e)^2 + 12*A*d^3*tan(f*x)^2*tan(e)^2 - 12*C*d^3*tan(f*x)^2*tan(e)^2 - 36*C*c^2*d*tan(f*x)*tan(e)^3 - 36*B*c*d^2*tan(f*x)*tan(e)^3 - 12*A*d^3*tan(f*x)*tan(e)^3 + 24*C*d^3*tan(f*x)*tan(e)^3 + 3*C*d^3*tan(e)^4 + 12*C*c*d^2*tan(f*x)^3 + 4*B*d^3*tan(f*x)^3 + 24*B*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 72*A*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 72*C*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 72*B*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 24*A*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 24*C*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 36*C*c^3*tan(f*x)^2*tan(e) - 108*B*c^2*d*tan(f*x)^2*tan(e) - 108*A*c*d^2*tan(f*x)^2*tan(e) + 144*C*c*d^2*tan(f*x)^2*tan(e) + 48*B*d^3*tan(f*x)^2*tan(e) - 36*C*c^3*tan(f*x)*tan(e)^2 - 108*B*c^2*d*tan(f*x)*tan(e)^2 - 108*A*c*d^2*tan(f*x)*tan(e)^2 + 144*C*c*d^2*tan(f*x)*tan(e)^2 + 48*B*d^3*tan(f*x)*tan(e)^2 + 12*C*c*d^2*tan(e)^3 + 4*B*d^3*tan(e)^3 + 12*A*c^3*f*x - 12*C*c^3*f*x - 36*B*c^2*d*f*x - 36*A*c*d^2*f*x + 36*C*c*d^2*f*x + 12*B*d^3*f*x + 18*C*c^2*d*tan(f*x)^2 + 18*B*c*d^2*tan(f*x)^2 + 6*A*d^3*tan(f*x)^2 - 6*C*d^3*tan(f*x)^2 - 36*C*c^2*d*tan(f*x)*tan(e) - 36*B*c*d^2*tan(f*x)*tan(e) - 12*A*d^3*tan(f*x)*tan(e) + 24*C*d^3*tan(f*x)*tan(e) + 18*C*c^2*d*tan(e)^2 + 18*B*c*d^2*tan(e)^2 + 6*A*d^3*tan(e)^2 - 6*C*d^3*tan(e)^2 - 6*B*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 18*A*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 18*C*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 18*B*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 6*A*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 6*C*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 12*C*c^3*tan(f*x) + 36*B*c^2*d*tan(f*x) + 36*A*c*d^2*tan(f*x) - 36*C*c*d^2*tan(f*x) - 12*B*d^3*tan(f*x) + 12*C*c^3*tan(e) + 36*B*c^2*d*tan(e) + 36*A*c*d^2*tan(e) - 36*C*c*d^2*tan(e) - 12*B*d^3*tan(e) + 18*C*c^2*d + 18*B*c*d^2 + 6*A*d^3 - 9*C*d^3)/(f*tan(f*x)^4*tan(e)^4 - 4*f*tan(f*x)^3*tan(e)^3 + 6*f*tan(f*x)^2*tan(e)^2 - 4*f*tan(f*x)*tan(e) + f)","B",0
67,1,573,0,3.407102," ","integrate((c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{6 \, {\left(A a c^{3} - C a c^{3} + B b c^{3} - 3 \, B a c^{2} d + 3 \, A b c^{2} d - 3 \, C b c^{2} d - 3 \, A a c d^{2} + 3 \, C a c d^{2} - 3 \, B b c d^{2} + B a d^{3} - A b d^{3} + C b d^{3}\right)} {\left(f x + e\right)}}{a^{2} + b^{2}} + \frac{3 \, {\left(B a c^{3} - A b c^{3} + C b c^{3} + 3 \, A a c^{2} d - 3 \, C a c^{2} d + 3 \, B b c^{2} d - 3 \, B a c d^{2} + 3 \, A b c d^{2} - 3 \, C b c d^{2} - A a d^{3} + C a d^{3} - B b d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{6 \, {\left(C a^{2} b^{3} c^{3} - B a b^{4} c^{3} + A b^{5} c^{3} - 3 \, C a^{3} b^{2} c^{2} d + 3 \, B a^{2} b^{3} c^{2} d - 3 \, A a b^{4} c^{2} d + 3 \, C a^{4} b c d^{2} - 3 \, B a^{3} b^{2} c d^{2} + 3 \, A a^{2} b^{3} c d^{2} - C a^{5} d^{3} + B a^{4} b d^{3} - A a^{3} b^{2} d^{3}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b^{4} + b^{6}} + \frac{2 \, C b^{2} d^{3} \tan\left(f x + e\right)^{3} + 9 \, C b^{2} c d^{2} \tan\left(f x + e\right)^{2} - 3 \, C a b d^{3} \tan\left(f x + e\right)^{2} + 3 \, B b^{2} d^{3} \tan\left(f x + e\right)^{2} + 18 \, C b^{2} c^{2} d \tan\left(f x + e\right) - 18 \, C a b c d^{2} \tan\left(f x + e\right) + 18 \, B b^{2} c d^{2} \tan\left(f x + e\right) + 6 \, C a^{2} d^{3} \tan\left(f x + e\right) - 6 \, B a b d^{3} \tan\left(f x + e\right) + 6 \, A b^{2} d^{3} \tan\left(f x + e\right) - 6 \, C b^{2} d^{3} \tan\left(f x + e\right)}{b^{3}}}{6 \, f}"," ",0,"1/6*(6*(A*a*c^3 - C*a*c^3 + B*b*c^3 - 3*B*a*c^2*d + 3*A*b*c^2*d - 3*C*b*c^2*d - 3*A*a*c*d^2 + 3*C*a*c*d^2 - 3*B*b*c*d^2 + B*a*d^3 - A*b*d^3 + C*b*d^3)*(f*x + e)/(a^2 + b^2) + 3*(B*a*c^3 - A*b*c^3 + C*b*c^3 + 3*A*a*c^2*d - 3*C*a*c^2*d + 3*B*b*c^2*d - 3*B*a*c*d^2 + 3*A*b*c*d^2 - 3*C*b*c*d^2 - A*a*d^3 + C*a*d^3 - B*b*d^3)*log(tan(f*x + e)^2 + 1)/(a^2 + b^2) + 6*(C*a^2*b^3*c^3 - B*a*b^4*c^3 + A*b^5*c^3 - 3*C*a^3*b^2*c^2*d + 3*B*a^2*b^3*c^2*d - 3*A*a*b^4*c^2*d + 3*C*a^4*b*c*d^2 - 3*B*a^3*b^2*c*d^2 + 3*A*a^2*b^3*c*d^2 - C*a^5*d^3 + B*a^4*b*d^3 - A*a^3*b^2*d^3)*log(abs(b*tan(f*x + e) + a))/(a^2*b^4 + b^6) + (2*C*b^2*d^3*tan(f*x + e)^3 + 9*C*b^2*c*d^2*tan(f*x + e)^2 - 3*C*a*b*d^3*tan(f*x + e)^2 + 3*B*b^2*d^3*tan(f*x + e)^2 + 18*C*b^2*c^2*d*tan(f*x + e) - 18*C*a*b*c*d^2*tan(f*x + e) + 18*B*b^2*c*d^2*tan(f*x + e) + 6*C*a^2*d^3*tan(f*x + e) - 6*B*a*b*d^3*tan(f*x + e) + 6*A*b^2*d^3*tan(f*x + e) - 6*C*b^2*d^3*tan(f*x + e))/b^3)/f","A",0
68,1,1357,0,7.279213," ","integrate((c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{2} c^{3} - C a^{2} c^{3} + 2 \, B a b c^{3} - A b^{2} c^{3} + C b^{2} c^{3} - 3 \, B a^{2} c^{2} d + 6 \, A a b c^{2} d - 6 \, C a b c^{2} d + 3 \, B b^{2} c^{2} d - 3 \, A a^{2} c d^{2} + 3 \, C a^{2} c d^{2} - 6 \, B a b c d^{2} + 3 \, A b^{2} c d^{2} - 3 \, C b^{2} c d^{2} + B a^{2} d^{3} - 2 \, A a b d^{3} + 2 \, C a b d^{3} - B b^{2} d^{3}\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(B a^{2} c^{3} - 2 \, A a b c^{3} + 2 \, C a b c^{3} - B b^{2} c^{3} + 3 \, A a^{2} c^{2} d - 3 \, C a^{2} c^{2} d + 6 \, B a b c^{2} d - 3 \, A b^{2} c^{2} d + 3 \, C b^{2} c^{2} d - 3 \, B a^{2} c d^{2} + 6 \, A a b c d^{2} - 6 \, C a b c d^{2} + 3 \, B b^{2} c d^{2} - A a^{2} d^{3} + C a^{2} d^{3} - 2 \, B a b d^{3} + A b^{2} d^{3} - C b^{2} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(B a^{2} b^{4} c^{3} - 2 \, A a b^{5} c^{3} + 2 \, C a b^{5} c^{3} - B b^{6} c^{3} - 3 \, C a^{4} b^{2} c^{2} d + 3 \, A a^{2} b^{4} c^{2} d - 9 \, C a^{2} b^{4} c^{2} d + 6 \, B a b^{5} c^{2} d - 3 \, A b^{6} c^{2} d + 6 \, C a^{5} b c d^{2} - 3 \, B a^{4} b^{2} c d^{2} + 12 \, C a^{3} b^{3} c d^{2} - 9 \, B a^{2} b^{4} c d^{2} + 6 \, A a b^{5} c d^{2} - 3 \, C a^{6} d^{3} + 2 \, B a^{5} b d^{3} - A a^{4} b^{2} d^{3} - 5 \, C a^{4} b^{2} d^{3} + 4 \, B a^{3} b^{3} d^{3} - 3 \, A a^{2} b^{4} d^{3}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}} + \frac{2 \, {\left(B a^{2} b^{5} c^{3} \tan\left(f x + e\right) - 2 \, A a b^{6} c^{3} \tan\left(f x + e\right) + 2 \, C a b^{6} c^{3} \tan\left(f x + e\right) - B b^{7} c^{3} \tan\left(f x + e\right) - 3 \, C a^{4} b^{3} c^{2} d \tan\left(f x + e\right) + 3 \, A a^{2} b^{5} c^{2} d \tan\left(f x + e\right) - 9 \, C a^{2} b^{5} c^{2} d \tan\left(f x + e\right) + 6 \, B a b^{6} c^{2} d \tan\left(f x + e\right) - 3 \, A b^{7} c^{2} d \tan\left(f x + e\right) + 6 \, C a^{5} b^{2} c d^{2} \tan\left(f x + e\right) - 3 \, B a^{4} b^{3} c d^{2} \tan\left(f x + e\right) + 12 \, C a^{3} b^{4} c d^{2} \tan\left(f x + e\right) - 9 \, B a^{2} b^{5} c d^{2} \tan\left(f x + e\right) + 6 \, A a b^{6} c d^{2} \tan\left(f x + e\right) - 3 \, C a^{6} b d^{3} \tan\left(f x + e\right) + 2 \, B a^{5} b^{2} d^{3} \tan\left(f x + e\right) - A a^{4} b^{3} d^{3} \tan\left(f x + e\right) - 5 \, C a^{4} b^{3} d^{3} \tan\left(f x + e\right) + 4 \, B a^{3} b^{4} d^{3} \tan\left(f x + e\right) - 3 \, A a^{2} b^{5} d^{3} \tan\left(f x + e\right) - C a^{4} b^{3} c^{3} + 2 \, B a^{3} b^{4} c^{3} - 3 \, A a^{2} b^{5} c^{3} + C a^{2} b^{5} c^{3} - A b^{7} c^{3} - 3 \, B a^{4} b^{3} c^{2} d + 6 \, A a^{3} b^{4} c^{2} d - 6 \, C a^{3} b^{4} c^{2} d + 3 \, B a^{2} b^{5} c^{2} d + 3 \, C a^{6} b c d^{2} - 3 \, A a^{4} b^{3} c d^{2} + 9 \, C a^{4} b^{3} c d^{2} - 6 \, B a^{3} b^{4} c d^{2} + 3 \, A a^{2} b^{5} c d^{2} - 2 \, C a^{7} d^{3} + B a^{6} b d^{3} - 4 \, C a^{5} b^{2} d^{3} + 3 \, B a^{4} b^{3} d^{3} - 2 \, A a^{3} b^{4} d^{3}\right)}}{{\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(f x + e\right) + a\right)}} + \frac{C b^{2} d^{3} \tan\left(f x + e\right)^{2} + 6 \, C b^{2} c d^{2} \tan\left(f x + e\right) - 4 \, C a b d^{3} \tan\left(f x + e\right) + 2 \, B b^{2} d^{3} \tan\left(f x + e\right)}{b^{4}}}{2 \, f}"," ",0,"1/2*(2*(A*a^2*c^3 - C*a^2*c^3 + 2*B*a*b*c^3 - A*b^2*c^3 + C*b^2*c^3 - 3*B*a^2*c^2*d + 6*A*a*b*c^2*d - 6*C*a*b*c^2*d + 3*B*b^2*c^2*d - 3*A*a^2*c*d^2 + 3*C*a^2*c*d^2 - 6*B*a*b*c*d^2 + 3*A*b^2*c*d^2 - 3*C*b^2*c*d^2 + B*a^2*d^3 - 2*A*a*b*d^3 + 2*C*a*b*d^3 - B*b^2*d^3)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) + (B*a^2*c^3 - 2*A*a*b*c^3 + 2*C*a*b*c^3 - B*b^2*c^3 + 3*A*a^2*c^2*d - 3*C*a^2*c^2*d + 6*B*a*b*c^2*d - 3*A*b^2*c^2*d + 3*C*b^2*c^2*d - 3*B*a^2*c*d^2 + 6*A*a*b*c*d^2 - 6*C*a*b*c*d^2 + 3*B*b^2*c*d^2 - A*a^2*d^3 + C*a^2*d^3 - 2*B*a*b*d^3 + A*b^2*d^3 - C*b^2*d^3)*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(B*a^2*b^4*c^3 - 2*A*a*b^5*c^3 + 2*C*a*b^5*c^3 - B*b^6*c^3 - 3*C*a^4*b^2*c^2*d + 3*A*a^2*b^4*c^2*d - 9*C*a^2*b^4*c^2*d + 6*B*a*b^5*c^2*d - 3*A*b^6*c^2*d + 6*C*a^5*b*c*d^2 - 3*B*a^4*b^2*c*d^2 + 12*C*a^3*b^3*c*d^2 - 9*B*a^2*b^4*c*d^2 + 6*A*a*b^5*c*d^2 - 3*C*a^6*d^3 + 2*B*a^5*b*d^3 - A*a^4*b^2*d^3 - 5*C*a^4*b^2*d^3 + 4*B*a^3*b^3*d^3 - 3*A*a^2*b^4*d^3)*log(abs(b*tan(f*x + e) + a))/(a^4*b^4 + 2*a^2*b^6 + b^8) + 2*(B*a^2*b^5*c^3*tan(f*x + e) - 2*A*a*b^6*c^3*tan(f*x + e) + 2*C*a*b^6*c^3*tan(f*x + e) - B*b^7*c^3*tan(f*x + e) - 3*C*a^4*b^3*c^2*d*tan(f*x + e) + 3*A*a^2*b^5*c^2*d*tan(f*x + e) - 9*C*a^2*b^5*c^2*d*tan(f*x + e) + 6*B*a*b^6*c^2*d*tan(f*x + e) - 3*A*b^7*c^2*d*tan(f*x + e) + 6*C*a^5*b^2*c*d^2*tan(f*x + e) - 3*B*a^4*b^3*c*d^2*tan(f*x + e) + 12*C*a^3*b^4*c*d^2*tan(f*x + e) - 9*B*a^2*b^5*c*d^2*tan(f*x + e) + 6*A*a*b^6*c*d^2*tan(f*x + e) - 3*C*a^6*b*d^3*tan(f*x + e) + 2*B*a^5*b^2*d^3*tan(f*x + e) - A*a^4*b^3*d^3*tan(f*x + e) - 5*C*a^4*b^3*d^3*tan(f*x + e) + 4*B*a^3*b^4*d^3*tan(f*x + e) - 3*A*a^2*b^5*d^3*tan(f*x + e) - C*a^4*b^3*c^3 + 2*B*a^3*b^4*c^3 - 3*A*a^2*b^5*c^3 + C*a^2*b^5*c^3 - A*b^7*c^3 - 3*B*a^4*b^3*c^2*d + 6*A*a^3*b^4*c^2*d - 6*C*a^3*b^4*c^2*d + 3*B*a^2*b^5*c^2*d + 3*C*a^6*b*c*d^2 - 3*A*a^4*b^3*c*d^2 + 9*C*a^4*b^3*c*d^2 - 6*B*a^3*b^4*c*d^2 + 3*A*a^2*b^5*c*d^2 - 2*C*a^7*d^3 + B*a^6*b*d^3 - 4*C*a^5*b^2*d^3 + 3*B*a^4*b^3*d^3 - 2*A*a^3*b^4*d^3)/((a^4*b^4 + 2*a^2*b^6 + b^8)*(b*tan(f*x + e) + a)) + (C*b^2*d^3*tan(f*x + e)^2 + 6*C*b^2*c*d^2*tan(f*x + e) - 4*C*a*b*d^3*tan(f*x + e) + 2*B*b^2*d^3*tan(f*x + e))/b^4)/f","B",0
69,1,2505,0,7.349041," ","integrate((c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, C d^{3} \tan\left(f x + e\right)}{b^{3}} + \frac{2 \, {\left(A a^{3} c^{3} - C a^{3} c^{3} + 3 \, B a^{2} b c^{3} - 3 \, A a b^{2} c^{3} + 3 \, C a b^{2} c^{3} - B b^{3} c^{3} - 3 \, B a^{3} c^{2} d + 9 \, A a^{2} b c^{2} d - 9 \, C a^{2} b c^{2} d + 9 \, B a b^{2} c^{2} d - 3 \, A b^{3} c^{2} d + 3 \, C b^{3} c^{2} d - 3 \, A a^{3} c d^{2} + 3 \, C a^{3} c d^{2} - 9 \, B a^{2} b c d^{2} + 9 \, A a b^{2} c d^{2} - 9 \, C a b^{2} c d^{2} + 3 \, B b^{3} c d^{2} + B a^{3} d^{3} - 3 \, A a^{2} b d^{3} + 3 \, C a^{2} b d^{3} - 3 \, B a b^{2} d^{3} + A b^{3} d^{3} - C b^{3} d^{3}\right)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(B a^{3} c^{3} - 3 \, A a^{2} b c^{3} + 3 \, C a^{2} b c^{3} - 3 \, B a b^{2} c^{3} + A b^{3} c^{3} - C b^{3} c^{3} + 3 \, A a^{3} c^{2} d - 3 \, C a^{3} c^{2} d + 9 \, B a^{2} b c^{2} d - 9 \, A a b^{2} c^{2} d + 9 \, C a b^{2} c^{2} d - 3 \, B b^{3} c^{2} d - 3 \, B a^{3} c d^{2} + 9 \, A a^{2} b c d^{2} - 9 \, C a^{2} b c d^{2} + 9 \, B a b^{2} c d^{2} - 3 \, A b^{3} c d^{2} + 3 \, C b^{3} c d^{2} - A a^{3} d^{3} + C a^{3} d^{3} - 3 \, B a^{2} b d^{3} + 3 \, A a b^{2} d^{3} - 3 \, C a b^{2} d^{3} + B b^{3} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(B a^{3} b^{4} c^{3} - 3 \, A a^{2} b^{5} c^{3} + 3 \, C a^{2} b^{5} c^{3} - 3 \, B a b^{6} c^{3} + A b^{7} c^{3} - C b^{7} c^{3} + 3 \, A a^{3} b^{4} c^{2} d - 3 \, C a^{3} b^{4} c^{2} d + 9 \, B a^{2} b^{5} c^{2} d - 9 \, A a b^{6} c^{2} d + 9 \, C a b^{6} c^{2} d - 3 \, B b^{7} c^{2} d - 3 \, C a^{6} b c d^{2} - 9 \, C a^{4} b^{3} c d^{2} - 3 \, B a^{3} b^{4} c d^{2} + 9 \, A a^{2} b^{5} c d^{2} - 18 \, C a^{2} b^{5} c d^{2} + 9 \, B a b^{6} c d^{2} - 3 \, A b^{7} c d^{2} + 3 \, C a^{7} d^{3} - B a^{6} b d^{3} + 9 \, C a^{5} b^{2} d^{3} - 3 \, B a^{4} b^{3} d^{3} - A a^{3} b^{4} d^{3} + 10 \, C a^{3} b^{4} d^{3} - 6 \, B a^{2} b^{5} d^{3} + 3 \, A a b^{6} d^{3}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}} + \frac{3 \, B a^{3} b^{6} c^{3} \tan\left(f x + e\right)^{2} - 9 \, A a^{2} b^{7} c^{3} \tan\left(f x + e\right)^{2} + 9 \, C a^{2} b^{7} c^{3} \tan\left(f x + e\right)^{2} - 9 \, B a b^{8} c^{3} \tan\left(f x + e\right)^{2} + 3 \, A b^{9} c^{3} \tan\left(f x + e\right)^{2} - 3 \, C b^{9} c^{3} \tan\left(f x + e\right)^{2} + 9 \, A a^{3} b^{6} c^{2} d \tan\left(f x + e\right)^{2} - 9 \, C a^{3} b^{6} c^{2} d \tan\left(f x + e\right)^{2} + 27 \, B a^{2} b^{7} c^{2} d \tan\left(f x + e\right)^{2} - 27 \, A a b^{8} c^{2} d \tan\left(f x + e\right)^{2} + 27 \, C a b^{8} c^{2} d \tan\left(f x + e\right)^{2} - 9 \, B b^{9} c^{2} d \tan\left(f x + e\right)^{2} - 9 \, C a^{6} b^{3} c d^{2} \tan\left(f x + e\right)^{2} - 27 \, C a^{4} b^{5} c d^{2} \tan\left(f x + e\right)^{2} - 9 \, B a^{3} b^{6} c d^{2} \tan\left(f x + e\right)^{2} + 27 \, A a^{2} b^{7} c d^{2} \tan\left(f x + e\right)^{2} - 54 \, C a^{2} b^{7} c d^{2} \tan\left(f x + e\right)^{2} + 27 \, B a b^{8} c d^{2} \tan\left(f x + e\right)^{2} - 9 \, A b^{9} c d^{2} \tan\left(f x + e\right)^{2} + 9 \, C a^{7} b^{2} d^{3} \tan\left(f x + e\right)^{2} - 3 \, B a^{6} b^{3} d^{3} \tan\left(f x + e\right)^{2} + 27 \, C a^{5} b^{4} d^{3} \tan\left(f x + e\right)^{2} - 9 \, B a^{4} b^{5} d^{3} \tan\left(f x + e\right)^{2} - 3 \, A a^{3} b^{6} d^{3} \tan\left(f x + e\right)^{2} + 30 \, C a^{3} b^{6} d^{3} \tan\left(f x + e\right)^{2} - 18 \, B a^{2} b^{7} d^{3} \tan\left(f x + e\right)^{2} + 9 \, A a b^{8} d^{3} \tan\left(f x + e\right)^{2} + 8 \, B a^{4} b^{5} c^{3} \tan\left(f x + e\right) - 22 \, A a^{3} b^{6} c^{3} \tan\left(f x + e\right) + 22 \, C a^{3} b^{6} c^{3} \tan\left(f x + e\right) - 18 \, B a^{2} b^{7} c^{3} \tan\left(f x + e\right) + 2 \, A a b^{8} c^{3} \tan\left(f x + e\right) - 2 \, C a b^{8} c^{3} \tan\left(f x + e\right) - 2 \, B b^{9} c^{3} \tan\left(f x + e\right) - 6 \, C a^{6} b^{3} c^{2} d \tan\left(f x + e\right) + 24 \, A a^{4} b^{5} c^{2} d \tan\left(f x + e\right) - 42 \, C a^{4} b^{5} c^{2} d \tan\left(f x + e\right) + 66 \, B a^{3} b^{6} c^{2} d \tan\left(f x + e\right) - 54 \, A a^{2} b^{7} c^{2} d \tan\left(f x + e\right) + 36 \, C a^{2} b^{7} c^{2} d \tan\left(f x + e\right) - 6 \, B a b^{8} c^{2} d \tan\left(f x + e\right) - 6 \, A b^{9} c^{2} d \tan\left(f x + e\right) - 6 \, C a^{7} b^{2} c d^{2} \tan\left(f x + e\right) - 6 \, B a^{6} b^{3} c d^{2} \tan\left(f x + e\right) - 18 \, C a^{5} b^{4} c d^{2} \tan\left(f x + e\right) - 42 \, B a^{4} b^{5} c d^{2} \tan\left(f x + e\right) + 66 \, A a^{3} b^{6} c d^{2} \tan\left(f x + e\right) - 84 \, C a^{3} b^{6} c d^{2} \tan\left(f x + e\right) + 36 \, B a^{2} b^{7} c d^{2} \tan\left(f x + e\right) - 6 \, A a b^{8} c d^{2} \tan\left(f x + e\right) + 12 \, C a^{8} b d^{3} \tan\left(f x + e\right) - 2 \, B a^{7} b^{2} d^{3} \tan\left(f x + e\right) - 2 \, A a^{6} b^{3} d^{3} \tan\left(f x + e\right) + 38 \, C a^{6} b^{3} d^{3} \tan\left(f x + e\right) - 6 \, B a^{5} b^{4} d^{3} \tan\left(f x + e\right) - 14 \, A a^{4} b^{5} d^{3} \tan\left(f x + e\right) + 50 \, C a^{4} b^{5} d^{3} \tan\left(f x + e\right) - 28 \, B a^{3} b^{6} d^{3} \tan\left(f x + e\right) + 12 \, A a^{2} b^{7} d^{3} \tan\left(f x + e\right) - C a^{6} b^{3} c^{3} + 6 \, B a^{5} b^{4} c^{3} - 14 \, A a^{4} b^{5} c^{3} + 11 \, C a^{4} b^{5} c^{3} - 7 \, B a^{3} b^{6} c^{3} - 3 \, A a^{2} b^{7} c^{3} - B a b^{8} c^{3} - A b^{9} c^{3} - 3 \, C a^{7} b^{2} c^{2} d - 3 \, B a^{6} b^{3} c^{2} d + 18 \, A a^{5} b^{4} c^{2} d - 27 \, C a^{5} b^{4} c^{2} d + 33 \, B a^{4} b^{5} c^{2} d - 21 \, A a^{3} b^{6} c^{2} d + 12 \, C a^{3} b^{6} c^{2} d - 3 \, A a b^{8} c^{2} d - 3 \, B a^{7} b^{2} c d^{2} - 3 \, A a^{6} b^{3} c d^{2} + 3 \, C a^{6} b^{3} c d^{2} - 27 \, B a^{5} b^{4} c