1,1,85,0,0.598026," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, C b \tan\left(d x + c\right)^{3} - 6 \, {\left(B a - C b\right)} d x + 3 \, {\left(C a + B b\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(C a + B b\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 6 \, {\left(B a - C b\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*C*b*tan(d*x + c)^3 - 6*(B*a - C*b)*d*x + 3*(C*a + B*b)*tan(d*x + c)^2 + 3*(C*a + B*b)*log(1/(tan(d*x + c)^2 + 1)) + 6*(B*a - C*b)*tan(d*x + c))/d","A",0
2,1,66,0,0.609375," ","integrate((a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""fricas"")","\frac{C b \tan\left(d x + c\right)^{2} - 2 \, {\left(C a + B b\right)} d x - {\left(B a - C b\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(C a + B b\right)} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(C*b*tan(d*x + c)^2 - 2*(C*a + B*b)*d*x - (B*a - C*b)*log(1/(tan(d*x + c)^2 + 1)) + 2*(C*a + B*b)*tan(d*x + c))/d","A",0
3,1,50,0,1.060416," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(B a - C b\right)} d x + 2 \, C b \tan\left(d x + c\right) - {\left(C a + B b\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(2*(B*a - C*b)*d*x + 2*C*b*tan(d*x + c) - (C*a + B*b)*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
4,1,59,0,0.461319," ","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=""fricas"")","\frac{2 \, {\left(C a + B b\right)} d x + B a \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - C b \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(2*(C*a + B*b)*d*x + B*a*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - C*b*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
5,1,73,0,1.550462," ","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=""fricas"")","-\frac{2 \, {\left(B a - C b\right)} d x \tan\left(d x + c\right) - {\left(C a + B b\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) + 2 \, B a}{2 \, d \tan\left(d x + c\right)}"," ",0,"-1/2*(2*(B*a - C*b)*d*x*tan(d*x + c) - (C*a + B*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) + 2*B*a)/(d*tan(d*x + c))","A",0
6,1,95,0,0.547155," ","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=""fricas"")","-\frac{{\left(B a - C b\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + {\left(2 \, {\left(C a + B b\right)} d x + B a\right)} \tan\left(d x + c\right)^{2} + B a + 2 \, {\left(C a + B b\right)} \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*((B*a - C*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + (2*(C*a + B*b)*d*x + B*a)*tan(d*x + c)^2 + B*a + 2*(C*a + B*b)*tan(d*x + c))/(d*tan(d*x + c)^2)","A",0
7,1,121,0,0.540076," ","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=""fricas"")","-\frac{3 \, {\left(C a + B b\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{3} - 3 \, {\left(2 \, {\left(B a - C b\right)} d x - C a - B b\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(B a - C b\right)} \tan\left(d x + c\right)^{2} + 2 \, B a + 3 \, {\left(C a + B b\right)} \tan\left(d x + c\right)}{6 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*(C*a + B*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 - 3*(2*(B*a - C*b)*d*x - C*a - B*b)*tan(d*x + c)^3 - 6*(B*a - C*b)*tan(d*x + c)^2 + 2*B*a + 3*(C*a + B*b)*tan(d*x + c))/(d*tan(d*x + c)^3)","A",0
8,1,138,0,0.693526," ","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=""fricas"")","\frac{6 \, {\left(B a - C b\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{4} + 3 \, {\left(4 \, {\left(C a + B b\right)} d x + 3 \, B a - 2 \, C b\right)} \tan\left(d x + c\right)^{4} + 12 \, {\left(C a + B b\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(B a - C b\right)} \tan\left(d x + c\right)^{2} - 3 \, B a - 4 \, {\left(C a + B b\right)} \tan\left(d x + c\right)}{12 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(B*a - C*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 + 3*(4*(C*a + B*b)*d*x + 3*B*a - 2*C*b)*tan(d*x + c)^4 + 12*(C*a + B*b)*tan(d*x + c)^3 + 6*(B*a - C*b)*tan(d*x + c)^2 - 3*B*a - 4*(C*a + B*b)*tan(d*x + c))/(d*tan(d*x + c)^4)","A",0
9,1,146,0,0.597881," ","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=""fricas"")","\frac{3 \, C b^{2} \tan\left(d x + c\right)^{4} + 4 \, {\left(2 \, C a b + B b^{2}\right)} \tan\left(d x + c\right)^{3} - 12 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} d x + 6 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 12 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*C*b^2*tan(d*x + c)^4 + 4*(2*C*a*b + B*b^2)*tan(d*x + c)^3 - 12*(B*a^2 - 2*C*a*b - B*b^2)*d*x + 6*(C*a^2 + 2*B*a*b - C*b^2)*tan(d*x + c)^2 + 6*(C*a^2 + 2*B*a*b - C*b^2)*log(1/(tan(d*x + c)^2 + 1)) + 12*(B*a^2 - 2*C*a*b - B*b^2)*tan(d*x + c))/d","A",0
10,1,119,0,0.666161," ","integrate((a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, C b^{2} \tan\left(d x + c\right)^{3} - 6 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} d x + 3 \, {\left(2 \, C a b + B b^{2}\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 6 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*C*b^2*tan(d*x + c)^3 - 6*(C*a^2 + 2*B*a*b - C*b^2)*d*x + 3*(2*C*a*b + B*b^2)*tan(d*x + c)^2 - 3*(B*a^2 - 2*C*a*b - B*b^2)*log(1/(tan(d*x + c)^2 + 1)) + 6*(C*a^2 + 2*B*a*b - C*b^2)*tan(d*x + c))/d","A",0
11,1,91,0,1.514554," ","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=""fricas"")","\frac{C b^{2} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} d x - {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(2 \, C a b + B b^{2}\right)} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(C*b^2*tan(d*x + c)^2 + 2*(B*a^2 - 2*C*a*b - B*b^2)*d*x - (C*a^2 + 2*B*a*b - C*b^2)*log(1/(tan(d*x + c)^2 + 1)) + 2*(2*C*a*b + B*b^2)*tan(d*x + c))/d","A",0
12,1,92,0,0.766464," ","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=""fricas"")","\frac{B a^{2} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, C b^{2} \tan\left(d x + c\right) + 2 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} d x - {\left(2 \, C a b + B b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(B*a^2*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + 2*C*b^2*tan(d*x + c) + 2*(C*a^2 + 2*B*a*b - C*b^2)*d*x - (2*C*a*b + B*b^2)*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
13,1,112,0,0.774999," ","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=""fricas"")","-\frac{C b^{2} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) + 2 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} d x \tan\left(d x + c\right) + 2 \, B a^{2} - {\left(C a^{2} + 2 \, B a b\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)}"," ",0,"-1/2*(C*b^2*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c) + 2*(B*a^2 - 2*C*a*b - B*b^2)*d*x*tan(d*x + c) + 2*B*a^2 - (C*a^2 + 2*B*a*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c))/(d*tan(d*x + c))","A",0
14,1,122,0,1.546034," ","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=""fricas"")","-\frac{{\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + B a^{2} + {\left(B a^{2} + 2 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(C a^{2} + 2 \, B a b\right)} \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*((B*a^2 - 2*C*a*b - B*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + B*a^2 + (B*a^2 + 2*(C*a^2 + 2*B*a*b - C*b^2)*d*x)*tan(d*x + c)^2 + 2*(C*a^2 + 2*B*a*b)*tan(d*x + c))/(d*tan(d*x + c)^2)","A",0
15,1,157,0,0.620189," ","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=""fricas"")","-\frac{3 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{3} + 3 \, {\left(C a^{2} + 2 \, B a b - 2 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 2 \, B a^{2} - 6 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(C a^{2} + 2 \, B a b\right)} \tan\left(d x + c\right)}{6 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*(C*a^2 + 2*B*a*b - C*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 + 3*(C*a^2 + 2*B*a*b - 2*(B*a^2 - 2*C*a*b - B*b^2)*d*x)*tan(d*x + c)^3 + 2*B*a^2 - 6*(B*a^2 - 2*C*a*b - B*b^2)*tan(d*x + c)^2 + 3*(C*a^2 + 2*B*a*b)*tan(d*x + c))/(d*tan(d*x + c)^3)","A",0
16,1,191,0,1.238697," ","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=""fricas"")","\frac{6 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{4} + 3 \, {\left(3 \, B a^{2} - 4 \, C a b - 2 \, B b^{2} + 4 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} d x\right)} \tan\left(d x + c\right)^{4} + 12 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \tan\left(d x + c\right)^{3} - 3 \, B a^{2} + 6 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \tan\left(d x + c\right)^{2} - 4 \, {\left(C a^{2} + 2 \, B a b\right)} \tan\left(d x + c\right)}{12 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(B*a^2 - 2*C*a*b - B*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 + 3*(3*B*a^2 - 4*C*a*b - 2*B*b^2 + 4*(C*a^2 + 2*B*a*b - C*b^2)*d*x)*tan(d*x + c)^4 + 12*(C*a^2 + 2*B*a*b - C*b^2)*tan(d*x + c)^3 - 3*B*a^2 + 6*(B*a^2 - 2*C*a*b - B*b^2)*tan(d*x + c)^2 - 4*(C*a^2 + 2*B*a*b)*tan(d*x + c))/(d*tan(d*x + c)^4)","A",0
17,1,178,0,0.592164," ","integrate((a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, C b^{3} \tan\left(d x + c\right)^{4} + 4 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \tan\left(d x + c\right)^{3} - 12 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} d x + 6 \, {\left(3 \, C a^{2} b + 3 \, B a b^{2} - C b^{3}\right)} \tan\left(d x + c\right)^{2} - 6 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 12 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*C*b^3*tan(d*x + c)^4 + 4*(3*C*a*b^2 + B*b^3)*tan(d*x + c)^3 - 12*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*d*x + 6*(3*C*a^2*b + 3*B*a*b^2 - C*b^3)*tan(d*x + c)^2 - 6*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(1/(tan(d*x + c)^2 + 1)) + 12*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*tan(d*x + c))/d","A",0
18,1,142,0,0.683379," ","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=""fricas"")","\frac{2 \, C b^{3} \tan\left(d x + c\right)^{3} + 6 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} d x + 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 6 \, {\left(3 \, C a^{2} b + 3 \, B a b^{2} - C b^{3}\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*C*b^3*tan(d*x + c)^3 + 6*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*d*x + 3*(3*C*a*b^2 + B*b^3)*tan(d*x + c)^2 - 3*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(1/(tan(d*x + c)^2 + 1)) + 6*(3*C*a^2*b + 3*B*a*b^2 - C*b^3)*tan(d*x + c))/d","A",0
19,1,133,0,0.646925," ","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=""fricas"")","\frac{C b^{3} \tan\left(d x + c\right)^{2} + B a^{3} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} d x - {\left(3 \, C a^{2} b + 3 \, B a b^{2} - C b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(C*b^3*tan(d*x + c)^2 + B*a^3*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + 2*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*d*x - (3*C*a^2*b + 3*B*a*b^2 - C*b^3)*log(1/(tan(d*x + c)^2 + 1)) + 2*(3*C*a*b^2 + B*b^3)*tan(d*x + c))/d","A",0
20,1,145,0,0.649319," ","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=""fricas"")","\frac{2 \, C b^{3} \tan\left(d x + c\right)^{2} - 2 \, B a^{3} - 2 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} d x \tan\left(d x + c\right) + {\left(C a^{3} + 3 \, B a^{2} b\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) - {\left(3 \, C a b^{2} + B b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)}"," ",0,"1/2*(2*C*b^3*tan(d*x + c)^2 - 2*B*a^3 - 2*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*d*x*tan(d*x + c) + (C*a^3 + 3*B*a^2*b)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) - (3*C*a*b^2 + B*b^3)*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c))/(d*tan(d*x + c))","A",0
21,1,162,0,0.917885," ","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=""fricas"")","-\frac{C b^{3} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + B a^{3} + {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + {\left(B a^{3} + 2 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \tan\left(d x + c\right)}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*(C*b^3*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + B*a^3 + (B*a^3 - 3*C*a^2*b - 3*B*a*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + (B*a^3 + 2*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*d*x)*tan(d*x + c)^2 + 2*(C*a^3 + 3*B*a^2*b)*tan(d*x + c))/(d*tan(d*x + c)^2)","A",0
22,1,181,0,0.625488," ","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=""fricas"")","-\frac{3 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{3} + 2 \, B a^{3} + 3 \, {\left(C a^{3} + 3 \, B a^{2} b - 2 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \tan\left(d x + c\right)}{6 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 + 2*B*a^3 + 3*(C*a^3 + 3*B*a^2*b - 2*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*d*x)*tan(d*x + c)^3 - 6*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2)*tan(d*x + c)^2 + 3*(C*a^3 + 3*B*a^2*b)*tan(d*x + c))/(d*tan(d*x + c)^3)","A",0
23,1,225,0,0.743860," ","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=""fricas"")","\frac{6 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{4} + 3 \, {\left(3 \, B a^{3} - 6 \, C a^{2} b - 6 \, B a b^{2} + 4 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{4} - 3 \, B a^{3} + 12 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2}\right)} \tan\left(d x + c\right)^{2} - 4 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \tan\left(d x + c\right)}{12 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 + 3*(3*B*a^3 - 6*C*a^2*b - 6*B*a*b^2 + 4*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*d*x)*tan(d*x + c)^4 - 3*B*a^3 + 12*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*tan(d*x + c)^3 + 6*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2)*tan(d*x + c)^2 - 4*(C*a^3 + 3*B*a^2*b)*tan(d*x + c))/(d*tan(d*x + c)^4)","A",0
24,1,266,0,1.406496," ","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=""fricas"")","\frac{30 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{5} + 15 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b - 6 \, C a b^{2} - 2 \, B b^{3} - 4 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{5} - 60 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \tan\left(d x + c\right)^{4} - 12 \, B a^{3} + 30 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)^{3} + 20 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2}\right)} \tan\left(d x + c\right)^{2} - 15 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \tan\left(d x + c\right)}{60 \, d \tan\left(d x + c\right)^{5}}"," ",0,"1/60*(30*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^5 + 15*(3*C*a^3 + 9*B*a^2*b - 6*C*a*b^2 - 2*B*b^3 - 4*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*d*x)*tan(d*x + c)^5 - 60*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*tan(d*x + c)^4 - 12*B*a^3 + 30*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*tan(d*x + c)^3 + 20*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2)*tan(d*x + c)^2 - 15*(C*a^3 + 3*B*a^2*b)*tan(d*x + c))/(d*tan(d*x + c)^5)","A",0
25,1,190,0,0.874346," ","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=""fricas"")","\frac{2 \, {\left(C a b^{3} - B b^{4}\right)} d x + {\left(C a^{2} b^{2} + C b^{4}\right)} \tan\left(d x + c\right)^{2} + {\left(C a^{4} - B a^{3} b\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(C a^{4} - B a^{3} b - B a b^{3} - C b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(C a^{3} b - B a^{2} b^{2} + C a b^{3} - B b^{4}\right)} \tan\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} + b^{5}\right)} d}"," ",0,"1/2*(2*(C*a*b^3 - B*b^4)*d*x + (C*a^2*b^2 + C*b^4)*tan(d*x + c)^2 + (C*a^4 - B*a^3*b)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (C*a^4 - B*a^3*b - B*a*b^3 - C*b^4)*log(1/(tan(d*x + c)^2 + 1)) - 2*(C*a^3*b - B*a^2*b^2 + C*a*b^3 - B*b^4)*tan(d*x + c))/((a^2*b^3 + b^5)*d)","A",0
26,1,149,0,0.667142," ","integrate(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(B a b^{2} + C b^{3}\right)} d x + {\left(C a^{3} - B a^{2} b\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(C a^{3} - B a^{2} b + C a b^{2} - B b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(C a^{2} b + C b^{3}\right)} \tan\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} + b^{4}\right)} d}"," ",0,"-1/2*(2*(B*a*b^2 + C*b^3)*d*x + (C*a^3 - B*a^2*b)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (C*a^3 - B*a^2*b + C*a*b^2 - B*b^3)*log(1/(tan(d*x + c)^2 + 1)) - 2*(C*a^2*b + C*b^3)*tan(d*x + c))/((a^2*b^2 + b^4)*d)","A",0
27,1,110,0,2.312557," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(C a b - B b^{2}\right)} d x - {\left(C a^{2} - B a b\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(C a^{2} + C b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, {\left(a^{2} b + b^{3}\right)} d}"," ",0,"-1/2*(2*(C*a*b - B*b^2)*d*x - (C*a^2 - B*a*b)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + (C*a^2 + C*b^2)*log(1/(tan(d*x + c)^2 + 1)))/((a^2*b + b^3)*d)","A",0
28,1,76,0,0.750554," ","integrate(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(B a + C b\right)} d x - {\left(C a - B b\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, {\left(a^{2} + b^{2}\right)} d}"," ",0,"1/2*(2*(B*a + C*b)*d*x - (C*a - B*b)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)))/((a^2 + b^2)*d)","A",0
29,1,118,0,0.666725," ","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=""fricas"")","\frac{2 \, {\left(C a^{2} - B a b\right)} d x + {\left(B a^{2} + B b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(C a b - B b^{2}\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, {\left(a^{3} + a b^{2}\right)} d}"," ",0,"1/2*(2*(C*a^2 - B*a*b)*d*x + (B*a^2 + B*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + (C*a*b - B*b^2)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)))/((a^3 + a*b^2)*d)","A",0
30,1,177,0,0.769287," ","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=""fricas"")","-\frac{2 \, B a^{3} + 2 \, B a b^{2} + 2 \, {\left(B a^{3} + C a^{2} b\right)} d x \tan\left(d x + c\right) - {\left(C a^{3} - B a^{2} b + C a b^{2} - B b^{3}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) + {\left(C a b^{2} - B b^{3}\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)}{2 \, {\left(a^{4} + a^{2} b^{2}\right)} d \tan\left(d x + c\right)}"," ",0,"-1/2*(2*B*a^3 + 2*B*a*b^2 + 2*(B*a^3 + C*a^2*b)*d*x*tan(d*x + c) - (C*a^3 - B*a^2*b + C*a*b^2 - B*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) + (C*a*b^2 - B*b^3)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1))*tan(d*x + c))/((a^4 + a^2*b^2)*d*tan(d*x + c))","A",0
31,1,234,0,0.634116," ","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=""fricas"")","-\frac{B a^{4} + B a^{2} b^{2} + {\left(B a^{4} + C a^{3} b + C a b^{3} - B b^{4}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} - {\left(C a b^{3} - B b^{4}\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + {\left(B a^{4} + B a^{2} b^{2} + 2 \, {\left(C a^{4} - B a^{3} b\right)} d x\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(C a^{4} - B a^{3} b + C a^{2} b^{2} - B a b^{3}\right)} \tan\left(d x + c\right)}{2 \, {\left(a^{5} + a^{3} b^{2}\right)} d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*(B*a^4 + B*a^2*b^2 + (B*a^4 + C*a^3*b + C*a*b^3 - B*b^4)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 - (C*a*b^3 - B*b^4)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + (B*a^4 + B*a^2*b^2 + 2*(C*a^4 - B*a^3*b)*d*x)*tan(d*x + c)^2 + 2*(C*a^4 - B*a^3*b + C*a^2*b^2 - B*a*b^3)*tan(d*x + c))/((a^5 + a^3*b^2)*d*tan(d*x + c)^2)","A",0
32,1,434,0,0.805167," ","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=""fricas"")","-\frac{2 \, C a^{4} b^{2} - 2 \, B a^{3} b^{3} - 2 \, {\left(C a^{3} b^{3} - 2 \, B a^{2} b^{4} - C a b^{5}\right)} d x - 2 \, {\left(C a^{4} b^{2} + 2 \, C a^{2} b^{4} + C b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(2 \, C a^{6} - B a^{5} b + 4 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} + {\left(2 \, C a^{5} b - B a^{4} b^{2} + 4 \, C a^{3} b^{3} - 3 \, B a^{2} b^{4}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(2 \, C a^{6} - B a^{5} b + 4 \, C a^{4} b^{2} - 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5} + {\left(2 \, C a^{5} b - B a^{4} b^{2} + 4 \, C a^{3} b^{3} - 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(2 \, C a^{5} b - B a^{4} b^{2} + 2 \, C a^{3} b^{3} + C a b^{5} + {\left(C a^{2} b^{4} - 2 \, B a b^{5} - C b^{6}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d \tan\left(d x + c\right) + {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d\right)}}"," ",0,"-1/2*(2*C*a^4*b^2 - 2*B*a^3*b^3 - 2*(C*a^3*b^3 - 2*B*a^2*b^4 - C*a*b^5)*d*x - 2*(C*a^4*b^2 + 2*C*a^2*b^4 + C*b^6)*tan(d*x + c)^2 + (2*C*a^6 - B*a^5*b + 4*C*a^4*b^2 - 3*B*a^3*b^3 + (2*C*a^5*b - B*a^4*b^2 + 4*C*a^3*b^3 - 3*B*a^2*b^4)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (2*C*a^6 - B*a^5*b + 4*C*a^4*b^2 - 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5 + (2*C*a^5*b - B*a^4*b^2 + 4*C*a^3*b^3 - 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(2*C*a^5*b - B*a^4*b^2 + 2*C*a^3*b^3 + C*a*b^5 + (C*a^2*b^4 - 2*B*a*b^5 - C*b^6)*d*x)*tan(d*x + c))/((a^4*b^4 + 2*a^2*b^6 + b^8)*d*tan(d*x + c) + (a^5*b^3 + 2*a^3*b^5 + a*b^7)*d)","B",0
33,1,311,0,0.822965," ","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=""fricas"")","\frac{2 \, C a^{3} b^{2} - 2 \, B a^{2} b^{3} - 2 \, {\left(B a^{3} b^{2} + 2 \, C a^{2} b^{3} - B a b^{4}\right)} d x + {\left(C a^{5} + 3 \, C a^{3} b^{2} - 2 \, B a^{2} b^{3} + {\left(C a^{4} b + 3 \, C a^{2} b^{3} - 2 \, B a b^{4}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(C a^{5} + 2 \, C a^{3} b^{2} + C a b^{4} + {\left(C a^{4} b + 2 \, C a^{2} b^{3} + C b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(C a^{4} b - B a^{3} b^{2} + {\left(B a^{2} b^{3} + 2 \, C a b^{4} - B b^{5}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d\right)}}"," ",0,"1/2*(2*C*a^3*b^2 - 2*B*a^2*b^3 - 2*(B*a^3*b^2 + 2*C*a^2*b^3 - B*a*b^4)*d*x + (C*a^5 + 3*C*a^3*b^2 - 2*B*a^2*b^3 + (C*a^4*b + 3*C*a^2*b^3 - 2*B*a*b^4)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (C*a^5 + 2*C*a^3*b^2 + C*a*b^4 + (C*a^4*b + 2*C*a^2*b^3 + C*b^5)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(C*a^4*b - B*a^3*b^2 + (B*a^2*b^3 + 2*C*a*b^4 - B*b^5)*d*x)*tan(d*x + c))/((a^4*b^3 + 2*a^2*b^5 + b^7)*d*tan(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d)","B",0
34,1,221,0,0.593662," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, C a^{2} b - 2 \, B a b^{2} + 2 \, {\left(C a^{3} - 2 \, B a^{2} b - C a b^{2}\right)} d x + {\left(B a^{3} + 2 \, C a^{2} b - B a b^{2} + {\left(B a^{2} b + 2 \, C a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(C a^{3} - B a^{2} b - {\left(C a^{2} b - 2 \, B a b^{2} - C b^{3}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \tan\left(d x + c\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}"," ",0,"-1/2*(2*C*a^2*b - 2*B*a*b^2 + 2*(C*a^3 - 2*B*a^2*b - C*a*b^2)*d*x + (B*a^3 + 2*C*a^2*b - B*a*b^2 + (B*a^2*b + 2*C*a*b^2 - B*b^3)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 2*(C*a^3 - B*a^2*b - (C*a^2*b - 2*B*a*b^2 - C*b^3)*d*x)*tan(d*x + c))/((a^4*b + 2*a^2*b^3 + b^5)*d*tan(d*x + c) + (a^5 + 2*a^3*b^2 + a*b^4)*d)","A",0
35,1,222,0,0.804142," ","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=""fricas"")","\frac{2 \, C a b^{2} - 2 \, B b^{3} + 2 \, {\left(B a^{3} + 2 \, C a^{2} b - B a b^{2}\right)} d x - {\left(C a^{3} - 2 \, B a^{2} b - C a b^{2} + {\left(C a^{2} b - 2 \, B a b^{2} - C b^{3}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(C a^{2} b - B a b^{2} - {\left(B a^{2} b + 2 \, C a b^{2} - B b^{3}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \tan\left(d x + c\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}"," ",0,"1/2*(2*C*a*b^2 - 2*B*b^3 + 2*(B*a^3 + 2*C*a^2*b - B*a*b^2)*d*x - (C*a^3 - 2*B*a^2*b - C*a*b^2 + (C*a^2*b - 2*B*a*b^2 - C*b^3)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 2*(C*a^2*b - B*a*b^2 - (B*a^2*b + 2*C*a*b^2 - B*b^3)*d*x)*tan(d*x + c))/((a^4*b + 2*a^2*b^3 + b^5)*d*tan(d*x + c) + (a^5 + 2*a^3*b^2 + a*b^4)*d)","A",0
36,1,323,0,0.919695," ","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=""fricas"")","-\frac{2 \, C a^{2} b^{3} - 2 \, B a b^{4} - 2 \, {\left(C a^{5} - 2 \, B a^{4} b - C a^{3} b^{2}\right)} d x - {\left(B a^{5} + 2 \, B a^{3} b^{2} + B a b^{4} + {\left(B a^{4} b + 2 \, B a^{2} b^{3} + B b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(2 \, C a^{4} b - 3 \, B a^{3} b^{2} - B a b^{4} + {\left(2 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - B b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} + {\left(C a^{4} b - 2 \, B a^{3} b^{2} - C a^{2} b^{3}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \tan\left(d x + c\right) + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d\right)}}"," ",0,"-1/2*(2*C*a^2*b^3 - 2*B*a*b^4 - 2*(C*a^5 - 2*B*a^4*b - C*a^3*b^2)*d*x - (B*a^5 + 2*B*a^3*b^2 + B*a*b^4 + (B*a^4*b + 2*B*a^2*b^3 + B*b^5)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - (2*C*a^4*b - 3*B*a^3*b^2 - B*a*b^4 + (2*C*a^3*b^2 - 3*B*a^2*b^3 - B*b^5)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 2*(C*a^3*b^2 - B*a^2*b^3 + (C*a^4*b - 2*B*a^3*b^2 - C*a^2*b^3)*d*x)*tan(d*x + c))/((a^6*b + 2*a^4*b^3 + a^2*b^5)*d*tan(d*x + c) + (a^7 + 2*a^5*b^2 + a^3*b^4)*d)","B",0
37,1,465,0,0.910028," ","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=""fricas"")","-\frac{2 \, B a^{6} + 4 \, B a^{4} b^{2} + 2 \, B a^{2} b^{4} + 2 \, {\left(C a^{3} b^{3} - B a^{2} b^{4} + {\left(B a^{5} b + 2 \, C a^{4} b^{2} - B a^{3} b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{2} - {\left({\left(C a^{5} b - 2 \, B a^{4} b^{2} + 2 \, C a^{3} b^{3} - 4 \, B a^{2} b^{4} + C a b^{5} - 2 \, B b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(C a^{6} - 2 \, B a^{5} b + 2 \, C a^{4} b^{2} - 4 \, B a^{3} b^{3} + C a^{2} b^{4} - 2 \, B a b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left({\left(3 \, C a^{3} b^{3} - 4 \, B a^{2} b^{4} + C a b^{5} - 2 \, B b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(3 \, C a^{4} b^{2} - 4 \, B a^{3} b^{3} + C a^{2} b^{4} - 2 \, B a b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(B a^{5} b + 2 \, B a^{3} b^{3} - C a^{2} b^{4} + 2 \, B a b^{5} + {\left(B a^{6} + 2 \, C a^{5} b - B a^{4} b^{2}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d \tan\left(d x + c\right)^{2} + {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \tan\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*B*a^6 + 4*B*a^4*b^2 + 2*B*a^2*b^4 + 2*(C*a^3*b^3 - B*a^2*b^4 + (B*a^5*b + 2*C*a^4*b^2 - B*a^3*b^3)*d*x)*tan(d*x + c)^2 - ((C*a^5*b - 2*B*a^4*b^2 + 2*C*a^3*b^3 - 4*B*a^2*b^4 + C*a*b^5 - 2*B*b^6)*tan(d*x + c)^2 + (C*a^6 - 2*B*a^5*b + 2*C*a^4*b^2 - 4*B*a^3*b^3 + C*a^2*b^4 - 2*B*a*b^5)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + ((3*C*a^3*b^3 - 4*B*a^2*b^4 + C*a*b^5 - 2*B*b^6)*tan(d*x + c)^2 + (3*C*a^4*b^2 - 4*B*a^3*b^3 + C*a^2*b^4 - 2*B*a*b^5)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + 2*(B*a^5*b + 2*B*a^3*b^3 - C*a^2*b^4 + 2*B*a*b^5 + (B*a^6 + 2*C*a^5*b - B*a^4*b^2)*d*x)*tan(d*x + c))/((a^7*b + 2*a^5*b^3 + a^3*b^5)*d*tan(d*x + c)^2 + (a^8 + 2*a^6*b^2 + a^4*b^4)*d*tan(d*x + c))","B",0