d^{2} + 33 \, A a^{4} b^{5} c d^{2} - 33 \, C a^{4} b^{5} c d^{2} + 12 \, B a^{3} b^{6} c d^{2} + 4 \, C a^{9} d^{3} - A a^{7} b^{2} d^{3} + 13 \, C a^{7} b^{2} d^{3} + B a^{6} b^{3} d^{3} - 9 \, A a^{5} b^{4} d^{3} + 21 \, C a^{5} b^{4} d^{3} - 11 \, B a^{4} b^{5} d^{3} + 4 \, A a^{3} b^{6} d^{3}}{{\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*C*d^3*tan(f*x + e)/b^3 + 2*(A*a^3*c^3 - C*a^3*c^3 + 3*B*a^2*b*c^3 - 3*A*a*b^2*c^3 + 3*C*a*b^2*c^3 - B*b^3*c^3 - 3*B*a^3*c^2*d + 9*A*a^2*b*c^2*d - 9*C*a^2*b*c^2*d + 9*B*a*b^2*c^2*d - 3*A*b^3*c^2*d + 3*C*b^3*c^2*d - 3*A*a^3*c*d^2 + 3*C*a^3*c*d^2 - 9*B*a^2*b*c*d^2 + 9*A*a*b^2*c*d^2 - 9*C*a*b^2*c*d^2 + 3*B*b^3*c*d^2 + B*a^3*d^3 - 3*A*a^2*b*d^3 + 3*C*a^2*b*d^3 - 3*B*a*b^2*d^3 + A*b^3*d^3 - C*b^3*d^3)*(f*x + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (B*a^3*c^3 - 3*A*a^2*b*c^3 + 3*C*a^2*b*c^3 - 3*B*a*b^2*c^3 + A*b^3*c^3 - C*b^3*c^3 + 3*A*a^3*c^2*d - 3*C*a^3*c^2*d + 9*B*a^2*b*c^2*d - 9*A*a*b^2*c^2*d + 9*C*a*b^2*c^2*d - 3*B*b^3*c^2*d - 3*B*a^3*c*d^2 + 9*A*a^2*b*c*d^2 - 9*C*a^2*b*c*d^2 + 9*B*a*b^2*c*d^2 - 3*A*b^3*c*d^2 + 3*C*b^3*c*d^2 - A*a^3*d^3 + C*a^3*d^3 - 3*B*a^2*b*d^3 + 3*A*a*b^2*d^3 - 3*C*a*b^2*d^3 + B*b^3*d^3)*log(tan(f*x + e)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(B*a^3*b^4*c^3 - 3*A*a^2*b^5*c^3 + 3*C*a^2*b^5*c^3 - 3*B*a*b^6*c^3 + A*b^7*c^3 - C*b^7*c^3 + 3*A*a^3*b^4*c^2*d - 3*C*a^3*b^4*c^2*d + 9*B*a^2*b^5*c^2*d - 9*A*a*b^6*c^2*d + 9*C*a*b^6*c^2*d - 3*B*b^7*c^2*d - 3*C*a^6*b*c*d^2 - 9*C*a^4*b^3*c*d^2 - 3*B*a^3*b^4*c*d^2 + 9*A*a^2*b^5*c*d^2 - 18*C*a^2*b^5*c*d^2 + 9*B*a*b^6*c*d^2 - 3*A*b^7*c*d^2 + 3*C*a^7*d^3 - B*a^6*b*d^3 + 9*C*a^5*b^2*d^3 - 3*B*a^4*b^3*d^3 - A*a^3*b^4*d^3 + 10*C*a^3*b^4*d^3 - 6*B*a^2*b^5*d^3 + 3*A*a*b^6*d^3)*log(abs(b*tan(f*x + e) + a))/(a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10) + (3*B*a^3*b^6*c^3*tan(f*x + e)^2 - 9*A*a^2*b^7*c^3*tan(f*x + e)^2 + 9*C*a^2*b^7*c^3*tan(f*x + e)^2 - 9*B*a*b^8*c^3*tan(f*x + e)^2 + 3*A*b^9*c^3*tan(f*x + e)^2 - 3*C*b^9*c^3*tan(f*x + e)^2 + 9*A*a^3*b^6*c^2*d*tan(f*x + e)^2 - 9*C*a^3*b^6*c^2*d*tan(f*x + e)^2 + 27*B*a^2*b^7*c^2*d*tan(f*x + e)^2 - 27*A*a*b^8*c^2*d*tan(f*x + e)^2 + 27*C*a*b^8*c^2*d*tan(f*x + e)^2 - 9*B*b^9*c^2*d*tan(f*x + e)^2 - 9*C*a^6*b^3*c*d^2*tan(f*x + e)^2 - 27*C*a^4*b^5*c*d^2*tan(f*x + e)^2 - 9*B*a^3*b^6*c*d^2*tan(f*x + e)^2 + 27*A*a^2*b^7*c*d^2*tan(f*x + e)^2 - 54*C*a^2*b^7*c*d^2*tan(f*x + e)^2 + 27*B*a*b^8*c*d^2*tan(f*x + e)^2 - 9*A*b^9*c*d^2*tan(f*x + e)^2 + 9*C*a^7*b^2*d^3*tan(f*x + e)^2 - 3*B*a^6*b^3*d^3*tan(f*x + e)^2 + 27*C*a^5*b^4*d^3*tan(f*x + e)^2 - 9*B*a^4*b^5*d^3*tan(f*x + e)^2 - 3*A*a^3*b^6*d^3*tan(f*x + e)^2 + 30*C*a^3*b^6*d^3*tan(f*x + e)^2 - 18*B*a^2*b^7*d^3*tan(f*x + e)^2 + 9*A*a*b^8*d^3*tan(f*x + e)^2 + 8*B*a^4*b^5*c^3*tan(f*x + e) - 22*A*a^3*b^6*c^3*tan(f*x + e) + 22*C*a^3*b^6*c^3*tan(f*x + e) - 18*B*a^2*b^7*c^3*tan(f*x + e) + 2*A*a*b^8*c^3*tan(f*x + e) - 2*C*a*b^8*c^3*tan(f*x + e) - 2*B*b^9*c^3*tan(f*x + e) - 6*C*a^6*b^3*c^2*d*tan(f*x + e) + 24*A*a^4*b^5*c^2*d*tan(f*x + e) - 42*C*a^4*b^5*c^2*d*tan(f*x + e) + 66*B*a^3*b^6*c^2*d*tan(f*x + e) - 54*A*a^2*b^7*c^2*d*tan(f*x + e) + 36*C*a^2*b^7*c^2*d*tan(f*x + e) - 6*B*a*b^8*c^2*d*tan(f*x + e) - 6*A*b^9*c^2*d*tan(f*x + e) - 6*C*a^7*b^2*c*d^2*tan(f*x + e) - 6*B*a^6*b^3*c*d^2*tan(f*x + e) - 18*C*a^5*b^4*c*d^2*tan(f*x + e) - 42*B*a^4*b^5*c*d^2*tan(f*x + e) + 66*A*a^3*b^6*c*d^2*tan(f*x + e) - 84*C*a^3*b^6*c*d^2*tan(f*x + e) + 36*B*a^2*b^7*c*d^2*tan(f*x + e) - 6*A*a*b^8*c*d^2*tan(f*x + e) + 12*C*a^8*b*d^3*tan(f*x + e) - 2*B*a^7*b^2*d^3*tan(f*x + e) - 2*A*a^6*b^3*d^3*tan(f*x + e) + 38*C*a^6*b^3*d^3*tan(f*x + e) - 6*B*a^5*b^4*d^3*tan(f*x + e) - 14*A*a^4*b^5*d^3*tan(f*x + e) + 50*C*a^4*b^5*d^3*tan(f*x + e) - 28*B*a^3*b^6*d^3*tan(f*x + e) + 12*A*a^2*b^7*d^3*tan(f*x + e) - C*a^6*b^3*c^3 + 6*B*a^5*b^4*c^3 - 14*A*a^4*b^5*c^3 + 11*C*a^4*b^5*c^3 - 7*B*a^3*b^6*c^3 - 3*A*a^2*b^7*c^3 - B*a*b^8*c^3 - A*b^9*c^3 - 3*C*a^7*b^2*c^2*d - 3*B*a^6*b^3*c^2*d + 18*A*a^5*b^4*c^2*d - 27*C*a^5*b^4*c^2*d + 33*B*a^4*b^5*c^2*d - 21*A*a^3*b^6*c^2*d + 12*C*a^3*b^6*c^2*d - 3*A*a*b^8*c^2*d - 3*B*a^7*b^2*c*d^2 - 3*A*a^6*b^3*c*d^2 + 3*C*a^6*b^3*c*d^2 - 27*B*a^5*b^4*c*d^2 + 33*A*a^4*b^5*c*d^2 - 33*C*a^4*b^5*c*d^2 + 12*B*a^3*b^6*c*d^2 + 4*C*a^9*d^3 - A*a^7*b^2*d^3 + 13*C*a^7*b^2*d^3 + B*a^6*b^3*d^3 - 9*A*a^5*b^4*d^3 + 21*C*a^5*b^4*d^3 - 11*B*a^4*b^5*d^3 + 4*A*a^3*b^6*d^3)/((a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10)*(b*tan(f*x + e) + a)^2))/f","B",0
70,1,573,0,5.521630," ","integrate((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{6 \, {\left(A a^{3} c - C a^{3} c - 3 \, B a^{2} b c - 3 \, A a b^{2} c + 3 \, C a b^{2} c + B b^{3} c + B a^{3} d + 3 \, A a^{2} b d - 3 \, C a^{2} b d - 3 \, B a b^{2} d - A b^{3} d + C b^{3} d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{3 \, {\left(B a^{3} c + 3 \, A a^{2} b c - 3 \, C a^{2} b c - 3 \, B a b^{2} c - A b^{3} c + C b^{3} c - A a^{3} d + C a^{3} d + 3 \, B a^{2} b d + 3 \, A a b^{2} d - 3 \, C a b^{2} d - B b^{3} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} - \frac{6 \, {\left(C b^{3} c^{5} - 3 \, C a b^{2} c^{4} d - B b^{3} c^{4} d + 3 \, C a^{2} b c^{3} d^{2} + 3 \, B a b^{2} c^{3} d^{2} + A b^{3} c^{3} d^{2} - C a^{3} c^{2} d^{3} - 3 \, B a^{2} b c^{2} d^{3} - 3 \, A a b^{2} c^{2} d^{3} + B a^{3} c d^{4} + 3 \, A a^{2} b c d^{4} - A a^{3} d^{5}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{2} d^{4} + d^{6}} + \frac{2 \, C b^{3} d^{2} \tan\left(f x + e\right)^{3} - 3 \, C b^{3} c d \tan\left(f x + e\right)^{2} + 9 \, C a b^{2} d^{2} \tan\left(f x + e\right)^{2} + 3 \, B b^{3} d^{2} \tan\left(f x + e\right)^{2} + 6 \, C b^{3} c^{2} \tan\left(f x + e\right) - 18 \, C a b^{2} c d \tan\left(f x + e\right) - 6 \, B b^{3} c d \tan\left(f x + e\right) + 18 \, C a^{2} b d^{2} \tan\left(f x + e\right) + 18 \, B a b^{2} d^{2} \tan\left(f x + e\right) + 6 \, A b^{3} d^{2} \tan\left(f x + e\right) - 6 \, C b^{3} d^{2} \tan\left(f x + e\right)}{d^{3}}}{6 \, f}"," ",0,"1/6*(6*(A*a^3*c - C*a^3*c - 3*B*a^2*b*c - 3*A*a*b^2*c + 3*C*a*b^2*c + B*b^3*c + B*a^3*d + 3*A*a^2*b*d - 3*C*a^2*b*d - 3*B*a*b^2*d - A*b^3*d + C*b^3*d)*(f*x + e)/(c^2 + d^2) + 3*(B*a^3*c + 3*A*a^2*b*c - 3*C*a^2*b*c - 3*B*a*b^2*c - A*b^3*c + C*b^3*c - A*a^3*d + C*a^3*d + 3*B*a^2*b*d + 3*A*a*b^2*d - 3*C*a*b^2*d - B*b^3*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2) - 6*(C*b^3*c^5 - 3*C*a*b^2*c^4*d - B*b^3*c^4*d + 3*C*a^2*b*c^3*d^2 + 3*B*a*b^2*c^3*d^2 + A*b^3*c^3*d^2 - C*a^3*c^2*d^3 - 3*B*a^2*b*c^2*d^3 - 3*A*a*b^2*c^2*d^3 + B*a^3*c*d^4 + 3*A*a^2*b*c*d^4 - A*a^3*d^5)*log(abs(d*tan(f*x + e) + c))/(c^2*d^4 + d^6) + (2*C*b^3*d^2*tan(f*x + e)^3 - 3*C*b^3*c*d*tan(f*x + e)^2 + 9*C*a*b^2*d^2*tan(f*x + e)^2 + 3*B*b^3*d^2*tan(f*x + e)^2 + 6*C*b^3*c^2*tan(f*x + e) - 18*C*a*b^2*c*d*tan(f*x + e) - 6*B*b^3*c*d*tan(f*x + e) + 18*C*a^2*b*d^2*tan(f*x + e) + 18*B*a*b^2*d^2*tan(f*x + e) + 6*A*b^3*d^2*tan(f*x + e) - 6*C*b^3*d^2*tan(f*x + e))/d^3)/f","A",0
71,1,338,0,3.055749," ","integrate((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{2} c - C a^{2} c - 2 \, B a b c - A b^{2} c + C b^{2} c + B a^{2} d + 2 \, A a b d - 2 \, C a b d - B b^{2} d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{{\left(B a^{2} c + 2 \, A a b c - 2 \, C a b c - B b^{2} c - A a^{2} d + C a^{2} d + 2 \, B a b d + A b^{2} d - C b^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} + \frac{2 \, {\left(C b^{2} c^{4} - 2 \, C a b c^{3} d - B b^{2} c^{3} d + C a^{2} c^{2} d^{2} + 2 \, B a b c^{2} d^{2} + A b^{2} c^{2} d^{2} - B a^{2} c d^{3} - 2 \, A a b c d^{3} + A a^{2} d^{4}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{2} d^{3} + d^{5}} + \frac{C b^{2} d \tan\left(f x + e\right)^{2} - 2 \, C b^{2} c \tan\left(f x + e\right) + 4 \, C a b d \tan\left(f x + e\right) + 2 \, B b^{2} d \tan\left(f x + e\right)}{d^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*a^2*c - C*a^2*c - 2*B*a*b*c - A*b^2*c + C*b^2*c + B*a^2*d + 2*A*a*b*d - 2*C*a*b*d - B*b^2*d)*(f*x + e)/(c^2 + d^2) + (B*a^2*c + 2*A*a*b*c - 2*C*a*b*c - B*b^2*c - A*a^2*d + C*a^2*d + 2*B*a*b*d + A*b^2*d - C*b^2*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2) + 2*(C*b^2*c^4 - 2*C*a*b*c^3*d - B*b^2*c^3*d + C*a^2*c^2*d^2 + 2*B*a*b*c^2*d^2 + A*b^2*c^2*d^2 - B*a^2*c*d^3 - 2*A*a*b*c*d^3 + A*a^2*d^4)*log(abs(d*tan(f*x + e) + c))/(c^2*d^3 + d^5) + (C*b^2*d*tan(f*x + e)^2 - 2*C*b^2*c*tan(f*x + e) + 4*C*a*b*d*tan(f*x + e) + 2*B*b^2*d*tan(f*x + e))/d^2)/f","A",0
72,1,186,0,1.929183," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, C b \tan\left(f x + e\right)}{d} + \frac{2 \, {\left(A a c - C a c - B b c + B a d + A b d - C b d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{{\left(B a c + A b c - C b c - A a d + C a d + B b d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} - \frac{2 \, {\left(C b c^{3} - C a c^{2} d - B b c^{2} d + B a c d^{2} + A b c d^{2} - A a d^{3}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{2} d^{2} + d^{4}}}{2 \, f}"," ",0,"1/2*(2*C*b*tan(f*x + e)/d + 2*(A*a*c - C*a*c - B*b*c + B*a*d + A*b*d - C*b*d)*(f*x + e)/(c^2 + d^2) + (B*a*c + A*b*c - C*b*c - A*a*d + C*a*d + B*b*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2) - 2*(C*b*c^3 - C*a*c^2*d - B*b*c^2*d + B*a*c*d^2 + A*b*c*d^2 - A*a*d^3)*log(abs(d*tan(f*x + e) + c))/(c^2*d^2 + d^4))/f","A",0
73,1,109,0,2.056865," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A c - C c + B d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{{\left(B c - A d + C d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} + \frac{2 \, {\left(C c^{2} - B c d + A d^{2}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{2} d + d^{3}}}{2 \, f}"," ",0,"1/2*(2*(A*c - C*c + B*d)*(f*x + e)/(c^2 + d^2) + (B*c - A*d + C*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2) + 2*(C*c^2 - B*c*d + A*d^2)*log(abs(d*tan(f*x + e) + c))/(c^2*d + d^3))/f","A",0
74,1,272,0,2.334286," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a c - C a c + B b c + B a d - A b d + C b d\right)} {\left(f x + e\right)}}{a^{2} c^{2} + b^{2} c^{2} + a^{2} d^{2} + b^{2} d^{2}} + \frac{{\left(B a c - A b c + C b c - A a d + C a d - B b d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} c^{2} + b^{2} c^{2} + a^{2} d^{2} + b^{2} d^{2}} + \frac{2 \, {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b^{2} c + b^{4} c - a^{3} b d - a b^{3} d} - \frac{2 \, {\left(C c^{2} d - B c d^{2} + A d^{3}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b c^{3} d - a c^{2} d^{2} + b c d^{3} - a d^{4}}}{2 \, f}"," ",0,"1/2*(2*(A*a*c - C*a*c + B*b*c + B*a*d - A*b*d + C*b*d)*(f*x + e)/(a^2*c^2 + b^2*c^2 + a^2*d^2 + b^2*d^2) + (B*a*c - A*b*c + C*b*c - A*a*d + C*a*d - B*b*d)*log(tan(f*x + e)^2 + 1)/(a^2*c^2 + b^2*c^2 + a^2*d^2 + b^2*d^2) + 2*(C*a^2*b - B*a*b^2 + A*b^3)*log(abs(b*tan(f*x + e) + a))/(a^2*b^2*c + b^4*c - a^3*b*d - a*b^3*d) - 2*(C*c^2*d - B*c*d^2 + A*d^3)*log(abs(d*tan(f*x + e) + c))/(b*c^3*d - a*c^2*d^2 + b*c*d^3 - a*d^4))/f","A",0
75,1,846,0,6.616525," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{2} c - C a^{2} c + 2 \, B a b c - A b^{2} c + C b^{2} c + B a^{2} d - 2 \, A a b d + 2 \, C a b d - B b^{2} d\right)} {\left(f x + e\right)}}{a^{4} c^{2} + 2 \, a^{2} b^{2} c^{2} + b^{4} c^{2} + a^{4} d^{2} + 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} + \frac{{\left(B a^{2} c - 2 \, A a b c + 2 \, C a b c - B b^{2} c - A a^{2} d + C a^{2} d - 2 \, B a b d + A b^{2} d - C b^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} c^{2} + 2 \, a^{2} b^{2} c^{2} + b^{4} c^{2} + a^{4} d^{2} + 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{2 \, {\left(B a^{2} b^{3} c - 2 \, A a b^{4} c + 2 \, C a b^{4} c - B b^{5} c + C a^{4} b d - 2 \, B a^{3} b^{2} d + 3 \, A a^{2} b^{3} d - C a^{2} b^{3} d + A b^{5} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b^{3} c^{2} + 2 \, a^{2} b^{5} c^{2} + b^{7} c^{2} - 2 \, a^{5} b^{2} c d - 4 \, a^{3} b^{4} c d - 2 \, a b^{6} c d + a^{6} b d^{2} + 2 \, a^{4} b^{3} d^{2} + a^{2} b^{5} d^{2}} + \frac{2 \, {\left(C c^{2} d^{2} - B c d^{3} + A d^{4}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}} + \frac{2 \, {\left(B a^{2} b^{3} c \tan\left(f x + e\right) - 2 \, A a b^{4} c \tan\left(f x + e\right) + 2 \, C a b^{4} c \tan\left(f x + e\right) - B b^{5} c \tan\left(f x + e\right) + C a^{4} b d \tan\left(f x + e\right) - 2 \, B a^{3} b^{2} d \tan\left(f x + e\right) + 3 \, A a^{2} b^{3} d \tan\left(f x + e\right) - C a^{2} b^{3} d \tan\left(f x + e\right) + A b^{5} d \tan\left(f x + e\right) - C a^{4} b c + 2 \, B a^{3} b^{2} c - 3 \, A a^{2} b^{3} c + C a^{2} b^{3} c - A b^{5} c + 2 \, C a^{5} d - 3 \, B a^{4} b d + 4 \, A a^{3} b^{2} d - B a^{2} b^{3} d + 2 \, A a b^{4} d\right)}}{{\left(a^{4} b^{2} c^{2} + 2 \, a^{2} b^{4} c^{2} + b^{6} c^{2} - 2 \, a^{5} b c d - 4 \, a^{3} b^{3} c d - 2 \, a b^{5} c d + a^{6} d^{2} + 2 \, a^{4} b^{2} d^{2} + a^{2} b^{4} d^{2}\right)} {\left(b \tan\left(f x + e\right) + a\right)}}}{2 \, f}"," ",0,"1/2*(2*(A*a^2*c - C*a^2*c + 2*B*a*b*c - A*b^2*c + C*b^2*c + B*a^2*d - 2*A*a*b*d + 2*C*a*b*d - B*b^2*d)*(f*x + e)/(a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 + a^4*d^2 + 2*a^2*b^2*d^2 + b^4*d^2) + (B*a^2*c - 2*A*a*b*c + 2*C*a*b*c - B*b^2*c - A*a^2*d + C*a^2*d - 2*B*a*b*d + A*b^2*d - C*b^2*d)*log(tan(f*x + e)^2 + 1)/(a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 + a^4*d^2 + 2*a^2*b^2*d^2 + b^4*d^2) - 2*(B*a^2*b^3*c - 2*A*a*b^4*c + 2*C*a*b^4*c - B*b^5*c + C*a^4*b*d - 2*B*a^3*b^2*d + 3*A*a^2*b^3*d - C*a^2*b^3*d + A*b^5*d)*log(abs(b*tan(f*x + e) + a))/(a^4*b^3*c^2 + 2*a^2*b^5*c^2 + b^7*c^2 - 2*a^5*b^2*c*d - 4*a^3*b^4*c*d - 2*a*b^6*c*d + a^6*b*d^2 + 2*a^4*b^3*d^2 + a^2*b^5*d^2) + 2*(C*c^2*d^2 - B*c*d^3 + A*d^4)*log(abs(d*tan(f*x + e) + c))/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5) + 2*(B*a^2*b^3*c*tan(f*x + e) - 2*A*a*b^4*c*tan(f*x + e) + 2*C*a*b^4*c*tan(f*x + e) - B*b^5*c*tan(f*x + e) + C*a^4*b*d*tan(f*x + e) - 2*B*a^3*b^2*d*tan(f*x + e) + 3*A*a^2*b^3*d*tan(f*x + e) - C*a^2*b^3*d*tan(f*x + e) + A*b^5*d*tan(f*x + e) - C*a^4*b*c + 2*B*a^3*b^2*c - 3*A*a^2*b^3*c + C*a^2*b^3*c - A*b^5*c + 2*C*a^5*d - 3*B*a^4*b*d + 4*A*a^3*b^2*d - B*a^2*b^3*d + 2*A*a*b^4*d)/((a^4*b^2*c^2 + 2*a^2*b^4*c^2 + b^6*c^2 - 2*a^5*b*c*d - 4*a^3*b^3*c*d - 2*a*b^5*c*d + a^6*d^2 + 2*a^4*b^2*d^2 + a^2*b^4*d^2)*(b*tan(f*x + e) + a)))/f","B",0