38,1,890,0,0.927304," ","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=""fricas"")","-\frac{3 \, C a^{7} b^{2} - B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 7 \, B a^{4} b^{5} - 2 \, {\left(C a^{6} b^{3} + 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} + C b^{9}\right)} \tan\left(d x + c\right)^{3} - 2 \, {\left(B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - C a^{2} b^{7}\right)} d x - {\left(9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} + 23 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} + 12 \, C a^{3} b^{6} + 4 \, C a b^{8} + 2 \, {\left(B a^{3} b^{6} + 3 \, C a^{2} b^{7} - 3 \, B a b^{8} - C b^{9}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(3 \, C a^{9} - B a^{8} b + 9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} + 10 \, C a^{5} b^{4} - 6 \, B a^{4} b^{5} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} + 10 \, C a^{3} b^{6} - 6 \, B a^{2} b^{7}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} + 9 \, C a^{6} b^{3} - 3 \, B a^{5} b^{4} + 10 \, C a^{4} b^{5} - 6 \, B a^{3} b^{6}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(3 \, C a^{9} - B a^{8} b + 9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - B a^{2} b^{7} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} + 3 \, C a b^{8} - B b^{9}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} + 9 \, C a^{6} b^{3} - 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} + 3 \, C a^{2} b^{7} - B a b^{8}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} + 6 \, C a^{6} b^{3} - 3 \, B a^{5} b^{4} - 2 \, C a^{4} b^{5} + 4 \, B a^{3} b^{6} + C a^{2} b^{7} + 2 \, {\left(B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - C a b^{8}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{6} + 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} + b^{12}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{5} + 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} + a b^{11}\right)} d \tan\left(d x + c\right) + {\left(a^{8} b^{4} + 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} + a^{2} b^{10}\right)} d\right)}}"," ",0,"-1/2*(3*C*a^7*b^2 - B*a^6*b^3 + 9*C*a^5*b^4 - 7*B*a^4*b^5 - 2*(C*a^6*b^3 + 3*C*a^4*b^5 + 3*C*a^2*b^7 + C*b^9)*tan(d*x + c)^3 - 2*(B*a^5*b^4 + 3*C*a^4*b^5 - 3*B*a^3*b^6 - C*a^2*b^7)*d*x - (9*C*a^7*b^2 - 3*B*a^6*b^3 + 23*C*a^5*b^4 - 9*B*a^4*b^5 + 12*C*a^3*b^6 + 4*C*a*b^8 + 2*(B*a^3*b^6 + 3*C*a^2*b^7 - 3*B*a*b^8 - C*b^9)*d*x)*tan(d*x + c)^2 + (3*C*a^9 - B*a^8*b + 9*C*a^7*b^2 - 3*B*a^6*b^3 + 10*C*a^5*b^4 - 6*B*a^4*b^5 + (3*C*a^7*b^2 - B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 + 10*C*a^3*b^6 - 6*B*a^2*b^7)*tan(d*x + c)^2 + 2*(3*C*a^8*b - B*a^7*b^2 + 9*C*a^6*b^3 - 3*B*a^5*b^4 + 10*C*a^4*b^5 - 6*B*a^3*b^6)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (3*C*a^9 - B*a^8*b + 9*C*a^7*b^2 - 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 + 3*C*a^3*b^6 - B*a^2*b^7 + (3*C*a^7*b^2 - B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 + 3*C*a*b^8 - B*b^9)*tan(d*x + c)^2 + 2*(3*C*a^8*b - B*a^7*b^2 + 9*C*a^6*b^3 - 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 + 3*C*a^2*b^7 - B*a*b^8)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(3*C*a^8*b - B*a^7*b^2 + 6*C*a^6*b^3 - 3*B*a^5*b^4 - 2*C*a^4*b^5 + 4*B*a^3*b^6 + C*a^2*b^7 + 2*(B*a^4*b^5 + 3*C*a^3*b^6 - 3*B*a^2*b^7 - C*a*b^8)*d*x)*tan(d*x + c))/((a^6*b^6 + 3*a^4*b^8 + 3*a^2*b^10 + b^12)*d*tan(d*x + c)^2 + 2*(a^7*b^5 + 3*a^5*b^7 + 3*a^3*b^9 + a*b^11)*d*tan(d*x + c) + (a^8*b^4 + 3*a^6*b^6 + 3*a^4*b^8 + a^2*b^10)*d)","B",0
39,1,666,0,1.459623," ","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=""fricas"")","\frac{C a^{6} b^{2} + B a^{5} b^{3} + 7 \, C a^{4} b^{4} - 5 \, B a^{3} b^{5} + 2 \, {\left(C a^{5} b^{3} - 3 \, B a^{4} b^{4} - 3 \, C a^{3} b^{5} + B a^{2} b^{6}\right)} d x - {\left(3 \, C a^{6} b^{2} - B a^{5} b^{3} + 9 \, C a^{4} b^{4} - 7 \, B a^{3} b^{5} - 2 \, {\left(C a^{3} b^{5} - 3 \, B a^{2} b^{6} - 3 \, C a b^{7} + B b^{8}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(C a^{8} + 3 \, C a^{6} b^{2} + B a^{5} b^{3} + 6 \, C a^{4} b^{4} - 3 \, B a^{3} b^{5} + {\left(C a^{6} b^{2} + 3 \, C a^{4} b^{4} + B a^{3} b^{5} + 6 \, C a^{2} b^{6} - 3 \, B a b^{7}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b + 3 \, C a^{5} b^{3} + B a^{4} b^{4} + 6 \, C a^{3} b^{5} - 3 \, B a^{2} b^{6}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(C a^{8} + 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} + C a^{2} b^{6} + {\left(C a^{6} b^{2} + 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} + C b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b + 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} + C a b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(C a^{7} b + 3 \, C a^{5} b^{3} - 3 \, B a^{4} b^{4} - 4 \, C a^{3} b^{5} + 3 \, B a^{2} b^{6} - 2 \, {\left(C a^{4} b^{4} - 3 \, B a^{3} b^{5} - 3 \, C a^{2} b^{6} + B a b^{7}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{5} + 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + b^{11}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{4} + 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} + a b^{10}\right)} d \tan\left(d x + c\right) + {\left(a^{8} b^{3} + 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} + a^{2} b^{9}\right)} d\right)}}"," ",0,"1/2*(C*a^6*b^2 + B*a^5*b^3 + 7*C*a^4*b^4 - 5*B*a^3*b^5 + 2*(C*a^5*b^3 - 3*B*a^4*b^4 - 3*C*a^3*b^5 + B*a^2*b^6)*d*x - (3*C*a^6*b^2 - B*a^5*b^3 + 9*C*a^4*b^4 - 7*B*a^3*b^5 - 2*(C*a^3*b^5 - 3*B*a^2*b^6 - 3*C*a*b^7 + B*b^8)*d*x)*tan(d*x + c)^2 + (C*a^8 + 3*C*a^6*b^2 + B*a^5*b^3 + 6*C*a^4*b^4 - 3*B*a^3*b^5 + (C*a^6*b^2 + 3*C*a^4*b^4 + B*a^3*b^5 + 6*C*a^2*b^6 - 3*B*a*b^7)*tan(d*x + c)^2 + 2*(C*a^7*b + 3*C*a^5*b^3 + B*a^4*b^4 + 6*C*a^3*b^5 - 3*B*a^2*b^6)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (C*a^8 + 3*C*a^6*b^2 + 3*C*a^4*b^4 + C*a^2*b^6 + (C*a^6*b^2 + 3*C*a^4*b^4 + 3*C*a^2*b^6 + C*b^8)*tan(d*x + c)^2 + 2*(C*a^7*b + 3*C*a^5*b^3 + 3*C*a^3*b^5 + C*a*b^7)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(C*a^7*b + 3*C*a^5*b^3 - 3*B*a^4*b^4 - 4*C*a^3*b^5 + 3*B*a^2*b^6 - 2*(C*a^4*b^4 - 3*B*a^3*b^5 - 3*C*a^2*b^6 + B*a*b^7)*d*x)*tan(d*x + c))/((a^6*b^5 + 3*a^4*b^7 + 3*a^2*b^9 + b^11)*d*tan(d*x + c)^2 + 2*(a^7*b^4 + 3*a^5*b^6 + 3*a^3*b^8 + a*b^10)*d*tan(d*x + c) + (a^8*b^3 + 3*a^6*b^5 + 3*a^4*b^7 + a^2*b^9)*d)","B",0
40,1,478,0,0.591568," ","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=""fricas"")","\frac{C a^{5} - 3 \, B a^{4} b - 5 \, C a^{3} b^{2} + 3 \, B a^{2} b^{3} - 2 \, {\left(B a^{5} + 3 \, C a^{4} b - 3 \, B a^{3} b^{2} - C a^{2} b^{3}\right)} d x + {\left(C a^{5} + B a^{4} b + 7 \, C a^{3} b^{2} - 5 \, B a^{2} b^{3} - 2 \, {\left(B a^{3} b^{2} + 3 \, C a^{2} b^{3} - 3 \, B a b^{4} - C b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(C a^{5} - 3 \, B a^{4} b - 3 \, C a^{3} b^{2} + B a^{2} b^{3} + {\left(C a^{3} b^{2} - 3 \, B a^{2} b^{3} - 3 \, C a b^{4} + B b^{5}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(C a^{4} b - 3 \, B a^{3} b^{2} - 3 \, C a^{2} b^{3} + B a b^{4}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(B a^{5} + 3 \, C a^{4} b - 3 \, B a^{3} b^{2} - 3 \, C a^{2} b^{3} + 2 \, B a b^{4} - 2 \, {\left(B a^{4} b + 3 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - C a b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d\right)}}"," ",0,"1/2*(C*a^5 - 3*B*a^4*b - 5*C*a^3*b^2 + 3*B*a^2*b^3 - 2*(B*a^5 + 3*C*a^4*b - 3*B*a^3*b^2 - C*a^2*b^3)*d*x + (C*a^5 + B*a^4*b + 7*C*a^3*b^2 - 5*B*a^2*b^3 - 2*(B*a^3*b^2 + 3*C*a^2*b^3 - 3*B*a*b^4 - C*b^5)*d*x)*tan(d*x + c)^2 + (C*a^5 - 3*B*a^4*b - 3*C*a^3*b^2 + B*a^2*b^3 + (C*a^3*b^2 - 3*B*a^2*b^3 - 3*C*a*b^4 + B*b^5)*tan(d*x + c)^2 + 2*(C*a^4*b - 3*B*a^3*b^2 - 3*C*a^2*b^3 + B*a*b^4)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + 2*(B*a^5 + 3*C*a^4*b - 3*B*a^3*b^2 - 3*C*a^2*b^3 + 2*B*a*b^4 - 2*(B*a^4*b + 3*C*a^3*b^2 - 3*B*a^2*b^3 - C*a*b^4)*d*x)*tan(d*x + c))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*tan(d*x + c) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d)","B",0
41,1,488,0,0.896838," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, C a^{4} b - 5 \, B a^{3} b^{2} - 3 \, C a^{2} b^{3} + B a b^{4} + 2 \, {\left(C a^{5} - 3 \, B a^{4} b - 3 \, C a^{3} b^{2} + B a^{2} b^{3}\right)} d x - {\left(C a^{4} b - 3 \, B a^{3} b^{2} - 5 \, C a^{2} b^{3} + 3 \, B a b^{4} - 2 \, {\left(C a^{3} b^{2} - 3 \, B a^{2} b^{3} - 3 \, C a b^{4} + B b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(B a^{5} + 3 \, C a^{4} b - 3 \, B a^{3} b^{2} - C a^{2} b^{3} + {\left(B a^{3} b^{2} + 3 \, C a^{2} b^{3} - 3 \, B a b^{4} - C b^{5}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{4} b + 3 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - C a b^{4}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(C a^{5} - 2 \, B a^{4} b - 3 \, C a^{3} b^{2} + 3 \, B a^{2} b^{3} + 2 \, C a b^{4} - B b^{5} - 2 \, {\left(C a^{4} b - 3 \, B a^{3} b^{2} - 3 \, C a^{2} b^{3} + B a b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d\right)}}"," ",0,"-1/2*(3*C*a^4*b - 5*B*a^3*b^2 - 3*C*a^2*b^3 + B*a*b^4 + 2*(C*a^5 - 3*B*a^4*b - 3*C*a^3*b^2 + B*a^2*b^3)*d*x - (C*a^4*b - 3*B*a^3*b^2 - 5*C*a^2*b^3 + 3*B*a*b^4 - 2*(C*a^3*b^2 - 3*B*a^2*b^3 - 3*C*a*b^4 + B*b^5)*d*x)*tan(d*x + c)^2 + (B*a^5 + 3*C*a^4*b - 3*B*a^3*b^2 - C*a^2*b^3 + (B*a^3*b^2 + 3*C*a^2*b^3 - 3*B*a*b^4 - C*b^5)*tan(d*x + c)^2 + 2*(B*a^4*b + 3*C*a^3*b^2 - 3*B*a^2*b^3 - C*a*b^4)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 2*(C*a^5 - 2*B*a^4*b - 3*C*a^3*b^2 + 3*B*a^2*b^3 + 2*C*a*b^4 - B*b^5 - 2*(C*a^4*b - 3*B*a^3*b^2 - 3*C*a^2*b^3 + B*a*b^4)*d*x)*tan(d*x + c))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*tan(d*x + c) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d)","B",0
42,1,482,0,0.784672," ","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=""fricas"")","\frac{5 \, C a^{3} b^{2} - 7 \, B a^{2} b^{3} - C a b^{4} - B b^{5} + 2 \, {\left(B a^{5} + 3 \, C a^{4} b - 3 \, B a^{3} b^{2} - C a^{2} b^{3}\right)} d x - {\left(3 \, C a^{3} b^{2} - 5 \, B a^{2} b^{3} - 3 \, C a b^{4} + B b^{5} - 2 \, {\left(B a^{3} b^{2} + 3 \, C a^{2} b^{3} - 3 \, B a b^{4} - C b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} - {\left(C a^{5} - 3 \, B a^{4} b - 3 \, C a^{3} b^{2} + B a^{2} b^{3} + {\left(C a^{3} b^{2} - 3 \, B a^{2} b^{3} - 3 \, C a b^{4} + B b^{5}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(C a^{4} b - 3 \, B a^{3} b^{2} - 3 \, C a^{2} b^{3} + B a b^{4}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(2 \, C a^{4} b - 3 \, B a^{3} b^{2} - 3 \, C a^{2} b^{3} + 3 \, B a b^{4} + C b^{5} - 2 \, {\left(B a^{4} b + 3 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - C a b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d\right)}}"," ",0,"1/2*(5*C*a^3*b^2 - 7*B*a^2*b^3 - C*a*b^4 - B*b^5 + 2*(B*a^5 + 3*C*a^4*b - 3*B*a^3*b^2 - C*a^2*b^3)*d*x - (3*C*a^3*b^2 - 5*B*a^2*b^3 - 3*C*a*b^4 + B*b^5 - 2*(B*a^3*b^2 + 3*C*a^2*b^3 - 3*B*a*b^4 - C*b^5)*d*x)*tan(d*x + c)^2 - (C*a^5 - 3*B*a^4*b - 3*C*a^3*b^2 + B*a^2*b^3 + (C*a^3*b^2 - 3*B*a^2*b^3 - 3*C*a*b^4 + B*b^5)*tan(d*x + c)^2 + 2*(C*a^4*b - 3*B*a^3*b^2 - 3*C*a^2*b^3 + B*a*b^4)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 2*(2*C*a^4*b - 3*B*a^3*b^2 - 3*C*a^2*b^3 + 3*B*a*b^4 + C*b^5 - 2*(B*a^4*b + 3*C*a^3*b^2 - 3*B*a^2*b^3 - C*a*b^4)*d*x)*tan(d*x + c))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*tan(d*x + c) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d)","B",0
43,1,683,0,0.725876," ","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=""fricas"")","-\frac{7 \, C a^{5} b^{3} - 9 \, B a^{4} b^{4} + C a^{3} b^{5} - 3 \, B a^{2} b^{6} - 2 \, {\left(C a^{8} - 3 \, B a^{7} b - 3 \, C a^{6} b^{2} + B a^{5} b^{3}\right)} d x - {\left(5 \, C a^{5} b^{3} - 7 \, B a^{4} b^{4} - C a^{3} b^{5} - B a^{2} b^{6} + 2 \, {\left(C a^{6} b^{2} - 3 \, B a^{5} b^{3} - 3 \, C a^{4} b^{4} + B a^{3} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} - {\left(B a^{8} + 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} + B a^{2} b^{6} + {\left(B a^{6} b^{2} + 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} + B b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b + 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} + B a b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(3 \, C a^{7} b - 6 \, B a^{6} b^{2} - C a^{5} b^{3} - 3 \, B a^{4} b^{4} - B a^{2} b^{6} + {\left(3 \, C a^{5} b^{3} - 6 \, B a^{4} b^{4} - C a^{3} b^{5} - 3 \, B a^{2} b^{6} - B b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, C a^{6} b^{2} - 6 \, B a^{5} b^{3} - C a^{4} b^{4} - 3 \, B a^{3} b^{5} - B a b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(3 \, C a^{6} b^{2} - 4 \, B a^{5} b^{3} - 3 \, C a^{4} b^{4} + 3 \, B a^{3} b^{5} + B a b^{7} + 2 \, {\left(C a^{7} b - 3 \, B a^{6} b^{2} - 3 \, C a^{5} b^{3} + B a^{4} b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{9} b^{2} + 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b + 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} + a^{4} b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{11} + 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} + a^{5} b^{6}\right)} d\right)}}"," ",0,"-1/2*(7*C*a^5*b^3 - 9*B*a^4*b^4 + C*a^3*b^5 - 3*B*a^2*b^6 - 2*(C*a^8 - 3*B*a^7*b - 3*C*a^6*b^2 + B*a^5*b^3)*d*x - (5*C*a^5*b^3 - 7*B*a^4*b^4 - C*a^3*b^5 - B*a^2*b^6 + 2*(C*a^6*b^2 - 3*B*a^5*b^3 - 3*C*a^4*b^4 + B*a^3*b^5)*d*x)*tan(d*x + c)^2 - (B*a^8 + 3*B*a^6*b^2 + 3*B*a^4*b^4 + B*a^2*b^6 + (B*a^6*b^2 + 3*B*a^4*b^4 + 3*B*a^2*b^6 + B*b^8)*tan(d*x + c)^2 + 2*(B*a^7*b + 3*B*a^5*b^3 + 3*B*a^3*b^5 + B*a*b^7)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - (3*C*a^7*b - 6*B*a^6*b^2 - C*a^5*b^3 - 3*B*a^4*b^4 - B*a^2*b^6 + (3*C*a^5*b^3 - 6*B*a^4*b^4 - C*a^3*b^5 - 3*B*a^2*b^6 - B*b^8)*tan(d*x + c)^2 + 2*(3*C*a^6*b^2 - 6*B*a^5*b^3 - C*a^4*b^4 - 3*B*a^3*b^5 - B*a*b^7)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 2*(3*C*a^6*b^2 - 4*B*a^5*b^3 - 3*C*a^4*b^4 + 3*B*a^3*b^5 + B*a*b^7 + 2*(C*a^7*b - 3*B*a^6*b^2 - 3*C*a^5*b^3 + B*a^4*b^4)*d*x)*tan(d*x + c))/((a^9*b^2 + 3*a^7*b^4 + 3*a^5*b^6 + a^3*b^8)*d*tan(d*x + c)^2 + 2*(a^10*b + 3*a^8*b^3 + 3*a^6*b^5 + a^4*b^7)*d*tan(d*x + c) + (a^11 + 3*a^9*b^2 + 3*a^7*b^4 + a^5*b^6)*d)","B",0