76,1,2127,0,26.162354," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{3} c - C a^{3} c + 3 \, B a^{2} b c - 3 \, A a b^{2} c + 3 \, C a b^{2} c - B b^{3} c + B a^{3} d - 3 \, A a^{2} b d + 3 \, C a^{2} b d - 3 \, B a b^{2} d + A b^{3} d - C b^{3} d\right)} {\left(f x + e\right)}}{a^{6} c^{2} + 3 \, a^{4} b^{2} c^{2} + 3 \, a^{2} b^{4} c^{2} + b^{6} c^{2} + a^{6} d^{2} + 3 \, a^{4} b^{2} d^{2} + 3 \, a^{2} b^{4} d^{2} + b^{6} d^{2}} + \frac{{\left(B a^{3} c - 3 \, A a^{2} b c + 3 \, C a^{2} b c - 3 \, B a b^{2} c + A b^{3} c - C b^{3} c - A a^{3} d + C a^{3} d - 3 \, B a^{2} b d + 3 \, A a b^{2} d - 3 \, C a b^{2} d + B b^{3} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} c^{2} + 3 \, a^{4} b^{2} c^{2} + 3 \, a^{2} b^{4} c^{2} + b^{6} c^{2} + a^{6} d^{2} + 3 \, a^{4} b^{2} d^{2} + 3 \, a^{2} b^{4} d^{2} + b^{6} d^{2}} - \frac{2 \, {\left(B a^{3} b^{4} c^{2} - 3 \, A a^{2} b^{5} c^{2} + 3 \, C a^{2} b^{5} c^{2} - 3 \, B a b^{6} c^{2} + A b^{7} c^{2} - C b^{7} c^{2} - 3 \, B a^{4} b^{3} c d + 8 \, A a^{3} b^{4} c d - 8 \, C a^{3} b^{4} c d + 6 \, B a^{2} b^{5} c d + B b^{7} c d - C a^{6} b d^{2} + 3 \, B a^{5} b^{2} d^{2} - 6 \, A a^{4} b^{3} d^{2} + 3 \, C a^{4} b^{3} d^{2} - B a^{3} b^{4} d^{2} - 3 \, A a^{2} b^{5} d^{2} - A b^{7} d^{2}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{6} b^{4} c^{3} + 3 \, a^{4} b^{6} c^{3} + 3 \, a^{2} b^{8} c^{3} + b^{10} c^{3} - 3 \, a^{7} b^{3} c^{2} d - 9 \, a^{5} b^{5} c^{2} d - 9 \, a^{3} b^{7} c^{2} d - 3 \, a b^{9} c^{2} d + 3 \, a^{8} b^{2} c d^{2} + 9 \, a^{6} b^{4} c d^{2} + 9 \, a^{4} b^{6} c d^{2} + 3 \, a^{2} b^{8} c d^{2} - a^{9} b d^{3} - 3 \, a^{7} b^{3} d^{3} - 3 \, a^{5} b^{5} d^{3} - a^{3} b^{7} d^{3}} - \frac{2 \, {\left(C c^{2} d^{3} - B c d^{4} + A d^{5}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{3} c^{5} d - 3 \, a b^{2} c^{4} d^{2} + 3 \, a^{2} b c^{3} d^{3} + b^{3} c^{3} d^{3} - a^{3} c^{2} d^{4} - 3 \, a b^{2} c^{2} d^{4} + 3 \, a^{2} b c d^{5} - a^{3} d^{6}} + \frac{3 \, B a^{3} b^{5} c^{2} \tan\left(f x + e\right)^{2} - 9 \, A a^{2} b^{6} c^{2} \tan\left(f x + e\right)^{2} + 9 \, C a^{2} b^{6} c^{2} \tan\left(f x + e\right)^{2} - 9 \, B a b^{7} c^{2} \tan\left(f x + e\right)^{2} + 3 \, A b^{8} c^{2} \tan\left(f x + e\right)^{2} - 3 \, C b^{8} c^{2} \tan\left(f x + e\right)^{2} - 9 \, B a^{4} b^{4} c d \tan\left(f x + e\right)^{2} + 24 \, A a^{3} b^{5} c d \tan\left(f x + e\right)^{2} - 24 \, C a^{3} b^{5} c d \tan\left(f x + e\right)^{2} + 18 \, B a^{2} b^{6} c d \tan\left(f x + e\right)^{2} + 3 \, B b^{8} c d \tan\left(f x + e\right)^{2} - 3 \, C a^{6} b^{2} d^{2} \tan\left(f x + e\right)^{2} + 9 \, B a^{5} b^{3} d^{2} \tan\left(f x + e\right)^{2} - 18 \, A a^{4} b^{4} d^{2} \tan\left(f x + e\right)^{2} + 9 \, C a^{4} b^{4} d^{2} \tan\left(f x + e\right)^{2} - 3 \, B a^{3} b^{5} d^{2} \tan\left(f x + e\right)^{2} - 9 \, A a^{2} b^{6} d^{2} \tan\left(f x + e\right)^{2} - 3 \, A b^{8} d^{2} \tan\left(f x + e\right)^{2} + 8 \, B a^{4} b^{4} c^{2} \tan\left(f x + e\right) - 22 \, A a^{3} b^{5} c^{2} \tan\left(f x + e\right) + 22 \, C a^{3} b^{5} c^{2} \tan\left(f x + e\right) - 18 \, B a^{2} b^{6} c^{2} \tan\left(f x + e\right) + 2 \, A a b^{7} c^{2} \tan\left(f x + e\right) - 2 \, C a b^{7} c^{2} \tan\left(f x + e\right) - 2 \, B b^{8} c^{2} \tan\left(f x + e\right) + 2 \, C a^{6} b^{2} c d \tan\left(f x + e\right) - 24 \, B a^{5} b^{3} c d \tan\left(f x + e\right) + 58 \, A a^{4} b^{4} c d \tan\left(f x + e\right) - 52 \, C a^{4} b^{4} c d \tan\left(f x + e\right) + 32 \, B a^{3} b^{5} c d \tan\left(f x + e\right) + 12 \, A a^{2} b^{6} c d \tan\left(f x + e\right) - 6 \, C a^{2} b^{6} c d \tan\left(f x + e\right) + 8 \, B a b^{7} c d \tan\left(f x + e\right) + 2 \, A b^{8} c d \tan\left(f x + e\right) - 8 \, C a^{7} b d^{2} \tan\left(f x + e\right) + 22 \, B a^{6} b^{2} d^{2} \tan\left(f x + e\right) - 42 \, A a^{5} b^{3} d^{2} \tan\left(f x + e\right) + 18 \, C a^{5} b^{3} d^{2} \tan\left(f x + e\right) - 2 \, B a^{4} b^{4} d^{2} \tan\left(f x + e\right) - 26 \, A a^{3} b^{5} d^{2} \tan\left(f x + e\right) + 2 \, C a^{3} b^{5} d^{2} \tan\left(f x + e\right) - 8 \, A a b^{7} d^{2} \tan\left(f x + e\right) - C a^{6} b^{2} c^{2} + 6 \, B a^{5} b^{3} c^{2} - 14 \, A a^{4} b^{4} c^{2} + 11 \, C a^{4} b^{4} c^{2} - 7 \, B a^{3} b^{5} c^{2} - 3 \, A a^{2} b^{6} c^{2} - B a b^{7} c^{2} - A b^{8} c^{2} + 4 \, C a^{7} b c d - 17 \, B a^{6} b^{2} c d + 36 \, A a^{5} b^{3} c d - 24 \, C a^{5} b^{3} c d + 10 \, B a^{4} b^{4} c d + 16 \, A a^{3} b^{5} c d - 4 \, C a^{3} b^{5} c d + 3 \, B a^{2} b^{6} c d + 4 \, A a b^{7} c d - 6 \, C a^{8} d^{2} + 14 \, B a^{7} b d^{2} - 25 \, A a^{6} b^{2} d^{2} + 7 \, C a^{6} b^{2} d^{2} + 3 \, B a^{5} b^{3} d^{2} - 19 \, A a^{4} b^{4} d^{2} + C a^{4} b^{4} d^{2} + B a^{3} b^{5} d^{2} - 6 \, A a^{2} b^{6} d^{2}}{{\left(a^{6} b^{3} c^{3} + 3 \, a^{4} b^{5} c^{3} + 3 \, a^{2} b^{7} c^{3} + b^{9} c^{3} - 3 \, a^{7} b^{2} c^{2} d - 9 \, a^{5} b^{4} c^{2} d - 9 \, a^{3} b^{6} c^{2} d - 3 \, a b^{8} c^{2} d + 3 \, a^{8} b c d^{2} + 9 \, a^{6} b^{3} c d^{2} + 9 \, a^{4} b^{5} c d^{2} + 3 \, a^{2} b^{7} c d^{2} - a^{9} d^{3} - 3 \, a^{7} b^{2} d^{3} - 3 \, a^{5} b^{4} d^{3} - a^{3} b^{6} d^{3}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*a^3*c - C*a^3*c + 3*B*a^2*b*c - 3*A*a*b^2*c + 3*C*a*b^2*c - B*b^3*c + B*a^3*d - 3*A*a^2*b*d + 3*C*a^2*b*d - 3*B*a*b^2*d + A*b^3*d - C*b^3*d)*(f*x + e)/(a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + b^6*c^2 + a^6*d^2 + 3*a^4*b^2*d^2 + 3*a^2*b^4*d^2 + b^6*d^2) + (B*a^3*c - 3*A*a^2*b*c + 3*C*a^2*b*c - 3*B*a*b^2*c + A*b^3*c - C*b^3*c - A*a^3*d + C*a^3*d - 3*B*a^2*b*d + 3*A*a*b^2*d - 3*C*a*b^2*d + B*b^3*d)*log(tan(f*x + e)^2 + 1)/(a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + b^6*c^2 + a^6*d^2 + 3*a^4*b^2*d^2 + 3*a^2*b^4*d^2 + b^6*d^2) - 2*(B*a^3*b^4*c^2 - 3*A*a^2*b^5*c^2 + 3*C*a^2*b^5*c^2 - 3*B*a*b^6*c^2 + A*b^7*c^2 - C*b^7*c^2 - 3*B*a^4*b^3*c*d + 8*A*a^3*b^4*c*d - 8*C*a^3*b^4*c*d + 6*B*a^2*b^5*c*d + B*b^7*c*d - C*a^6*b*d^2 + 3*B*a^5*b^2*d^2 - 6*A*a^4*b^3*d^2 + 3*C*a^4*b^3*d^2 - B*a^3*b^4*d^2 - 3*A*a^2*b^5*d^2 - A*b^7*d^2)*log(abs(b*tan(f*x + e) + a))/(a^6*b^4*c^3 + 3*a^4*b^6*c^3 + 3*a^2*b^8*c^3 + b^10*c^3 - 3*a^7*b^3*c^2*d - 9*a^5*b^5*c^2*d - 9*a^3*b^7*c^2*d - 3*a*b^9*c^2*d + 3*a^8*b^2*c*d^2 + 9*a^6*b^4*c*d^2 + 9*a^4*b^6*c*d^2 + 3*a^2*b^8*c*d^2 - a^9*b*d^3 - 3*a^7*b^3*d^3 - 3*a^5*b^5*d^3 - a^3*b^7*d^3) - 2*(C*c^2*d^3 - B*c*d^4 + A*d^5)*log(abs(d*tan(f*x + e) + c))/(b^3*c^5*d - 3*a*b^2*c^4*d^2 + 3*a^2*b*c^3*d^3 + b^3*c^3*d^3 - a^3*c^2*d^4 - 3*a*b^2*c^2*d^4 + 3*a^2*b*c*d^5 - a^3*d^6) + (3*B*a^3*b^5*c^2*tan(f*x + e)^2 - 9*A*a^2*b^6*c^2*tan(f*x + e)^2 + 9*C*a^2*b^6*c^2*tan(f*x + e)^2 - 9*B*a*b^7*c^2*tan(f*x + e)^2 + 3*A*b^8*c^2*tan(f*x + e)^2 - 3*C*b^8*c^2*tan(f*x + e)^2 - 9*B*a^4*b^4*c*d*tan(f*x + e)^2 + 24*A*a^3*b^5*c*d*tan(f*x + e)^2 - 24*C*a^3*b^5*c*d*tan(f*x + e)^2 + 18*B*a^2*b^6*c*d*tan(f*x + e)^2 + 3*B*b^8*c*d*tan(f*x + e)^2 - 3*C*a^6*b^2*d^2*tan(f*x + e)^2 + 9*B*a^5*b^3*d^2*tan(f*x + e)^2 - 18*A*a^4*b^4*d^2*tan(f*x + e)^2 + 9*C*a^4*b^4*d^2*tan(f*x + e)^2 - 3*B*a^3*b^5*d^2*tan(f*x + e)^2 - 9*A*a^2*b^6*d^2*tan(f*x + e)^2 - 3*A*b^8*d^2*tan(f*x + e)^2 + 8*B*a^4*b^4*c^2*tan(f*x + e) - 22*A*a^3*b^5*c^2*tan(f*x + e) + 22*C*a^3*b^5*c^2*tan(f*x + e) - 18*B*a^2*b^6*c^2*tan(f*x + e) + 2*A*a*b^7*c^2*tan(f*x + e) - 2*C*a*b^7*c^2*tan(f*x + e) - 2*B*b^8*c^2*tan(f*x + e) + 2*C*a^6*b^2*c*d*tan(f*x + e) - 24*B*a^5*b^3*c*d*tan(f*x + e) + 58*A*a^4*b^4*c*d*tan(f*x + e) - 52*C*a^4*b^4*c*d*tan(f*x + e) + 32*B*a^3*b^5*c*d*tan(f*x + e) + 12*A*a^2*b^6*c*d*tan(f*x + e) - 6*C*a^2*b^6*c*d*tan(f*x + e) + 8*B*a*b^7*c*d*tan(f*x + e) + 2*A*b^8*c*d*tan(f*x + e) - 8*C*a^7*b*d^2*tan(f*x + e) + 22*B*a^6*b^2*d^2*tan(f*x + e) - 42*A*a^5*b^3*d^2*tan(f*x + e) + 18*C*a^5*b^3*d^2*tan(f*x + e) - 2*B*a^4*b^4*d^2*tan(f*x + e) - 26*A*a^3*b^5*d^2*tan(f*x + e) + 2*C*a^3*b^5*d^2*tan(f*x + e) - 8*A*a*b^7*d^2*tan(f*x + e) - C*a^6*b^2*c^2 + 6*B*a^5*b^3*c^2 - 14*A*a^4*b^4*c^2 + 11*C*a^4*b^4*c^2 - 7*B*a^3*b^5*c^2 - 3*A*a^2*b^6*c^2 - B*a*b^7*c^2 - A*b^8*c^2 + 4*C*a^7*b*c*d - 17*B*a^6*b^2*c*d + 36*A*a^5*b^3*c*d - 24*C*a^5*b^3*c*d + 10*B*a^4*b^4*c*d + 16*A*a^3*b^5*c*d - 4*C*a^3*b^5*c*d + 3*B*a^2*b^6*c*d + 4*A*a*b^7*c*d - 6*C*a^8*d^2 + 14*B*a^7*b*d^2 - 25*A*a^6*b^2*d^2 + 7*C*a^6*b^2*d^2 + 3*B*a^5*b^3*d^2 - 19*A*a^4*b^4*d^2 + C*a^4*b^4*d^2 + B*a^3*b^5*d^2 - 6*A*a^2*b^6*d^2)/((a^6*b^3*c^3 + 3*a^4*b^5*c^3 + 3*a^2*b^7*c^3 + b^9*c^3 - 3*a^7*b^2*c^2*d - 9*a^5*b^4*c^2*d - 9*a^3*b^6*c^2*d - 3*a*b^8*c^2*d + 3*a^8*b*c*d^2 + 9*a^6*b^3*c*d^2 + 9*a^4*b^5*c*d^2 + 3*a^2*b^7*c*d^2 - a^9*d^3 - 3*a^7*b^2*d^3 - 3*a^5*b^4*d^3 - a^3*b^6*d^3)*(b*tan(f*x + e) + a)^2))/f","B",0
77,1,1355,0,3.652841," ","integrate((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{3} c^{2} - C a^{3} c^{2} - 3 \, B a^{2} b c^{2} - 3 \, A a b^{2} c^{2} + 3 \, C a b^{2} c^{2} + B b^{3} c^{2} + 2 \, B a^{3} c d + 6 \, A a^{2} b c d - 6 \, C a^{2} b c d - 6 \, B a b^{2} c d - 2 \, A b^{3} c d + 2 \, C b^{3} c d - A a^{3} d^{2} + C a^{3} d^{2} + 3 \, B a^{2} b d^{2} + 3 \, A a b^{2} d^{2} - 3 \, C a b^{2} d^{2} - B b^{3} d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(B a^{3} c^{2} + 3 \, A a^{2} b c^{2} - 3 \, C a^{2} b c^{2} - 3 \, B a b^{2} c^{2} - A b^{3} c^{2} + C b^{3} c^{2} - 2 \, A a^{3} c d + 2 \, C a^{3} c d + 6 \, B a^{2} b c d + 6 \, A a b^{2} c d - 6 \, C a b^{2} c d - 2 \, B b^{3} c d - B a^{3} d^{2} - 3 \, A a^{2} b d^{2} + 3 \, C a^{2} b d^{2} + 3 \, B a b^{2} d^{2} + A b^{3} d^{2} - C b^{3} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{2 \, {\left(3 \, C b^{3} c^{6} - 6 \, C a b^{2} c^{5} d - 2 \, B b^{3} c^{5} d + 3 \, C a^{2} b c^{4} d^{2} + 3 \, B a b^{2} c^{4} d^{2} + A b^{3} c^{4} d^{2} + 5 \, C b^{3} c^{4} d^{2} - 12 \, C a b^{2} c^{3} d^{3} - 4 \, B b^{3} c^{3} d^{3} - B a^{3} c^{2} d^{4} - 3 \, A a^{2} b c^{2} d^{4} + 9 \, C a^{2} b c^{2} d^{4} + 9 \, B a b^{2} c^{2} d^{4} + 3 \, A b^{3} c^{2} d^{4} + 2 \, A a^{3} c d^{5} - 2 \, C a^{3} c d^{5} - 6 \, B a^{2} b c d^{5} - 6 \, A a b^{2} c d^{5} + B a^{3} d^{6} + 3 \, A a^{2} b d^{6}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{4} d^{4} + 2 \, c^{2} d^{6} + d^{8}} - \frac{2 \, {\left(3 \, C b^{3} c^{6} d \tan\left(f x + e\right) - 6 \, C a b^{2} c^{5} d^{2} \tan\left(f x + e\right) - 2 \, B b^{3} c^{5} d^{2} \tan\left(f x + e\right) + 3 \, C a^{2} b c^{4} d^{3} \tan\left(f x + e\right) + 3 \, B a b^{2} c^{4} d^{3} \tan\left(f x + e\right) + A b^{3} c^{4} d^{3} \tan\left(f x + e\right) + 5 \, C b^{3} c^{4} d^{3} \tan\left(f x + e\right) - 12 \, C a b^{2} c^{3} d^{4} \tan\left(f x + e\right) - 4 \, B b^{3} c^{3} d^{4} \tan\left(f x + e\right) - B a^{3} c^{2} d^{5} \tan\left(f x + e\right) - 3 \, A a^{2} b c^{2} d^{5} \tan\left(f x + e\right) + 9 \, C a^{2} b c^{2} d^{5} \tan\left(f x + e\right) + 9 \, B a b^{2} c^{2} d^{5} \tan\left(f x + e\right) + 3 \, A b^{3} c^{2} d^{5} \tan\left(f x + e\right) + 2 \, A a^{3} c d^{6} \tan\left(f x + e\right) - 2 \, C a^{3} c d^{6} \tan\left(f x + e\right) - 6 \, B a^{2} b c d^{6} \tan\left(f x + e\right) - 6 \, A a b^{2} c d^{6} \tan\left(f x + e\right) + B a^{3} d^{7} \tan\left(f x + e\right) + 3 \, A a^{2} b d^{7} \tan\left(f x + e\right) + 2 \, C b^{3} c^{7} - 3 \, C a b^{2} c^{6} d - B b^{3} c^{6} d + 4 \, C b^{3} c^{5} d^{2} + C a^{3} c^{4} d^{3} + 3 \, B a^{2} b c^{4} d^{3} + 3 \, A a b^{2} c^{4} d^{3} - 9 \, C a b^{2} c^{4} d^{3} - 3 \, B b^{3} c^{4} d^{3} - 2 \, B a^{3} c^{3} d^{4} - 6 \, A a^{2} b c^{3} d^{4} + 6 \, C a^{2} b c^{3} d^{4} + 6 \, B a b^{2} c^{3} d^{4} + 2 \, A b^{3} c^{3} d^{4} + 3 \, A a^{3} c^{2} d^{5} - C a^{3} c^{2} d^{5} - 3 \, B a^{2} b c^{2} d^{5} - 3 \, A a b^{2} c^{2} d^{5} + A a^{3} d^{7}\right)}}{{\left(c^{4} d^{4} + 2 \, c^{2} d^{6} + d^{8}\right)} {\left(d \tan\left(f x + e\right) + c\right)}} + \frac{C b^{3} d^{2} \tan\left(f x + e\right)^{2} - 4 \, C b^{3} c d \tan\left(f x + e\right) + 6 \, C a b^{2} d^{2} \tan\left(f x + e\right) + 2 \, B b^{3} d^{2} \tan\left(f x + e\right)}{d^{4}}}{2 \, f}"," ",0,"1/2*(2*(A*a^3*c^2 - C*a^3*c^2 - 3*B*a^2*b*c^2 - 3*A*a*b^2*c^2 + 3*C*a*b^2*c^2 + B*b^3*c^2 + 2*B*a^3*c*d + 6*A*a^2*b*c*d - 6*C*a^2*b*c*d - 6*B*a*b^2*c*d - 2*A*b^3*c*d + 2*C*b^3*c*d - A*a^3*d^2 + C*a^3*d^2 + 3*B*a^2*b*d^2 + 3*A*a*b^2*d^2 - 3*C*a*b^2*d^2 - B*b^3*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + (B*a^3*c^2 + 3*A*a^2*b*c^2 - 3*C*a^2*b*c^2 - 3*B*a*b^2*c^2 - A*b^3*c^2 + C*b^3*c^2 - 2*A*a^3*c*d + 2*C*a^3*c*d + 6*B*a^2*b*c*d + 6*A*a*b^2*c*d - 6*C*a*b^2*c*d - 2*B*b^3*c*d - B*a^3*d^2 - 3*A*a^2*b*d^2 + 3*C*a^2*b*d^2 + 3*B*a*b^2*d^2 + A*b^3*d^2 - C*b^3*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) + 2*(3*C*b^3*c^6 - 6*C*a*b^2*c^5*d - 2*B*b^3*c^5*d + 3*C*a^2*b*c^4*d^2 + 3*B*a*b^2*c^4*d^2 + A*b^3*c^4*d^2 + 5*C*b^3*c^4*d^2 - 12*C*a*b^2*c^3*d^3 - 4*B*b^3*c^3*d^3 - B*a^3*c^2*d^4 - 3*A*a^2*b*c^2*d^4 + 9*C*a^2*b*c^2*d^4 + 9*B*a*b^2*c^2*d^4 + 3*A*b^3*c^2*d^4 + 2*A*a^3*c*d^5 - 2*C*a^3*c*d^5 - 6*B*a^2*b*c*d^5 - 6*A*a*b^2*c*d^5 + B*a^3*d^6 + 3*A*a^2*b*d^6)*log(abs(d*tan(f*x + e) + c))/(c^4*d^4 + 2*c^2*d^6 + d^8) - 2*(3*C*b^3*c^6*d*tan(f*x + e) - 6*C*a*b^2*c^5*d^2*tan(f*x + e) - 2*B*b^3*c^5*d^2*tan(f*x + e) + 3*C*a^2*b*c^4*d^3*tan(f*x + e) + 3*B*a*b^2*c^4*d^3*tan(f*x + e) + A*b^3*c^4*d^3*tan(f*x + e) + 5*C*b^3*c^4*d^3*tan(f*x + e) - 12*C*a*b^2*c^3*d^4*tan(f*x + e) - 4*B*b^3*c^3*d^4*tan(f*x + e) - B*a^3*c^2*d^5*tan(f*x + e) - 3*A*a^2*b*c^2*d^5*tan(f*x + e) + 9*C*a^2*b*c^2*d^5*tan(f*x + e) + 9*B*a*b^2*c^2*d^5*tan(f*x + e) + 3*A*b^3*c^2*d^5*tan(f*x + e) + 2*A*a^3*c*d^6*tan(f*x + e) - 2*C*a^3*c*d^6*tan(f*x + e) - 6*B*a^2*b*c*d^6*tan(f*x + e) - 6*A*a*b^2*c*d^6*tan(f*x + e) + B*a^3*d^7*tan(f*x + e) + 3*A*a^2*b*d^7*tan(f*x + e) + 2*C*b^3*c^7 - 3*C*a*b^2*c^6*d - B*b^3*c^6*d + 4*C*b^3*c^5*d^2 + C*a^3*c^4*d^3 + 3*B*a^2*b*c^4*d^3 + 3*A*a*b^2*c^4*d^3 - 9*C*a*b^2*c^4*d^3 - 3*B*b^3*c^4*d^3 - 2*B*a^3*c^3*d^4 - 6*A*a^2*b*c^3*d^4 + 6*C*a^2*b*c^3*d^4 + 6*B*a*b^2*c^3*d^4 + 2*A*b^3*c^3*d^4 + 3*A*a^3*c^2*d^5 - C*a^3*c^2*d^5 - 3*B*a^2*b*c^2*d^5 - 3*A*a*b^2*c^2*d^5 + A*a^3*d^7)/((c^4*d^4 + 2*c^2*d^6 + d^8)*(d*tan(f*x + e) + c)) + (C*b^3*d^2*tan(f*x + e)^2 - 4*C*b^3*c*d*tan(f*x + e) + 6*C*a*b^2*d^2*tan(f*x + e) + 2*B*b^3*d^2*tan(f*x + e))/d^4)/f","B",0
78,1,912,0,3.089704," ","integrate((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, C b^{2} \tan\left(f x + e\right)}{d^{2}} + \frac{2 \, {\left(A a^{2} c^{2} - C a^{2} c^{2} - 2 \, B a b c^{2} - A b^{2} c^{2} + C b^{2} c^{2} + 2 \, B a^{2} c d + 4 \, A a b c d - 4 \, C a b c d - 2 \, B b^{2} c d - A a^{2} d^{2} + C a^{2} d^{2} + 2 \, B a b d^{2} + A b^{2} d^{2} - C b^{2} d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(B a^{2} c^{2} + 2 \, A a b c^{2} - 2 \, C a b c^{2} - B b^{2} c^{2} - 2 \, A a^{2} c d + 2 \, C a^{2} c d + 4 \, B a b c d + 2 \, A b^{2} c d - 2 \, C b^{2} c d - B a^{2} d^{2} - 2 \, A a b d^{2} + 2 \, C a b d^{2} + B b^{2} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{2 \, {\left(2 \, C b^{2} c^{5} - 2 \, C a b c^{4} d - B b^{2} c^{4} d + 4 \, C b^{2} c^{3} d^{2} + B a^{2} c^{2} d^{3} + 2 \, A a b c^{2} d^{3} - 6 \, C a b c^{2} d^{3} - 3 \, B b^{2} c^{2} d^{3} - 2 \, A a^{2} c d^{4} + 2 \, C a^{2} c d^{4} + 4 \, B a b c d^{4} + 2 \, A b^{2} c d^{4} - B a^{2} d^{5} - 2 \, A a b d^{5}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}} + \frac{2 \, {\left(2 \, C b^{2} c^{5} d \tan\left(f x + e\right) - 2 \, C a b c^{4} d^{2} \tan\left(f x + e\right) - B b^{2} c^{4} d^{2} \tan\left(f x + e\right) + 4 \, C b^{2} c^{3} d^{3} \tan\left(f x + e\right) + B a^{2} c^{2} d^{4} \tan\left(f x + e\right) + 2 \, A a b c^{2} d^{4} \tan\left(f x + e\right) - 6 \, C a b c^{2} d^{4} \tan\left(f x + e\right) - 3 \, B b^{2} c^{2} d^{4} \tan\left(f x + e\right) - 2 \, A a^{2} c d^{5} \tan\left(f x + e\right) + 2 \, C a^{2} c d^{5} \tan\left(f x + e\right) + 4 \, B a b c d^{5} \tan\left(f x + e\right) + 2 \, A b^{2} c d^{5} \tan\left(f x + e\right) - B a^{2} d^{6} \tan\left(f x + e\right) - 2 \, A a b d^{6} \tan\left(f x + e\right) + C b^{2} c^{6} - C a^{2} c^{4} d^{2} - 2 \, B a b c^{4} d^{2} - A b^{2} c^{4} d^{2} + 3 \, C b^{2} c^{4} d^{2} + 2 \, B a^{2} c^{3} d^{3} + 4 \, A a b c^{3} d^{3} - 4 \, C a b c^{3} d^{3} - 2 \, B b^{2} c^{3} d^{3} - 3 \, A a^{2} c^{2} d^{4} + C a^{2} c^{2} d^{4} + 2 \, B a b c^{2} d^{4} + A b^{2} c^{2} d^{4} - A a^{2} d^{6}\right)}}{{\left(c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}\right)} {\left(d \tan\left(f x + e\right) + c\right)}}}{2 \, f}"," ",0,"1/2*(2*C*b^2*tan(f*x + e)/d^2 + 2*(A*a^2*c^2 - C*a^2*c^2 - 2*B*a*b*c^2 - A*b^2*c^2 + C*b^2*c^2 + 2*B*a^2*c*d + 4*A*a*b*c*d - 4*C*a*b*c*d - 2*B*b^2*c*d - A*a^2*d^2 + C*a^2*d^2 + 2*B*a*b*d^2 + A*b^2*d^2 - C*b^2*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + (B*a^2*c^2 + 2*A*a*b*c^2 - 2*C*a*b*c^2 - B*b^2*c^2 - 2*A*a^2*c*d + 2*C*a^2*c*d + 4*B*a*b*c*d + 2*A*b^2*c*d - 2*C*b^2*c*d - B*a^2*d^2 - 2*A*a*b*d^2 + 2*C*a*b*d^2 + B*b^2*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) - 2*(2*C*b^2*c^5 - 2*C*a*b*c^4*d - B*b^2*c^4*d + 4*C*b^2*c^3*d^2 + B*a^2*c^2*d^3 + 2*A*a*b*c^2*d^3 - 6*C*a*b*c^2*d^3 - 3*B*b^2*c^2*d^3 - 2*A*a^2*c*d^4 + 2*C*a^2*c*d^4 + 4*B*a*b*c*d^4 + 2*A*b^2*c*d^4 - B*a^2*d^5 - 2*A*a*b*d^5)*log(abs(d*tan(f*x + e) + c))/(c^4*d^3 + 2*c^2*d^5 + d^7) + 2*(2*C*b^2*c^5*d*tan(f*x + e) - 2*C*a*b*c^4*d^2*tan(f*x + e) - B*b^2*c^4*d^2*tan(f*x + e) + 4*C*b^2*c^3*d^3*tan(f*x + e) + B*a^2*c^2*d^4*tan(f*x + e) + 2*A*a*b*c^2*d^4*tan(f*x + e) - 6*C*a*b*c^2*d^4*tan(f*x + e) - 3*B*b^2*c^2*d^4*tan(f*x + e) - 2*A*a^2*c*d^5*tan(f*x + e) + 2*C*a^2*c*d^5*tan(f*x + e) + 4*B*a*b*c*d^5*tan(f*x + e) + 2*A*b^2*c*d^5*tan(f*x + e) - B*a^2*d^6*tan(f*x + e) - 2*A*a*b*d^6*tan(f*x + e) + C*b^2*c^6 - C*a^2*c^4*d^2 - 2*B*a*b*c^4*d^2 - A*b^2*c^4*d^2 + 3*C*b^2*c^4*d^2 + 2*B*a^2*c^3*d^3 + 4*A*a*b*c^3*d^3 - 4*C*a*b*c^3*d^3 - 2*B*b^2*c^3*d^3 - 3*A*a^2*c^2*d^4 + C*a^2*c^2*d^4 + 2*B*a*b*c^2*d^4 + A*b^2*c^2*d^4 - A*a^2*d^6)/((c^4*d^3 + 2*c^2*d^5 + d^7)*(d*tan(f*x + e) + c)))/f","B",0