44,1,917,0,0.889512," ","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=""fricas"")","-\frac{2 \, B a^{9} + 6 \, B a^{7} b^{2} + 6 \, B a^{5} b^{4} + 2 \, B a^{3} b^{6} + {\left(7 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} + C a^{3} b^{6} - 3 \, B a^{2} b^{7} + 2 \, {\left(B a^{7} b^{2} + 3 \, C a^{6} b^{3} - 3 \, B a^{5} b^{4} - C a^{4} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(B a^{7} b^{2} + 4 \, C a^{6} b^{3} - 2 \, B a^{5} b^{4} - 3 \, C a^{4} b^{5} + 6 \, B a^{3} b^{6} - C a^{2} b^{7} + 3 \, B a b^{8} + 2 \, {\left(B a^{8} b + 3 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} - C a^{5} b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{2} - {\left({\left(C a^{7} b^{2} - 3 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B a^{2} b^{7} + C a b^{8} - 3 \, B b^{9}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(C a^{8} b - 3 \, B a^{7} b^{2} + 3 \, C a^{6} b^{3} - 9 \, B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 9 \, B a^{3} b^{6} + C a^{2} b^{7} - 3 \, B a b^{8}\right)} \tan\left(d x + c\right)^{2} + {\left(C a^{9} - 3 \, B a^{8} b + 3 \, C a^{7} b^{2} - 9 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} + C a^{3} b^{6} - 3 \, B a^{2} b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left({\left(6 \, C a^{5} b^{4} - 10 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B a^{2} b^{7} + C a b^{8} - 3 \, B b^{9}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(6 \, C a^{6} b^{3} - 10 \, B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 9 \, B a^{3} b^{6} + C a^{2} b^{7} - 3 \, B a b^{8}\right)} \tan\left(d x + c\right)^{2} + {\left(6 \, C a^{7} b^{2} - 10 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} + C a^{3} b^{6} - 3 \, B a^{2} b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(4 \, B a^{8} b + 12 \, B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 23 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + 9 \, B a^{2} b^{7} + 2 \, {\left(B a^{9} + 3 \, C a^{8} b - 3 \, B a^{7} b^{2} - C a^{6} b^{3}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{10} b^{2} + 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} + a^{4} b^{8}\right)} d \tan\left(d x + c\right)^{3} + 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} d \tan\left(d x + c\right)^{2} + {\left(a^{12} + 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} + a^{6} b^{6}\right)} d \tan\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*B*a^9 + 6*B*a^7*b^2 + 6*B*a^5*b^4 + 2*B*a^3*b^6 + (7*C*a^5*b^4 - 9*B*a^4*b^5 + C*a^3*b^6 - 3*B*a^2*b^7 + 2*(B*a^7*b^2 + 3*C*a^6*b^3 - 3*B*a^5*b^4 - C*a^4*b^5)*d*x)*tan(d*x + c)^3 + 2*(B*a^7*b^2 + 4*C*a^6*b^3 - 2*B*a^5*b^4 - 3*C*a^4*b^5 + 6*B*a^3*b^6 - C*a^2*b^7 + 3*B*a*b^8 + 2*(B*a^8*b + 3*C*a^7*b^2 - 3*B*a^6*b^3 - C*a^5*b^4)*d*x)*tan(d*x + c)^2 - ((C*a^7*b^2 - 3*B*a^6*b^3 + 3*C*a^5*b^4 - 9*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*a^2*b^7 + C*a*b^8 - 3*B*b^9)*tan(d*x + c)^3 + 2*(C*a^8*b - 3*B*a^7*b^2 + 3*C*a^6*b^3 - 9*B*a^5*b^4 + 3*C*a^4*b^5 - 9*B*a^3*b^6 + C*a^2*b^7 - 3*B*a*b^8)*tan(d*x + c)^2 + (C*a^9 - 3*B*a^8*b + 3*C*a^7*b^2 - 9*B*a^6*b^3 + 3*C*a^5*b^4 - 9*B*a^4*b^5 + C*a^3*b^6 - 3*B*a^2*b^7)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + ((6*C*a^5*b^4 - 10*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*a^2*b^7 + C*a*b^8 - 3*B*b^9)*tan(d*x + c)^3 + 2*(6*C*a^6*b^3 - 10*B*a^5*b^4 + 3*C*a^4*b^5 - 9*B*a^3*b^6 + C*a^2*b^7 - 3*B*a*b^8)*tan(d*x + c)^2 + (6*C*a^7*b^2 - 10*B*a^6*b^3 + 3*C*a^5*b^4 - 9*B*a^4*b^5 + C*a^3*b^6 - 3*B*a^2*b^7)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + (4*B*a^8*b + 12*B*a^6*b^3 - 9*C*a^5*b^4 + 23*B*a^4*b^5 - 3*C*a^3*b^6 + 9*B*a^2*b^7 + 2*(B*a^9 + 3*C*a^8*b - 3*B*a^7*b^2 - C*a^6*b^3)*d*x)*tan(d*x + c))/((a^10*b^2 + 3*a^8*b^4 + 3*a^6*b^6 + a^4*b^8)*d*tan(d*x + c)^3 + 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*d*tan(d*x + c)^2 + (a^12 + 3*a^10*b^2 + 3*a^8*b^4 + a^6*b^6)*d*tan(d*x + c))","B",0
45,0,0,0,1.121511," ","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=""fricas"")","{\rm integral}\left({\left(C \tan\left(d x + c\right)^{4} + B \tan\left(d x + c\right)^{3} + A \tan\left(d x + c\right)^{2}\right)} \left(b \tan\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((C*tan(d*x + c)^4 + B*tan(d*x + c)^3 + A*tan(d*x + c)^2)*(b*tan(d*x + c))^n, x)","F",0
46,0,0,0,0.759960," ","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=""fricas"")","{\rm integral}\left({\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}, x\right)"," ",0,"integral((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
47,0,0,0,0.551757," ","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=""fricas"")","{\rm integral}\left({\left(C \tan\left(d x + c\right)^{2} + B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right)} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*tan(d*x + c)^2 + B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c))*tan(d*x + c)^m, x)","F",0
48,0,0,0,0.663869," ","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=""fricas"")","{\rm integral}\left(\frac{{\left(C \tan\left(d x + c\right)^{2} + B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right)} \tan\left(d x + c\right)^{m}}{b \tan\left(d x + c\right)}, x\right)"," ",0,"integral((C*tan(d*x + c)^2 + B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c))*tan(d*x + c)^m/(b*tan(d*x + c)), x)","F",0
49,0,0,0,0.818511," ","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=""fricas"")","{\rm integral}\left(\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) + a}}, x\right)"," ",0,"integral((C*tan(d*x + c)^2 + B*tan(d*x + c) + A)*tan(d*x + c)^m/sqrt(b*tan(d*x + c) + a), x)","F",0
50,1,415,0,1.037546," ","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=""fricas"")","\frac{12 \, C b^{3} d \tan\left(f x + e\right)^{5} + 15 \, {\left(C b^{3} c + {\left(3 \, C a b^{2} + B b^{3}\right)} d\right)} \tan\left(f x + e\right)^{4} + 20 \, {\left({\left(3 \, C a b^{2} + B b^{3}\right)} c + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A - C\right)} b^{3}\right)} d\right)} \tan\left(f x + e\right)^{3} + 60 \, {\left({\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c - {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} d\right)} f x + 30 \, {\left({\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A - C\right)} b^{3}\right)} c + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, {\left(A - C\right)} a b^{2} - B b^{3}\right)} d\right)} \tan\left(f x + e\right)^{2} - 30 \, {\left({\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c + {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} d\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 60 \, {\left({\left(C a^{3} + 3 \, B a^{2} b + 3 \, {\left(A - C\right)} a b^{2} - B b^{3}\right)} c + {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} d\right)} \tan\left(f x + e\right)}{60 \, f}"," ",0,"1/60*(12*C*b^3*d*tan(f*x + e)^5 + 15*(C*b^3*c + (3*C*a*b^2 + B*b^3)*d)*tan(f*x + e)^4 + 20*((3*C*a*b^2 + B*b^3)*c + (3*C*a^2*b + 3*B*a*b^2 + (A - C)*b^3)*d)*tan(f*x + e)^3 + 60*(((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c - (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*d)*f*x + 30*((3*C*a^2*b + 3*B*a*b^2 + (A - C)*b^3)*c + (C*a^3 + 3*B*a^2*b + 3*(A - C)*a*b^2 - B*b^3)*d)*tan(f*x + e)^2 - 30*((B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c + ((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*d)*log(1/(tan(f*x + e)^2 + 1)) + 60*((C*a^3 + 3*B*a^2*b + 3*(A - C)*a*b^2 - B*b^3)*c + (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*d)*tan(f*x + e))/f","A",0
51,1,273,0,0.572069," ","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=""fricas"")","\frac{3 \, C b^{2} d \tan\left(f x + e\right)^{4} + 4 \, {\left(C b^{2} c + {\left(2 \, C a b + B b^{2}\right)} d\right)} \tan\left(f x + e\right)^{3} + 12 \, {\left({\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c - {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} d\right)} f x + 6 \, {\left({\left(2 \, C a b + B b^{2}\right)} c + {\left(C a^{2} + 2 \, B a b + {\left(A - C\right)} b^{2}\right)} d\right)} \tan\left(f x + e\right)^{2} - 6 \, {\left({\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c + {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} d\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 12 \, {\left({\left(C a^{2} + 2 \, B a b + {\left(A - C\right)} b^{2}\right)} c + {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} d\right)} \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*C*b^2*d*tan(f*x + e)^4 + 4*(C*b^2*c + (2*C*a*b + B*b^2)*d)*tan(f*x + e)^3 + 12*(((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c - (B*a^2 + 2*(A - C)*a*b - B*b^2)*d)*f*x + 6*((2*C*a*b + B*b^2)*c + (C*a^2 + 2*B*a*b + (A - C)*b^2)*d)*tan(f*x + e)^2 - 6*((B*a^2 + 2*(A - C)*a*b - B*b^2)*c + ((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*d)*log(1/(tan(f*x + e)^2 + 1)) + 12*((C*a^2 + 2*B*a*b + (A - C)*b^2)*c + (B*a^2 + 2*(A - C)*a*b - B*b^2)*d)*tan(f*x + e))/f","A",0
52,1,150,0,0.588099," ","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=""fricas"")","\frac{2 \, C b d \tan\left(f x + e\right)^{3} + 6 \, {\left({\left({\left(A - C\right)} a - B b\right)} c - {\left(B a + {\left(A - C\right)} b\right)} d\right)} f x + 3 \, {\left(C b c + {\left(C a + B b\right)} d\right)} \tan\left(f x + e\right)^{2} - 3 \, {\left({\left(B a + {\left(A - C\right)} b\right)} c + {\left({\left(A - C\right)} a - B b\right)} d\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left({\left(C a + B b\right)} c + {\left(B a + {\left(A - C\right)} b\right)} d\right)} \tan\left(f x + e\right)}{6 \, f}"," ",0,"1/6*(2*C*b*d*tan(f*x + e)^3 + 6*(((A - C)*a - B*b)*c - (B*a + (A - C)*b)*d)*f*x + 3*(C*b*c + (C*a + B*b)*d)*tan(f*x + e)^2 - 3*((B*a + (A - C)*b)*c + ((A - C)*a - B*b)*d)*log(1/(tan(f*x + e)^2 + 1)) + 6*((C*a + B*b)*c + (B*a + (A - C)*b)*d)*tan(f*x + e))/f","A",0
53,1,74,0,1.329283," ","integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""fricas"")","\frac{C d \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(A - C\right)} c - B d\right)} f x - {\left(B c + {\left(A - C\right)} d\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(C c + B d\right)} \tan\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(C*d*tan(f*x + e)^2 + 2*((A - C)*c - B*d)*f*x - (B*c + (A - C)*d)*log(1/(tan(f*x + e)^2 + 1)) + 2*(C*c + B*d)*tan(f*x + e))/f","A",0
54,1,226,0,1.440962," ","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=""fricas"")","\frac{2 \, {\left({\left({\left(A - C\right)} a b^{2} + B b^{3}\right)} c - {\left(B a b^{2} - {\left(A - C\right)} b^{3}\right)} d\right)} f x + 2 \, {\left(C a^{2} b + C b^{3}\right)} d \tan\left(f x + e\right) + {\left({\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c - {\left(C a^{3} - B a^{2} b + A a b^{2}\right)} d\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left({\left(C a^{2} b + C b^{3}\right)} c - {\left(C a^{3} - B a^{2} b + C a b^{2} - B b^{3}\right)} d\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, {\left(a^{2} b^{2} + b^{4}\right)} f}"," ",0,"1/2*(2*(((A - C)*a*b^2 + B*b^3)*c - (B*a*b^2 - (A - C)*b^3)*d)*f*x + 2*(C*a^2*b + C*b^3)*d*tan(f*x + e) + ((C*a^2*b - B*a*b^2 + A*b^3)*c - (C*a^3 - B*a^2*b + A*a*b^2)*d)*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - ((C*a^2*b + C*b^3)*c - (C*a^3 - B*a^2*b + C*a*b^2 - B*b^3)*d)*log(1/(tan(f*x + e)^2 + 1)))/((a^2*b^2 + b^4)*f)","A",0
55,1,556,0,1.341913," ","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=""fricas"")","\frac{2 \, {\left({\left({\left(A - C\right)} a^{3} b^{2} + 2 \, B a^{2} b^{3} - {\left(A - C\right)} a b^{4}\right)} c - {\left(B a^{3} b^{2} - 2 \, {\left(A - C\right)} a^{2} b^{3} - B a b^{4}\right)} d\right)} f x - 2 \, {\left(C a^{2} b^{3} - B a b^{4} + A b^{5}\right)} c + 2 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} d - {\left({\left(B a^{3} b^{2} - 2 \, {\left(A - C\right)} a^{2} b^{3} - B a b^{4}\right)} c - {\left(C a^{5} - {\left(A - 3 \, C\right)} a^{3} b^{2} - 2 \, B a^{2} b^{3} + A a b^{4}\right)} d + {\left({\left(B a^{2} b^{3} - 2 \, {\left(A - C\right)} a b^{4} - B b^{5}\right)} c - {\left(C a^{4} b - {\left(A - 3 \, C\right)} a^{2} b^{3} - 2 \, B a b^{4} + A b^{5}\right)} d\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left({\left(C a^{4} b + 2 \, C a^{2} b^{3} + C b^{5}\right)} d \tan\left(f x + e\right) + {\left(C a^{5} + 2 \, C a^{3} b^{2} + C a b^{4}\right)} d\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left({\left({\left({\left(A - C\right)} a^{2} b^{3} + 2 \, B a b^{4} - {\left(A - C\right)} b^{5}\right)} c - {\left(B a^{2} b^{3} - 2 \, {\left(A - C\right)} a b^{4} - B b^{5}\right)} d\right)} f x + {\left(C a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} c - {\left(C a^{4} b - B a^{3} b^{2} + A a^{2} b^{3}\right)} d\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} f \tan\left(f x + e\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} f\right)}}"," ",0,"1/2*(2*(((A - C)*a^3*b^2 + 2*B*a^2*b^3 - (A - C)*a*b^4)*c - (B*a^3*b^2 - 2*(A - C)*a^2*b^3 - B*a*b^4)*d)*f*x - 2*(C*a^2*b^3 - B*a*b^4 + A*b^5)*c + 2*(C*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*d - ((B*a^3*b^2 - 2*(A - C)*a^2*b^3 - B*a*b^4)*c - (C*a^5 - (A - 3*C)*a^3*b^2 - 2*B*a^2*b^3 + A*a*b^4)*d + ((B*a^2*b^3 - 2*(A - C)*a*b^4 - B*b^5)*c - (C*a^4*b - (A - 3*C)*a^2*b^3 - 2*B*a*b^4 + A*b^5)*d)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - ((C*a^4*b + 2*C*a^2*b^3 + C*b^5)*d*tan(f*x + e) + (C*a^5 + 2*C*a^3*b^2 + C*a*b^4)*d)*log(1/(tan(f*x + e)^2 + 1)) + 2*((((A - C)*a^2*b^3 + 2*B*a*b^4 - (A - C)*b^5)*c - (B*a^2*b^3 - 2*(A - C)*a*b^4 - B*b^5)*d)*f*x + (C*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*c - (C*a^4*b - B*a^3*b^2 + A*a^2*b^3)*d)*tan(f*x + e))/((a^4*b^3 + 2*a^2*b^5 + b^7)*f*tan(f*x + e) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*f)","B",0