79,1,528,0,6.680665," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a c^{2} - C a c^{2} - B b c^{2} + 2 \, B a c d + 2 \, A b c d - 2 \, C b c d - A a d^{2} + C a d^{2} + B b d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(B a c^{2} + A b c^{2} - C b c^{2} - 2 \, A a c d + 2 \, C a c d + 2 \, B b c d - B a d^{2} - A b d^{2} + C b d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{2 \, {\left(C b c^{4} - B a c^{2} d^{2} - A b c^{2} d^{2} + 3 \, C b c^{2} d^{2} + 2 \, A a c d^{3} - 2 \, C a c d^{3} - 2 \, B b c d^{3} + B a d^{4} + A b d^{4}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{4} d^{2} + 2 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left(C b c^{4} \tan\left(f x + e\right) - B a c^{2} d^{2} \tan\left(f x + e\right) - A b c^{2} d^{2} \tan\left(f x + e\right) + 3 \, C b c^{2} d^{2} \tan\left(f x + e\right) + 2 \, A a c d^{3} \tan\left(f x + e\right) - 2 \, C a c d^{3} \tan\left(f x + e\right) - 2 \, B b c d^{3} \tan\left(f x + e\right) + B a d^{4} \tan\left(f x + e\right) + A b d^{4} \tan\left(f x + e\right) + C a c^{4} + B b c^{4} - 2 \, B a c^{3} d - 2 \, A b c^{3} d + 2 \, C b c^{3} d + 3 \, A a c^{2} d^{2} - C a c^{2} d^{2} - B b c^{2} d^{2} + A a d^{4}\right)}}{{\left(c^{4} d + 2 \, c^{2} d^{3} + d^{5}\right)} {\left(d \tan\left(f x + e\right) + c\right)}}}{2 \, f}"," ",0,"1/2*(2*(A*a*c^2 - C*a*c^2 - B*b*c^2 + 2*B*a*c*d + 2*A*b*c*d - 2*C*b*c*d - A*a*d^2 + C*a*d^2 + B*b*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + (B*a*c^2 + A*b*c^2 - C*b*c^2 - 2*A*a*c*d + 2*C*a*c*d + 2*B*b*c*d - B*a*d^2 - A*b*d^2 + C*b*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) + 2*(C*b*c^4 - B*a*c^2*d^2 - A*b*c^2*d^2 + 3*C*b*c^2*d^2 + 2*A*a*c*d^3 - 2*C*a*c*d^3 - 2*B*b*c*d^3 + B*a*d^4 + A*b*d^4)*log(abs(d*tan(f*x + e) + c))/(c^4*d^2 + 2*c^2*d^4 + d^6) - 2*(C*b*c^4*tan(f*x + e) - B*a*c^2*d^2*tan(f*x + e) - A*b*c^2*d^2*tan(f*x + e) + 3*C*b*c^2*d^2*tan(f*x + e) + 2*A*a*c*d^3*tan(f*x + e) - 2*C*a*c*d^3*tan(f*x + e) - 2*B*b*c*d^3*tan(f*x + e) + B*a*d^4*tan(f*x + e) + A*b*d^4*tan(f*x + e) + C*a*c^4 + B*b*c^4 - 2*B*a*c^3*d - 2*A*b*c^3*d + 2*C*b*c^3*d + 3*A*a*c^2*d^2 - C*a*c^2*d^2 - B*b*c^2*d^2 + A*a*d^4)/((c^4*d + 2*c^2*d^3 + d^5)*(d*tan(f*x + e) + c)))/f","A",0
80,1,299,0,3.991164," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A c^{2} - C c^{2} + 2 \, B c d - A d^{2} + C d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(B c^{2} - 2 \, A c d + 2 \, C c d - B d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{2 \, {\left(B c^{2} d - 2 \, A c d^{2} + 2 \, C c d^{2} - B d^{3}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{4} d + 2 \, c^{2} d^{3} + d^{5}} + \frac{2 \, {\left(B c^{2} d^{2} \tan\left(f x + e\right) - 2 \, A c d^{3} \tan\left(f x + e\right) + 2 \, C c d^{3} \tan\left(f x + e\right) - B d^{4} \tan\left(f x + e\right) - C c^{4} + 2 \, B c^{3} d - 3 \, A c^{2} d^{2} + C c^{2} d^{2} - A d^{4}\right)}}{{\left(c^{4} d + 2 \, c^{2} d^{3} + d^{5}\right)} {\left(d \tan\left(f x + e\right) + c\right)}}}{2 \, f}"," ",0,"1/2*(2*(A*c^2 - C*c^2 + 2*B*c*d - A*d^2 + C*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + (B*c^2 - 2*A*c*d + 2*C*c*d - B*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) - 2*(B*c^2*d - 2*A*c*d^2 + 2*C*c*d^2 - B*d^3)*log(abs(d*tan(f*x + e) + c))/(c^4*d + 2*c^2*d^3 + d^5) + 2*(B*c^2*d^2*tan(f*x + e) - 2*A*c*d^3*tan(f*x + e) + 2*C*c*d^3*tan(f*x + e) - B*d^4*tan(f*x + e) - C*c^4 + 2*B*c^3*d - 3*A*c^2*d^2 + C*c^2*d^2 - A*d^4)/((c^4*d + 2*c^2*d^3 + d^5)*(d*tan(f*x + e) + c)))/f","B",0
81,1,846,0,5.672940," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a c^{2} - C a c^{2} + B b c^{2} + 2 \, B a c d - 2 \, A b c d + 2 \, C b c d - A a d^{2} + C a d^{2} - B b d^{2}\right)} {\left(f x + e\right)}}{a^{2} c^{4} + b^{2} c^{4} + 2 \, a^{2} c^{2} d^{2} + 2 \, b^{2} c^{2} d^{2} + a^{2} d^{4} + b^{2} d^{4}} + \frac{{\left(B a c^{2} - A b c^{2} + C b c^{2} - 2 \, A a c d + 2 \, C a c d - 2 \, B b c d - B a d^{2} + A b d^{2} - C b d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} c^{4} + b^{2} c^{4} + 2 \, a^{2} c^{2} d^{2} + 2 \, b^{2} c^{2} d^{2} + a^{2} d^{4} + b^{2} d^{4}} + \frac{2 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b^{3} c^{2} + b^{5} c^{2} - 2 \, a^{3} b^{2} c d - 2 \, a b^{4} c d + a^{4} b d^{2} + a^{2} b^{3} d^{2}} - \frac{2 \, {\left(C b c^{4} d - 2 \, B b c^{3} d^{2} + B a c^{2} d^{3} + 3 \, A b c^{2} d^{3} - C b c^{2} d^{3} - 2 \, A a c d^{4} + 2 \, C a c d^{4} - B a d^{5} + A b d^{5}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{2} c^{6} d - 2 \, a b c^{5} d^{2} + a^{2} c^{4} d^{3} + 2 \, b^{2} c^{4} d^{3} - 4 \, a b c^{3} d^{4} + 2 \, a^{2} c^{2} d^{5} + b^{2} c^{2} d^{5} - 2 \, a b c d^{6} + a^{2} d^{7}} + \frac{2 \, {\left(C b c^{4} d \tan\left(f x + e\right) - 2 \, B b c^{3} d^{2} \tan\left(f x + e\right) + B a c^{2} d^{3} \tan\left(f x + e\right) + 3 \, A b c^{2} d^{3} \tan\left(f x + e\right) - C b c^{2} d^{3} \tan\left(f x + e\right) - 2 \, A a c d^{4} \tan\left(f x + e\right) + 2 \, C a c d^{4} \tan\left(f x + e\right) - B a d^{5} \tan\left(f x + e\right) + A b d^{5} \tan\left(f x + e\right) + 2 \, C b c^{5} - C a c^{4} d - 3 \, B b c^{4} d + 2 \, B a c^{3} d^{2} + 4 \, A b c^{3} d^{2} - 3 \, A a c^{2} d^{3} + C a c^{2} d^{3} - B b c^{2} d^{3} + 2 \, A b c d^{4} - A a d^{5}\right)}}{{\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2} + 2 \, b^{2} c^{4} d^{2} - 4 \, a b c^{3} d^{3} + 2 \, a^{2} c^{2} d^{4} + b^{2} c^{2} d^{4} - 2 \, a b c d^{5} + a^{2} d^{6}\right)} {\left(d \tan\left(f x + e\right) + c\right)}}}{2 \, f}"," ",0,"1/2*(2*(A*a*c^2 - C*a*c^2 + B*b*c^2 + 2*B*a*c*d - 2*A*b*c*d + 2*C*b*c*d - A*a*d^2 + C*a*d^2 - B*b*d^2)*(f*x + e)/(a^2*c^4 + b^2*c^4 + 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2 + a^2*d^4 + b^2*d^4) + (B*a*c^2 - A*b*c^2 + C*b*c^2 - 2*A*a*c*d + 2*C*a*c*d - 2*B*b*c*d - B*a*d^2 + A*b*d^2 - C*b*d^2)*log(tan(f*x + e)^2 + 1)/(a^2*c^4 + b^2*c^4 + 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2 + a^2*d^4 + b^2*d^4) + 2*(C*a^2*b^2 - B*a*b^3 + A*b^4)*log(abs(b*tan(f*x + e) + a))/(a^2*b^3*c^2 + b^5*c^2 - 2*a^3*b^2*c*d - 2*a*b^4*c*d + a^4*b*d^2 + a^2*b^3*d^2) - 2*(C*b*c^4*d - 2*B*b*c^3*d^2 + B*a*c^2*d^3 + 3*A*b*c^2*d^3 - C*b*c^2*d^3 - 2*A*a*c*d^4 + 2*C*a*c*d^4 - B*a*d^5 + A*b*d^5)*log(abs(d*tan(f*x + e) + c))/(b^2*c^6*d - 2*a*b*c^5*d^2 + a^2*c^4*d^3 + 2*b^2*c^4*d^3 - 4*a*b*c^3*d^4 + 2*a^2*c^2*d^5 + b^2*c^2*d^5 - 2*a*b*c*d^6 + a^2*d^7) + 2*(C*b*c^4*d*tan(f*x + e) - 2*B*b*c^3*d^2*tan(f*x + e) + B*a*c^2*d^3*tan(f*x + e) + 3*A*b*c^2*d^3*tan(f*x + e) - C*b*c^2*d^3*tan(f*x + e) - 2*A*a*c*d^4*tan(f*x + e) + 2*C*a*c*d^4*tan(f*x + e) - B*a*d^5*tan(f*x + e) + A*b*d^5*tan(f*x + e) + 2*C*b*c^5 - C*a*c^4*d - 3*B*b*c^4*d + 2*B*a*c^3*d^2 + 4*A*b*c^3*d^2 - 3*A*a*c^2*d^3 + C*a*c^2*d^3 - B*b*c^2*d^3 + 2*A*b*c*d^4 - A*a*d^5)/((b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2 + 2*b^2*c^4*d^2 - 4*a*b*c^3*d^3 + 2*a^2*c^2*d^4 + b^2*c^2*d^4 - 2*a*b*c*d^5 + a^2*d^6)*(d*tan(f*x + e) + c)))/f","B",0
82,1,2893,0,4.534001," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{2} c^{2} - C a^{2} c^{2} + 2 \, B a b c^{2} - A b^{2} c^{2} + C b^{2} c^{2} + 2 \, B a^{2} c d - 4 \, A a b c d + 4 \, C a b c d - 2 \, B b^{2} c d - A a^{2} d^{2} + C a^{2} d^{2} - 2 \, B a b d^{2} + A b^{2} d^{2} - C b^{2} d^{2}\right)} {\left(f x + e\right)}}{a^{4} c^{4} + 2 \, a^{2} b^{2} c^{4} + b^{4} c^{4} + 2 \, a^{4} c^{2} d^{2} + 4 \, a^{2} b^{2} c^{2} d^{2} + 2 \, b^{4} c^{2} d^{2} + a^{4} d^{4} + 2 \, a^{2} b^{2} d^{4} + b^{4} d^{4}} + \frac{{\left(B a^{2} c^{2} - 2 \, A a b c^{2} + 2 \, C a b c^{2} - B b^{2} c^{2} - 2 \, A a^{2} c d + 2 \, C a^{2} c d - 4 \, B a b c d + 2 \, A b^{2} c d - 2 \, C b^{2} c d - B a^{2} d^{2} + 2 \, A a b d^{2} - 2 \, C a b d^{2} + B b^{2} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} c^{4} + 2 \, a^{2} b^{2} c^{4} + b^{4} c^{4} + 2 \, a^{4} c^{2} d^{2} + 4 \, a^{2} b^{2} c^{2} d^{2} + 2 \, b^{4} c^{2} d^{2} + a^{4} d^{4} + 2 \, a^{2} b^{2} d^{4} + b^{4} d^{4}} - \frac{2 \, {\left(B a^{2} b^{4} c - 2 \, A a b^{5} c + 2 \, C a b^{5} c - B b^{6} c + 2 \, C a^{4} b^{2} d - 3 \, B a^{3} b^{3} d + 4 \, A a^{2} b^{4} d - B a b^{5} d + 2 \, A b^{6} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b^{4} c^{3} + 2 \, a^{2} b^{6} c^{3} + b^{8} c^{3} - 3 \, a^{5} b^{3} c^{2} d - 6 \, a^{3} b^{5} c^{2} d - 3 \, a b^{7} c^{2} d + 3 \, a^{6} b^{2} c d^{2} + 6 \, a^{4} b^{4} c d^{2} + 3 \, a^{2} b^{6} c d^{2} - a^{7} b d^{3} - 2 \, a^{5} b^{3} d^{3} - a^{3} b^{5} d^{3}} + \frac{2 \, {\left(2 \, C b c^{4} d^{2} - 3 \, B b c^{3} d^{3} + B a c^{2} d^{4} + 4 \, A b c^{2} d^{4} - 2 \, A a c d^{5} + 2 \, C a c d^{5} - B b c d^{5} - B a d^{6} + 2 \, A b d^{6}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} + 2 \, b^{3} c^{5} d^{3} - a^{3} c^{4} d^{4} - 6 \, a b^{2} c^{4} d^{4} + 6 \, a^{2} b c^{3} d^{5} + b^{3} c^{3} d^{5} - 2 \, a^{3} c^{2} d^{6} - 3 \, a b^{2} c^{2} d^{6} + 3 \, a^{2} b c d^{7} - a^{3} d^{8}} + \frac{B a^{2} b^{3} c^{4} d \tan\left(f x + e\right)^{2} - 2 \, A a b^{4} c^{4} d \tan\left(f x + e\right)^{2} + 2 \, C a b^{4} c^{4} d \tan\left(f x + e\right)^{2} - B b^{5} c^{4} d \tan\left(f x + e\right)^{2} - 2 \, B a^{3} b^{2} c^{3} d^{2} \tan\left(f x + e\right)^{2} + 2 \, A a^{2} b^{3} c^{3} d^{2} \tan\left(f x + e\right)^{2} - 2 \, C a^{2} b^{3} c^{3} d^{2} \tan\left(f x + e\right)^{2} - 2 \, B a b^{4} c^{3} d^{2} \tan\left(f x + e\right)^{2} + 2 \, A b^{5} c^{3} d^{2} \tan\left(f x + e\right)^{2} - 2 \, C b^{5} c^{3} d^{2} \tan\left(f x + e\right)^{2} + B a^{4} b c^{2} d^{3} \tan\left(f x + e\right)^{2} + 2 \, A a^{3} b^{2} c^{2} d^{3} \tan\left(f x + e\right)^{2} - 2 \, C a^{3} b^{2} c^{2} d^{3} \tan\left(f x + e\right)^{2} + 6 \, B a^{2} b^{3} c^{2} d^{3} \tan\left(f x + e\right)^{2} - 2 \, A a b^{4} c^{2} d^{3} \tan\left(f x + e\right)^{2} + 2 \, C a b^{4} c^{2} d^{3} \tan\left(f x + e\right)^{2} + B b^{5} c^{2} d^{3} \tan\left(f x + e\right)^{2} - 2 \, A a^{4} b c d^{4} \tan\left(f x + e\right)^{2} + 2 \, C a^{4} b c d^{4} \tan\left(f x + e\right)^{2} - 2 \, B a^{3} b^{2} c d^{4} \tan\left(f x + e\right)^{2} - 2 \, A a^{2} b^{3} c d^{4} \tan\left(f x + e\right)^{2} + 2 \, C a^{2} b^{3} c d^{4} \tan\left(f x + e\right)^{2} - 2 \, B a b^{4} c d^{4} \tan\left(f x + e\right)^{2} - B a^{4} b d^{5} \tan\left(f x + e\right)^{2} + 2 \, A a^{3} b^{2} d^{5} \tan\left(f x + e\right)^{2} - 2 \, C a^{3} b^{2} d^{5} \tan\left(f x + e\right)^{2} + B a^{2} b^{3} d^{5} \tan\left(f x + e\right)^{2} + B a^{2} b^{3} c^{5} \tan\left(f x + e\right) - 2 \, A a b^{4} c^{5} \tan\left(f x + e\right) + 2 \, C a b^{4} c^{5} \tan\left(f x + e\right) - B b^{5} c^{5} \tan\left(f x + e\right) - 4 \, C a^{4} b c^{4} d \tan\left(f x + e\right) + B a^{3} b^{2} c^{4} d \tan\left(f x + e\right) - 2 \, A a^{2} b^{3} c^{4} d \tan\left(f x + e\right) - 6 \, C a^{2} b^{3} c^{4} d \tan\left(f x + e\right) - B a b^{4} c^{4} d \tan\left(f x + e\right) - 4 \, C b^{5} c^{4} d \tan\left(f x + e\right) + B a^{4} b c^{3} d^{2} \tan\left(f x + e\right) + 4 \, A a^{3} b^{2} c^{3} d^{2} \tan\left(f x + e\right) - 4 \, C a^{3} b^{2} c^{3} d^{2} \tan\left(f x + e\right) + 8 \, B a^{2} b^{3} c^{3} d^{2} \tan\left(f x + e\right) + 3 \, B b^{5} c^{3} d^{2} \tan\left(f x + e\right) + B a^{5} c^{2} d^{3} \tan\left(f x + e\right) - 2 \, A a^{4} b c^{2} d^{3} \tan\left(f x + e\right) - 6 \, C a^{4} b c^{2} d^{3} \tan\left(f x + e\right) + 8 \, B a^{3} b^{2} c^{2} d^{3} \tan\left(f x + e\right) - 12 \, A a^{2} b^{3} c^{2} d^{3} \tan\left(f x + e\right) - 4 \, C a^{2} b^{3} c^{2} d^{3} \tan\left(f x + e\right) + 3 \, B a b^{4} c^{2} d^{3} \tan\left(f x + e\right) - 6 \, A b^{5} c^{2} d^{3} \tan\left(f x + e\right) - 2 \, C b^{5} c^{2} d^{3} \tan\left(f x + e\right) - 2 \, A a^{5} c d^{4} \tan\left(f x + e\right) + 2 \, C a^{5} c d^{4} \tan\left(f x + e\right) - B a^{4} b c d^{4} \tan\left(f x + e\right) + 3 \, B a^{2} b^{3} c d^{4} \tan\left(f x + e\right) + 2 \, B b^{5} c d^{4} \tan\left(f x + e\right) - B a^{5} d^{5} \tan\left(f x + e\right) - 4 \, C a^{4} b d^{5} \tan\left(f x + e\right) + 3 \, B a^{3} b^{2} d^{5} \tan\left(f x + e\right) - 6 \, A a^{2} b^{3} d^{5} \tan\left(f x + e\right) - 2 \, C a^{2} b^{3} d^{5} \tan\left(f x + e\right) + 2 \, B a b^{4} d^{5} \tan\left(f x + e\right) - 4 \, A b^{5} d^{5} \tan\left(f x + e\right) - 2 \, C a^{4} b c^{5} + 3 \, B a^{3} b^{2} c^{5} - 4 \, A a^{2} b^{3} c^{5} + B a b^{4} c^{5} - 2 \, A b^{5} c^{5} - 2 \, C a^{5} c^{4} d - 2 \, B a^{4} b c^{4} d + 2 \, A a^{3} b^{2} c^{4} d - 6 \, C a^{3} b^{2} c^{4} d - 2 \, B a^{2} b^{3} c^{4} d + 2 \, A a b^{4} c^{4} d - 4 \, C a b^{4} c^{4} d + 3 \, B a^{5} c^{3} d^{2} + 2 \, A a^{4} b c^{3} d^{2} - 6 \, C a^{4} b c^{3} d^{2} + 14 \, B a^{3} b^{2} c^{3} d^{2} - 6 \, A a^{2} b^{3} c^{3} d^{2} - 2 \, C a^{2} b^{3} c^{3} d^{2} + 7 \, B a b^{4} c^{3} d^{2} - 4 \, A b^{5} c^{3} d^{2} - 4 \, A a^{5} c^{2} d^{3} - 2 \, B a^{4} b c^{2} d^{3} - 6 \, A a^{3} b^{2} c^{2} d^{3} - 2 \, C a^{3} b^{2} c^{2} d^{3} - 2 \, B a^{2} b^{3} c^{2} d^{3} - 2 \, A a b^{4} c^{2} d^{3} - 2 \, C a b^{4} c^{2} d^{3} + B a^{5} c d^{4} + 2 \, A a^{4} b c d^{4} - 4 \, C a^{4} b c d^{4} + 7 \, B a^{3} b^{2} c d^{4} - 2 \, A a^{2} b^{3} c d^{4} - 2 \, C a^{2} b^{3} c d^{4} + 4 \, B a b^{4} c d^{4} - 2 \, A b^{5} c d^{4} - 2 \, A a^{5} d^{5} - 4 \, A a^{3} b^{2} d^{5} - 2 \, A a b^{4} d^{5}}{{\left(a^{4} b^{2} c^{6} + 2 \, a^{2} b^{4} c^{6} + b^{6} c^{6} - 2 \, a^{5} b c^{5} d - 4 \, a^{3} b^{3} c^{5} d - 2 \, a b^{5} c^{5} d + a^{6} c^{4} d^{2} + 4 \, a^{4} b^{2} c^{4} d^{2} + 5 \, a^{2} b^{4} c^{4} d^{2} + 2 \, b^{6} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} - 8 \, a^{3} b^{3} c^{3} d^{3} - 4 \, a b^{5} c^{3} d^{3} + 2 \, a^{6} c^{2} d^{4} + 5 \, a^{4} b^{2} c^{2} d^{4} + 4 \, a^{2} b^{4} c^{2} d^{4} + b^{6} c^{2} d^{4} - 2 \, a^{5} b c d^{5} - 4 \, a^{3} b^{3} c d^{5} - 2 \, a b^{5} c d^{5} + a^{6} d^{6} + 2 \, a^{4} b^{2} d^{6} + a^{2} b^{4} d^{6}\right)} {\left(b d \tan\left(f x + e\right)^{2} + b c \tan\left(f x + e\right) + a d \tan\left(f x + e\right) + a c\right)}}}{2 \, f}"," ",0,"1/2*(2*(A*a^2*c^2 - C*a^2*c^2 + 2*B*a*b*c^2 - A*b^2*c^2 + C*b^2*c^2 + 2*B*a^2*c*d - 4*A*a*b*c*d + 4*C*a*b*c*d - 2*B*b^2*c*d - A*a^2*d^2 + C*a^2*d^2 - 2*B*a*b*d^2 + A*b^2*d^2 - C*b^2*d^2)*(f*x + e)/(a^4*c^4 + 2*a^2*b^2*c^4 + b^4*c^4 + 2*a^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2 + 2*b^4*c^2*d^2 + a^4*d^4 + 2*a^2*b^2*d^4 + b^4*d^4) + (B*a^2*c^2 - 2*A*a*b*c^2 + 2*C*a*b*c^2 - B*b^2*c^2 - 2*A*a^2*c*d + 2*C*a^2*c*d - 4*B*a*b*c*d + 2*A*b^2*c*d - 2*C*b^2*c*d - B*a^2*d^2 + 2*A*a*b*d^2 - 2*C*a*b*d^2 + B*b^2*d^2)*log(tan(f*x + e)^2 + 1)/(a^4*c^4 + 2*a^2*b^2*c^4 + b^4*c^4 + 2*a^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2 + 2*b^4*c^2*d^2 + a^4*d^4 + 2*a^2*b^2*d^4 + b^4*d^4) - 2*(B*a^2*b^4*c - 2*A*a*b^5*c + 2*C*a*b^5*c - B*b^6*c + 2*C*a^4*b^2*d - 3*B*a^3*b^3*d + 4*A*a^2*b^4*d - B*a*b^5*d + 2*A*b^6*d)*log(abs(b*tan(f*x + e) + a))/(a^4*b^4*c^3 + 2*a^2*b^6*c^3 + b^8*c^3 - 3*a^5*b^3*c^2*d - 6*a^3*b^5*c^2*d - 3*a*b^7*c^2*d + 3*a^6*b^2*c*d^2 + 6*a^4*b^4*c*d^2 + 3*a^2*b^6*c*d^2 - a^7*b*d^3 - 2*a^5*b^3*d^3 - a^3*b^5*d^3) + 2*(2*C*b*c^4*d^2 - 3*B*b*c^3*d^3 + B*a*c^2*d^4 + 4*A*b*c^2*d^4 - 2*A*a*c*d^5 + 2*C*a*c*d^5 - B*b*c*d^5 - B*a*d^6 + 2*A*b*d^6)*log(abs(d*tan(f*x + e) + c))/(b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 + 2*b^3*c^5*d^3 - a^3*c^4*d^4 - 6*a*b^2*c^4*d^4 + 6*a^2*b*c^3*d^5 + b^3*c^3*d^5 - 2*a^3*c^2*d^6 - 3*a*b^2*c^2*d^6 + 3*a^2*b*c*d^7 - a^3*d^8) + (B*a^2*b^3*c^4*d*tan(f*x + e)^2 - 2*A*a*b^4*c^4*d*tan(f*x + e)^2 + 2*C*a*b^4*c^4*d*tan(f*x + e)^2 - B*b^5*c^4*d*tan(f*x + e)^2 - 2*B*a^3*b^2*c^3*d^2*tan(f*x + e)^2 + 2*A*a^2*b^3*c^3*d^2*tan(f*x + e)^2 - 2*C*a^2*b^3*c^3*d^2*tan(f*x + e)^2 - 2*B*a*b^4*c^3*d^2*tan(f*x + e)^2 + 2*A*b^5*c^3*d^2*tan(f*x + e)^2 - 2*C*b^5*c^3*d^2*tan(f*x + e)^2 + B*a^4*b*c^2*d^3*tan(f*x + e)^2 + 2*A*a^3*b^2*c^2*d^3*tan(f*x + e)^2 - 2*C*a^3*b^2*c^2*d^3*tan(f*x + e)^2 + 6*B*a^2*b^3*c^2*d^3*tan(f*x + e)^2 - 2*A*a*b^4*c^2*d^3*tan(f*x + e)^2 + 2*C*a*b^4*c^2*d^3*tan(f*x + e)^2 + B*b^5*c^2*d^3*tan(f*x + e)^2 - 2*A*a^4*b*c*d^4*tan(f*x + e)^2 + 2*C*a^4*b*c*d^4*tan(f*x + e)^2 - 2*B*a^3*b^2*c*d^4*tan(f*x + e)^2 - 2*A*a^2*b^3*c*d^4*tan(f*x + e)^2 + 2*C*a^2*b^3*c*d^4*tan(f*x + e)^2 - 2*B*a*b^4*c*d^4*tan(f*x + e)^2 - B*a^4*b*d^5*tan(f*x + e)^2 + 2*A*a^3*b^2*d^5*tan(f*x + e)^2 - 2*C*a^3*b^2*d^5*tan(f*x + e)^2 + B*a^2*b^3*d^5*tan(f*x + e)^2 + B*a^2*b^3*c^5*tan(f*x + e) - 2*A*a*b^4*c^5*tan(f*x + e) + 2*C*a*b^4*c^5*tan(f*x + e) - B*b^5*c^5*tan(f*x + e) - 4*C*a^4*b*c^4*d*tan(f*x + e) + B*a^3*b^2*c^4*d*tan(f*x + e) - 2*A*a^2*b^3*c^4*d*tan(f*x + e) - 6*C*a^2*b^3*c^4*d*tan(f*x + e) - B*a*b^4*c^4*d*tan(f*x + e) - 4*C*b^5*c^4*d*tan(f*x + e) + B*a^4*b*c^3*d^2*tan(f*x + e) + 4*A*a^3*b^2*c^3*d^2*tan(f*x + e) - 4*C*a^3*b^2*c^3*d^2*tan(f*x + e) + 8*B*a^2*b^3*c^3*d^2*tan(f*x + e) + 3*B*b^5*c^3*d^2*tan(f*x + e) + B*a^5*c^2*d^3*tan(f*x + e) - 2*A*a^4*b*c^2*d^3*tan(f*x + e) - 6*C*a^4*b*c^2*d^3*tan(f*x + e) + 8*B*a^3*b^2*c^2*d^3*tan(f*x + e) - 12*A*a^2*b^3*c^2*d^3*tan(f*x + e) - 4*C*a^2*b^3*c^2*d^3*tan(f*x + e) + 3*B*a*b^4*c^2*d^3*tan(f*x + e) - 6*A*b^5*c^2*d^3*tan(f*x + e) - 2*C*b^5*c^2*d^3*tan(f*x + e) - 2*A*a^5*c*d^4*tan(f*x + e) + 2*C*a^5*c*d^4*tan(f*x + e) - B*a^4*b*c*d^4*tan(f*x + e) + 3*B*a^2*b^3*c*d^4*tan(f*x + e) + 2*B*b^5*c*d^4*tan(f*x + e) - B*a^5*d^5*tan(f*x + e) - 4*C*a^4*b*d^5*tan(f*x + e) + 3*B*a^3*b^2*d^5*tan(f*x + e) - 6*A*a^2*b^3*d^5*tan(f*x + e) - 2*C*a^2*b^3*d^5*tan(f*x + e) + 2*B*a*b^4*d^5*tan(f*x + e) - 4*A*b^5*d^5*tan(f*x + e) - 2*C*a^4*b*c^5 + 3*B*a^3*b^2*c^5 - 4*A*a^2*b^3*c^5 + B*a*b^4*c^5 - 2*A*b^5*c^5 - 2*C*a^5*c^4*d - 2*B*a^4*b*c^4*d + 2*A*a^3*b^2*c^4*d - 6*C*a^3*b^2*c^4*d - 2*B*a^2*b^3*c^4*d + 2*A*a*b^4*c^4*d - 4*C*a*b^4*c^4*d + 3*B*a^5*c^3*d^2 + 2*A*a^4*b*c^3*d^2 - 6*C*a^4*b*c^3*d^2 + 14*B*a^3*b^2*c^3*d^2 - 6*A*a^2*b^3*c^3*d^2 - 2*C*a^2*b^3*c^3*d^2 + 7*B*a*b^4*c^3*d^2 - 4*A*b^5*c^3*d^2 - 4*A*a^5*c^2*d^3 - 2*B*a^4*b*c^2*d^3 - 6*A*a^3*b^2*c^2*d^3 - 2*C*a^3*b^2*c^2*d^3 - 2*B*a^2*b^3*c^2*d^3 - 2*A*a*b^4*c^2*d^3 - 2*C*a*b^4*c^2*d^3 + B*a^5*c*d^4 + 2*A*a^4*b*c*d^4 - 4*C*a^4*b*c*d^4 + 7*B*a^3*b^2*c*d^4 - 2*A*a^2*b^3*c*d^4 - 2*C*a^2*b^3*c*d^4 + 4*B*a*b^4*c*d^4 - 2*A*b^5*c*d^4 - 2*A*a^5*d^5 - 4*A*a^3*b^2*d^5 - 2*A*a*b^4*d^5)/((a^4*b^2*c^6 + 2*a^2*b^4*c^6 + b^6*c^6 - 2*a^5*b*c^5*d - 4*a^3*b^3*c^5*d - 2*a*b^5*c^5*d + a^6*c^4*d^2 + 4*a^4*b^2*c^4*d^2 + 5*a^2*b^4*c^4*d^2 + 2*b^6*c^4*d^2 - 4*a^5*b*c^3*d^3 - 8*a^3*b^3*c^3*d^3 - 4*a*b^5*c^3*d^3 + 2*a^6*c^2*d^4 + 5*a^4*b^2*c^2*d^4 + 4*a^2*b^4*c^2*d^4 + b^6*c^2*d^4 - 2*a^5*b*c*d^5 - 4*a^3*b^3*c*d^5 - 2*a*b^5*c*d^5 + a^6*d^6 + 2*a^4*b^2*d^6 + a^2*b^4*d^6)*(b*d*tan(f*x + e)^2 + b*c*tan(f*x + e) + a*d*tan(f*x + e) + a*c)))/f","B",0
83,1,3176,0,25.977513," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{3} c^{2} - C a^{3} c^{2} + 3 \, B a^{2} b c^{2} - 3 \, A a b^{2} c^{2} + 3 \, C a b^{2} c^{2} - B b^{3} c^{2} + 2 \, B a^{3} c d - 6 \, A a^{2} b c d + 6 \, C a^{2} b c d - 6 \, B a b^{2} c d + 2 \, A b^{3} c d - 2 \, C b^{3} c d - A a^{3} d^{2} + C a^{3} d^{2} - 3 \, B a^{2} b d^{2} + 3 \, A a b^{2} d^{2} - 3 \, C a b^{2} d^{2} + B b^{3} d^{2}\right)} {\left(f x + e\right)}}{a^{6} c^{4} + 3 \, a^{4} b^{2} c^{4} + 3 \, a^{2} b^{4} c^{4} + b^{6} c^{4} + 2 \, a^{6} c^{2} d^{2} + 6 \, a^{4} b^{2} c^{2} d^{2} + 6 \, a^{2} b^{4} c^{2} d^{2} + 2 \, b^{6} c^{2} d^{2} + a^{6} d^{4} + 3 \, a^{4} b^{2} d^{4} + 3 \, a^{2} b^{4} d^{4} + b^{6} d^{4}} + \frac{{\left(B a^{3} c^{2} - 3 \, A a^{2} b c^{2} + 3 \, C a^{2} b c^{2} - 3 \, B a b^{2} c^{2} + A b^{3} c^{2} - C b^{3} c^{2} - 2 \, A a^{3} c d + 2 \, C a^{3} c d - 6 \, B a^{2} b c d + 6 \, A a b^{2} c d - 6 \, C a b^{2} c d + 2 \, B b^{3} c d - B a^{3} d^{2} + 3 \, A a^{2} b d^{2} - 3 \, C a^{2} b d^{2} + 3 \, B a b^{2} d^{2} - A b^{3} d^{2} + C b^{3} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} c^{4} + 3 \, a^{4} b^{2} c^{4} + 3 \, a^{2} b^{4} c^{4} + b^{6} c^{4} + 2 \, a^{6} c^{2} d^{2} + 6 \, a^{4} b^{2} c^{2} d^{2} + 6 \, a^{2} b^{4} c^{2} d^{2} + 2 \, b^{6} c^{2} d^{2} + a^{6} d^{4} + 3 \, a^{4} b^{2} d^{4} + 3 \, a^{2} b^{4} d^{4} + b^{6} d^{4}} - \frac{2 \, {\left(B a^{3} b^{5} c^{2} - 3 \, A a^{2} b^{6} c^{2} + 3 \, C a^{2} b^{6} c^{2} - 3 \, B a b^{7} c^{2} + A b^{8} c^{2} - C b^{8} c^{2} - 4 \, B a^{4} b^{4} c d + 10 \, A a^{3} b^{5} c d - 10 \, C a^{3} b^{5} c d + 6 \, B a^{2} b^{6} c d + 2 \, A a b^{7} c d - 2 \, C a b^{7} c d + 2 \, B b^{8} c d - 3 \, C a^{6} b^{2} d^{2} + 6 \, B a^{5} b^{3} d^{2} - 10 \, A a^{4} b^{4} d^{2} + C a^{4} b^{4} d^{2} + 3 \, B a^{3} b^{5} d^{2} - 9 \, A a^{2} b^{6} d^{2} + B a b^{7} d^{2} - 3 \, A b^{8} d^{2}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{6} b^{5} c^{4} + 3 \, a^{4} b^{7} c^{4} + 3 \, a^{2} b^{9} c^{4} + b^{11} c^{4} - 4 \, a^{7} b^{4} c^{3} d - 12 \, a^{5} b^{6} c^{3} d - 12 \, a^{3} b^{8} c^{3} d - 4 \, a b^{10} c^{3} d + 6 \, a^{8} b^{3} c^{2} d^{2} + 18 \, a^{6} b^{5} c^{2} d^{2} + 18 \, a^{4} b^{7} c^{2} d^{2} + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{9} b^{2} c d^{3} - 12 \, a^{7} b^{4} c d^{3} - 12 \, a^{5} b^{6} c d^{3} - 4 \, a^{3} b^{8} c d^{3} + a^{10} b d^{4} + 3 \, a^{8} b^{3} d^{4} + 3 \, a^{6} b^{5} d^{4} + a^{4} b^{7} d^{4}} - \frac{2 \, {\left(3 \, C b c^{4} d^{3} - 4 \, B b c^{3} d^{4} + B a c^{2} d^{5} + 5 \, A b c^{2} d^{5} + C b c^{2} d^{5} - 2 \, A a c d^{6} + 2 \, C a c d^{6} - 2 \, B b c d^{6} - B a d^{7} + 3 \, A b d^{7}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{4} c^{8} d - 4 \, a b^{3} c^{7} d^{2} + 6 \, a^{2} b^{2} c^{6} d^{3} + 2 \, b^{4} c^{6} d^{3} - 4 \, a^{3} b c^{5} d^{4} - 8 \, a b^{3} c^{5} d^{4} + a^{4} c^{4} d^{5} + 12 \, a^{2} b^{2} c^{4} d^{5} + b^{4} c^{4} d^{5} - 8 \, a^{3} b c^{3} d^{6} - 4 \, a b^{3} c^{3} d^{6} + 2 \, a^{4} c^{2} d^{7} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}} + \frac{2 \, {\left(3 \, C b c^{4} d^{3} \tan\left(f x + e\right) - 4 \, B b c^{3} d^{4} \tan\left(f x + e\right) + B a c^{2} d^{5} \tan\left(f x + e\right) + 5 \, A b c^{2} d^{5} \tan\left(f x + e\right) + C b c^{2} d^{5} \tan\left(f x + e\right) - 2 \, A a c d^{6} \tan\left(f x + e\right) + 2 \, C a c d^{6} \tan\left(f x + e\right) - 2 \, B b c d^{6} \tan\left(f x + e\right) - B a d^{7} \tan\left(f x + e\right) + 3 \, A b d^{7} \tan\left(f x + e\right) + 4 \, C b c^{5} d^{2} - C a c^{4} d^{3} - 5 \, B b c^{4} d^{3} + 2 \, B a c^{3} d^{4} + 6 \, A b c^{3} d^{4} + 2 \, C b c^{3} d^{4} - 3 \, A a c^{2} d^{5} + C a c^{2} d^{5} - 3 \, B b c^{2} d^{5} + 4 \, A b c d^{6} - A a d^{7}\right)}}{{\left(b^{4} c^{8} - 4 \, a b^{3} c^{7} d + 6 \, a^{2} b^{2} c^{6} d^{2} + 2 \, b^{4} c^{6} d^{2} - 4 \, a^{3} b c^{5} d^{3} - 8 \, a b^{3} c^{5} d^{3} + a^{4} c^{4} d^{4} + 12 \, a^{2} b^{2} c^{4} d^{4} + b^{4} c^{4} d^{4} - 8 \, a^{3} b c^{3} d^{5} - 4 \, a b^{3} c^{3} d^{5} + 2 \, a^{4} c^{2} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{6} - 4 \, a^{3} b c d^{7} + a^{4} d^{8}\right)} {\left(d \tan\left(f x + e\right) + c\right)}} + \frac{3 \, B a^{3} b^{6} c^{2} \tan\left(f x + e\right)^{2} - 9 \, A a^{2} b^{7} c^{2} \tan\left(f x + e\right)^{2} + 9 \, C a^{2} b^{7} c^{2} \tan\left(f x + e\right)^{2} - 9 \, B a b^{8} c^{2} \tan\left(f x + e\right)^{2} + 3 \, A b^{9} c^{2} \tan\left(f x + e\right)^{2} - 3 \, C b^{9} c^{2} \tan\left(f x + e\right)^{2} - 12 \, B a^{4} b^{5} c d \tan\left(f x + e\right)^{2} + 30 \, A a^{3} b^{6} c d \tan\left(f x + e\right)^{2} - 30 \, C a^{3} b^{6} c d \tan\left(f x + e\right)^{2} + 18 \, B a^{2} b^{7} c d \tan\left(f x + e\right)^{2} + 6 \, A a b^{8} c d \tan\left(f x + e\right)^{2} - 6 \, C a b^{8} c d \tan\left(f x + e\right)^{2} + 6 \, B b^{9} c d \tan\left(f x + e\right)^{2} - 9 \, C a^{6} b^{3} d^{2} \tan\left(f x + e\right)^{2} + 18 \, B a^{5} b^{4} d^{2} \tan\left(f x + e\right)^{2} - 30 \, A a^{4} b^{5} d^{2} \tan\left(f x + e\right)^{2} + 3 \, C a^{4} b^{5} d^{2} \tan\left(f x + e\right)^{2} + 9 \, B a^{3} b^{6} d^{2} \tan\left(f x + e\right)^{2} - 27 \, A a^{2} b^{7} d^{2} \tan\left(f x + e\right)^{2} + 3 \, B a b^{8} d^{2} \tan\left(f x + e\right)^{2} - 9 \, A b^{9} d^{2} \tan\left(f x + e\right)^{2} + 8 \, B a^{4} b^{5} c^{2} \tan\left(f x + e\right) - 22 \, A a^{3} b^{6} c^{2} \tan\left(f x + e\right) + 22 \, C a^{3} b^{6} c^{2} \tan\left(f x + e\right) - 18 \, B a^{2} b^{7} c^{2} \tan\left(f x + e\right) + 2 \, A a b^{8} c^{2} \tan\left(f x + e\right) - 2 \, C a b^{8} c^{2} \tan\left(f x + e\right) - 2 \, B b^{9} c^{2} \tan\left(f x + e\right) + 4 \, C a^{6} b^{3} c d \tan\left(f x + e\right) - 32 \, B a^{5} b^{4} c d \tan\left(f x + e\right) + 72 \, A a^{4} b^{5} c d \tan\left(f x + e\right) - 60 \, C a^{4} b^{5} c d \tan\left(f x + e\right) + 28 \, B a^{3} b^{6} c d \tan\left(f x + e\right) + 28 \, A a^{2} b^{7} c d \tan\left(f x + e\right) - 16 \, C a^{2} b^{7} c d \tan\left(f x + e\right) + 12 \, B a b^{8} c d \tan\left(f x + e\right) + 4 \, A b^{9} c d \tan\left(f x + e\right) - 22 \, C a^{7} b^{2} d^{2} \tan\left(f x + e\right) + 42 \, B a^{6} b^{3} d^{2} \tan\left(f x + e\right) - 68 \, A a^{5} b^{4} d^{2} \tan\left(f x + e\right) + 2 \, C a^{5} b^{4} d^{2} \tan\left(f x + e\right) + 26 \, B a^{4} b^{5} d^{2} \tan\left(f x + e\right) - 66 \, A a^{3} b^{6} d^{2} \tan\left(f x + e\right) + 8 \, B a^{2} b^{7} d^{2} \tan\left(f x + e\right) - 22 \, A a b^{8} d^{2} \tan\left(f x + e\right) - C a^{6} b^{3} c^{2} + 6 \, B a^{5} b^{4} c^{2} - 14 \, A a^{4} b^{5} c^{2} + 11 \, C a^{4} b^{5} c^{2} - 7 \, B a^{3} b^{6} c^{2} - 3 \, A a^{2} b^{7} c^{2} - B a b^{8} c^{2} - A b^{9} c^{2} + 6 \, C a^{7} b^{2} c d - 22 \, B a^{6} b^{3} c d + 44 \, A a^{5} b^{4} c d - 26 \, C a^{5} b^{4} c d + 6 \, B a^{4} b^{5} c d + 26 \, A a^{3} b^{6} c d - 8 \, C a^{3} b^{6} c d + 4 \, B a^{2} b^{7} c d + 6 \, A a b^{8} c d - 14 \, C a^{8} b d^{2} + 25 \, B a^{7} b^{2} d^{2} - 39 \, A a^{6} b^{3} d^{2} - 3 \, C a^{6} b^{3} d^{2} + 19 \, B a^{5} b^{4} d^{2} - 41 \, A a^{4} b^{5} d^{2} - C a^{4} b^{5} d^{2} + 6 \, B a^{3} b^{6} d^{2} - 14 \, A a^{2} b^{7} d^{2}}{{\left(a^{6} b^{4} c^{4} + 3 \, a^{4} b^{6} c^{4} + 3 \, a^{2} b^{8} c^{4} + b^{10} c^{4} - 4 \, a^{7} b^{3} c^{3} d - 12 \, a^{5} b^{5} c^{3} d - 12 \, a^{3} b^{7} c^{3} d - 4 \, a b^{9} c^{3} d + 6 \, a^{8} b^{2} c^{2} d^{2} + 18 \, a^{6} b^{4} c^{2} d^{2} + 18 \, a^{4} b^{6} c^{2} d^{2} + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{9} b c d^{3} - 12 \, a^{7} b^{3} c d^{3} - 12 \, a^{5} b^{5} c d^{3} - 4 \, a^{3} b^{7} c d^{3} + a^{10} d^{4} + 3 \, a^{8} b^{2} d^{4} + 3 \, a^{6} b^{4} d^{4} + a^{4} b^{6} d^{4}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*a^3*c^2 - C*a^3*c^2 + 3*B*a^2*b*c^2 - 3*A*a*b^2*c^2 + 3*C*a*b^2*c^2 - B*b^3*c^2 + 2*B*a^3*c*d - 6*A*a^2*b*c*d + 6*C*a^2*b*c*d - 6*B*a*b^2*c*d + 2*A*b^3*c*d - 2*C*b^3*c*d - A*a^3*d^2 + C*a^3*d^2 - 3*B*a^2*b*d^2 + 3*A*a*b^2*d^2 - 3*C*a*b^2*d^2 + B*b^3*d^2)*(f*x + e)/(a^6*c^4 + 3*a^4*b^2*c^4 + 3*a^2*b^4*c^4 + b^6*c^4 + 2*a^6*c^2*d^2 + 6*a^4*b^2*c^2*d^2 + 6*a^2*b^4*c^2*d^2 + 2*b^6*c^2*d^2 + a^6*d^4 + 3*a^4*b^2*d^4 + 3*a^2*b^4*d^4 + b^6*d^4) + (B*a^3*c^2 - 3*A*a^2*b*c^2 + 3*C*a^2*b*c^2 - 3*B*a*b^2*c^2 + A*b^3*c^2 - C*b^3*c^2 - 2*A*a^3*c*d + 2*C*a^3*c*d - 6*B*a^2*b*c*d + 6*A*a*b^2*c*d - 6*C*a*b^2*c*d + 2*B*b^3*c*d - B*a^3*d^2 + 3*A*a^2*b*d^2 - 3*C*a^2*b*d^2 + 3*B*a*b^2*d^2 - A*b^3*d^2 + C*b^3*d^2)*log(tan(f*x + e)^2 + 1)/(a^6*c^4 + 3*a^4*b^2*c^4 + 3*a^2*b^4*c^4 + b^6*c^4 + 2*a^6*c^2*d^2 + 6*a^4*b^2*c^2*d^2 + 6*a^2*b^4*c^2*d^2 + 2*b^6*c^2*d^2 + a^6*d^4 + 3*a^4*b^2*d^4 + 3*a^2*b^4*d^4 + b^6*d^4) - 2*(B*a^3*b^5*c^2 - 3*A*a^2*b^6*c^2 + 3*C*a^2*b^6*c^2 - 3*B*a*b^7*c^2 + A*b^8*c^2 - C*b^8*c^2 - 4*B*a^4*b^4*c*d + 10*A*a^3*b^5*c*d - 10*C*a^3*b^5*c*d + 6*B*a^2*b^6*c*d + 2*A*a*b^7*c*d - 2*C*a*b^7*c*d + 2*B*b^8*c*d - 3*C*a^6*b^2*d^2 + 6*B*a^5*b^3*d^2 - 10*A*a^4*b^4*d^2 + C*a^4*b^4*d^2 + 3*B*a^3*b^5*d^2 - 9*A*a^2*b^6*d^2 + B*a*b^7*d^2 - 3*A*b^8*d^2)*log(abs(b*tan(f*x + e) + a))/(a^6*b^5*c^4 + 3*a^4*b^7*c^4 + 3*a^2*b^9*c^4 + b^11*c^4 - 4*a^7*b^4*c^3*d - 12*a^5*b^6*c^3*d - 12*a^3*b^8*c^3*d - 4*a*b^10*c^3*d + 6*a^8*b^3*c^2*d^2 + 18*a^6*b^5*c^2*d^2 + 18*a^4*b^7*c^2*d^2 + 6*a^2*b^9*c^2*d^2 - 4*a^9*b^2*c*d^3 - 12*a^7*b^4*c*d^3 - 12*a^5*b^6*c*d^3 - 4*a^3*b^8*c*d^3 + a^10*b*d^4 + 3*a^8*b^3*d^4 + 3*a^6*b^5*d^4 + a^4*b^7*d^4) - 2*(3*C*b*c^4*d^3 - 4*B*b*c^3*d^4 + B*a*c^2*d^5 + 5*A*b*c^2*d^5 + C*b*c^2*d^5 - 2*A*a*c*d^6 + 2*C*a*c*d^6 - 2*B*b*c*d^6 - B*a*d^7 + 3*A*b*d^7)*log(abs(d*tan(f*x + e) + c))/(b^4*c^8*d - 4*a*b^3*c^7*d^2 + 6*a^2*b^2*c^6*d^3 + 2*b^4*c^6*d^3 - 4*a^3*b*c^5*d^4 - 8*a*b^3*c^5*d^4 + a^4*c^4*d^5 + 12*a^2*b^2*c^4*d^5 + b^4*c^4*d^5 - 8*a^3*b*c^3*d^6 - 4*a*b^3*c^3*d^6 + 2*a^4*c^2*d^7 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9) + 2*(3*C*b*c^4*d^3*tan(f*x + e) - 4*B*b*c^3*d^4*tan(f*x + e) + B*a*c^2*d^5*tan(f*x + e) + 5*A*b*c^2*d^5*tan(f*x + e) + C*b*c^2*d^5*tan(f*x + e) - 2*A*a*c*d^6*tan(f*x + e) + 2*C*a*c*d^6*tan(f*x + e) - 2*B*b*c*d^6*tan(f*x + e) - B*a*d^7*tan(f*x + e) + 3*A*b*d^7*tan(f*x + e) + 4*C*b*c^5*d^2 - C*a*c^4*d^3 - 5*B*b*c^4*d^3 + 2*B*a*c^3*d^4 + 6*A*b*c^3*d^4 + 2*C*b*c^3*d^4 - 3*A*a*c^2*d^5 + C*a*c^2*d^5 - 3*B*b*c^2*d^5 + 4*A*b*c*d^6 - A*a*d^7)/((b^4*c^8 - 4*a*b^3*c^7*d + 6*a^2*b^2*c^6*d^2 + 2*b^4*c^6*d^2 - 4*a^3*b*c^5*d^3 - 8*a*b^3*c^5*d^3 + a^4*c^4*d^4 + 12*a^2*b^2*c^4*d^4 + b^4*c^4*d^4 - 8*a^3*b*c^3*d^5 - 4*a*b^3*c^3*d^5 + 2*a^4*c^2*d^6 + 6*a^2*b^2*c^2*d^6 - 4*a^3*b*c*d^7 + a^4*d^8)*(d*tan(f*x + e) + c)) + (3*B*a^3*b^6*c^2*tan(f*x + e)^2 - 9*A*a^2*b^7*c^2*tan(f*x + e)^2 + 9*C*a^2*b^7*c^2*tan(f*x + e)^2 - 9*B*a*b^8*c^2*tan(f*x + e)^2 + 3*A*b^9*c^2*tan(f*x + e)^2 - 3*C*b^9*c^2*tan(f*x + e)^2 - 12*B*a^4*b^5*c*d*tan(f*x + e)^2 + 30*A*a^3*b^6*c*d*tan(f*x + e)^2 - 30*C*a^3*b^6*c*d*tan(f*x + e)^2 + 18*B*a^2*b^7*c*d*tan(f*x + e)^2 + 6*A*a*b^8*c*d*tan(f*x + e)^2 - 6*C*a*b^8*c*d*tan(f*x + e)^2 + 6*B*b^9*c*d*tan(f*x + e)^2 - 9*C*a^6*b^3*d^2*tan(f*x + e)^2 + 18*B*a^5*b^4*d^2*tan(f*x + e)^2 - 30*A*a^4*b^5*d^2*tan(f*x + e)^2 + 3*C*a^4*b^5*d^2*tan(f*x + e)^2 + 9*B*a^3*b^6*d^2*tan(f*x + e)^2 - 27*A*a^2*b^7*d^2*tan(f*x + e)^2 + 3*B*a*b^8*d^2*tan(f*x + e)^2 - 9*A*b^9*d^2*tan(f*x + e)^2 + 8*B*a^4*b^5*c^2*tan(f*x + e) - 22*A*a^3*b^6*c^2*tan(f*x + e) + 22*C*a^3*b^6*c^2*tan(f*x + e) - 18*B*a^2*b^7*c^2*tan(f*x + e) + 2*A*a*b^8*c^2*tan(f*x + e) - 2*C*a*b^8*c^2*tan(f*x + e) - 2*B*b^9*c^2*tan(f*x + e) + 4*C*a^6*b^3*c*d*tan(f*x + e) - 32*B*a^5*b^4*c*d*tan(f*x + e) + 72*A*a^4*b^5*c*d*tan(f*x + e) - 60*C*a^4*b^5*c*d*tan(f*x + e) + 28*B*a^3*b^6*c*d*tan(f*x + e) + 28*A*a^2*b^7*c*d*tan(f*x + e) - 16*C*a^2*b^7*c*d*tan(f*x + e) + 12*B*a*b^8*c*d*tan(f*x + e) + 4*A*b^9*c*d*tan(f*x + e) - 22*C*a^7*b^2*d^2*tan(f*x + e) + 42*B*a^6*b^3*d^2*tan(f*x + e) - 68*A*a^5*b^4*d^2*tan(f*x + e) + 2*C*a^5*b^4*d^2*tan(f*x + e) + 26*B*a^4*b^5*d^2*tan(f*x + e) - 66*A*a^3*b^6*d^2*tan(f*x + e) + 8*B*a^2*b^7*d^2*tan(f*x + e) - 22*A*a*b^8*d^2*tan(f*x + e) - C*a^6*b^3*c^2 + 6*B*a^5*b^4*c^2 - 14*A*a^4*b^5*c^2 + 11*C*a^4*b^5*c^2 - 7*B*a^3*b^6*c^2 - 3*A*a^2*b^7*c^2 - B*a*b^8*c^2 - A*b^9*c^2 + 6*C*a^7*b^2*c*d - 22*B*a^6*b^3*c*d + 44*A*a^5*b^4*c*d - 26*C*a^5*b^4*c*d + 6*B*a^4*b^5*c*d + 26*A*a^3*b^6*c*d - 8*C*a^3*b^6*c*d + 4*B*a^2*b^7*c*d + 6*A*a*b^8*c*d - 14*C*a^8*b*d^2 + 25*B*a^7*b^2*d^2 - 39*A*a^6*b^3*d^2 - 3*C*a^6*b^3*d^2 + 19*B*a^5*b^4*d^2 - 41*A*a^4*b^5*d^2 - C*a^4*b^5*d^2 + 6*B*a^3*b^6*d^2 - 14*A*a^2*b^7*d^2)/((a^6*b^4*c^4 + 3*a^4*b^6*c^4 + 3*a^2*b^8*c^4 + b^10*c^4 - 4*a^7*b^3*c^3*d - 12*a^5*b^5*c^3*d - 12*a^3*b^7*c^3*d - 4*a*b^9*c^3*d + 6*a^8*b^2*c^2*d^2 + 18*a^6*b^4*c^2*d^2 + 18*a^4*b^6*c^2*d^2 + 6*a^2*b^8*c^2*d^2 - 4*a^9*b*c*d^3 - 12*a^7*b^3*c*d^3 - 12*a^5*b^5*c*d^3 - 4*a^3*b^7*c*d^3 + a^10*d^4 + 3*a^8*b^2*d^4 + 3*a^6*b^4*d^4 + a^4*b^6*d^4)*(b*tan(f*x + e) + a)^2))/f","B",0