56,1,987,0,2.056122," ","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=""fricas"")","\frac{2 \, {\left({\left({\left(A - C\right)} a^{5} + 3 \, B a^{4} b - 3 \, {\left(A - C\right)} a^{3} b^{2} - B a^{2} b^{3}\right)} c - {\left(B a^{5} - 3 \, {\left(A - C\right)} a^{4} b - 3 \, B a^{3} b^{2} + {\left(A - C\right)} a^{2} b^{3}\right)} d\right)} f x + {\left(2 \, {\left({\left({\left(A - C\right)} a^{3} b^{2} + 3 \, B a^{2} b^{3} - 3 \, {\left(A - C\right)} a b^{4} - B b^{5}\right)} c - {\left(B a^{3} b^{2} - 3 \, {\left(A - C\right)} a^{2} b^{3} - 3 \, B a b^{4} + {\left(A - C\right)} b^{5}\right)} d\right)} f x + {\left(C a^{4} b - 3 \, B a^{3} b^{2} + 5 \, {\left(A - C\right)} a^{2} b^{3} + 3 \, B a b^{4} - A b^{5}\right)} c + {\left(C a^{5} + B a^{4} b - {\left(3 \, A - 7 \, C\right)} a^{3} b^{2} - 5 \, B a^{2} b^{3} + 3 \, A a b^{4}\right)} d\right)} \tan\left(f x + e\right)^{2} - {\left(3 \, C a^{4} b - 5 \, B a^{3} b^{2} + {\left(7 \, A - 3 \, C\right)} a^{2} b^{3} + B a b^{4} + A b^{5}\right)} c + {\left(C a^{5} - 3 \, B a^{4} b + 5 \, {\left(A - C\right)} a^{3} b^{2} + 3 \, B a^{2} b^{3} - A a b^{4}\right)} d - {\left({\left({\left(B a^{3} b^{2} - 3 \, {\left(A - C\right)} a^{2} b^{3} - 3 \, B a b^{4} + {\left(A - C\right)} b^{5}\right)} c + {\left({\left(A - C\right)} a^{3} b^{2} + 3 \, B a^{2} b^{3} - 3 \, {\left(A - C\right)} a b^{4} - B b^{5}\right)} d\right)} \tan\left(f x + e\right)^{2} + {\left(B a^{5} - 3 \, {\left(A - C\right)} a^{4} b - 3 \, B a^{3} b^{2} + {\left(A - C\right)} a^{2} b^{3}\right)} c + {\left({\left(A - C\right)} a^{5} + 3 \, B a^{4} b - 3 \, {\left(A - C\right)} a^{3} b^{2} - B a^{2} b^{3}\right)} d + 2 \, {\left({\left(B a^{4} b - 3 \, {\left(A - C\right)} a^{3} b^{2} - 3 \, B a^{2} b^{3} + {\left(A - C\right)} a b^{4}\right)} c + {\left({\left(A - C\right)} a^{4} b + 3 \, B a^{3} b^{2} - 3 \, {\left(A - C\right)} a^{2} b^{3} - B a b^{4}\right)} d\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(2 \, {\left({\left({\left(A - C\right)} a^{4} b + 3 \, B a^{3} b^{2} - 3 \, {\left(A - C\right)} a^{2} b^{3} - B a b^{4}\right)} c - {\left(B a^{4} b - 3 \, {\left(A - C\right)} a^{3} b^{2} - 3 \, B a^{2} b^{3} + {\left(A - C\right)} a b^{4}\right)} d\right)} f x + {\left(C a^{5} - 2 \, B a^{4} b + 3 \, {\left(A - C\right)} a^{3} b^{2} + 3 \, B a^{2} b^{3} - {\left(3 \, A - 2 \, C\right)} a b^{4} - B b^{5}\right)} c + {\left(B a^{5} - {\left(2 \, A - 3 \, C\right)} a^{4} b - 3 \, B a^{3} b^{2} + 3 \, {\left(A - C\right)} a^{2} b^{3} + 2 \, B a b^{4} - A b^{5}\right)} d\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} f \tan\left(f x + e\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} f\right)}}"," ",0,"1/2*(2*(((A - C)*a^5 + 3*B*a^4*b - 3*(A - C)*a^3*b^2 - B*a^2*b^3)*c - (B*a^5 - 3*(A - C)*a^4*b - 3*B*a^3*b^2 + (A - C)*a^2*b^3)*d)*f*x + (2*(((A - C)*a^3*b^2 + 3*B*a^2*b^3 - 3*(A - C)*a*b^4 - B*b^5)*c - (B*a^3*b^2 - 3*(A - C)*a^2*b^3 - 3*B*a*b^4 + (A - C)*b^5)*d)*f*x + (C*a^4*b - 3*B*a^3*b^2 + 5*(A - C)*a^2*b^3 + 3*B*a*b^4 - A*b^5)*c + (C*a^5 + B*a^4*b - (3*A - 7*C)*a^3*b^2 - 5*B*a^2*b^3 + 3*A*a*b^4)*d)*tan(f*x + e)^2 - (3*C*a^4*b - 5*B*a^3*b^2 + (7*A - 3*C)*a^2*b^3 + B*a*b^4 + A*b^5)*c + (C*a^5 - 3*B*a^4*b + 5*(A - C)*a^3*b^2 + 3*B*a^2*b^3 - A*a*b^4)*d - (((B*a^3*b^2 - 3*(A - C)*a^2*b^3 - 3*B*a*b^4 + (A - C)*b^5)*c + ((A - C)*a^3*b^2 + 3*B*a^2*b^3 - 3*(A - C)*a*b^4 - B*b^5)*d)*tan(f*x + e)^2 + (B*a^5 - 3*(A - C)*a^4*b - 3*B*a^3*b^2 + (A - C)*a^2*b^3)*c + ((A - C)*a^5 + 3*B*a^4*b - 3*(A - C)*a^3*b^2 - B*a^2*b^3)*d + 2*((B*a^4*b - 3*(A - C)*a^3*b^2 - 3*B*a^2*b^3 + (A - C)*a*b^4)*c + ((A - C)*a^4*b + 3*B*a^3*b^2 - 3*(A - C)*a^2*b^3 - B*a*b^4)*d)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) + 2*(2*(((A - C)*a^4*b + 3*B*a^3*b^2 - 3*(A - C)*a^2*b^3 - B*a*b^4)*c - (B*a^4*b - 3*(A - C)*a^3*b^2 - 3*B*a^2*b^3 + (A - C)*a*b^4)*d)*f*x + (C*a^5 - 2*B*a^4*b + 3*(A - C)*a^3*b^2 + 3*B*a^2*b^3 - (3*A - 2*C)*a*b^4 - B*b^5)*c + (B*a^5 - (2*A - 3*C)*a^4*b - 3*B*a^3*b^2 + 3*(A - C)*a^2*b^3 + 2*B*a*b^4 - A*b^5)*d)*tan(f*x + e))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*f*tan(f*x + e)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*f*tan(f*x + e) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*f)","B",0
57,1,690,0,1.235966," ","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=""fricas"")","\frac{10 \, C b^{3} d^{2} \tan\left(f x + e\right)^{6} + 12 \, {\left(2 \, C b^{3} c d + {\left(3 \, C a b^{2} + B b^{3}\right)} d^{2}\right)} \tan\left(f x + e\right)^{5} + 15 \, {\left(C b^{3} c^{2} + 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c d + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A - C\right)} b^{3}\right)} d^{2}\right)} \tan\left(f x + e\right)^{4} + 20 \, {\left({\left(3 \, C a b^{2} + B b^{3}\right)} c^{2} + 2 \, {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A - C\right)} b^{3}\right)} c d + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, {\left(A - C\right)} a b^{2} - B b^{3}\right)} d^{2}\right)} \tan\left(f x + e\right)^{3} + 60 \, {\left({\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c^{2} - 2 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c d - {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} d^{2}\right)} f x + 30 \, {\left({\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A - C\right)} b^{3}\right)} c^{2} + 2 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, {\left(A - C\right)} a b^{2} - B b^{3}\right)} c d + {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} d^{2}\right)} \tan\left(f x + e\right)^{2} - 30 \, {\left({\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c^{2} + 2 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c d - {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} d^{2}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 60 \, {\left({\left(C a^{3} + 3 \, B a^{2} b + 3 \, {\left(A - C\right)} a b^{2} - B b^{3}\right)} c^{2} + 2 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c d + {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} d^{2}\right)} \tan\left(f x + e\right)}{60 \, f}"," ",0,"1/60*(10*C*b^3*d^2*tan(f*x + e)^6 + 12*(2*C*b^3*c*d + (3*C*a*b^2 + B*b^3)*d^2)*tan(f*x + e)^5 + 15*(C*b^3*c^2 + 2*(3*C*a*b^2 + B*b^3)*c*d + (3*C*a^2*b + 3*B*a*b^2 + (A - C)*b^3)*d^2)*tan(f*x + e)^4 + 20*((3*C*a*b^2 + B*b^3)*c^2 + 2*(3*C*a^2*b + 3*B*a*b^2 + (A - C)*b^3)*c*d + (C*a^3 + 3*B*a^2*b + 3*(A - C)*a*b^2 - B*b^3)*d^2)*tan(f*x + e)^3 + 60*(((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c^2 - 2*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c*d - ((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*d^2)*f*x + 30*((3*C*a^2*b + 3*B*a*b^2 + (A - C)*b^3)*c^2 + 2*(C*a^3 + 3*B*a^2*b + 3*(A - C)*a*b^2 - B*b^3)*c*d + (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*d^2)*tan(f*x + e)^2 - 30*((B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c^2 + 2*((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c*d - (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*d^2)*log(1/(tan(f*x + e)^2 + 1)) + 60*((C*a^3 + 3*B*a^2*b + 3*(A - C)*a*b^2 - B*b^3)*c^2 + 2*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c*d + ((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*d^2)*tan(f*x + e))/f","A",0
58,1,462,0,1.154960," ","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=""fricas"")","\frac{12 \, C b^{2} d^{2} \tan\left(f x + e\right)^{5} + 15 \, {\left(2 \, C b^{2} c d + {\left(2 \, C a b + B b^{2}\right)} d^{2}\right)} \tan\left(f x + e\right)^{4} + 20 \, {\left(C b^{2} c^{2} + 2 \, {\left(2 \, C a b + B b^{2}\right)} c d + {\left(C a^{2} + 2 \, B a b + {\left(A - C\right)} b^{2}\right)} d^{2}\right)} \tan\left(f x + e\right)^{3} + 60 \, {\left({\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c^{2} - 2 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c d - {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} d^{2}\right)} f x + 30 \, {\left({\left(2 \, C a b + B b^{2}\right)} c^{2} + 2 \, {\left(C a^{2} + 2 \, B a b + {\left(A - C\right)} b^{2}\right)} c d + {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} d^{2}\right)} \tan\left(f x + e\right)^{2} - 30 \, {\left({\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{2} + 2 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c d - {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} d^{2}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 60 \, {\left({\left(C a^{2} + 2 \, B a b + {\left(A - C\right)} b^{2}\right)} c^{2} + 2 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c d + {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} d^{2}\right)} \tan\left(f x + e\right)}{60 \, f}"," ",0,"1/60*(12*C*b^2*d^2*tan(f*x + e)^5 + 15*(2*C*b^2*c*d + (2*C*a*b + B*b^2)*d^2)*tan(f*x + e)^4 + 20*(C*b^2*c^2 + 2*(2*C*a*b + B*b^2)*c*d + (C*a^2 + 2*B*a*b + (A - C)*b^2)*d^2)*tan(f*x + e)^3 + 60*(((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c^2 - 2*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c*d - ((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*d^2)*f*x + 30*((2*C*a*b + B*b^2)*c^2 + 2*(C*a^2 + 2*B*a*b + (A - C)*b^2)*c*d + (B*a^2 + 2*(A - C)*a*b - B*b^2)*d^2)*tan(f*x + e)^2 - 30*((B*a^2 + 2*(A - C)*a*b - B*b^2)*c^2 + 2*((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c*d - (B*a^2 + 2*(A - C)*a*b - B*b^2)*d^2)*log(1/(tan(f*x + e)^2 + 1)) + 60*((C*a^2 + 2*B*a*b + (A - C)*b^2)*c^2 + 2*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c*d + ((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*d^2)*tan(f*x + e))/f","A",0
59,1,259,0,0.599153," ","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=""fricas"")","\frac{3 \, C b d^{2} \tan\left(f x + e\right)^{4} + 4 \, {\left(2 \, C b c d + {\left(C a + B b\right)} d^{2}\right)} \tan\left(f x + e\right)^{3} + 12 \, {\left({\left({\left(A - C\right)} a - B b\right)} c^{2} - 2 \, {\left(B a + {\left(A - C\right)} b\right)} c d - {\left({\left(A - C\right)} a - B b\right)} d^{2}\right)} f x + 6 \, {\left(C b c^{2} + 2 \, {\left(C a + B b\right)} c d + {\left(B a + {\left(A - C\right)} b\right)} d^{2}\right)} \tan\left(f x + e\right)^{2} - 6 \, {\left({\left(B a + {\left(A - C\right)} b\right)} c^{2} + 2 \, {\left({\left(A - C\right)} a - B b\right)} c d - {\left(B a + {\left(A - C\right)} b\right)} d^{2}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 12 \, {\left({\left(C a + B b\right)} c^{2} + 2 \, {\left(B a + {\left(A - C\right)} b\right)} c d + {\left({\left(A - C\right)} a - B b\right)} d^{2}\right)} \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*C*b*d^2*tan(f*x + e)^4 + 4*(2*C*b*c*d + (C*a + B*b)*d^2)*tan(f*x + e)^3 + 12*(((A - C)*a - B*b)*c^2 - 2*(B*a + (A - C)*b)*c*d - ((A - C)*a - B*b)*d^2)*f*x + 6*(C*b*c^2 + 2*(C*a + B*b)*c*d + (B*a + (A - C)*b)*d^2)*tan(f*x + e)^2 - 6*((B*a + (A - C)*b)*c^2 + 2*((A - C)*a - B*b)*c*d - (B*a + (A - C)*b)*d^2)*log(1/(tan(f*x + e)^2 + 1)) + 12*((C*a + B*b)*c^2 + 2*(B*a + (A - C)*b)*c*d + ((A - C)*a - B*b)*d^2)*tan(f*x + e))/f","A",0
60,1,134,0,0.556512," ","integrate((c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""fricas"")","\frac{2 \, C d^{2} \tan\left(f x + e\right)^{3} + 6 \, {\left({\left(A - C\right)} c^{2} - 2 \, B c d - {\left(A - C\right)} d^{2}\right)} f x + 3 \, {\left(2 \, C c d + B d^{2}\right)} \tan\left(f x + e\right)^{2} - 3 \, {\left(B c^{2} + 2 \, {\left(A - C\right)} c d - B d^{2}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(C c^{2} + 2 \, B c d + {\left(A - C\right)} d^{2}\right)} \tan\left(f x + e\right)}{6 \, f}"," ",0,"1/6*(2*C*d^2*tan(f*x + e)^3 + 6*((A - C)*c^2 - 2*B*c*d - (A - C)*d^2)*f*x + 3*(2*C*c*d + B*d^2)*tan(f*x + e)^2 - 3*(B*c^2 + 2*(A - C)*c*d - B*d^2)*log(1/(tan(f*x + e)^2 + 1)) + 6*(C*c^2 + 2*B*c*d + (A - C)*d^2)*tan(f*x + e))/f","A",0
61,1,397,0,1.650340," ","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=""fricas"")","\frac{{\left(C a^{2} b^{2} + C b^{4}\right)} d^{2} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left({\left(A - C\right)} a b^{3} + B b^{4}\right)} c^{2} - 2 \, {\left(B a b^{3} - {\left(A - C\right)} b^{4}\right)} c d - {\left({\left(A - C\right)} a b^{3} + B b^{4}\right)} d^{2}\right)} f x + {\left({\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{2} - 2 \, {\left(C a^{3} b - B a^{2} b^{2} + A a b^{3}\right)} c d + {\left(C a^{4} - B a^{3} b + A a^{2} b^{2}\right)} d^{2}\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left({\left(C a^{2} b^{2} + C b^{4}\right)} c^{2} - 2 \, {\left(C a^{3} b - B a^{2} b^{2} + C a b^{3} - B b^{4}\right)} c d + {\left(C a^{4} - B a^{3} b + A a^{2} b^{2} - B a b^{3} + {\left(A - C\right)} b^{4}\right)} d^{2}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(2 \, {\left(C a^{2} b^{2} + C b^{4}\right)} c d - {\left(C a^{3} b - B a^{2} b^{2} + C a b^{3} - B b^{4}\right)} d^{2}\right)} \tan\left(f x + e\right)}{2 \, {\left(a^{2} b^{3} + b^{5}\right)} f}"," ",0,"1/2*((C*a^2*b^2 + C*b^4)*d^2*tan(f*x + e)^2 + 2*(((A - C)*a*b^3 + B*b^4)*c^2 - 2*(B*a*b^3 - (A - C)*b^4)*c*d - ((A - C)*a*b^3 + B*b^4)*d^2)*f*x + ((C*a^2*b^2 - B*a*b^3 + A*b^4)*c^2 - 2*(C*a^3*b - B*a^2*b^2 + A*a*b^3)*c*d + (C*a^4 - B*a^3*b + A*a^2*b^2)*d^2)*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - ((C*a^2*b^2 + C*b^4)*c^2 - 2*(C*a^3*b - B*a^2*b^2 + C*a*b^3 - B*b^4)*c*d + (C*a^4 - B*a^3*b + A*a^2*b^2 - B*a*b^3 + (A - C)*b^4)*d^2)*log(1/(tan(f*x + e)^2 + 1)) + 2*(2*(C*a^2*b^2 + C*b^4)*c*d - (C*a^3*b - B*a^2*b^2 + C*a*b^3 - B*b^4)*d^2)*tan(f*x + e))/((a^2*b^3 + b^5)*f)","A",0