84,1,2505,0,5.088346," ","integrate((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, C b^{3} \tan\left(f x + e\right)}{d^{3}} + \frac{2 \, {\left(A a^{3} c^{3} - C a^{3} c^{3} - 3 \, B a^{2} b c^{3} - 3 \, A a b^{2} c^{3} + 3 \, C a b^{2} c^{3} + B b^{3} c^{3} + 3 \, B a^{3} c^{2} d + 9 \, A a^{2} b c^{2} d - 9 \, C a^{2} b c^{2} d - 9 \, B a b^{2} c^{2} d - 3 \, A b^{3} c^{2} d + 3 \, C b^{3} c^{2} d - 3 \, A a^{3} c d^{2} + 3 \, C a^{3} c d^{2} + 9 \, B a^{2} b c d^{2} + 9 \, A a b^{2} c d^{2} - 9 \, C a b^{2} c d^{2} - 3 \, B b^{3} c d^{2} - B a^{3} d^{3} - 3 \, A a^{2} b d^{3} + 3 \, C a^{2} b d^{3} + 3 \, B a b^{2} d^{3} + A b^{3} d^{3} - C b^{3} d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(B a^{3} c^{3} + 3 \, A a^{2} b c^{3} - 3 \, C a^{2} b c^{3} - 3 \, B a b^{2} c^{3} - A b^{3} c^{3} + C b^{3} c^{3} - 3 \, A a^{3} c^{2} d + 3 \, C a^{3} c^{2} d + 9 \, B a^{2} b c^{2} d + 9 \, A a b^{2} c^{2} d - 9 \, C a b^{2} c^{2} d - 3 \, B b^{3} c^{2} d - 3 \, B a^{3} c d^{2} - 9 \, A a^{2} b c d^{2} + 9 \, C a^{2} b c d^{2} + 9 \, B a b^{2} c d^{2} + 3 \, A b^{3} c d^{2} - 3 \, C b^{3} c d^{2} + A a^{3} d^{3} - C a^{3} d^{3} - 3 \, B a^{2} b d^{3} - 3 \, A a b^{2} d^{3} + 3 \, C a b^{2} d^{3} + B b^{3} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left(3 \, C b^{3} c^{7} - 3 \, C a b^{2} c^{6} d - B b^{3} c^{6} d + 9 \, C b^{3} c^{5} d^{2} - 9 \, C a b^{2} c^{4} d^{3} - 3 \, B b^{3} c^{4} d^{3} + B a^{3} c^{3} d^{4} + 3 \, A a^{2} b c^{3} d^{4} - 3 \, C a^{2} b c^{3} d^{4} - 3 \, B a b^{2} c^{3} d^{4} - A b^{3} c^{3} d^{4} + 10 \, C b^{3} c^{3} d^{4} - 3 \, A a^{3} c^{2} d^{5} + 3 \, C a^{3} c^{2} d^{5} + 9 \, B a^{2} b c^{2} d^{5} + 9 \, A a b^{2} c^{2} d^{5} - 18 \, C a b^{2} c^{2} d^{5} - 6 \, B b^{3} c^{2} d^{5} - 3 \, B a^{3} c d^{6} - 9 \, A a^{2} b c d^{6} + 9 \, C a^{2} b c d^{6} + 9 \, B a b^{2} c d^{6} + 3 \, A b^{3} c d^{6} + A a^{3} d^{7} - C a^{3} d^{7} - 3 \, B a^{2} b d^{7} - 3 \, A a b^{2} d^{7}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{6} d^{4} + 3 \, c^{4} d^{6} + 3 \, c^{2} d^{8} + d^{10}} + \frac{9 \, C b^{3} c^{7} d^{2} \tan\left(f x + e\right)^{2} - 9 \, C a b^{2} c^{6} d^{3} \tan\left(f x + e\right)^{2} - 3 \, B b^{3} c^{6} d^{3} \tan\left(f x + e\right)^{2} + 27 \, C b^{3} c^{5} d^{4} \tan\left(f x + e\right)^{2} - 27 \, C a b^{2} c^{4} d^{5} \tan\left(f x + e\right)^{2} - 9 \, B b^{3} c^{4} d^{5} \tan\left(f x + e\right)^{2} + 3 \, B a^{3} c^{3} d^{6} \tan\left(f x + e\right)^{2} + 9 \, A a^{2} b c^{3} d^{6} \tan\left(f x + e\right)^{2} - 9 \, C a^{2} b c^{3} d^{6} \tan\left(f x + e\right)^{2} - 9 \, B a b^{2} c^{3} d^{6} \tan\left(f x + e\right)^{2} - 3 \, A b^{3} c^{3} d^{6} \tan\left(f x + e\right)^{2} + 30 \, C b^{3} c^{3} d^{6} \tan\left(f x + e\right)^{2} - 9 \, A a^{3} c^{2} d^{7} \tan\left(f x + e\right)^{2} + 9 \, C a^{3} c^{2} d^{7} \tan\left(f x + e\right)^{2} + 27 \, B a^{2} b c^{2} d^{7} \tan\left(f x + e\right)^{2} + 27 \, A a b^{2} c^{2} d^{7} \tan\left(f x + e\right)^{2} - 54 \, C a b^{2} c^{2} d^{7} \tan\left(f x + e\right)^{2} - 18 \, B b^{3} c^{2} d^{7} \tan\left(f x + e\right)^{2} - 9 \, B a^{3} c d^{8} \tan\left(f x + e\right)^{2} - 27 \, A a^{2} b c d^{8} \tan\left(f x + e\right)^{2} + 27 \, C a^{2} b c d^{8} \tan\left(f x + e\right)^{2} + 27 \, B a b^{2} c d^{8} \tan\left(f x + e\right)^{2} + 9 \, A b^{3} c d^{8} \tan\left(f x + e\right)^{2} + 3 \, A a^{3} d^{9} \tan\left(f x + e\right)^{2} - 3 \, C a^{3} d^{9} \tan\left(f x + e\right)^{2} - 9 \, B a^{2} b d^{9} \tan\left(f x + e\right)^{2} - 9 \, A a b^{2} d^{9} \tan\left(f x + e\right)^{2} + 12 \, C b^{3} c^{8} d \tan\left(f x + e\right) - 6 \, C a b^{2} c^{7} d^{2} \tan\left(f x + e\right) - 2 \, B b^{3} c^{7} d^{2} \tan\left(f x + e\right) - 6 \, C a^{2} b c^{6} d^{3} \tan\left(f x + e\right) - 6 \, B a b^{2} c^{6} d^{3} \tan\left(f x + e\right) - 2 \, A b^{3} c^{6} d^{3} \tan\left(f x + e\right) + 38 \, C b^{3} c^{6} d^{3} \tan\left(f x + e\right) - 18 \, C a b^{2} c^{5} d^{4} \tan\left(f x + e\right) - 6 \, B b^{3} c^{5} d^{4} \tan\left(f x + e\right) + 8 \, B a^{3} c^{4} d^{5} \tan\left(f x + e\right) + 24 \, A a^{2} b c^{4} d^{5} \tan\left(f x + e\right) - 42 \, C a^{2} b c^{4} d^{5} \tan\left(f x + e\right) - 42 \, B a b^{2} c^{4} d^{5} \tan\left(f x + e\right) - 14 \, A b^{3} c^{4} d^{5} \tan\left(f x + e\right) + 50 \, C b^{3} c^{4} d^{5} \tan\left(f x + e\right) - 22 \, A a^{3} c^{3} d^{6} \tan\left(f x + e\right) + 22 \, C a^{3} c^{3} d^{6} \tan\left(f x + e\right) + 66 \, B a^{2} b c^{3} d^{6} \tan\left(f x + e\right) + 66 \, A a b^{2} c^{3} d^{6} \tan\left(f x + e\right) - 84 \, C a b^{2} c^{3} d^{6} \tan\left(f x + e\right) - 28 \, B b^{3} c^{3} d^{6} \tan\left(f x + e\right) - 18 \, B a^{3} c^{2} d^{7} \tan\left(f x + e\right) - 54 \, A a^{2} b c^{2} d^{7} \tan\left(f x + e\right) + 36 \, C a^{2} b c^{2} d^{7} \tan\left(f x + e\right) + 36 \, B a b^{2} c^{2} d^{7} \tan\left(f x + e\right) + 12 \, A b^{3} c^{2} d^{7} \tan\left(f x + e\right) + 2 \, A a^{3} c d^{8} \tan\left(f x + e\right) - 2 \, C a^{3} c d^{8} \tan\left(f x + e\right) - 6 \, B a^{2} b c d^{8} \tan\left(f x + e\right) - 6 \, A a b^{2} c d^{8} \tan\left(f x + e\right) - 2 \, B a^{3} d^{9} \tan\left(f x + e\right) - 6 \, A a^{2} b d^{9} \tan\left(f x + e\right) + 4 \, C b^{3} c^{9} - 3 \, C a^{2} b c^{7} d^{2} - 3 \, B a b^{2} c^{7} d^{2} - A b^{3} c^{7} d^{2} + 13 \, C b^{3} c^{7} d^{2} - C a^{3} c^{6} d^{3} - 3 \, B a^{2} b c^{6} d^{3} - 3 \, A a b^{2} c^{6} d^{3} + 3 \, C a b^{2} c^{6} d^{3} + B b^{3} c^{6} d^{3} + 6 \, B a^{3} c^{5} d^{4} + 18 \, A a^{2} b c^{5} d^{4} - 27 \, C a^{2} b c^{5} d^{4} - 27 \, B a b^{2} c^{5} d^{4} - 9 \, A b^{3} c^{5} d^{4} + 21 \, C b^{3} c^{5} d^{4} - 14 \, A a^{3} c^{4} d^{5} + 11 \, C a^{3} c^{4} d^{5} + 33 \, B a^{2} b c^{4} d^{5} + 33 \, A a b^{2} c^{4} d^{5} - 33 \, C a b^{2} c^{4} d^{5} - 11 \, B b^{3} c^{4} d^{5} - 7 \, B a^{3} c^{3} d^{6} - 21 \, A a^{2} b c^{3} d^{6} + 12 \, C a^{2} b c^{3} d^{6} + 12 \, B a b^{2} c^{3} d^{6} + 4 \, A b^{3} c^{3} d^{6} - 3 \, A a^{3} c^{2} d^{7} - B a^{3} c d^{8} - 3 \, A a^{2} b c d^{8} - A a^{3} d^{9}}{{\left(c^{6} d^{4} + 3 \, c^{4} d^{6} + 3 \, c^{2} d^{8} + d^{10}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*C*b^3*tan(f*x + e)/d^3 + 2*(A*a^3*c^3 - C*a^3*c^3 - 3*B*a^2*b*c^3 - 3*A*a*b^2*c^3 + 3*C*a*b^2*c^3 + B*b^3*c^3 + 3*B*a^3*c^2*d + 9*A*a^2*b*c^2*d - 9*C*a^2*b*c^2*d - 9*B*a*b^2*c^2*d - 3*A*b^3*c^2*d + 3*C*b^3*c^2*d - 3*A*a^3*c*d^2 + 3*C*a^3*c*d^2 + 9*B*a^2*b*c*d^2 + 9*A*a*b^2*c*d^2 - 9*C*a*b^2*c*d^2 - 3*B*b^3*c*d^2 - B*a^3*d^3 - 3*A*a^2*b*d^3 + 3*C*a^2*b*d^3 + 3*B*a*b^2*d^3 + A*b^3*d^3 - C*b^3*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (B*a^3*c^3 + 3*A*a^2*b*c^3 - 3*C*a^2*b*c^3 - 3*B*a*b^2*c^3 - A*b^3*c^3 + C*b^3*c^3 - 3*A*a^3*c^2*d + 3*C*a^3*c^2*d + 9*B*a^2*b*c^2*d + 9*A*a*b^2*c^2*d - 9*C*a*b^2*c^2*d - 3*B*b^3*c^2*d - 3*B*a^3*c*d^2 - 9*A*a^2*b*c*d^2 + 9*C*a^2*b*c*d^2 + 9*B*a*b^2*c*d^2 + 3*A*b^3*c*d^2 - 3*C*b^3*c*d^2 + A*a^3*d^3 - C*a^3*d^3 - 3*B*a^2*b*d^3 - 3*A*a*b^2*d^3 + 3*C*a*b^2*d^3 + B*b^3*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*(3*C*b^3*c^7 - 3*C*a*b^2*c^6*d - B*b^3*c^6*d + 9*C*b^3*c^5*d^2 - 9*C*a*b^2*c^4*d^3 - 3*B*b^3*c^4*d^3 + B*a^3*c^3*d^4 + 3*A*a^2*b*c^3*d^4 - 3*C*a^2*b*c^3*d^4 - 3*B*a*b^2*c^3*d^4 - A*b^3*c^3*d^4 + 10*C*b^3*c^3*d^4 - 3*A*a^3*c^2*d^5 + 3*C*a^3*c^2*d^5 + 9*B*a^2*b*c^2*d^5 + 9*A*a*b^2*c^2*d^5 - 18*C*a*b^2*c^2*d^5 - 6*B*b^3*c^2*d^5 - 3*B*a^3*c*d^6 - 9*A*a^2*b*c*d^6 + 9*C*a^2*b*c*d^6 + 9*B*a*b^2*c*d^6 + 3*A*b^3*c*d^6 + A*a^3*d^7 - C*a^3*d^7 - 3*B*a^2*b*d^7 - 3*A*a*b^2*d^7)*log(abs(d*tan(f*x + e) + c))/(c^6*d^4 + 3*c^4*d^6 + 3*c^2*d^8 + d^10) + (9*C*b^3*c^7*d^2*tan(f*x + e)^2 - 9*C*a*b^2*c^6*d^3*tan(f*x + e)^2 - 3*B*b^3*c^6*d^3*tan(f*x + e)^2 + 27*C*b^3*c^5*d^4*tan(f*x + e)^2 - 27*C*a*b^2*c^4*d^5*tan(f*x + e)^2 - 9*B*b^3*c^4*d^5*tan(f*x + e)^2 + 3*B*a^3*c^3*d^6*tan(f*x + e)^2 + 9*A*a^2*b*c^3*d^6*tan(f*x + e)^2 - 9*C*a^2*b*c^3*d^6*tan(f*x + e)^2 - 9*B*a*b^2*c^3*d^6*tan(f*x + e)^2 - 3*A*b^3*c^3*d^6*tan(f*x + e)^2 + 30*C*b^3*c^3*d^6*tan(f*x + e)^2 - 9*A*a^3*c^2*d^7*tan(f*x + e)^2 + 9*C*a^3*c^2*d^7*tan(f*x + e)^2 + 27*B*a^2*b*c^2*d^7*tan(f*x + e)^2 + 27*A*a*b^2*c^2*d^7*tan(f*x + e)^2 - 54*C*a*b^2*c^2*d^7*tan(f*x + e)^2 - 18*B*b^3*c^2*d^7*tan(f*x + e)^2 - 9*B*a^3*c*d^8*tan(f*x + e)^2 - 27*A*a^2*b*c*d^8*tan(f*x + e)^2 + 27*C*a^2*b*c*d^8*tan(f*x + e)^2 + 27*B*a*b^2*c*d^8*tan(f*x + e)^2 + 9*A*b^3*c*d^8*tan(f*x + e)^2 + 3*A*a^3*d^9*tan(f*x + e)^2 - 3*C*a^3*d^9*tan(f*x + e)^2 - 9*B*a^2*b*d^9*tan(f*x + e)^2 - 9*A*a*b^2*d^9*tan(f*x + e)^2 + 12*C*b^3*c^8*d*tan(f*x + e) - 6*C*a*b^2*c^7*d^2*tan(f*x + e) - 2*B*b^3*c^7*d^2*tan(f*x + e) - 6*C*a^2*b*c^6*d^3*tan(f*x + e) - 6*B*a*b^2*c^6*d^3*tan(f*x + e) - 2*A*b^3*c^6*d^3*tan(f*x + e) + 38*C*b^3*c^6*d^3*tan(f*x + e) - 18*C*a*b^2*c^5*d^4*tan(f*x + e) - 6*B*b^3*c^5*d^4*tan(f*x + e) + 8*B*a^3*c^4*d^5*tan(f*x + e) + 24*A*a^2*b*c^4*d^5*tan(f*x + e) - 42*C*a^2*b*c^4*d^5*tan(f*x + e) - 42*B*a*b^2*c^4*d^5*tan(f*x + e) - 14*A*b^3*c^4*d^5*tan(f*x + e) + 50*C*b^3*c^4*d^5*tan(f*x + e) - 22*A*a^3*c^3*d^6*tan(f*x + e) + 22*C*a^3*c^3*d^6*tan(f*x + e) + 66*B*a^2*b*c^3*d^6*tan(f*x + e) + 66*A*a*b^2*c^3*d^6*tan(f*x + e) - 84*C*a*b^2*c^3*d^6*tan(f*x + e) - 28*B*b^3*c^3*d^6*tan(f*x + e) - 18*B*a^3*c^2*d^7*tan(f*x + e) - 54*A*a^2*b*c^2*d^7*tan(f*x + e) + 36*C*a^2*b*c^2*d^7*tan(f*x + e) + 36*B*a*b^2*c^2*d^7*tan(f*x + e) + 12*A*b^3*c^2*d^7*tan(f*x + e) + 2*A*a^3*c*d^8*tan(f*x + e) - 2*C*a^3*c*d^8*tan(f*x + e) - 6*B*a^2*b*c*d^8*tan(f*x + e) - 6*A*a*b^2*c*d^8*tan(f*x + e) - 2*B*a^3*d^9*tan(f*x + e) - 6*A*a^2*b*d^9*tan(f*x + e) + 4*C*b^3*c^9 - 3*C*a^2*b*c^7*d^2 - 3*B*a*b^2*c^7*d^2 - A*b^3*c^7*d^2 + 13*C*b^3*c^7*d^2 - C*a^3*c^6*d^3 - 3*B*a^2*b*c^6*d^3 - 3*A*a*b^2*c^6*d^3 + 3*C*a*b^2*c^6*d^3 + B*b^3*c^6*d^3 + 6*B*a^3*c^5*d^4 + 18*A*a^2*b*c^5*d^4 - 27*C*a^2*b*c^5*d^4 - 27*B*a*b^2*c^5*d^4 - 9*A*b^3*c^5*d^4 + 21*C*b^3*c^5*d^4 - 14*A*a^3*c^4*d^5 + 11*C*a^3*c^4*d^5 + 33*B*a^2*b*c^4*d^5 + 33*A*a*b^2*c^4*d^5 - 33*C*a*b^2*c^4*d^5 - 11*B*b^3*c^4*d^5 - 7*B*a^3*c^3*d^6 - 21*A*a^2*b*c^3*d^6 + 12*C*a^2*b*c^3*d^6 + 12*B*a*b^2*c^3*d^6 + 4*A*b^3*c^3*d^6 - 3*A*a^3*c^2*d^7 - B*a^3*c*d^8 - 3*A*a^2*b*c*d^8 - A*a^3*d^9)/((c^6*d^4 + 3*c^4*d^6 + 3*c^2*d^8 + d^10)*(d*tan(f*x + e) + c)^2))/f","B",0
85,1,1709,0,4.651095," ","integrate((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{2} c^{3} - C a^{2} c^{3} - 2 \, B a b c^{3} - A b^{2} c^{3} + C b^{2} c^{3} + 3 \, B a^{2} c^{2} d + 6 \, A a b c^{2} d - 6 \, C a b c^{2} d - 3 \, B b^{2} c^{2} d - 3 \, A a^{2} c d^{2} + 3 \, C a^{2} c d^{2} + 6 \, B a b c d^{2} + 3 \, A b^{2} c d^{2} - 3 \, C b^{2} c d^{2} - B a^{2} d^{3} - 2 \, A a b d^{3} + 2 \, C a b d^{3} + B b^{2} d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(B a^{2} c^{3} + 2 \, A a b c^{3} - 2 \, C a b c^{3} - B b^{2} c^{3} - 3 \, A a^{2} c^{2} d + 3 \, C a^{2} c^{2} d + 6 \, B a b c^{2} d + 3 \, A b^{2} c^{2} d - 3 \, C b^{2} c^{2} d - 3 \, B a^{2} c d^{2} - 6 \, A a b c d^{2} + 6 \, C a b c d^{2} + 3 \, B b^{2} c d^{2} + A a^{2} d^{3} - C a^{2} d^{3} - 2 \, B a b d^{3} - A b^{2} d^{3} + C b^{2} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{2 \, {\left(C b^{2} c^{6} + 3 \, C b^{2} c^{4} d^{2} - B a^{2} c^{3} d^{3} - 2 \, A a b c^{3} d^{3} + 2 \, C a b c^{3} d^{3} + B b^{2} c^{3} d^{3} + 3 \, A a^{2} c^{2} d^{4} - 3 \, C a^{2} c^{2} d^{4} - 6 \, B a b c^{2} d^{4} - 3 \, A b^{2} c^{2} d^{4} + 6 \, C b^{2} c^{2} d^{4} + 3 \, B a^{2} c d^{5} + 6 \, A a b c d^{5} - 6 \, C a b c d^{5} - 3 \, B b^{2} c d^{5} - A a^{2} d^{6} + C a^{2} d^{6} + 2 \, B a b d^{6} + A b^{2} d^{6}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{6} d^{3} + 3 \, c^{4} d^{5} + 3 \, c^{2} d^{7} + d^{9}} - \frac{3 \, C b^{2} c^{6} d \tan\left(f x + e\right)^{2} + 9 \, C b^{2} c^{4} d^{3} \tan\left(f x + e\right)^{2} - 3 \, B a^{2} c^{3} d^{4} \tan\left(f x + e\right)^{2} - 6 \, A a b c^{3} d^{4} \tan\left(f x + e\right)^{2} + 6 \, C a b c^{3} d^{4} \tan\left(f x + e\right)^{2} + 3 \, B b^{2} c^{3} d^{4} \tan\left(f x + e\right)^{2} + 9 \, A a^{2} c^{2} d^{5} \tan\left(f x + e\right)^{2} - 9 \, C a^{2} c^{2} d^{5} \tan\left(f x + e\right)^{2} - 18 \, B a b c^{2} d^{5} \tan\left(f x + e\right)^{2} - 9 \, A b^{2} c^{2} d^{5} \tan\left(f x + e\right)^{2} + 18 \, C b^{2} c^{2} d^{5} \tan\left(f x + e\right)^{2} + 9 \, B a^{2} c d^{6} \tan\left(f x + e\right)^{2} + 18 \, A a b c d^{6} \tan\left(f x + e\right)^{2} - 18 \, C a b c d^{6} \tan\left(f x + e\right)^{2} - 9 \, B b^{2} c d^{6} \tan\left(f x + e\right)^{2} - 3 \, A a^{2} d^{7} \tan\left(f x + e\right)^{2} + 3 \, C a^{2} d^{7} \tan\left(f x + e\right)^{2} + 6 \, B a b d^{7} \tan\left(f x + e\right)^{2} + 3 \, A b^{2} d^{7} \tan\left(f x + e\right)^{2} + 2 \, C b^{2} c^{7} \tan\left(f x + e\right) + 4 \, C a b c^{6} d \tan\left(f x + e\right) + 2 \, B b^{2} c^{6} d \tan\left(f x + e\right) + 6 \, C b^{2} c^{5} d^{2} \tan\left(f x + e\right) - 8 \, B a^{2} c^{4} d^{3} \tan\left(f x + e\right) - 16 \, A a b c^{4} d^{3} \tan\left(f x + e\right) + 28 \, C a b c^{4} d^{3} \tan\left(f x + e\right) + 14 \, B b^{2} c^{4} d^{3} \tan\left(f x + e\right) + 22 \, A a^{2} c^{3} d^{4} \tan\left(f x + e\right) - 22 \, C a^{2} c^{3} d^{4} \tan\left(f x + e\right) - 44 \, B a b c^{3} d^{4} \tan\left(f x + e\right) - 22 \, A b^{2} c^{3} d^{4} \tan\left(f x + e\right) + 28 \, C b^{2} c^{3} d^{4} \tan\left(f x + e\right) + 18 \, B a^{2} c^{2} d^{5} \tan\left(f x + e\right) + 36 \, A a b c^{2} d^{5} \tan\left(f x + e\right) - 24 \, C a b c^{2} d^{5} \tan\left(f x + e\right) - 12 \, B b^{2} c^{2} d^{5} \tan\left(f x + e\right) - 2 \, A a^{2} c d^{6} \tan\left(f x + e\right) + 2 \, C a^{2} c d^{6} \tan\left(f x + e\right) + 4 \, B a b c d^{6} \tan\left(f x + e\right) + 2 \, A b^{2} c d^{6} \tan\left(f x + e\right) + 2 \, B a^{2} d^{7} \tan\left(f x + e\right) + 4 \, A a b d^{7} \tan\left(f x + e\right) + 2 \, C a b c^{7} + B b^{2} c^{7} + C a^{2} c^{6} d + 2 \, B a b c^{6} d + A b^{2} c^{6} d - C b^{2} c^{6} d - 6 \, B a^{2} c^{5} d^{2} - 12 \, A a b c^{5} d^{2} + 18 \, C a b c^{5} d^{2} + 9 \, B b^{2} c^{5} d^{2} + 14 \, A a^{2} c^{4} d^{3} - 11 \, C a^{2} c^{4} d^{3} - 22 \, B a b c^{4} d^{3} - 11 \, A b^{2} c^{4} d^{3} + 11 \, C b^{2} c^{4} d^{3} + 7 \, B a^{2} c^{3} d^{4} + 14 \, A a b c^{3} d^{4} - 8 \, C a b c^{3} d^{4} - 4 \, B b^{2} c^{3} d^{4} + 3 \, A a^{2} c^{2} d^{5} + B a^{2} c d^{6} + 2 \, A a b c d^{6} + A a^{2} d^{7}}{{\left(c^{6} d^{2} + 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} + d^{8}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*a^2*c^3 - C*a^2*c^3 - 2*B*a*b*c^3 - A*b^2*c^3 + C*b^2*c^3 + 3*B*a^2*c^2*d + 6*A*a*b*c^2*d - 6*C*a*b*c^2*d - 3*B*b^2*c^2*d - 3*A*a^2*c*d^2 + 3*C*a^2*c*d^2 + 6*B*a*b*c*d^2 + 3*A*b^2*c*d^2 - 3*C*b^2*c*d^2 - B*a^2*d^3 - 2*A*a*b*d^3 + 2*C*a*b*d^3 + B*b^2*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (B*a^2*c^3 + 2*A*a*b*c^3 - 2*C*a*b*c^3 - B*b^2*c^3 - 3*A*a^2*c^2*d + 3*C*a^2*c^2*d + 6*B*a*b*c^2*d + 3*A*b^2*c^2*d - 3*C*b^2*c^2*d - 3*B*a^2*c*d^2 - 6*A*a*b*c*d^2 + 6*C*a*b*c*d^2 + 3*B*b^2*c*d^2 + A*a^2*d^3 - C*a^2*d^3 - 2*B*a*b*d^3 - A*b^2*d^3 + C*b^2*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + 2*(C*b^2*c^6 + 3*C*b^2*c^4*d^2 - B*a^2*c^3*d^3 - 2*A*a*b*c^3*d^3 + 2*C*a*b*c^3*d^3 + B*b^2*c^3*d^3 + 3*A*a^2*c^2*d^4 - 3*C*a^2*c^2*d^4 - 6*B*a*b*c^2*d^4 - 3*A*b^2*c^2*d^4 + 6*C*b^2*c^2*d^4 + 3*B*a^2*c*d^5 + 6*A*a*b*c*d^5 - 6*C*a*b*c*d^5 - 3*B*b^2*c*d^5 - A*a^2*d^6 + C*a^2*d^6 + 2*B*a*b*d^6 + A*b^2*d^6)*log(abs(d*tan(f*x + e) + c))/(c^6*d^3 + 3*c^4*d^5 + 3*c^2*d^7 + d^9) - (3*C*b^2*c^6*d*tan(f*x + e)^2 + 9*C*b^2*c^4*d^3*tan(f*x + e)^2 - 3*B*a^2*c^3*d^4*tan(f*x + e)^2 - 6*A*a*b*c^3*d^4*tan(f*x + e)^2 + 6*C*a*b*c^3*d^4*tan(f*x + e)^2 + 3*B*b^2*c^3*d^4*tan(f*x + e)^2 + 9*A*a^2*c^2*d^5*tan(f*x + e)^2 - 9*C*a^2*c^2*d^5*tan(f*x + e)^2 - 18*B*a*b*c^2*d^5*tan(f*x + e)^2 - 9*A*b^2*c^2*d^5*tan(f*x + e)^2 + 18*C*b^2*c^2*d^5*tan(f*x + e)^2 + 9*B*a^2*c*d^6*tan(f*x + e)^2 + 18*A*a*b*c*d^6*tan(f*x + e)^2 - 18*C*a*b*c*d^6*tan(f*x + e)^2 - 9*B*b^2*c*d^6*tan(f*x + e)^2 - 3*A*a^2*d^7*tan(f*x + e)^2 + 3*C*a^2*d^7*tan(f*x + e)^2 + 6*B*a*b*d^7*tan(f*x + e)^2 + 3*A*b^2*d^7*tan(f*x + e)^2 + 2*C*b^2*c^7*tan(f*x + e) + 4*C*a*b*c^6*d*tan(f*x + e) + 2*B*b^2*c^6*d*tan(f*x + e) + 6*C*b^2*c^5*d^2*tan(f*x + e) - 8*B*a^2*c^4*d^3*tan(f*x + e) - 16*A*a*b*c^4*d^3*tan(f*x + e) + 28*C*a*b*c^4*d^3*tan(f*x + e) + 14*B*b^2*c^4*d^3*tan(f*x + e) + 22*A*a^2*c^3*d^4*tan(f*x + e) - 22*C*a^2*c^3*d^4*tan(f*x + e) - 44*B*a*b*c^3*d^4*tan(f*x + e) - 22*A*b^2*c^3*d^4*tan(f*x + e) + 28*C*b^2*c^3*d^4*tan(f*x + e) + 18*B*a^2*c^2*d^5*tan(f*x + e) + 36*A*a*b*c^2*d^5*tan(f*x + e) - 24*C*a*b*c^2*d^5*tan(f*x + e) - 12*B*b^2*c^2*d^5*tan(f*x + e) - 2*A*a^2*c*d^6*tan(f*x + e) + 2*C*a^2*c*d^6*tan(f*x + e) + 4*B*a*b*c*d^6*tan(f*x + e) + 2*A*b^2*c*d^6*tan(f*x + e) + 2*B*a^2*d^7*tan(f*x + e) + 4*A*a*b*d^7*tan(f*x + e) + 2*C*a*b*c^7 + B*b^2*c^7 + C*a^2*c^6*d + 2*B*a*b*c^6*d + A*b^2*c^6*d - C*b^2*c^6*d - 6*B*a^2*c^5*d^2 - 12*A*a*b*c^5*d^2 + 18*C*a*b*c^5*d^2 + 9*B*b^2*c^5*d^2 + 14*A*a^2*c^4*d^3 - 11*C*a^2*c^4*d^3 - 22*B*a*b*c^4*d^3 - 11*A*b^2*c^4*d^3 + 11*C*b^2*c^4*d^3 + 7*B*a^2*c^3*d^4 + 14*A*a*b*c^3*d^4 - 8*C*a*b*c^3*d^4 - 4*B*b^2*c^3*d^4 + 3*A*a^2*c^2*d^5 + B*a^2*c*d^6 + 2*A*a*b*c*d^6 + A*a^2*d^7)/((c^6*d^2 + 3*c^4*d^4 + 3*c^2*d^6 + d^8)*(d*tan(f*x + e) + c)^2))/f","B",0