62,1,964,0,2.999684," ","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=""fricas"")","\frac{2 \, {\left(C a^{4} b^{2} + 2 \, C a^{2} b^{4} + C b^{6}\right)} d^{2} \tan\left(f x + e\right)^{2} - 2 \, {\left(C a^{2} b^{4} - B a b^{5} + A b^{6}\right)} c^{2} + 4 \, {\left(C a^{3} b^{3} - B a^{2} b^{4} + A a b^{5}\right)} c d - 2 \, {\left(C a^{4} b^{2} - B a^{3} b^{3} + A a^{2} b^{4}\right)} d^{2} + 2 \, {\left({\left({\left(A - C\right)} a^{3} b^{3} + 2 \, B a^{2} b^{4} - {\left(A - C\right)} a b^{5}\right)} c^{2} - 2 \, {\left(B a^{3} b^{3} - 2 \, {\left(A - C\right)} a^{2} b^{4} - B a b^{5}\right)} c d - {\left({\left(A - C\right)} a^{3} b^{3} + 2 \, B a^{2} b^{4} - {\left(A - C\right)} a b^{5}\right)} d^{2}\right)} f x - {\left({\left(B a^{3} b^{3} - 2 \, {\left(A - C\right)} a^{2} b^{4} - B a b^{5}\right)} c^{2} - 2 \, {\left(C a^{5} b - {\left(A - 3 \, C\right)} a^{3} b^{3} - 2 \, B a^{2} b^{4} + A a b^{5}\right)} c d + {\left(2 \, C a^{6} - B a^{5} b + 4 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4}\right)} d^{2} + {\left({\left(B a^{2} b^{4} - 2 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c^{2} - 2 \, {\left(C a^{4} b^{2} - {\left(A - 3 \, C\right)} a^{2} b^{4} - 2 \, B a b^{5} + A b^{6}\right)} c d + {\left(2 \, C a^{5} b - B a^{4} b^{2} + 4 \, C a^{3} b^{3} - 3 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(2 \, {\left(C a^{5} b + 2 \, C a^{3} b^{3} + C a b^{5}\right)} c d - {\left(2 \, C a^{6} - B a^{5} b + 4 \, C a^{4} b^{2} - 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} d^{2} + {\left(2 \, {\left(C a^{4} b^{2} + 2 \, C a^{2} b^{4} + C b^{6}\right)} c d - {\left(2 \, C a^{5} b - B a^{4} b^{2} + 4 \, C a^{3} b^{3} - 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} d^{2}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left({\left(C a^{3} b^{3} - B a^{2} b^{4} + A a b^{5}\right)} c^{2} - 2 \, {\left(C a^{4} b^{2} - B a^{3} b^{3} + A a^{2} b^{4}\right)} c d + {\left(2 \, C a^{5} b - B a^{4} b^{2} + {\left(A + 2 \, C\right)} a^{3} b^{3} + C a b^{5}\right)} d^{2} + {\left({\left({\left(A - C\right)} a^{2} b^{4} + 2 \, B a b^{5} - {\left(A - C\right)} b^{6}\right)} c^{2} - 2 \, {\left(B a^{2} b^{4} - 2 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c d - {\left({\left(A - C\right)} a^{2} b^{4} + 2 \, B a b^{5} - {\left(A - C\right)} b^{6}\right)} d^{2}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} f \tan\left(f x + e\right) + {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} f\right)}}"," ",0,"1/2*(2*(C*a^4*b^2 + 2*C*a^2*b^4 + C*b^6)*d^2*tan(f*x + e)^2 - 2*(C*a^2*b^4 - B*a*b^5 + A*b^6)*c^2 + 4*(C*a^3*b^3 - B*a^2*b^4 + A*a*b^5)*c*d - 2*(C*a^4*b^2 - B*a^3*b^3 + A*a^2*b^4)*d^2 + 2*(((A - C)*a^3*b^3 + 2*B*a^2*b^4 - (A - C)*a*b^5)*c^2 - 2*(B*a^3*b^3 - 2*(A - C)*a^2*b^4 - B*a*b^5)*c*d - ((A - C)*a^3*b^3 + 2*B*a^2*b^4 - (A - C)*a*b^5)*d^2)*f*x - ((B*a^3*b^3 - 2*(A - C)*a^2*b^4 - B*a*b^5)*c^2 - 2*(C*a^5*b - (A - 3*C)*a^3*b^3 - 2*B*a^2*b^4 + A*a*b^5)*c*d + (2*C*a^6 - B*a^5*b + 4*C*a^4*b^2 - 3*B*a^3*b^3 + 2*A*a^2*b^4)*d^2 + ((B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c^2 - 2*(C*a^4*b^2 - (A - 3*C)*a^2*b^4 - 2*B*a*b^5 + A*b^6)*c*d + (2*C*a^5*b - B*a^4*b^2 + 4*C*a^3*b^3 - 3*B*a^2*b^4 + 2*A*a*b^5)*d^2)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (2*(C*a^5*b + 2*C*a^3*b^3 + C*a*b^5)*c*d - (2*C*a^6 - B*a^5*b + 4*C*a^4*b^2 - 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*d^2 + (2*(C*a^4*b^2 + 2*C*a^2*b^4 + C*b^6)*c*d - (2*C*a^5*b - B*a^4*b^2 + 4*C*a^3*b^3 - 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*d^2)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) + 2*((C*a^3*b^3 - B*a^2*b^4 + A*a*b^5)*c^2 - 2*(C*a^4*b^2 - B*a^3*b^3 + A*a^2*b^4)*c*d + (2*C*a^5*b - B*a^4*b^2 + (A + 2*C)*a^3*b^3 + C*a*b^5)*d^2 + (((A - C)*a^2*b^4 + 2*B*a*b^5 - (A - C)*b^6)*c^2 - 2*(B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c*d - ((A - C)*a^2*b^4 + 2*B*a*b^5 - (A - C)*b^6)*d^2)*f*x)*tan(f*x + e))/((a^4*b^4 + 2*a^2*b^6 + b^8)*f*tan(f*x + e) + (a^5*b^3 + 2*a^3*b^5 + a*b^7)*f)","B",0
63,1,1699,0,2.650842," ","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=""fricas"")","-\frac{{\left(3 \, C a^{4} b^{4} - 5 \, B a^{3} b^{5} + {\left(7 \, A - 3 \, C\right)} a^{2} b^{6} + B a b^{7} + A b^{8}\right)} c^{2} - 2 \, {\left(C a^{5} b^{3} - 3 \, B a^{4} b^{4} + 5 \, {\left(A - C\right)} a^{3} b^{5} + 3 \, B a^{2} b^{6} - A a b^{7}\right)} c d - {\left(C a^{6} b^{2} + B a^{5} b^{3} - {\left(3 \, A - 7 \, C\right)} a^{4} b^{4} - 5 \, B a^{3} b^{5} + 3 \, A a^{2} b^{6}\right)} d^{2} - 2 \, {\left({\left({\left(A - C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} - 3 \, {\left(A - C\right)} a^{3} b^{5} - B a^{2} b^{6}\right)} c^{2} - 2 \, {\left(B a^{5} b^{3} - 3 \, {\left(A - C\right)} a^{4} b^{4} - 3 \, B a^{3} b^{5} + {\left(A - C\right)} a^{2} b^{6}\right)} c d - {\left({\left(A - C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} - 3 \, {\left(A - C\right)} a^{3} b^{5} - B a^{2} b^{6}\right)} d^{2}\right)} f x - {\left({\left(C a^{4} b^{4} - 3 \, B a^{3} b^{5} + 5 \, {\left(A - C\right)} a^{2} b^{6} + 3 \, B a b^{7} - A b^{8}\right)} c^{2} + 2 \, {\left(C a^{5} b^{3} + B a^{4} b^{4} - {\left(3 \, A - 7 \, C\right)} a^{3} b^{5} - 5 \, B a^{2} b^{6} + 3 \, A a b^{7}\right)} c d - {\left(3 \, C a^{6} b^{2} - B a^{5} b^{3} - {\left(A - 9 \, C\right)} a^{4} b^{4} - 7 \, B a^{3} b^{5} + 5 \, A a^{2} b^{6}\right)} d^{2} + 2 \, {\left({\left({\left(A - C\right)} a^{3} b^{5} + 3 \, B a^{2} b^{6} - 3 \, {\left(A - C\right)} a b^{7} - B b^{8}\right)} c^{2} - 2 \, {\left(B a^{3} b^{5} - 3 \, {\left(A - C\right)} a^{2} b^{6} - 3 \, B a b^{7} + {\left(A - C\right)} b^{8}\right)} c d - {\left({\left(A - C\right)} a^{3} b^{5} + 3 \, B a^{2} b^{6} - 3 \, {\left(A - C\right)} a b^{7} - B b^{8}\right)} d^{2}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left({\left(B a^{5} b^{3} - 3 \, {\left(A - C\right)} a^{4} b^{4} - 3 \, B a^{3} b^{5} + {\left(A - C\right)} a^{2} b^{6}\right)} c^{2} + 2 \, {\left({\left(A - C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} - 3 \, {\left(A - C\right)} a^{3} b^{5} - B a^{2} b^{6}\right)} c d - {\left(C a^{8} + 3 \, C a^{6} b^{2} + B a^{5} b^{3} - 3 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - 3 \, B a^{3} b^{5} + A a^{2} b^{6}\right)} d^{2} + {\left({\left(B a^{3} b^{5} - 3 \, {\left(A - C\right)} a^{2} b^{6} - 3 \, B a b^{7} + {\left(A - C\right)} b^{8}\right)} c^{2} + 2 \, {\left({\left(A - C\right)} a^{3} b^{5} + 3 \, B a^{2} b^{6} - 3 \, {\left(A - C\right)} a b^{7} - B b^{8}\right)} c d - {\left(C a^{6} b^{2} + 3 \, C a^{4} b^{4} + B a^{3} b^{5} - 3 \, {\left(A - 2 \, C\right)} a^{2} b^{6} - 3 \, B a b^{7} + A b^{8}\right)} d^{2}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(B a^{4} b^{4} - 3 \, {\left(A - C\right)} a^{3} b^{5} - 3 \, B a^{2} b^{6} + {\left(A - C\right)} a b^{7}\right)} c^{2} + 2 \, {\left({\left(A - C\right)} a^{4} b^{4} + 3 \, B a^{3} b^{5} - 3 \, {\left(A - C\right)} a^{2} b^{6} - B a b^{7}\right)} c d - {\left(C a^{7} b + 3 \, C a^{5} b^{3} + B a^{4} b^{4} - 3 \, {\left(A - 2 \, C\right)} a^{3} b^{5} - 3 \, B a^{2} b^{6} + A a b^{7}\right)} d^{2}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left({\left(C a^{6} b^{2} + 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} + C b^{8}\right)} d^{2} \tan\left(f x + e\right)^{2} + 2 \, {\left(C a^{7} b + 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} + C a b^{7}\right)} d^{2} \tan\left(f x + e\right) + {\left(C a^{8} + 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} + C a^{2} b^{6}\right)} d^{2}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left({\left(C a^{5} b^{3} - 2 \, B a^{4} b^{4} + 3 \, {\left(A - C\right)} a^{3} b^{5} + 3 \, B a^{2} b^{6} - {\left(3 \, A - 2 \, C\right)} a b^{7} - B b^{8}\right)} c^{2} + 2 \, {\left(B a^{5} b^{3} - {\left(2 \, A - 3 \, C\right)} a^{4} b^{4} - 3 \, B a^{3} b^{5} + 3 \, {\left(A - C\right)} a^{2} b^{6} + 2 \, B a b^{7} - A b^{8}\right)} c d - {\left(C a^{7} b - {\left(A - 3 \, C\right)} a^{5} b^{3} - 3 \, B a^{4} b^{4} + {\left(3 \, A - 4 \, C\right)} a^{3} b^{5} + 3 \, B a^{2} b^{6} - 2 \, A a b^{7}\right)} d^{2} + 2 \, {\left({\left({\left(A - C\right)} a^{4} b^{4} + 3 \, B a^{3} b^{5} - 3 \, {\left(A - C\right)} a^{2} b^{6} - B a b^{7}\right)} c^{2} - 2 \, {\left(B a^{4} b^{4} - 3 \, {\left(A - C\right)} a^{3} b^{5} - 3 \, B a^{2} b^{6} + {\left(A - C\right)} a b^{7}\right)} c d - {\left({\left(A - C\right)} a^{4} b^{4} + 3 \, B a^{3} b^{5} - 3 \, {\left(A - C\right)} a^{2} b^{6} - B a b^{7}\right)} d^{2}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{6} b^{5} + 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + b^{11}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{7} b^{4} + 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} + a b^{10}\right)} f \tan\left(f x + e\right) + {\left(a^{8} b^{3} + 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} + a^{2} b^{9}\right)} f\right)}}"," ",0,"-1/2*((3*C*a^4*b^4 - 5*B*a^3*b^5 + (7*A - 3*C)*a^2*b^6 + B*a*b^7 + A*b^8)*c^2 - 2*(C*a^5*b^3 - 3*B*a^4*b^4 + 5*(A - C)*a^3*b^5 + 3*B*a^2*b^6 - A*a*b^7)*c*d - (C*a^6*b^2 + B*a^5*b^3 - (3*A - 7*C)*a^4*b^4 - 5*B*a^3*b^5 + 3*A*a^2*b^6)*d^2 - 2*(((A - C)*a^5*b^3 + 3*B*a^4*b^4 - 3*(A - C)*a^3*b^5 - B*a^2*b^6)*c^2 - 2*(B*a^5*b^3 - 3*(A - C)*a^4*b^4 - 3*B*a^3*b^5 + (A - C)*a^2*b^6)*c*d - ((A - C)*a^5*b^3 + 3*B*a^4*b^4 - 3*(A - C)*a^3*b^5 - B*a^2*b^6)*d^2)*f*x - ((C*a^4*b^4 - 3*B*a^3*b^5 + 5*(A - C)*a^2*b^6 + 3*B*a*b^7 - A*b^8)*c^2 + 2*(C*a^5*b^3 + B*a^4*b^4 - (3*A - 7*C)*a^3*b^5 - 5*B*a^2*b^6 + 3*A*a*b^7)*c*d - (3*C*a^6*b^2 - B*a^5*b^3 - (A - 9*C)*a^4*b^4 - 7*B*a^3*b^5 + 5*A*a^2*b^6)*d^2 + 2*(((A - C)*a^3*b^5 + 3*B*a^2*b^6 - 3*(A - C)*a*b^7 - B*b^8)*c^2 - 2*(B*a^3*b^5 - 3*(A - C)*a^2*b^6 - 3*B*a*b^7 + (A - C)*b^8)*c*d - ((A - C)*a^3*b^5 + 3*B*a^2*b^6 - 3*(A - C)*a*b^7 - B*b^8)*d^2)*f*x)*tan(f*x + e)^2 + ((B*a^5*b^3 - 3*(A - C)*a^4*b^4 - 3*B*a^3*b^5 + (A - C)*a^2*b^6)*c^2 + 2*((A - C)*a^5*b^3 + 3*B*a^4*b^4 - 3*(A - C)*a^3*b^5 - B*a^2*b^6)*c*d - (C*a^8 + 3*C*a^6*b^2 + B*a^5*b^3 - 3*(A - 2*C)*a^4*b^4 - 3*B*a^3*b^5 + A*a^2*b^6)*d^2 + ((B*a^3*b^5 - 3*(A - C)*a^2*b^6 - 3*B*a*b^7 + (A - C)*b^8)*c^2 + 2*((A - C)*a^3*b^5 + 3*B*a^2*b^6 - 3*(A - C)*a*b^7 - B*b^8)*c*d - (C*a^6*b^2 + 3*C*a^4*b^4 + B*a^3*b^5 - 3*(A - 2*C)*a^2*b^6 - 3*B*a*b^7 + A*b^8)*d^2)*tan(f*x + e)^2 + 2*((B*a^4*b^4 - 3*(A - C)*a^3*b^5 - 3*B*a^2*b^6 + (A - C)*a*b^7)*c^2 + 2*((A - C)*a^4*b^4 + 3*B*a^3*b^5 - 3*(A - C)*a^2*b^6 - B*a*b^7)*c*d - (C*a^7*b + 3*C*a^5*b^3 + B*a^4*b^4 - 3*(A - 2*C)*a^3*b^5 - 3*B*a^2*b^6 + A*a*b^7)*d^2)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) + ((C*a^6*b^2 + 3*C*a^4*b^4 + 3*C*a^2*b^6 + C*b^8)*d^2*tan(f*x + e)^2 + 2*(C*a^7*b + 3*C*a^5*b^3 + 3*C*a^3*b^5 + C*a*b^7)*d^2*tan(f*x + e) + (C*a^8 + 3*C*a^6*b^2 + 3*C*a^4*b^4 + C*a^2*b^6)*d^2)*log(1/(tan(f*x + e)^2 + 1)) - 2*((C*a^5*b^3 - 2*B*a^4*b^4 + 3*(A - C)*a^3*b^5 + 3*B*a^2*b^6 - (3*A - 2*C)*a*b^7 - B*b^8)*c^2 + 2*(B*a^5*b^3 - (2*A - 3*C)*a^4*b^4 - 3*B*a^3*b^5 + 3*(A - C)*a^2*b^6 + 2*B*a*b^7 - A*b^8)*c*d - (C*a^7*b - (A - 3*C)*a^5*b^3 - 3*B*a^4*b^4 + (3*A - 4*C)*a^3*b^5 + 3*B*a^2*b^6 - 2*A*a*b^7)*d^2 + 2*(((A - C)*a^4*b^4 + 3*B*a^3*b^5 - 3*(A - C)*a^2*b^6 - B*a*b^7)*c^2 - 2*(B*a^4*b^4 - 3*(A - C)*a^3*b^5 - 3*B*a^2*b^6 + (A - C)*a*b^7)*c*d - ((A - C)*a^4*b^4 + 3*B*a^3*b^5 - 3*(A - C)*a^2*b^6 - B*a*b^7)*d^2)*f*x)*tan(f*x + e))/((a^6*b^5 + 3*a^4*b^7 + 3*a^2*b^9 + b^11)*f*tan(f*x + e)^2 + 2*(a^7*b^4 + 3*a^5*b^6 + 3*a^3*b^8 + a*b^10)*f*tan(f*x + e) + (a^8*b^3 + 3*a^6*b^5 + 3*a^4*b^7 + a^2*b^9)*f)","B",0
64,1,679,0,0.642568," ","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=""fricas"")","\frac{10 \, C b^{2} d^{3} \tan\left(f x + e\right)^{6} + 12 \, {\left(3 \, C b^{2} c d^{2} + {\left(2 \, C a b + B b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)^{5} + 15 \, {\left(3 \, C b^{2} c^{2} d + 3 \, {\left(2 \, C a b + B b^{2}\right)} c d^{2} + {\left(C a^{2} + 2 \, B a b + {\left(A - C\right)} b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)^{4} + 20 \, {\left(C b^{2} c^{3} + 3 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d + 3 \, {\left(C a^{2} + 2 \, B a b + {\left(A - C\right)} b^{2}\right)} c d^{2} + {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)^{3} + 60 \, {\left({\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c^{3} - 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{2} d - 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c d^{2} + {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} d^{3}\right)} f x + 30 \, {\left({\left(2 \, C a b + B b^{2}\right)} c^{3} + 3 \, {\left(C a^{2} + 2 \, B a b + {\left(A - C\right)} b^{2}\right)} c^{2} d + 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c d^{2} + {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} - 30 \, {\left({\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{3} + 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c^{2} d - 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c d^{2} - {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 60 \, {\left({\left(C a^{2} + 2 \, B a b + {\left(A - C\right)} b^{2}\right)} c^{3} + 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{2} d + 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c d^{2} - {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)}{60 \, f}"," ",0,"1/60*(10*C*b^2*d^3*tan(f*x + e)^6 + 12*(3*C*b^2*c*d^2 + (2*C*a*b + B*b^2)*d^3)*tan(f*x + e)^5 + 15*(3*C*b^2*c^2*d + 3*(2*C*a*b + B*b^2)*c*d^2 + (C*a^2 + 2*B*a*b + (A - C)*b^2)*d^3)*tan(f*x + e)^4 + 20*(C*b^2*c^3 + 3*(2*C*a*b + B*b^2)*c^2*d + 3*(C*a^2 + 2*B*a*b + (A - C)*b^2)*c*d^2 + (B*a^2 + 2*(A - C)*a*b - B*b^2)*d^3)*tan(f*x + e)^3 + 60*(((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c^3 - 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c^2*d - 3*((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c*d^2 + (B*a^2 + 2*(A - C)*a*b - B*b^2)*d^3)*f*x + 30*((2*C*a*b + B*b^2)*c^3 + 3*(C*a^2 + 2*B*a*b + (A - C)*b^2)*c^2*d + 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c*d^2 + ((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*d^3)*tan(f*x + e)^2 - 30*((B*a^2 + 2*(A - C)*a*b - B*b^2)*c^3 + 3*((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c^2*d - 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c*d^2 - ((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*d^3)*log(1/(tan(f*x + e)^2 + 1)) + 60*((C*a^2 + 2*B*a*b + (A - C)*b^2)*c^3 + 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c^2*d + 3*((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c*d^2 - (B*a^2 + 2*(A - C)*a*b - B*b^2)*d^3)*tan(f*x + e))/f","A",0
65,1,386,0,1.480567," ","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=""fricas"")","\frac{12 \, C b d^{3} \tan\left(f x + e\right)^{5} + 15 \, {\left(3 \, C b c d^{2} + {\left(C a + B b\right)} d^{3}\right)} \tan\left(f x + e\right)^{4} + 20 \, {\left(3 \, C b c^{2} d + 3 \, {\left(C a + B b\right)} c d^{2} + {\left(B a + {\left(A - C\right)} b\right)} d^{3}\right)} \tan\left(f x + e\right)^{3} + 60 \, {\left({\left({\left(A - C\right)} a - B b\right)} c^{3} - 3 \, {\left(B a + {\left(A - C\right)} b\right)} c^{2} d - 3 \, {\left({\left(A - C\right)} a - B b\right)} c d^{2} + {\left(B a + {\left(A - C\right)} b\right)} d^{3}\right)} f x + 30 \, {\left(C b c^{3} + 3 \, {\left(C a + B b\right)} c^{2} d + 3 \, {\left(B a + {\left(A - C\right)} b\right)} c d^{2} + {\left({\left(A - C\right)} a - B b\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} - 30 \, {\left({\left(B a + {\left(A - C\right)} b\right)} c^{3} + 3 \, {\left({\left(A - C\right)} a - B b\right)} c^{2} d - 3 \, {\left(B a + {\left(A - C\right)} b\right)} c d^{2} - {\left({\left(A - C\right)} a - B b\right)} d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 60 \, {\left({\left(C a + B b\right)} c^{3} + 3 \, {\left(B a + {\left(A - C\right)} b\right)} c^{2} d + 3 \, {\left({\left(A - C\right)} a - B b\right)} c d^{2} - {\left(B a + {\left(A - C\right)} b\right)} d^{3}\right)} \tan\left(f x + e\right)}{60 \, f}"," ",0,"1/60*(12*C*b*d^3*tan(f*x + e)^5 + 15*(3*C*b*c*d^2 + (C*a + B*b)*d^3)*tan(f*x + e)^4 + 20*(3*C*b*c^2*d + 3*(C*a + B*b)*c*d^2 + (B*a + (A - C)*b)*d^3)*tan(f*x + e)^3 + 60*(((A - C)*a - B*b)*c^3 - 3*(B*a + (A - C)*b)*c^2*d - 3*((A - C)*a - B*b)*c*d^2 + (B*a + (A - C)*b)*d^3)*f*x + 30*(C*b*c^3 + 3*(C*a + B*b)*c^2*d + 3*(B*a + (A - C)*b)*c*d^2 + ((A - C)*a - B*b)*d^3)*tan(f*x + e)^2 - 30*((B*a + (A - C)*b)*c^3 + 3*((A - C)*a - B*b)*c^2*d - 3*(B*a + (A - C)*b)*c*d^2 - ((A - C)*a - B*b)*d^3)*log(1/(tan(f*x + e)^2 + 1)) + 60*((C*a + B*b)*c^3 + 3*(B*a + (A - C)*b)*c^2*d + 3*((A - C)*a - B*b)*c*d^2 - (B*a + (A - C)*b)*d^3)*tan(f*x + e))/f","A",0