86,1,1037,0,2.699301," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a c^{3} - C a c^{3} - B b c^{3} + 3 \, B a c^{2} d + 3 \, A b c^{2} d - 3 \, C b c^{2} d - 3 \, A a c d^{2} + 3 \, C a c d^{2} + 3 \, B b c d^{2} - B a d^{3} - A b d^{3} + C b d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(B a c^{3} + A b c^{3} - C b c^{3} - 3 \, A a c^{2} d + 3 \, C a c^{2} d + 3 \, B b c^{2} d - 3 \, B a c d^{2} - 3 \, A b c d^{2} + 3 \, C b c d^{2} + A a d^{3} - C a d^{3} - B b d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left(B a c^{3} d + A b c^{3} d - C b c^{3} d - 3 \, A a c^{2} d^{2} + 3 \, C a c^{2} d^{2} + 3 \, B b c^{2} d^{2} - 3 \, B a c d^{3} - 3 \, A b c d^{3} + 3 \, C b c d^{3} + A a d^{4} - C a d^{4} - B b d^{4}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{6} d + 3 \, c^{4} d^{3} + 3 \, c^{2} d^{5} + d^{7}} + \frac{3 \, B a c^{3} d^{4} \tan\left(f x + e\right)^{2} + 3 \, A b c^{3} d^{4} \tan\left(f x + e\right)^{2} - 3 \, C b c^{3} d^{4} \tan\left(f x + e\right)^{2} - 9 \, A a c^{2} d^{5} \tan\left(f x + e\right)^{2} + 9 \, C a c^{2} d^{5} \tan\left(f x + e\right)^{2} + 9 \, B b c^{2} d^{5} \tan\left(f x + e\right)^{2} - 9 \, B a c d^{6} \tan\left(f x + e\right)^{2} - 9 \, A b c d^{6} \tan\left(f x + e\right)^{2} + 9 \, C b c d^{6} \tan\left(f x + e\right)^{2} + 3 \, A a d^{7} \tan\left(f x + e\right)^{2} - 3 \, C a d^{7} \tan\left(f x + e\right)^{2} - 3 \, B b d^{7} \tan\left(f x + e\right)^{2} - 2 \, C b c^{6} d \tan\left(f x + e\right) + 8 \, B a c^{4} d^{3} \tan\left(f x + e\right) + 8 \, A b c^{4} d^{3} \tan\left(f x + e\right) - 14 \, C b c^{4} d^{3} \tan\left(f x + e\right) - 22 \, A a c^{3} d^{4} \tan\left(f x + e\right) + 22 \, C a c^{3} d^{4} \tan\left(f x + e\right) + 22 \, B b c^{3} d^{4} \tan\left(f x + e\right) - 18 \, B a c^{2} d^{5} \tan\left(f x + e\right) - 18 \, A b c^{2} d^{5} \tan\left(f x + e\right) + 12 \, C b c^{2} d^{5} \tan\left(f x + e\right) + 2 \, A a c d^{6} \tan\left(f x + e\right) - 2 \, C a c d^{6} \tan\left(f x + e\right) - 2 \, B b c d^{6} \tan\left(f x + e\right) - 2 \, B a d^{7} \tan\left(f x + e\right) - 2 \, A b d^{7} \tan\left(f x + e\right) - C b c^{7} - C a c^{6} d - B b c^{6} d + 6 \, B a c^{5} d^{2} + 6 \, A b c^{5} d^{2} - 9 \, C b c^{5} d^{2} - 14 \, A a c^{4} d^{3} + 11 \, C a c^{4} d^{3} + 11 \, B b c^{4} d^{3} - 7 \, B a c^{3} d^{4} - 7 \, A b c^{3} d^{4} + 4 \, C b c^{3} d^{4} - 3 \, A a c^{2} d^{5} - B a c d^{6} - A b c d^{6} - A a d^{7}}{{\left(c^{6} d^{2} + 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} + d^{8}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*a*c^3 - C*a*c^3 - B*b*c^3 + 3*B*a*c^2*d + 3*A*b*c^2*d - 3*C*b*c^2*d - 3*A*a*c*d^2 + 3*C*a*c*d^2 + 3*B*b*c*d^2 - B*a*d^3 - A*b*d^3 + C*b*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (B*a*c^3 + A*b*c^3 - C*b*c^3 - 3*A*a*c^2*d + 3*C*a*c^2*d + 3*B*b*c^2*d - 3*B*a*c*d^2 - 3*A*b*c*d^2 + 3*C*b*c*d^2 + A*a*d^3 - C*a*d^3 - B*b*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*(B*a*c^3*d + A*b*c^3*d - C*b*c^3*d - 3*A*a*c^2*d^2 + 3*C*a*c^2*d^2 + 3*B*b*c^2*d^2 - 3*B*a*c*d^3 - 3*A*b*c*d^3 + 3*C*b*c*d^3 + A*a*d^4 - C*a*d^4 - B*b*d^4)*log(abs(d*tan(f*x + e) + c))/(c^6*d + 3*c^4*d^3 + 3*c^2*d^5 + d^7) + (3*B*a*c^3*d^4*tan(f*x + e)^2 + 3*A*b*c^3*d^4*tan(f*x + e)^2 - 3*C*b*c^3*d^4*tan(f*x + e)^2 - 9*A*a*c^2*d^5*tan(f*x + e)^2 + 9*C*a*c^2*d^5*tan(f*x + e)^2 + 9*B*b*c^2*d^5*tan(f*x + e)^2 - 9*B*a*c*d^6*tan(f*x + e)^2 - 9*A*b*c*d^6*tan(f*x + e)^2 + 9*C*b*c*d^6*tan(f*x + e)^2 + 3*A*a*d^7*tan(f*x + e)^2 - 3*C*a*d^7*tan(f*x + e)^2 - 3*B*b*d^7*tan(f*x + e)^2 - 2*C*b*c^6*d*tan(f*x + e) + 8*B*a*c^4*d^3*tan(f*x + e) + 8*A*b*c^4*d^3*tan(f*x + e) - 14*C*b*c^4*d^3*tan(f*x + e) - 22*A*a*c^3*d^4*tan(f*x + e) + 22*C*a*c^3*d^4*tan(f*x + e) + 22*B*b*c^3*d^4*tan(f*x + e) - 18*B*a*c^2*d^5*tan(f*x + e) - 18*A*b*c^2*d^5*tan(f*x + e) + 12*C*b*c^2*d^5*tan(f*x + e) + 2*A*a*c*d^6*tan(f*x + e) - 2*C*a*c*d^6*tan(f*x + e) - 2*B*b*c*d^6*tan(f*x + e) - 2*B*a*d^7*tan(f*x + e) - 2*A*b*d^7*tan(f*x + e) - C*b*c^7 - C*a*c^6*d - B*b*c^6*d + 6*B*a*c^5*d^2 + 6*A*b*c^5*d^2 - 9*C*b*c^5*d^2 - 14*A*a*c^4*d^3 + 11*C*a*c^4*d^3 + 11*B*b*c^4*d^3 - 7*B*a*c^3*d^4 - 7*A*b*c^3*d^4 + 4*C*b*c^3*d^4 - 3*A*a*c^2*d^5 - B*a*c*d^6 - A*b*c*d^6 - A*a*d^7)/((c^6*d^2 + 3*c^4*d^4 + 3*c^2*d^6 + d^8)*(d*tan(f*x + e) + c)^2))/f","B",0
87,1,548,0,1.386151," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A c^{3} - C c^{3} + 3 \, B c^{2} d - 3 \, A c d^{2} + 3 \, C c d^{2} - B d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(B c^{3} - 3 \, A c^{2} d + 3 \, C c^{2} d - 3 \, B c d^{2} + A d^{3} - C d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left(B c^{3} d - 3 \, A c^{2} d^{2} + 3 \, C c^{2} d^{2} - 3 \, B c d^{3} + A d^{4} - C d^{4}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{6} d + 3 \, c^{4} d^{3} + 3 \, c^{2} d^{5} + d^{7}} + \frac{3 \, B c^{3} d^{3} \tan\left(f x + e\right)^{2} - 9 \, A c^{2} d^{4} \tan\left(f x + e\right)^{2} + 9 \, C c^{2} d^{4} \tan\left(f x + e\right)^{2} - 9 \, B c d^{5} \tan\left(f x + e\right)^{2} + 3 \, A d^{6} \tan\left(f x + e\right)^{2} - 3 \, C d^{6} \tan\left(f x + e\right)^{2} + 8 \, B c^{4} d^{2} \tan\left(f x + e\right) - 22 \, A c^{3} d^{3} \tan\left(f x + e\right) + 22 \, C c^{3} d^{3} \tan\left(f x + e\right) - 18 \, B c^{2} d^{4} \tan\left(f x + e\right) + 2 \, A c d^{5} \tan\left(f x + e\right) - 2 \, C c d^{5} \tan\left(f x + e\right) - 2 \, B d^{6} \tan\left(f x + e\right) - C c^{6} + 6 \, B c^{5} d - 14 \, A c^{4} d^{2} + 11 \, C c^{4} d^{2} - 7 \, B c^{3} d^{3} - 3 \, A c^{2} d^{4} - B c d^{5} - A d^{6}}{{\left(c^{6} d + 3 \, c^{4} d^{3} + 3 \, c^{2} d^{5} + d^{7}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*c^3 - C*c^3 + 3*B*c^2*d - 3*A*c*d^2 + 3*C*c*d^2 - B*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (B*c^3 - 3*A*c^2*d + 3*C*c^2*d - 3*B*c*d^2 + A*d^3 - C*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*(B*c^3*d - 3*A*c^2*d^2 + 3*C*c^2*d^2 - 3*B*c*d^3 + A*d^4 - C*d^4)*log(abs(d*tan(f*x + e) + c))/(c^6*d + 3*c^4*d^3 + 3*c^2*d^5 + d^7) + (3*B*c^3*d^3*tan(f*x + e)^2 - 9*A*c^2*d^4*tan(f*x + e)^2 + 9*C*c^2*d^4*tan(f*x + e)^2 - 9*B*c*d^5*tan(f*x + e)^2 + 3*A*d^6*tan(f*x + e)^2 - 3*C*d^6*tan(f*x + e)^2 + 8*B*c^4*d^2*tan(f*x + e) - 22*A*c^3*d^3*tan(f*x + e) + 22*C*c^3*d^3*tan(f*x + e) - 18*B*c^2*d^4*tan(f*x + e) + 2*A*c*d^5*tan(f*x + e) - 2*C*c*d^5*tan(f*x + e) - 2*B*d^6*tan(f*x + e) - C*c^6 + 6*B*c^5*d - 14*A*c^4*d^2 + 11*C*c^4*d^2 - 7*B*c^3*d^3 - 3*A*c^2*d^4 - B*c*d^5 - A*d^6)/((c^6*d + 3*c^4*d^3 + 3*c^2*d^5 + d^7)*(d*tan(f*x + e) + c)^2))/f","B",0
88,1,2125,0,17.821277," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a c^{3} - C a c^{3} + B b c^{3} + 3 \, B a c^{2} d - 3 \, A b c^{2} d + 3 \, C b c^{2} d - 3 \, A a c d^{2} + 3 \, C a c d^{2} - 3 \, B b c d^{2} - B a d^{3} + A b d^{3} - C b d^{3}\right)} {\left(f x + e\right)}}{a^{2} c^{6} + b^{2} c^{6} + 3 \, a^{2} c^{4} d^{2} + 3 \, b^{2} c^{4} d^{2} + 3 \, a^{2} c^{2} d^{4} + 3 \, b^{2} c^{2} d^{4} + a^{2} d^{6} + b^{2} d^{6}} + \frac{{\left(B a c^{3} - A b c^{3} + C b c^{3} - 3 \, A a c^{2} d + 3 \, C a c^{2} d - 3 \, B b c^{2} d - 3 \, B a c d^{2} + 3 \, A b c d^{2} - 3 \, C b c d^{2} + A a d^{3} - C a d^{3} + B b d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} c^{6} + b^{2} c^{6} + 3 \, a^{2} c^{4} d^{2} + 3 \, b^{2} c^{4} d^{2} + 3 \, a^{2} c^{2} d^{4} + 3 \, b^{2} c^{2} d^{4} + a^{2} d^{6} + b^{2} d^{6}} + \frac{2 \, {\left(C a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b^{4} c^{3} + b^{6} c^{3} - 3 \, a^{3} b^{3} c^{2} d - 3 \, a b^{5} c^{2} d + 3 \, a^{4} b^{2} c d^{2} + 3 \, a^{2} b^{4} c d^{2} - a^{5} b d^{3} - a^{3} b^{3} d^{3}} - \frac{2 \, {\left(C b^{2} c^{6} d - 3 \, B b^{2} c^{5} d^{2} + 3 \, B a b c^{4} d^{3} + 6 \, A b^{2} c^{4} d^{3} - 3 \, C b^{2} c^{4} d^{3} - B a^{2} c^{3} d^{4} - 8 \, A a b c^{3} d^{4} + 8 \, C a b c^{3} d^{4} + B b^{2} c^{3} d^{4} + 3 \, A a^{2} c^{2} d^{5} - 3 \, C a^{2} c^{2} d^{5} - 6 \, B a b c^{2} d^{5} + 3 \, A b^{2} c^{2} d^{5} + 3 \, B a^{2} c d^{6} - A a^{2} d^{7} + C a^{2} d^{7} - B a b d^{7} + A b^{2} d^{7}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{3} c^{9} d - 3 \, a b^{2} c^{8} d^{2} + 3 \, a^{2} b c^{7} d^{3} + 3 \, b^{3} c^{7} d^{3} - a^{3} c^{6} d^{4} - 9 \, a b^{2} c^{6} d^{4} + 9 \, a^{2} b c^{5} d^{5} + 3 \, b^{3} c^{5} d^{5} - 3 \, a^{3} c^{4} d^{6} - 9 \, a b^{2} c^{4} d^{6} + 9 \, a^{2} b c^{3} d^{7} + b^{3} c^{3} d^{7} - 3 \, a^{3} c^{2} d^{8} - 3 \, a b^{2} c^{2} d^{8} + 3 \, a^{2} b c d^{9} - a^{3} d^{10}} + \frac{3 \, C b^{2} c^{6} d^{2} \tan\left(f x + e\right)^{2} - 9 \, B b^{2} c^{5} d^{3} \tan\left(f x + e\right)^{2} + 9 \, B a b c^{4} d^{4} \tan\left(f x + e\right)^{2} + 18 \, A b^{2} c^{4} d^{4} \tan\left(f x + e\right)^{2} - 9 \, C b^{2} c^{4} d^{4} \tan\left(f x + e\right)^{2} - 3 \, B a^{2} c^{3} d^{5} \tan\left(f x + e\right)^{2} - 24 \, A a b c^{3} d^{5} \tan\left(f x + e\right)^{2} + 24 \, C a b c^{3} d^{5} \tan\left(f x + e\right)^{2} + 3 \, B b^{2} c^{3} d^{5} \tan\left(f x + e\right)^{2} + 9 \, A a^{2} c^{2} d^{6} \tan\left(f x + e\right)^{2} - 9 \, C a^{2} c^{2} d^{6} \tan\left(f x + e\right)^{2} - 18 \, B a b c^{2} d^{6} \tan\left(f x + e\right)^{2} + 9 \, A b^{2} c^{2} d^{6} \tan\left(f x + e\right)^{2} + 9 \, B a^{2} c d^{7} \tan\left(f x + e\right)^{2} - 3 \, A a^{2} d^{8} \tan\left(f x + e\right)^{2} + 3 \, C a^{2} d^{8} \tan\left(f x + e\right)^{2} - 3 \, B a b d^{8} \tan\left(f x + e\right)^{2} + 3 \, A b^{2} d^{8} \tan\left(f x + e\right)^{2} + 8 \, C b^{2} c^{7} d \tan\left(f x + e\right) - 2 \, C a b c^{6} d^{2} \tan\left(f x + e\right) - 22 \, B b^{2} c^{6} d^{2} \tan\left(f x + e\right) + 24 \, B a b c^{5} d^{3} \tan\left(f x + e\right) + 42 \, A b^{2} c^{5} d^{3} \tan\left(f x + e\right) - 18 \, C b^{2} c^{5} d^{3} \tan\left(f x + e\right) - 8 \, B a^{2} c^{4} d^{4} \tan\left(f x + e\right) - 58 \, A a b c^{4} d^{4} \tan\left(f x + e\right) + 52 \, C a b c^{4} d^{4} \tan\left(f x + e\right) + 2 \, B b^{2} c^{4} d^{4} \tan\left(f x + e\right) + 22 \, A a^{2} c^{3} d^{5} \tan\left(f x + e\right) - 22 \, C a^{2} c^{3} d^{5} \tan\left(f x + e\right) - 32 \, B a b c^{3} d^{5} \tan\left(f x + e\right) + 26 \, A b^{2} c^{3} d^{5} \tan\left(f x + e\right) - 2 \, C b^{2} c^{3} d^{5} \tan\left(f x + e\right) + 18 \, B a^{2} c^{2} d^{6} \tan\left(f x + e\right) - 12 \, A a b c^{2} d^{6} \tan\left(f x + e\right) + 6 \, C a b c^{2} d^{6} \tan\left(f x + e\right) - 2 \, A a^{2} c d^{7} \tan\left(f x + e\right) + 2 \, C a^{2} c d^{7} \tan\left(f x + e\right) - 8 \, B a b c d^{7} \tan\left(f x + e\right) + 8 \, A b^{2} c d^{7} \tan\left(f x + e\right) + 2 \, B a^{2} d^{8} \tan\left(f x + e\right) - 2 \, A a b d^{8} \tan\left(f x + e\right) + 6 \, C b^{2} c^{8} - 4 \, C a b c^{7} d - 14 \, B b^{2} c^{7} d + C a^{2} c^{6} d^{2} + 17 \, B a b c^{6} d^{2} + 25 \, A b^{2} c^{6} d^{2} - 7 \, C b^{2} c^{6} d^{2} - 6 \, B a^{2} c^{5} d^{3} - 36 \, A a b c^{5} d^{3} + 24 \, C a b c^{5} d^{3} - 3 \, B b^{2} c^{5} d^{3} + 14 \, A a^{2} c^{4} d^{4} - 11 \, C a^{2} c^{4} d^{4} - 10 \, B a b c^{4} d^{4} + 19 \, A b^{2} c^{4} d^{4} - C b^{2} c^{4} d^{4} + 7 \, B a^{2} c^{3} d^{5} - 16 \, A a b c^{3} d^{5} + 4 \, C a b c^{3} d^{5} - B b^{2} c^{3} d^{5} + 3 \, A a^{2} c^{2} d^{6} - 3 \, B a b c^{2} d^{6} + 6 \, A b^{2} c^{2} d^{6} + B a^{2} c d^{7} - 4 \, A a b c d^{7} + A a^{2} d^{8}}{{\left(b^{3} c^{9} - 3 \, a b^{2} c^{8} d + 3 \, a^{2} b c^{7} d^{2} + 3 \, b^{3} c^{7} d^{2} - a^{3} c^{6} d^{3} - 9 \, a b^{2} c^{6} d^{3} + 9 \, a^{2} b c^{5} d^{4} + 3 \, b^{3} c^{5} d^{4} - 3 \, a^{3} c^{4} d^{5} - 9 \, a b^{2} c^{4} d^{5} + 9 \, a^{2} b c^{3} d^{6} + b^{3} c^{3} d^{6} - 3 \, a^{3} c^{2} d^{7} - 3 \, a b^{2} c^{2} d^{7} + 3 \, a^{2} b c d^{8} - a^{3} d^{9}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*a*c^3 - C*a*c^3 + B*b*c^3 + 3*B*a*c^2*d - 3*A*b*c^2*d + 3*C*b*c^2*d - 3*A*a*c*d^2 + 3*C*a*c*d^2 - 3*B*b*c*d^2 - B*a*d^3 + A*b*d^3 - C*b*d^3)*(f*x + e)/(a^2*c^6 + b^2*c^6 + 3*a^2*c^4*d^2 + 3*b^2*c^4*d^2 + 3*a^2*c^2*d^4 + 3*b^2*c^2*d^4 + a^2*d^6 + b^2*d^6) + (B*a*c^3 - A*b*c^3 + C*b*c^3 - 3*A*a*c^2*d + 3*C*a*c^2*d - 3*B*b*c^2*d - 3*B*a*c*d^2 + 3*A*b*c*d^2 - 3*C*b*c*d^2 + A*a*d^3 - C*a*d^3 + B*b*d^3)*log(tan(f*x + e)^2 + 1)/(a^2*c^6 + b^2*c^6 + 3*a^2*c^4*d^2 + 3*b^2*c^4*d^2 + 3*a^2*c^2*d^4 + 3*b^2*c^2*d^4 + a^2*d^6 + b^2*d^6) + 2*(C*a^2*b^3 - B*a*b^4 + A*b^5)*log(abs(b*tan(f*x + e) + a))/(a^2*b^4*c^3 + b^6*c^3 - 3*a^3*b^3*c^2*d - 3*a*b^5*c^2*d + 3*a^4*b^2*c*d^2 + 3*a^2*b^4*c*d^2 - a^5*b*d^3 - a^3*b^3*d^3) - 2*(C*b^2*c^6*d - 3*B*b^2*c^5*d^2 + 3*B*a*b*c^4*d^3 + 6*A*b^2*c^4*d^3 - 3*C*b^2*c^4*d^3 - B*a^2*c^3*d^4 - 8*A*a*b*c^3*d^4 + 8*C*a*b*c^3*d^4 + B*b^2*c^3*d^4 + 3*A*a^2*c^2*d^5 - 3*C*a^2*c^2*d^5 - 6*B*a*b*c^2*d^5 + 3*A*b^2*c^2*d^5 + 3*B*a^2*c*d^6 - A*a^2*d^7 + C*a^2*d^7 - B*a*b*d^7 + A*b^2*d^7)*log(abs(d*tan(f*x + e) + c))/(b^3*c^9*d - 3*a*b^2*c^8*d^2 + 3*a^2*b*c^7*d^3 + 3*b^3*c^7*d^3 - a^3*c^6*d^4 - 9*a*b^2*c^6*d^4 + 9*a^2*b*c^5*d^5 + 3*b^3*c^5*d^5 - 3*a^3*c^4*d^6 - 9*a*b^2*c^4*d^6 + 9*a^2*b*c^3*d^7 + b^3*c^3*d^7 - 3*a^3*c^2*d^8 - 3*a*b^2*c^2*d^8 + 3*a^2*b*c*d^9 - a^3*d^10) + (3*C*b^2*c^6*d^2*tan(f*x + e)^2 - 9*B*b^2*c^5*d^3*tan(f*x + e)^2 + 9*B*a*b*c^4*d^4*tan(f*x + e)^2 + 18*A*b^2*c^4*d^4*tan(f*x + e)^2 - 9*C*b^2*c^4*d^4*tan(f*x + e)^2 - 3*B*a^2*c^3*d^5*tan(f*x + e)^2 - 24*A*a*b*c^3*d^5*tan(f*x + e)^2 + 24*C*a*b*c^3*d^5*tan(f*x + e)^2 + 3*B*b^2*c^3*d^5*tan(f*x + e)^2 + 9*A*a^2*c^2*d^6*tan(f*x + e)^2 - 9*C*a^2*c^2*d^6*tan(f*x + e)^2 - 18*B*a*b*c^2*d^6*tan(f*x + e)^2 + 9*A*b^2*c^2*d^6*tan(f*x + e)^2 + 9*B*a^2*c*d^7*tan(f*x + e)^2 - 3*A*a^2*d^8*tan(f*x + e)^2 + 3*C*a^2*d^8*tan(f*x + e)^2 - 3*B*a*b*d^8*tan(f*x + e)^2 + 3*A*b^2*d^8*tan(f*x + e)^2 + 8*C*b^2*c^7*d*tan(f*x + e) - 2*C*a*b*c^6*d^2*tan(f*x + e) - 22*B*b^2*c^6*d^2*tan(f*x + e) + 24*B*a*b*c^5*d^3*tan(f*x + e) + 42*A*b^2*c^5*d^3*tan(f*x + e) - 18*C*b^2*c^5*d^3*tan(f*x + e) - 8*B*a^2*c^4*d^4*tan(f*x + e) - 58*A*a*b*c^4*d^4*tan(f*x + e) + 52*C*a*b*c^4*d^4*tan(f*x + e) + 2*B*b^2*c^4*d^4*tan(f*x + e) + 22*A*a^2*c^3*d^5*tan(f*x + e) - 22*C*a^2*c^3*d^5*tan(f*x + e) - 32*B*a*b*c^3*d^5*tan(f*x + e) + 26*A*b^2*c^3*d^5*tan(f*x + e) - 2*C*b^2*c^3*d^5*tan(f*x + e) + 18*B*a^2*c^2*d^6*tan(f*x + e) - 12*A*a*b*c^2*d^6*tan(f*x + e) + 6*C*a*b*c^2*d^6*tan(f*x + e) - 2*A*a^2*c*d^7*tan(f*x + e) + 2*C*a^2*c*d^7*tan(f*x + e) - 8*B*a*b*c*d^7*tan(f*x + e) + 8*A*b^2*c*d^7*tan(f*x + e) + 2*B*a^2*d^8*tan(f*x + e) - 2*A*a*b*d^8*tan(f*x + e) + 6*C*b^2*c^8 - 4*C*a*b*c^7*d - 14*B*b^2*c^7*d + C*a^2*c^6*d^2 + 17*B*a*b*c^6*d^2 + 25*A*b^2*c^6*d^2 - 7*C*b^2*c^6*d^2 - 6*B*a^2*c^5*d^3 - 36*A*a*b*c^5*d^3 + 24*C*a*b*c^5*d^3 - 3*B*b^2*c^5*d^3 + 14*A*a^2*c^4*d^4 - 11*C*a^2*c^4*d^4 - 10*B*a*b*c^4*d^4 + 19*A*b^2*c^4*d^4 - C*b^2*c^4*d^4 + 7*B*a^2*c^3*d^5 - 16*A*a*b*c^3*d^5 + 4*C*a*b*c^3*d^5 - B*b^2*c^3*d^5 + 3*A*a^2*c^2*d^6 - 3*B*a*b*c^2*d^6 + 6*A*b^2*c^2*d^6 + B*a^2*c*d^7 - 4*A*a*b*c*d^7 + A*a^2*d^8)/((b^3*c^9 - 3*a*b^2*c^8*d + 3*a^2*b*c^7*d^2 + 3*b^3*c^7*d^2 - a^3*c^6*d^3 - 9*a*b^2*c^6*d^3 + 9*a^2*b*c^5*d^4 + 3*b^3*c^5*d^4 - 3*a^3*c^4*d^5 - 9*a*b^2*c^4*d^5 + 9*a^2*b*c^3*d^6 + b^3*c^3*d^6 - 3*a^3*c^2*d^7 - 3*a*b^2*c^2*d^7 + 3*a^2*b*c*d^8 - a^3*d^9)*(d*tan(f*x + e) + c)^2))/f","B",0
89,1,3176,0,90.117208," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A a^{2} c^{3} - C a^{2} c^{3} + 2 \, B a b c^{3} - A b^{2} c^{3} + C b^{2} c^{3} + 3 \, B a^{2} c^{2} d - 6 \, A a b c^{2} d + 6 \, C a b c^{2} d - 3 \, B b^{2} c^{2} d - 3 \, A a^{2} c d^{2} + 3 \, C a^{2} c d^{2} - 6 \, B a b c d^{2} + 3 \, A b^{2} c d^{2} - 3 \, C b^{2} c d^{2} - B a^{2} d^{3} + 2 \, A a b d^{3} - 2 \, C a b d^{3} + B b^{2} d^{3}\right)} {\left(f x + e\right)}}{a^{4} c^{6} + 2 \, a^{2} b^{2} c^{6} + b^{4} c^{6} + 3 \, a^{4} c^{4} d^{2} + 6 \, a^{2} b^{2} c^{4} d^{2} + 3 \, b^{4} c^{4} d^{2} + 3 \, a^{4} c^{2} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{4} + 3 \, b^{4} c^{2} d^{4} + a^{4} d^{6} + 2 \, a^{2} b^{2} d^{6} + b^{4} d^{6}} + \frac{{\left(B a^{2} c^{3} - 2 \, A a b c^{3} + 2 \, C a b c^{3} - B b^{2} c^{3} - 3 \, A a^{2} c^{2} d + 3 \, C a^{2} c^{2} d - 6 \, B a b c^{2} d + 3 \, A b^{2} c^{2} d - 3 \, C b^{2} c^{2} d - 3 \, B a^{2} c d^{2} + 6 \, A a b c d^{2} - 6 \, C a b c d^{2} + 3 \, B b^{2} c d^{2} + A a^{2} d^{3} - C a^{2} d^{3} + 2 \, B a b d^{3} - A b^{2} d^{3} + C b^{2} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} c^{6} + 2 \, a^{2} b^{2} c^{6} + b^{4} c^{6} + 3 \, a^{4} c^{4} d^{2} + 6 \, a^{2} b^{2} c^{4} d^{2} + 3 \, b^{4} c^{4} d^{2} + 3 \, a^{4} c^{2} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{4} + 3 \, b^{4} c^{2} d^{4} + a^{4} d^{6} + 2 \, a^{2} b^{2} d^{6} + b^{4} d^{6}} - \frac{2 \, {\left(B a^{2} b^{5} c - 2 \, A a b^{6} c + 2 \, C a b^{6} c - B b^{7} c + 3 \, C a^{4} b^{3} d - 4 \, B a^{3} b^{4} d + 5 \, A a^{2} b^{5} d + C a^{2} b^{5} d - 2 \, B a b^{6} d + 3 \, A b^{7} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b^{5} c^{4} + 2 \, a^{2} b^{7} c^{4} + b^{9} c^{4} - 4 \, a^{5} b^{4} c^{3} d - 8 \, a^{3} b^{6} c^{3} d - 4 \, a b^{8} c^{3} d + 6 \, a^{6} b^{3} c^{2} d^{2} + 12 \, a^{4} b^{5} c^{2} d^{2} + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{7} b^{2} c d^{3} - 8 \, a^{5} b^{4} c d^{3} - 4 \, a^{3} b^{6} c d^{3} + a^{8} b d^{4} + 2 \, a^{6} b^{3} d^{4} + a^{4} b^{5} d^{4}} + \frac{2 \, {\left(3 \, C b^{2} c^{6} d^{2} - 6 \, B b^{2} c^{5} d^{3} + 4 \, B a b c^{4} d^{4} + 10 \, A b^{2} c^{4} d^{4} - C b^{2} c^{4} d^{4} - B a^{2} c^{3} d^{5} - 10 \, A a b c^{3} d^{5} + 10 \, C a b c^{3} d^{5} - 3 \, B b^{2} c^{3} d^{5} + 3 \, A a^{2} c^{2} d^{6} - 3 \, C a^{2} c^{2} d^{6} - 6 \, B a b c^{2} d^{6} + 9 \, A b^{2} c^{2} d^{6} + 3 \, B a^{2} c d^{7} - 2 \, A a b c d^{7} + 2 \, C a b c d^{7} - B b^{2} c d^{7} - A a^{2} d^{8} + C a^{2} d^{8} - 2 \, B a b d^{8} + 3 \, A b^{2} d^{8}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{4} c^{10} d - 4 \, a b^{3} c^{9} d^{2} + 6 \, a^{2} b^{2} c^{8} d^{3} + 3 \, b^{4} c^{8} d^{3} - 4 \, a^{3} b c^{7} d^{4} - 12 \, a b^{3} c^{7} d^{4} + a^{4} c^{6} d^{5} + 18 \, a^{2} b^{2} c^{6} d^{5} + 3 \, b^{4} c^{6} d^{5} - 12 \, a^{3} b c^{5} d^{6} - 12 \, a b^{3} c^{5} d^{6} + 3 \, a^{4} c^{4} d^{7} + 18 \, a^{2} b^{2} c^{4} d^{7} + b^{4} c^{4} d^{7} - 12 \, a^{3} b c^{3} d^{8} - 4 \, a b^{3} c^{3} d^{8} + 3 \, a^{4} c^{2} d^{9} + 6 \, a^{2} b^{2} c^{2} d^{9} - 4 \, a^{3} b c d^{10} + a^{4} d^{11}} + \frac{2 \, {\left(B a^{2} b^{5} c \tan\left(f x + e\right) - 2 \, A a b^{6} c \tan\left(f x + e\right) + 2 \, C a b^{6} c \tan\left(f x + e\right) - B b^{7} c \tan\left(f x + e\right) + 3 \, C a^{4} b^{3} d \tan\left(f x + e\right) - 4 \, B a^{3} b^{4} d \tan\left(f x + e\right) + 5 \, A a^{2} b^{5} d \tan\left(f x + e\right) + C a^{2} b^{5} d \tan\left(f x + e\right) - 2 \, B a b^{6} d \tan\left(f x + e\right) + 3 \, A b^{7} d \tan\left(f x + e\right) - C a^{4} b^{3} c + 2 \, B a^{3} b^{4} c - 3 \, A a^{2} b^{5} c + C a^{2} b^{5} c - A b^{7} c + 4 \, C a^{5} b^{2} d - 5 \, B a^{4} b^{3} d + 6 \, A a^{3} b^{4} d + 2 \, C a^{3} b^{4} d - 3 \, B a^{2} b^{5} d + 4 \, A a b^{6} d\right)}}{{\left(a^{4} b^{4} c^{4} + 2 \, a^{2} b^{6} c^{4} + b^{8} c^{4} - 4 \, a^{5} b^{3} c^{3} d - 8 \, a^{3} b^{5} c^{3} d - 4 \, a b^{7} c^{3} d + 6 \, a^{6} b^{2} c^{2} d^{2} + 12 \, a^{4} b^{4} c^{2} d^{2} + 6 \, a^{2} b^{6} c^{2} d^{2} - 4 \, a^{7} b c d^{3} - 8 \, a^{5} b^{3} c d^{3} - 4 \, a^{3} b^{5} c d^{3} + a^{8} d^{4} + 2 \, a^{6} b^{2} d^{4} + a^{4} b^{4} d^{4}\right)} {\left(b \tan\left(f x + e\right) + a\right)}} - \frac{9 \, C b^{2} c^{6} d^{3} \tan\left(f x + e\right)^{2} - 18 \, B b^{2} c^{5} d^{4} \tan\left(f x + e\right)^{2} + 12 \, B a b c^{4} d^{5} \tan\left(f x + e\right)^{2} + 30 \, A b^{2} c^{4} d^{5} \tan\left(f x + e\right)^{2} - 3 \, C b^{2} c^{4} d^{5} \tan\left(f x + e\right)^{2} - 3 \, B a^{2} c^{3} d^{6} \tan\left(f x + e\right)^{2} - 30 \, A a b c^{3} d^{6} \tan\left(f x + e\right)^{2} + 30 \, C a b c^{3} d^{6} \tan\left(f x + e\right)^{2} - 9 \, B b^{2} c^{3} d^{6} \tan\left(f x + e\right)^{2} + 9 \, A a^{2} c^{2} d^{7} \tan\left(f x + e\right)^{2} - 9 \, C a^{2} c^{2} d^{7} \tan\left(f x + e\right)^{2} - 18 \, B a b c^{2} d^{7} \tan\left(f x + e\right)^{2} + 27 \, A b^{2} c^{2} d^{7} \tan\left(f x + e\right)^{2} + 9 \, B a^{2} c d^{8} \tan\left(f x + e\right)^{2} - 6 \, A a b c d^{8} \tan\left(f x + e\right)^{2} + 6 \, C a b c d^{8} \tan\left(f x + e\right)^{2} - 3 \, B b^{2} c d^{8} \tan\left(f x + e\right)^{2} - 3 \, A a^{2} d^{9} \tan\left(f x + e\right)^{2} + 3 \, C a^{2} d^{9} \tan\left(f x + e\right)^{2} - 6 \, B a b d^{9} \tan\left(f x + e\right)^{2} + 9 \, A b^{2} d^{9} \tan\left(f x + e\right)^{2} + 22 \, C b^{2} c^{7} d^{2} \tan\left(f x + e\right) - 4 \, C a b c^{6} d^{3} \tan\left(f x + e\right) - 42 \, B b^{2} c^{6} d^{3} \tan\left(f x + e\right) + 32 \, B a b c^{5} d^{4} \tan\left(f x + e\right) + 68 \, A b^{2} c^{5} d^{4} \tan\left(f x + e\right) - 2 \, C b^{2} c^{5} d^{4} \tan\left(f x + e\right) - 8 \, B a^{2} c^{4} d^{5} \tan\left(f x + e\right) - 72 \, A a b c^{4} d^{5} \tan\left(f x + e\right) + 60 \, C a b c^{4} d^{5} \tan\left(f x + e\right) - 26 \, B b^{2} c^{4} d^{5} \tan\left(f x + e\right) + 22 \, A a^{2} c^{3} d^{6} \tan\left(f x + e\right) - 22 \, C a^{2} c^{3} d^{6} \tan\left(f x + e\right) - 28 \, B a b c^{3} d^{6} \tan\left(f x + e\right) + 66 \, A b^{2} c^{3} d^{6} \tan\left(f x + e\right) + 18 \, B a^{2} c^{2} d^{7} \tan\left(f x + e\right) - 28 \, A a b c^{2} d^{7} \tan\left(f x + e\right) + 16 \, C a b c^{2} d^{7} \tan\left(f x + e\right) - 8 \, B b^{2} c^{2} d^{7} \tan\left(f x + e\right) - 2 \, A a^{2} c d^{8} \tan\left(f x + e\right) + 2 \, C a^{2} c d^{8} \tan\left(f x + e\right) - 12 \, B a b c d^{8} \tan\left(f x + e\right) + 22 \, A b^{2} c d^{8} \tan\left(f x + e\right) + 2 \, B a^{2} d^{9} \tan\left(f x + e\right) - 4 \, A a b d^{9} \tan\left(f x + e\right) + 14 \, C b^{2} c^{8} d - 6 \, C a b c^{7} d^{2} - 25 \, B b^{2} c^{7} d^{2} + C a^{2} c^{6} d^{3} + 22 \, B a b c^{6} d^{3} + 39 \, A b^{2} c^{6} d^{3} + 3 \, C b^{2} c^{6} d^{3} - 6 \, B a^{2} c^{5} d^{4} - 44 \, A a b c^{5} d^{4} + 26 \, C a b c^{5} d^{4} - 19 \, B b^{2} c^{5} d^{4} + 14 \, A a^{2} c^{4} d^{5} - 11 \, C a^{2} c^{4} d^{5} - 6 \, B a b c^{4} d^{5} + 41 \, A b^{2} c^{4} d^{5} + C b^{2} c^{4} d^{5} + 7 \, B a^{2} c^{3} d^{6} - 26 \, A a b c^{3} d^{6} + 8 \, C a b c^{3} d^{6} - 6 \, B b^{2} c^{3} d^{6} + 3 \, A a^{2} c^{2} d^{7} - 4 \, B a b c^{2} d^{7} + 14 \, A b^{2} c^{2} d^{7} + B a^{2} c d^{8} - 6 \, A a b c d^{8} + A a^{2} d^{9}}{{\left(b^{4} c^{10} - 4 \, a b^{3} c^{9} d + 6 \, a^{2} b^{2} c^{8} d^{2} + 3 \, b^{4} c^{8} d^{2} - 4 \, a^{3} b c^{7} d^{3} - 12 \, a b^{3} c^{7} d^{3} + a^{4} c^{6} d^{4} + 18 \, a^{2} b^{2} c^{6} d^{4} + 3 \, b^{4} c^{6} d^{4} - 12 \, a^{3} b c^{5} d^{5} - 12 \, a b^{3} c^{5} d^{5} + 3 \, a^{4} c^{4} d^{6} + 18 \, a^{2} b^{2} c^{4} d^{6} + b^{4} c^{4} d^{6} - 12 \, a^{3} b c^{3} d^{7} - 4 \, a b^{3} c^{3} d^{7} + 3 \, a^{4} c^{2} d^{8} + 6 \, a^{2} b^{2} c^{2} d^{8} - 4 \, a^{3} b c d^{9} + a^{4} d^{10}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(A*a^2*c^3 - C*a^2*c^3 + 2*B*a*b*c^3 - A*b^2*c^3 + C*b^2*c^3 + 3*B*a^2*c^2*d - 6*A*a*b*c^2*d + 6*C*a*b*c^2*d - 3*B*b^2*c^2*d - 3*A*a^2*c*d^2 + 3*C*a^2*c*d^2 - 6*B*a*b*c*d^2 + 3*A*b^2*c*d^2 - 3*C*b^2*c*d^2 - B*a^2*d^3 + 2*A*a*b*d^3 - 2*C*a*b*d^3 + B*b^2*d^3)*(f*x + e)/(a^4*c^6 + 2*a^2*b^2*c^6 + b^4*c^6 + 3*a^4*c^4*d^2 + 6*a^2*b^2*c^4*d^2 + 3*b^4*c^4*d^2 + 3*a^4*c^2*d^4 + 6*a^2*b^2*c^2*d^4 + 3*b^4*c^2*d^4 + a^4*d^6 + 2*a^2*b^2*d^6 + b^4*d^6) + (B*a^2*c^3 - 2*A*a*b*c^3 + 2*C*a*b*c^3 - B*b^2*c^3 - 3*A*a^2*c^2*d + 3*C*a^2*c^2*d - 6*B*a*b*c^2*d + 3*A*b^2*c^2*d - 3*C*b^2*c^2*d - 3*B*a^2*c*d^2 + 6*A*a*b*c*d^2 - 6*C*a*b*c*d^2 + 3*B*b^2*c*d^2 + A*a^2*d^3 - C*a^2*d^3 + 2*B*a*b*d^3 - A*b^2*d^3 + C*b^2*d^3)*log(tan(f*x + e)^2 + 1)/(a^4*c^6 + 2*a^2*b^2*c^6 + b^4*c^6 + 3*a^4*c^4*d^2 + 6*a^2*b^2*c^4*d^2 + 3*b^4*c^4*d^2 + 3*a^4*c^2*d^4 + 6*a^2*b^2*c^2*d^4 + 3*b^4*c^2*d^4 + a^4*d^6 + 2*a^2*b^2*d^6 + b^4*d^6) - 2*(B*a^2*b^5*c - 2*A*a*b^6*c + 2*C*a*b^6*c - B*b^7*c + 3*C*a^4*b^3*d - 4*B*a^3*b^4*d + 5*A*a^2*b^5*d + C*a^2*b^5*d - 2*B*a*b^6*d + 3*A*b^7*d)*log(abs(b*tan(f*x + e) + a))/(a^4*b^5*c^4 + 2*a^2*b^7*c^4 + b^9*c^4 - 4*a^5*b^4*c^3*d - 8*a^3*b^6*c^3*d - 4*a*b^8*c^3*d + 6*a^6*b^3*c^2*d^2 + 12*a^4*b^5*c^2*d^2 + 6*a^2*b^7*c^2*d^2 - 4*a^7*b^2*c*d^3 - 8*a^5*b^4*c*d^3 - 4*a^3*b^6*c*d^3 + a^8*b*d^4 + 2*a^6*b^3*d^4 + a^4*b^5*d^4) + 2*(3*C*b^2*c^6*d^2 - 6*B*b^2*c^5*d^3 + 4*B*a*b*c^4*d^4 + 10*A*b^2*c^4*d^4 - C*b^2*c^4*d^4 - B*a^2*c^3*d^5 - 10*A*a*b*c^3*d^5 + 10*C*a*b*c^3*d^5 - 3*B*b^2*c^3*d^5 + 3*A*a^2*c^2*d^6 - 3*C*a^2*c^2*d^6 - 6*B*a*b*c^2*d^6 + 9*A*b^2*c^2*d^6 + 3*B*a^2*c*d^7 - 2*A*a*b*c*d^7 + 2*C*a*b*c*d^7 - B*b^2*c*d^7 - A*a^2*d^8 + C*a^2*d^8 - 2*B*a*b*d^8 + 3*A*b^2*d^8)*log(abs(d*tan(f*x + e) + c))/(b^4*c^10*d - 4*a*b^3*c^9*d^2 + 6*a^2*b^2*c^8*d^3 + 3*b^4*c^8*d^3 - 4*a^3*b*c^7*d^4 - 12*a*b^3*c^7*d^4 + a^4*c^6*d^5 + 18*a^2*b^2*c^6*d^5 + 3*b^4*c^6*d^5 - 12*a^3*b*c^5*d^6 - 12*a*b^3*c^5*d^6 + 3*a^4*c^4*d^7 + 18*a^2*b^2*c^4*d^7 + b^4*c^4*d^7 - 12*a^3*b*c^3*d^8 - 4*a*b^3*c^3*d^8 + 3*a^4*c^2*d^9 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11) + 2*(B*a^2*b^5*c*tan(f*x + e) - 2*A*a*b^6*c*tan(f*x + e) + 2*C*a*b^6*c*tan(f*x + e) - B*b^7*c*tan(f*x + e) + 3*C*a^4*b^3*d*tan(f*x + e) - 4*B*a^3*b^4*d*tan(f*x + e) + 5*A*a^2*b^5*d*tan(f*x + e) + C*a^2*b^5*d*tan(f*x + e) - 2*B*a*b^6*d*tan(f*x + e) + 3*A*b^7*d*tan(f*x + e) - C*a^4*b^3*c + 2*B*a^3*b^4*c - 3*A*a^2*b^5*c + C*a^2*b^5*c - A*b^7*c + 4*C*a^5*b^2*d - 5*B*a^4*b^3*d + 6*A*a^3*b^4*d + 2*C*a^3*b^4*d - 3*B*a^2*b^5*d + 4*A*a*b^6*d)/((a^4*b^4*c^4 + 2*a^2*b^6*c^4 + b^8*c^4 - 4*a^5*b^3*c^3*d - 8*a^3*b^5*c^3*d - 4*a*b^7*c^3*d + 6*a^6*b^2*c^2*d^2 + 12*a^4*b^4*c^2*d^2 + 6*a^2*b^6*c^2*d^2 - 4*a^7*b*c*d^3 - 8*a^5*b^3*c*d^3 - 4*a^3*b^5*c*d^3 + a^8*d^4 + 2*a^6*b^2*d^4 + a^4*b^4*d^4)*(b*tan(f*x + e) + a)) - (9*C*b^2*c^6*d^3*tan(f*x + e)^2 - 18*B*b^2*c^5*d^4*tan(f*x + e)^2 + 12*B*a*b*c^4*d^5*tan(f*x + e)^2 + 30*A*b^2*c^4*d^5*tan(f*x + e)^2 - 3*C*b^2*c^4*d^5*tan(f*x + e)^2 - 3*B*a^2*c^3*d^6*tan(f*x + e)^2 - 30*A*a*b*c^3*d^6*tan(f*x + e)^2 + 30*C*a*b*c^3*d^6*tan(f*x + e)^2 - 9*B*b^2*c^3*d^6*tan(f*x + e)^2 + 9*A*a^2*c^2*d^7*tan(f*x + e)^2 - 9*C*a^2*c^2*d^7*tan(f*x + e)^2 - 18*B*a*b*c^2*d^7*tan(f*x + e)^2 + 27*A*b^2*c^2*d^7*tan(f*x + e)^2 + 9*B*a^2*c*d^8*tan(f*x + e)^2 - 6*A*a*b*c*d^8*tan(f*x + e)^2 + 6*C*a*b*c*d^8*tan(f*x + e)^2 - 3*B*b^2*c*d^8*tan(f*x + e)^2 - 3*A*a^2*d^9*tan(f*x + e)^2 + 3*C*a^2*d^9*tan(f*x + e)^2 - 6*B*a*b*d^9*tan(f*x + e)^2 + 9*A*b^2*d^9*tan(f*x + e)^2 + 22*C*b^2*c^7*d^2*tan(f*x + e) - 4*C*a*b*c^6*d^3*tan(f*x + e) - 42*B*b^2*c^6*d^3*tan(f*x + e) + 32*B*a*b*c^5*d^4*tan(f*x + e) + 68*A*b^2*c^5*d^4*tan(f*x + e) - 2*C*b^2*c^5*d^4*tan(f*x + e) - 8*B*a^2*c^4*d^5*tan(f*x + e) - 72*A*a*b*c^4*d^5*tan(f*x + e) + 60*C*a*b*c^4*d^5*tan(f*x + e) - 26*B*b^2*c^4*d^5*tan(f*x + e) + 22*A*a^2*c^3*d^6*tan(f*x + e) - 22*C*a^2*c^3*d^6*tan(f*x + e) - 28*B*a*b*c^3*d^6*tan(f*x + e) + 66*A*b^2*c^3*d^6*tan(f*x + e) + 18*B*a^2*c^2*d^7*tan(f*x + e) - 28*A*a*b*c^2*d^7*tan(f*x + e) + 16*C*a*b*c^2*d^7*tan(f*x + e) - 8*B*b^2*c^2*d^7*tan(f*x + e) - 2*A*a^2*c*d^8*tan(f*x + e) + 2*C*a^2*c*d^8*tan(f*x + e) - 12*B*a*b*c*d^8*tan(f*x + e) + 22*A*b^2*c*d^8*tan(f*x + e) + 2*B*a^2*d^9*tan(f*x + e) - 4*A*a*b*d^9*tan(f*x + e) + 14*C*b^2*c^8*d - 6*C*a*b*c^7*d^2 - 25*B*b^2*c^7*d^2 + C*a^2*c^6*d^3 + 22*B*a*b*c^6*d^3 + 39*A*b^2*c^6*d^3 + 3*C*b^2*c^6*d^3 - 6*B*a^2*c^5*d^4 - 44*A*a*b*c^5*d^4 + 26*C*a*b*c^5*d^4 - 19*B*b^2*c^5*d^4 + 14*A*a^2*c^4*d^5 - 11*C*a^2*c^4*d^5 - 6*B*a*b*c^4*d^5 + 41*A*b^2*c^4*d^5 + C*b^2*c^4*d^5 + 7*B*a^2*c^3*d^6 - 26*A*a*b*c^3*d^6 + 8*C*a*b*c^3*d^6 - 6*B*b^2*c^3*d^6 + 3*A*a^2*c^2*d^7 - 4*B*a*b*c^2*d^7 + 14*A*b^2*c^2*d^7 + B*a^2*c*d^8 - 6*A*a*b*c*d^8 + A*a^2*d^9)/((b^4*c^10 - 4*a*b^3*c^9*d + 6*a^2*b^2*c^8*d^2 + 3*b^4*c^8*d^2 - 4*a^3*b*c^7*d^3 - 12*a*b^3*c^7*d^3 + a^4*c^6*d^4 + 18*a^2*b^2*c^6*d^4 + 3*b^4*c^6*d^4 - 12*a^3*b*c^5*d^5 - 12*a*b^3*c^5*d^5 + 3*a^4*c^4*d^6 + 18*a^2*b^2*c^4*d^6 + b^4*c^4*d^6 - 12*a^3*b*c^3*d^7 - 4*a*b^3*c^3*d^7 + 3*a^4*c^2*d^8 + 6*a^2*b^2*c^2*d^8 - 4*a^3*b*c*d^9 + a^4*d^10)*(d*tan(f*x + e) + c)^2))/f","B",0
90,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^n*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m} {\left(d \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m*(d*tan(f*x + e) + c)^n, x)","F",0
165,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{3} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(d*tan(f*x + e) + c)^3*(b*tan(f*x + e) + a)^m, x)","F",0
166,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(d*tan(f*x + e) + c)^2*(b*tan(f*x + e) + a)^m, x)","F",0
167,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(d \tan\left(f x + e\right) + c\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(d*tan(f*x + e) + c)*(b*tan(f*x + e) + a)^m, x)","F",0
168,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""giac"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m, x)","F",0
169,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}}{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c), x)","F",0
170,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^2, x)","F",0
171,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^3, x)","F",0