66,1,201,0,1.573869," ","integrate((c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""fricas"")","\frac{3 \, C d^{3} \tan\left(f x + e\right)^{4} + 4 \, {\left(3 \, C c d^{2} + B d^{3}\right)} \tan\left(f x + e\right)^{3} + 12 \, {\left({\left(A - C\right)} c^{3} - 3 \, B c^{2} d - 3 \, {\left(A - C\right)} c d^{2} + B d^{3}\right)} f x + 6 \, {\left(3 \, C c^{2} d + 3 \, B c d^{2} + {\left(A - C\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} - 6 \, {\left(B c^{3} + 3 \, {\left(A - C\right)} c^{2} d - 3 \, B c d^{2} - {\left(A - C\right)} d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 12 \, {\left(C c^{3} + 3 \, B c^{2} d + 3 \, {\left(A - C\right)} c d^{2} - B d^{3}\right)} \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*C*d^3*tan(f*x + e)^4 + 4*(3*C*c*d^2 + B*d^3)*tan(f*x + e)^3 + 12*((A - C)*c^3 - 3*B*c^2*d - 3*(A - C)*c*d^2 + B*d^3)*f*x + 6*(3*C*c^2*d + 3*B*c*d^2 + (A - C)*d^3)*tan(f*x + e)^2 - 6*(B*c^3 + 3*(A - C)*c^2*d - 3*B*c*d^2 - (A - C)*d^3)*log(1/(tan(f*x + e)^2 + 1)) + 12*(C*c^3 + 3*B*c^2*d + 3*(A - C)*c*d^2 - B*d^3)*tan(f*x + e))/f","A",0
67,1,623,0,3.138689," ","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=""fricas"")","\frac{2 \, {\left(C a^{2} b^{3} + C b^{5}\right)} d^{3} \tan\left(f x + e\right)^{3} + 6 \, {\left({\left({\left(A - C\right)} a b^{4} + B b^{5}\right)} c^{3} - 3 \, {\left(B a b^{4} - {\left(A - C\right)} b^{5}\right)} c^{2} d - 3 \, {\left({\left(A - C\right)} a b^{4} + B b^{5}\right)} c d^{2} + {\left(B a b^{4} - {\left(A - C\right)} b^{5}\right)} d^{3}\right)} f x + 3 \, {\left(3 \, {\left(C a^{2} b^{3} + C b^{5}\right)} c d^{2} - {\left(C a^{3} b^{2} - B a^{2} b^{3} + C a b^{4} - B b^{5}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} + 3 \, {\left({\left(C a^{2} b^{3} - B a b^{4} + A b^{5}\right)} c^{3} - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} c^{2} d + 3 \, {\left(C a^{4} b - B a^{3} b^{2} + A a^{2} b^{3}\right)} c d^{2} - {\left(C a^{5} - B a^{4} b + A a^{3} b^{2}\right)} d^{3}\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 3 \, {\left({\left(C a^{2} b^{3} + C b^{5}\right)} c^{3} - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} + C a b^{4} - B b^{5}\right)} c^{2} d + 3 \, {\left(C a^{4} b - B a^{3} b^{2} + A a^{2} b^{3} - B a b^{4} + {\left(A - C\right)} b^{5}\right)} c d^{2} - {\left(C a^{5} - B a^{4} b + A a^{3} b^{2} + {\left(A - C\right)} a b^{4} + B b^{5}\right)} d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(3 \, {\left(C a^{2} b^{3} + C b^{5}\right)} c^{2} d - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} + C a b^{4} - B b^{5}\right)} c d^{2} + {\left(C a^{4} b - B a^{3} b^{2} + A a^{2} b^{3} - B a b^{4} + {\left(A - C\right)} b^{5}\right)} d^{3}\right)} \tan\left(f x + e\right)}{6 \, {\left(a^{2} b^{4} + b^{6}\right)} f}"," ",0,"1/6*(2*(C*a^2*b^3 + C*b^5)*d^3*tan(f*x + e)^3 + 6*(((A - C)*a*b^4 + B*b^5)*c^3 - 3*(B*a*b^4 - (A - C)*b^5)*c^2*d - 3*((A - C)*a*b^4 + B*b^5)*c*d^2 + (B*a*b^4 - (A - C)*b^5)*d^3)*f*x + 3*(3*(C*a^2*b^3 + C*b^5)*c*d^2 - (C*a^3*b^2 - B*a^2*b^3 + C*a*b^4 - B*b^5)*d^3)*tan(f*x + e)^2 + 3*((C*a^2*b^3 - B*a*b^4 + A*b^5)*c^3 - 3*(C*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*c^2*d + 3*(C*a^4*b - B*a^3*b^2 + A*a^2*b^3)*c*d^2 - (C*a^5 - B*a^4*b + A*a^3*b^2)*d^3)*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - 3*((C*a^2*b^3 + C*b^5)*c^3 - 3*(C*a^3*b^2 - B*a^2*b^3 + C*a*b^4 - B*b^5)*c^2*d + 3*(C*a^4*b - B*a^3*b^2 + A*a^2*b^3 - B*a*b^4 + (A - C)*b^5)*c*d^2 - (C*a^5 - B*a^4*b + A*a^3*b^2 + (A - C)*a*b^4 + B*b^5)*d^3)*log(1/(tan(f*x + e)^2 + 1)) + 6*(3*(C*a^2*b^3 + C*b^5)*c^2*d - 3*(C*a^3*b^2 - B*a^2*b^3 + C*a*b^4 - B*b^5)*c*d^2 + (C*a^4*b - B*a^3*b^2 + A*a^2*b^3 - B*a*b^4 + (A - C)*b^5)*d^3)*tan(f*x + e))/((a^2*b^4 + b^6)*f)","A",0
68,1,1512,0,3.085598," ","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=""fricas"")","\frac{{\left(C a^{4} b^{3} + 2 \, C a^{2} b^{5} + C b^{7}\right)} d^{3} \tan\left(f x + e\right)^{3} - 2 \, {\left(C a^{2} b^{5} - B a b^{6} + A b^{7}\right)} c^{3} + 6 \, {\left(C a^{3} b^{4} - B a^{2} b^{5} + A a b^{6}\right)} c^{2} d - 6 \, {\left(C a^{4} b^{3} - B a^{3} b^{4} + A a^{2} b^{5}\right)} c d^{2} + {\left(3 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} + 2 \, {\left(A + C\right)} a^{3} b^{4} + C a b^{6}\right)} d^{3} + 2 \, {\left({\left({\left(A - C\right)} a^{3} b^{4} + 2 \, B a^{2} b^{5} - {\left(A - C\right)} a b^{6}\right)} c^{3} - 3 \, {\left(B a^{3} b^{4} - 2 \, {\left(A - C\right)} a^{2} b^{5} - B a b^{6}\right)} c^{2} d - 3 \, {\left({\left(A - C\right)} a^{3} b^{4} + 2 \, B a^{2} b^{5} - {\left(A - C\right)} a b^{6}\right)} c d^{2} + {\left(B a^{3} b^{4} - 2 \, {\left(A - C\right)} a^{2} b^{5} - B a b^{6}\right)} d^{3}\right)} f x + {\left(6 \, {\left(C a^{4} b^{3} + 2 \, C a^{2} b^{5} + C b^{7}\right)} c d^{2} - {\left(3 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} + 6 \, C a^{3} b^{4} - 4 \, B a^{2} b^{5} + 3 \, C a b^{6} - 2 \, B b^{7}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} - {\left({\left(B a^{3} b^{4} - 2 \, {\left(A - C\right)} a^{2} b^{5} - B a b^{6}\right)} c^{3} - 3 \, {\left(C a^{5} b^{2} - {\left(A - 3 \, C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + A a b^{6}\right)} c^{2} d + 3 \, {\left(2 \, C a^{6} b - B a^{5} b^{2} + 4 \, C a^{4} b^{3} - 3 \, B a^{3} b^{4} + 2 \, A a^{2} b^{5}\right)} c d^{2} - {\left(3 \, C a^{7} - 2 \, B a^{6} b + {\left(A + 5 \, C\right)} a^{5} b^{2} - 4 \, B a^{4} b^{3} + 3 \, A a^{3} b^{4}\right)} d^{3} + {\left({\left(B a^{2} b^{5} - 2 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c^{3} - 3 \, {\left(C a^{4} b^{3} - {\left(A - 3 \, C\right)} a^{2} b^{5} - 2 \, B a b^{6} + A b^{7}\right)} c^{2} d + 3 \, {\left(2 \, C a^{5} b^{2} - B a^{4} b^{3} + 4 \, C a^{3} b^{4} - 3 \, B a^{2} b^{5} + 2 \, A a b^{6}\right)} c d^{2} - {\left(3 \, C a^{6} b - 2 \, B a^{5} b^{2} + {\left(A + 5 \, C\right)} a^{4} b^{3} - 4 \, B a^{3} b^{4} + 3 \, A a^{2} b^{5}\right)} d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(3 \, {\left(C a^{5} b^{2} + 2 \, C a^{3} b^{4} + C a b^{6}\right)} c^{2} d - 3 \, {\left(2 \, C a^{6} b - B a^{5} b^{2} + 4 \, C a^{4} b^{3} - 2 \, B a^{3} b^{4} + 2 \, C a^{2} b^{5} - B a b^{6}\right)} c d^{2} + {\left(3 \, C a^{7} - 2 \, B a^{6} b + {\left(A + 5 \, C\right)} a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(2 \, A + C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + {\left(A - C\right)} a b^{6}\right)} d^{3} + {\left(3 \, {\left(C a^{4} b^{3} + 2 \, C a^{2} b^{5} + C b^{7}\right)} c^{2} d - 3 \, {\left(2 \, C a^{5} b^{2} - B a^{4} b^{3} + 4 \, C a^{3} b^{4} - 2 \, B a^{2} b^{5} + 2 \, C a b^{6} - B b^{7}\right)} c d^{2} + {\left(3 \, C a^{6} b - 2 \, B a^{5} b^{2} + {\left(A + 5 \, C\right)} a^{4} b^{3} - 4 \, B a^{3} b^{4} + {\left(2 \, A + C\right)} a^{2} b^{5} - 2 \, B a b^{6} + {\left(A - C\right)} b^{7}\right)} d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(2 \, {\left(C a^{3} b^{4} - B a^{2} b^{5} + A a b^{6}\right)} c^{3} - 6 \, {\left(C a^{4} b^{3} - B a^{3} b^{4} + A a^{2} b^{5}\right)} c^{2} d + 6 \, {\left(2 \, C a^{5} b^{2} - B a^{4} b^{3} + {\left(A + 2 \, C\right)} a^{3} b^{4} + C a b^{6}\right)} c d^{2} - {\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} + {\left(2 \, A + 7 \, C\right)} a^{4} b^{3} - 4 \, B a^{3} b^{4} + 2 \, C a^{2} b^{5} - 2 \, B a b^{6} - C b^{7}\right)} d^{3} + 2 \, {\left({\left({\left(A - C\right)} a^{2} b^{5} + 2 \, B a b^{6} - {\left(A - C\right)} b^{7}\right)} c^{3} - 3 \, {\left(B a^{2} b^{5} - 2 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c^{2} d - 3 \, {\left({\left(A - C\right)} a^{2} b^{5} + 2 \, B a b^{6} - {\left(A - C\right)} b^{7}\right)} c d^{2} + {\left(B a^{2} b^{5} - 2 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} d^{3}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} f \tan\left(f x + e\right) + {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} f\right)}}"," ",0,"1/2*((C*a^4*b^3 + 2*C*a^2*b^5 + C*b^7)*d^3*tan(f*x + e)^3 - 2*(C*a^2*b^5 - B*a*b^6 + A*b^7)*c^3 + 6*(C*a^3*b^4 - B*a^2*b^5 + A*a*b^6)*c^2*d - 6*(C*a^4*b^3 - B*a^3*b^4 + A*a^2*b^5)*c*d^2 + (3*C*a^5*b^2 - 2*B*a^4*b^3 + 2*(A + C)*a^3*b^4 + C*a*b^6)*d^3 + 2*(((A - C)*a^3*b^4 + 2*B*a^2*b^5 - (A - C)*a*b^6)*c^3 - 3*(B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^2*d - 3*((A - C)*a^3*b^4 + 2*B*a^2*b^5 - (A - C)*a*b^6)*c*d^2 + (B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*d^3)*f*x + (6*(C*a^4*b^3 + 2*C*a^2*b^5 + C*b^7)*c*d^2 - (3*C*a^5*b^2 - 2*B*a^4*b^3 + 6*C*a^3*b^4 - 4*B*a^2*b^5 + 3*C*a*b^6 - 2*B*b^7)*d^3)*tan(f*x + e)^2 - ((B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^3 - 3*(C*a^5*b^2 - (A - 3*C)*a^3*b^4 - 2*B*a^2*b^5 + A*a*b^6)*c^2*d + 3*(2*C*a^6*b - B*a^5*b^2 + 4*C*a^4*b^3 - 3*B*a^3*b^4 + 2*A*a^2*b^5)*c*d^2 - (3*C*a^7 - 2*B*a^6*b + (A + 5*C)*a^5*b^2 - 4*B*a^4*b^3 + 3*A*a^3*b^4)*d^3 + ((B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^3 - 3*(C*a^4*b^3 - (A - 3*C)*a^2*b^5 - 2*B*a*b^6 + A*b^7)*c^2*d + 3*(2*C*a^5*b^2 - B*a^4*b^3 + 4*C*a^3*b^4 - 3*B*a^2*b^5 + 2*A*a*b^6)*c*d^2 - (3*C*a^6*b - 2*B*a^5*b^2 + (A + 5*C)*a^4*b^3 - 4*B*a^3*b^4 + 3*A*a^2*b^5)*d^3)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (3*(C*a^5*b^2 + 2*C*a^3*b^4 + C*a*b^6)*c^2*d - 3*(2*C*a^6*b - B*a^5*b^2 + 4*C*a^4*b^3 - 2*B*a^3*b^4 + 2*C*a^2*b^5 - B*a*b^6)*c*d^2 + (3*C*a^7 - 2*B*a^6*b + (A + 5*C)*a^5*b^2 - 4*B*a^4*b^3 + (2*A + C)*a^3*b^4 - 2*B*a^2*b^5 + (A - C)*a*b^6)*d^3 + (3*(C*a^4*b^3 + 2*C*a^2*b^5 + C*b^7)*c^2*d - 3*(2*C*a^5*b^2 - B*a^4*b^3 + 4*C*a^3*b^4 - 2*B*a^2*b^5 + 2*C*a*b^6 - B*b^7)*c*d^2 + (3*C*a^6*b - 2*B*a^5*b^2 + (A + 5*C)*a^4*b^3 - 4*B*a^3*b^4 + (2*A + C)*a^2*b^5 - 2*B*a*b^6 + (A - C)*b^7)*d^3)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) + (2*(C*a^3*b^4 - B*a^2*b^5 + A*a*b^6)*c^3 - 6*(C*a^4*b^3 - B*a^3*b^4 + A*a^2*b^5)*c^2*d + 6*(2*C*a^5*b^2 - B*a^4*b^3 + (A + 2*C)*a^3*b^4 + C*a*b^6)*c*d^2 - (6*C*a^6*b - 4*B*a^5*b^2 + (2*A + 7*C)*a^4*b^3 - 4*B*a^3*b^4 + 2*C*a^2*b^5 - 2*B*a*b^6 - C*b^7)*d^3 + 2*(((A - C)*a^2*b^5 + 2*B*a*b^6 - (A - C)*b^7)*c^3 - 3*(B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^2*d - 3*((A - C)*a^2*b^5 + 2*B*a*b^6 - (A - C)*b^7)*c*d^2 + (B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*d^3)*f*x)*tan(f*x + e))/((a^4*b^5 + 2*a^2*b^7 + b^9)*f*tan(f*x + e) + (a^5*b^4 + 2*a^3*b^6 + a*b^8)*f)","B",0
69,1,2549,0,4.313809," ","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=""fricas"")","\frac{2 \, {\left(C a^{6} b^{3} + 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} + C b^{9}\right)} d^{3} \tan\left(f x + e\right)^{3} - {\left(3 \, C a^{4} b^{5} - 5 \, B a^{3} b^{6} + {\left(7 \, A - 3 \, C\right)} a^{2} b^{7} + B a b^{8} + A b^{9}\right)} c^{3} + 3 \, {\left(C a^{5} b^{4} - 3 \, B a^{4} b^{5} + 5 \, {\left(A - C\right)} a^{3} b^{6} + 3 \, B a^{2} b^{7} - A a b^{8}\right)} c^{2} d + 3 \, {\left(C a^{6} b^{3} + B a^{5} b^{4} - {\left(3 \, A - 7 \, C\right)} a^{4} b^{5} - 5 \, B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} c d^{2} - {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - {\left(A - 9 \, C\right)} a^{5} b^{4} - 7 \, B a^{4} b^{5} + 5 \, A a^{3} b^{6}\right)} d^{3} + 2 \, {\left({\left({\left(A - C\right)} a^{5} b^{4} + 3 \, B a^{4} b^{5} - 3 \, {\left(A - C\right)} a^{3} b^{6} - B a^{2} b^{7}\right)} c^{3} - 3 \, {\left(B a^{5} b^{4} - 3 \, {\left(A - C\right)} a^{4} b^{5} - 3 \, B a^{3} b^{6} + {\left(A - C\right)} a^{2} b^{7}\right)} c^{2} d - 3 \, {\left({\left(A - C\right)} a^{5} b^{4} + 3 \, B a^{4} b^{5} - 3 \, {\left(A - C\right)} a^{3} b^{6} - B a^{2} b^{7}\right)} c d^{2} + {\left(B a^{5} b^{4} - 3 \, {\left(A - C\right)} a^{4} b^{5} - 3 \, B a^{3} b^{6} + {\left(A - C\right)} a^{2} b^{7}\right)} d^{3}\right)} f x + {\left({\left(C a^{4} b^{5} - 3 \, B a^{3} b^{6} + 5 \, {\left(A - C\right)} a^{2} b^{7} + 3 \, B a b^{8} - A b^{9}\right)} c^{3} + 3 \, {\left(C a^{5} b^{4} + B a^{4} b^{5} - {\left(3 \, A - 7 \, C\right)} a^{3} b^{6} - 5 \, B a^{2} b^{7} + 3 \, A a b^{8}\right)} c^{2} d - 3 \, {\left(3 \, C a^{6} b^{3} - B a^{5} b^{4} - {\left(A - 9 \, C\right)} a^{4} b^{5} - 7 \, B a^{3} b^{6} + 5 \, A a^{2} b^{7}\right)} c d^{2} + {\left(9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} + {\left(A + 23 \, C\right)} a^{5} b^{4} - 9 \, B a^{4} b^{5} + {\left(7 \, A + 12 \, C\right)} a^{3} b^{6} + 4 \, C a b^{8}\right)} d^{3} + 2 \, {\left({\left({\left(A - C\right)} a^{3} b^{6} + 3 \, B a^{2} b^{7} - 3 \, {\left(A - C\right)} a b^{8} - B b^{9}\right)} c^{3} - 3 \, {\left(B a^{3} b^{6} - 3 \, {\left(A - C\right)} a^{2} b^{7} - 3 \, B a b^{8} + {\left(A - C\right)} b^{9}\right)} c^{2} d - 3 \, {\left({\left(A - C\right)} a^{3} b^{6} + 3 \, B a^{2} b^{7} - 3 \, {\left(A - C\right)} a b^{8} - B b^{9}\right)} c d^{2} + {\left(B a^{3} b^{6} - 3 \, {\left(A - C\right)} a^{2} b^{7} - 3 \, B a b^{8} + {\left(A - C\right)} b^{9}\right)} d^{3}\right)} f x\right)} \tan\left(f x + e\right)^{2} - {\left({\left(B a^{5} b^{4} - 3 \, {\left(A - C\right)} a^{4} b^{5} - 3 \, B a^{3} b^{6} + {\left(A - C\right)} a^{2} b^{7}\right)} c^{3} + 3 \, {\left({\left(A - C\right)} a^{5} b^{4} + 3 \, B a^{4} b^{5} - 3 \, {\left(A - C\right)} a^{3} b^{6} - B a^{2} b^{7}\right)} c^{2} d - 3 \, {\left(C a^{8} b + 3 \, C a^{6} b^{3} + B a^{5} b^{4} - 3 \, {\left(A - 2 \, C\right)} a^{4} b^{5} - 3 \, B a^{3} b^{6} + A a^{2} b^{7}\right)} c d^{2} + {\left(3 \, C a^{9} - B a^{8} b + 9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} - {\left(A - 10 \, C\right)} a^{5} b^{4} - 6 \, B a^{4} b^{5} + 3 \, A a^{3} b^{6}\right)} d^{3} + {\left({\left(B a^{3} b^{6} - 3 \, {\left(A - C\right)} a^{2} b^{7} - 3 \, B a b^{8} + {\left(A - C\right)} b^{9}\right)} c^{3} + 3 \, {\left({\left(A - C\right)} a^{3} b^{6} + 3 \, B a^{2} b^{7} - 3 \, {\left(A - C\right)} a b^{8} - B b^{9}\right)} c^{2} d - 3 \, {\left(C a^{6} b^{3} + 3 \, C a^{4} b^{5} + B a^{3} b^{6} - 3 \, {\left(A - 2 \, C\right)} a^{2} b^{7} - 3 \, B a b^{8} + A b^{9}\right)} c d^{2} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - {\left(A - 10 \, C\right)} a^{3} b^{6} - 6 \, B a^{2} b^{7} + 3 \, A a b^{8}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(B a^{4} b^{5} - 3 \, {\left(A - C\right)} a^{3} b^{6} - 3 \, B a^{2} b^{7} + {\left(A - C\right)} a b^{8}\right)} c^{3} + 3 \, {\left({\left(A - C\right)} a^{4} b^{5} + 3 \, B a^{3} b^{6} - 3 \, {\left(A - C\right)} a^{2} b^{7} - B a b^{8}\right)} c^{2} d - 3 \, {\left(C a^{7} b^{2} + 3 \, C a^{5} b^{4} + B a^{4} b^{5} - 3 \, {\left(A - 2 \, C\right)} a^{3} b^{6} - 3 \, B a^{2} b^{7} + A a b^{8}\right)} c d^{2} + {\left(3 \, C a^{8} b - B a^{7} b^{2} + 9 \, C a^{6} b^{3} - 3 \, B a^{5} b^{4} - {\left(A - 10 \, C\right)} a^{4} b^{5} - 6 \, B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(3 \, {\left(C a^{8} b + 3 \, C a^{6} b^{3} + 3 \, C a^{4} b^{5} + C a^{2} b^{7}\right)} c d^{2} - {\left(3 \, C a^{9} - B a^{8} b + 9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - B a^{2} b^{7}\right)} d^{3} + {\left(3 \, {\left(C a^{6} b^{3} + 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} + C b^{9}\right)} c d^{2} - {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} + 3 \, C a b^{8} - B b^{9}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(C a^{7} b^{2} + 3 \, C a^{5} b^{4} + 3 \, C a^{3} b^{6} + C a b^{8}\right)} c d^{2} - {\left(3 \, C a^{8} b - B a^{7} b^{2} + 9 \, C a^{6} b^{3} - 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} + 3 \, C a^{2} b^{7} - B a b^{8}\right)} d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left({\left(C a^{5} b^{4} - 2 \, B a^{4} b^{5} + 3 \, {\left(A - C\right)} a^{3} b^{6} + 3 \, B a^{2} b^{7} - {\left(3 \, A - 2 \, C\right)} a b^{8} - B b^{9}\right)} c^{3} + 3 \, {\left(B a^{5} b^{4} - {\left(2 \, A - 3 \, C\right)} a^{4} b^{5} - 3 \, B a^{3} b^{6} + 3 \, {\left(A - C\right)} a^{2} b^{7} + 2 \, B a b^{8} - A b^{9}\right)} c^{2} d - 3 \, {\left(C a^{7} b^{2} - {\left(A - 3 \, C\right)} a^{5} b^{4} - 3 \, B a^{4} b^{5} + {\left(3 \, A - 4 \, C\right)} a^{3} b^{6} + 3 \, B a^{2} b^{7} - 2 \, A a b^{8}\right)} c d^{2} + {\left(3 \, C a^{8} b - B a^{7} b^{2} + 6 \, C a^{6} b^{3} - 3 \, B a^{5} b^{4} + {\left(3 \, A - 2 \, C\right)} a^{4} b^{5} + 4 \, B a^{3} b^{6} - {\left(3 \, A - C\right)} a^{2} b^{7}\right)} d^{3} + 2 \, {\left({\left({\left(A - C\right)} a^{4} b^{5} + 3 \, B a^{3} b^{6} - 3 \, {\left(A - C\right)} a^{2} b^{7} - B a b^{8}\right)} c^{3} - 3 \, {\left(B a^{4} b^{5} - 3 \, {\left(A - C\right)} a^{3} b^{6} - 3 \, B a^{2} b^{7} + {\left(A - C\right)} a b^{8}\right)} c^{2} d - 3 \, {\left({\left(A - C\right)} a^{4} b^{5} + 3 \, B a^{3} b^{6} - 3 \, {\left(A - C\right)} a^{2} b^{7} - B a b^{8}\right)} c d^{2} + {\left(B a^{4} b^{5} - 3 \, {\left(A - C\right)} a^{3} b^{6} - 3 \, B a^{2} b^{7} + {\left(A - C\right)} a b^{8}\right)} d^{3}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{6} b^{6} + 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} + b^{12}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{7} b^{5} + 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} + a b^{11}\right)} f \tan\left(f x + e\right) + {\left(a^{8} b^{4} + 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} + a^{2} b^{10}\right)} f\right)}}"," ",0,"1/2*(2*(C*a^6*b^3 + 3*C*a^4*b^5 + 3*C*a^2*b^7 + C*b^9)*d^3*tan(f*x + e)^3 - (3*C*a^4*b^5 - 5*B*a^3*b^6 + (7*A - 3*C)*a^2*b^7 + B*a*b^8 + A*b^9)*c^3 + 3*(C*a^5*b^4 - 3*B*a^4*b^5 + 5*(A - C)*a^3*b^6 + 3*B*a^2*b^7 - A*a*b^8)*c^2*d + 3*(C*a^6*b^3 + B*a^5*b^4 - (3*A - 7*C)*a^4*b^5 - 5*B*a^3*b^6 + 3*A*a^2*b^7)*c*d^2 - (3*C*a^7*b^2 - B*a^6*b^3 - (A - 9*C)*a^5*b^4 - 7*B*a^4*b^5 + 5*A*a^3*b^6)*d^3 + 2*(((A - C)*a^5*b^4 + 3*B*a^4*b^5 - 3*(A - C)*a^3*b^6 - B*a^2*b^7)*c^3 - 3*(B*a^5*b^4 - 3*(A - C)*a^4*b^5 - 3*B*a^3*b^6 + (A - C)*a^2*b^7)*c^2*d - 3*((A - C)*a^5*b^4 + 3*B*a^4*b^5 - 3*(A - C)*a^3*b^6 - B*a^2*b^7)*c*d^2 + (B*a^5*b^4 - 3*(A - C)*a^4*b^5 - 3*B*a^3*b^6 + (A - C)*a^2*b^7)*d^3)*f*x + ((C*a^4*b^5 - 3*B*a^3*b^6 + 5*(A - C)*a^2*b^7 + 3*B*a*b^8 - A*b^9)*c^3 + 3*(C*a^5*b^4 + B*a^4*b^5 - (3*A - 7*C)*a^3*b^6 - 5*B*a^2*b^7 + 3*A*a*b^8)*c^2*d - 3*(3*C*a^6*b^3 - B*a^5*b^4 - (A - 9*C)*a^4*b^5 - 7*B*a^3*b^6 + 5*A*a^2*b^7)*c*d^2 + (9*C*a^7*b^2 - 3*B*a^6*b^3 + (A + 23*C)*a^5*b^4 - 9*B*a^4*b^5 + (7*A + 12*C)*a^3*b^6 + 4*C*a*b^8)*d^3 + 2*(((A - C)*a^3*b^6 + 3*B*a^2*b^7 - 3*(A - C)*a*b^8 - B*b^9)*c^3 - 3*(B*a^3*b^6 - 3*(A - C)*a^2*b^7 - 3*B*a*b^8 + (A - C)*b^9)*c^2*d - 3*((A - C)*a^3*b^6 + 3*B*a^2*b^7 - 3*(A - C)*a*b^8 - B*b^9)*c*d^2 + (B*a^3*b^6 - 3*(A - C)*a^2*b^7 - 3*B*a*b^8 + (A - C)*b^9)*d^3)*f*x)*tan(f*x + e)^2 - ((B*a^5*b^4 - 3*(A - C)*a^4*b^5 - 3*B*a^3*b^6 + (A - C)*a^2*b^7)*c^3 + 3*((A - C)*a^5*b^4 + 3*B*a^4*b^5 - 3*(A - C)*a^3*b^6 - B*a^2*b^7)*c^2*d - 3*(C*a^8*b + 3*C*a^6*b^3 + B*a^5*b^4 - 3*(A - 2*C)*a^4*b^5 - 3*B*a^3*b^6 + A*a^2*b^7)*c*d^2 + (3*C*a^9 - B*a^8*b + 9*C*a^7*b^2 - 3*B*a^6*b^3 - (A - 10*C)*a^5*b^4 - 6*B*a^4*b^5 + 3*A*a^3*b^6)*d^3 + ((B*a^3*b^6 - 3*(A - C)*a^2*b^7 - 3*B*a*b^8 + (A - C)*b^9)*c^3 + 3*((A - C)*a^3*b^6 + 3*B*a^2*b^7 - 3*(A - C)*a*b^8 - B*b^9)*c^2*d - 3*(C*a^6*b^3 + 3*C*a^4*b^5 + B*a^3*b^6 - 3*(A - 2*C)*a^2*b^7 - 3*B*a*b^8 + A*b^9)*c*d^2 + (3*C*a^7*b^2 - B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - (A - 10*C)*a^3*b^6 - 6*B*a^2*b^7 + 3*A*a*b^8)*d^3)*tan(f*x + e)^2 + 2*((B*a^4*b^5 - 3*(A - C)*a^3*b^6 - 3*B*a^2*b^7 + (A - C)*a*b^8)*c^3 + 3*((A - C)*a^4*b^5 + 3*B*a^3*b^6 - 3*(A - C)*a^2*b^7 - B*a*b^8)*c^2*d - 3*(C*a^7*b^2 + 3*C*a^5*b^4 + B*a^4*b^5 - 3*(A - 2*C)*a^3*b^6 - 3*B*a^2*b^7 + A*a*b^8)*c*d^2 + (3*C*a^8*b - B*a^7*b^2 + 9*C*a^6*b^3 - 3*B*a^5*b^4 - (A - 10*C)*a^4*b^5 - 6*B*a^3*b^6 + 3*A*a^2*b^7)*d^3)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (3*(C*a^8*b + 3*C*a^6*b^3 + 3*C*a^4*b^5 + C*a^2*b^7)*c*d^2 - (3*C*a^9 - B*a^8*b + 9*C*a^7*b^2 - 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 + 3*C*a^3*b^6 - B*a^2*b^7)*d^3 + (3*(C*a^6*b^3 + 3*C*a^4*b^5 + 3*C*a^2*b^7 + C*b^9)*c*d^2 - (3*C*a^7*b^2 - B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 + 3*C*a*b^8 - B*b^9)*d^3)*tan(f*x + e)^2 + 2*(3*(C*a^7*b^2 + 3*C*a^5*b^4 + 3*C*a^3*b^6 + C*a*b^8)*c*d^2 - (3*C*a^8*b - B*a^7*b^2 + 9*C*a^6*b^3 - 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 + 3*C*a^2*b^7 - B*a*b^8)*d^3)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) + 2*((C*a^5*b^4 - 2*B*a^4*b^5 + 3*(A - C)*a^3*b^6 + 3*B*a^2*b^7 - (3*A - 2*C)*a*b^8 - B*b^9)*c^3 + 3*(B*a^5*b^4 - (2*A - 3*C)*a^4*b^5 - 3*B*a^3*b^6 + 3*(A - C)*a^2*b^7 + 2*B*a*b^8 - A*b^9)*c^2*d - 3*(C*a^7*b^2 - (A - 3*C)*a^5*b^4 - 3*B*a^4*b^5 + (3*A - 4*C)*a^3*b^6 + 3*B*a^2*b^7 - 2*A*a*b^8)*c*d^2 + (3*C*a^8*b - B*a^7*b^2 + 6*C*a^6*b^3 - 3*B*a^5*b^4 + (3*A - 2*C)*a^4*b^5 + 4*B*a^3*b^6 - (3*A - C)*a^2*b^7)*d^3 + 2*(((A - C)*a^4*b^5 + 3*B*a^3*b^6 - 3*(A - C)*a^2*b^7 - B*a*b^8)*c^3 - 3*(B*a^4*b^5 - 3*(A - C)*a^3*b^6 - 3*B*a^2*b^7 + (A - C)*a*b^8)*c^2*d - 3*((A - C)*a^4*b^5 + 3*B*a^3*b^6 - 3*(A - C)*a^2*b^7 - B*a*b^8)*c*d^2 + (B*a^4*b^5 - 3*(A - C)*a^3*b^6 - 3*B*a^2*b^7 + (A - C)*a*b^8)*d^3)*f*x)*tan(f*x + e))/((a^6*b^6 + 3*a^4*b^8 + 3*a^2*b^10 + b^12)*f*tan(f*x + e)^2 + 2*(a^7*b^5 + 3*a^5*b^7 + 3*a^3*b^9 + a*b^11)*f*tan(f*x + e) + (a^8*b^4 + 3*a^6*b^6 + 3*a^4*b^8 + a^2*b^10)*f)","B",0
70,1,627,0,2.732484," ","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=""fricas"")","\frac{2 \, {\left(C b^{3} c^{2} d^{3} + C b^{3} d^{5}\right)} \tan\left(f x + e\right)^{3} + 6 \, {\left({\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c d^{4} + {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} d^{5}\right)} f x - 3 \, {\left(C b^{3} c^{3} d^{2} + C b^{3} c d^{4} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2} d^{3} - {\left(3 \, C a b^{2} + B b^{3}\right)} d^{5}\right)} \tan\left(f x + e\right)^{2} - 3 \, {\left(C b^{3} c^{5} - A a^{3} d^{5} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4} d + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{3} d^{2} - {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{4}\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + 3 \, {\left(C b^{3} c^{5} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4} d + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{3} d^{2} - {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A - C\right)} b^{3}\right)} c d^{4} - {\left(C a^{3} + 3 \, B a^{2} b + 3 \, {\left(A - C\right)} a b^{2} - B b^{3}\right)} d^{5}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(C b^{3} c^{4} d - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3} d^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{2} d^{3} - {\left(3 \, C a b^{2} + B b^{3}\right)} c d^{4} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A - C\right)} b^{3}\right)} d^{5}\right)} \tan\left(f x + e\right)}{6 \, {\left(c^{2} d^{4} + d^{6}\right)} f}"," ",0,"1/6*(2*(C*b^3*c^2*d^3 + C*b^3*d^5)*tan(f*x + e)^3 + 6*(((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c*d^4 + (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*d^5)*f*x - 3*(C*b^3*c^3*d^2 + C*b^3*c*d^4 - (3*C*a*b^2 + B*b^3)*c^2*d^3 - (3*C*a*b^2 + B*b^3)*d^5)*tan(f*x + e)^2 - 3*(C*b^3*c^5 - A*a^3*d^5 - (3*C*a*b^2 + B*b^3)*c^4*d + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^3*d^2 - (C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^3 + (B*a^3 + 3*A*a^2*b)*c*d^4)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) + 3*(C*b^3*c^5 - (3*C*a*b^2 + B*b^3)*c^4*d + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^3*d^2 - (C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^3 + (3*C*a^2*b + 3*B*a*b^2 + (A - C)*b^3)*c*d^4 - (C*a^3 + 3*B*a^2*b + 3*(A - C)*a*b^2 - B*b^3)*d^5)*log(1/(tan(f*x + e)^2 + 1)) + 6*(C*b^3*c^4*d - (3*C*a*b^2 + B*b^3)*c^3*d^2 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^2*d^3 - (3*C*a*b^2 + B*b^3)*c*d^4 + (3*C*a^2*b + 3*B*a*b^2 + (A - C)*b^3)*d^5)*tan(f*x + e))/((c^2*d^4 + d^6)*f)","A",0
71,1,390,0,1.174479," ","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=""fricas"")","\frac{2 \, {\left({\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c d^{3} + {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} d^{4}\right)} f x + {\left(C b^{2} c^{2} d^{2} + C b^{2} d^{4}\right)} \tan\left(f x + e\right)^{2} + {\left(C b^{2} c^{4} + A a^{2} d^{4} - {\left(2 \, C a b + B b^{2}\right)} c^{3} d + {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{2} - {\left(B a^{2} + 2 \, A a b\right)} c d^{3}\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(C b^{2} c^{4} - {\left(2 \, C a b + B b^{2}\right)} c^{3} d + {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{2} - {\left(2 \, C a b + B b^{2}\right)} c d^{3} + {\left(C a^{2} + 2 \, B a b + {\left(A - C\right)} b^{2}\right)} d^{4}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(C b^{2} c^{3} d + C b^{2} c d^{3} - {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{2} - {\left(2 \, C a b + B b^{2}\right)} d^{4}\right)} \tan\left(f x + e\right)}{2 \, {\left(c^{2} d^{3} + d^{5}\right)} f}"," ",0,"1/2*(2*(((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c*d^3 + (B*a^2 + 2*(A - C)*a*b - B*b^2)*d^4)*f*x + (C*b^2*c^2*d^2 + C*b^2*d^4)*tan(f*x + e)^2 + (C*b^2*c^4 + A*a^2*d^4 - (2*C*a*b + B*b^2)*c^3*d + (C*a^2 + 2*B*a*b + A*b^2)*c^2*d^2 - (B*a^2 + 2*A*a*b)*c*d^3)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (C*b^2*c^4 - (2*C*a*b + B*b^2)*c^3*d + (C*a^2 + 2*B*a*b + A*b^2)*c^2*d^2 - (2*C*a*b + B*b^2)*c*d^3 + (C*a^2 + 2*B*a*b + (A - C)*b^2)*d^4)*log(1/(tan(f*x + e)^2 + 1)) - 2*(C*b^2*c^3*d + C*b^2*c*d^3 - (2*C*a*b + B*b^2)*c^2*d^2 - (2*C*a*b + B*b^2)*d^4)*tan(f*x + e))/((c^2*d^3 + d^5)*f)","A",0
72,1,212,0,0.846162," ","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=""fricas"")","\frac{2 \, {\left({\left({\left(A - C\right)} a - B b\right)} c d^{2} + {\left(B a + {\left(A - C\right)} b\right)} d^{3}\right)} f x - {\left(C b c^{3} - A a d^{3} - {\left(C a + B b\right)} c^{2} d + {\left(B a + A b\right)} c d^{2}\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(C b c^{3} + C b c d^{2} - {\left(C a + B b\right)} c^{2} d - {\left(C a + B b\right)} d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(C b c^{2} d + C b d^{3}\right)} \tan\left(f x + e\right)}{2 \, {\left(c^{2} d^{2} + d^{4}\right)} f}"," ",0,"1/2*(2*(((A - C)*a - B*b)*c*d^2 + (B*a + (A - C)*b)*d^3)*f*x - (C*b*c^3 - A*a*d^3 - (C*a + B*b)*c^2*d + (B*a + A*b)*c*d^2)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) + (C*b*c^3 + C*b*c*d^2 - (C*a + B*b)*c^2*d - (C*a + B*b)*d^3)*log(1/(tan(f*x + e)^2 + 1)) + 2*(C*b*c^2*d + C*b*d^3)*tan(f*x + e))/((c^2*d^2 + d^4)*f)","A",0
73,1,118,0,1.177271," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(A - C\right)} c d + B d^{2}\right)} f x + {\left(C c^{2} - B c d + A d^{2}\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(C c^{2} + C d^{2}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, {\left(c^{2} d + d^{3}\right)} f}"," ",0,"1/2*(2*((A - C)*c*d + B*d^2)*f*x + (C*c^2 - B*c*d + A*d^2)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (C*c^2 + C*d^2)*log(1/(tan(f*x + e)^2 + 1)))/((c^2*d + d^3)*f)","A",0
74,1,301,0,0.922253," ","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=""fricas"")","\frac{2 \, {\left({\left({\left(A - C\right)} a b + B b^{2}\right)} c^{2} - {\left({\left(A - C\right)} a^{2} + {\left(A - C\right)} b^{2}\right)} c d - {\left(B a^{2} - {\left(A - C\right)} a b\right)} d^{2}\right)} f x + {\left({\left(C a^{2} - B a b + A b^{2}\right)} c^{2} + {\left(C a^{2} - B a b + A b^{2}\right)} d^{2}\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left({\left(C a^{2} + C b^{2}\right)} c^{2} - {\left(B a^{2} + B b^{2}\right)} c d + {\left(A a^{2} + A b^{2}\right)} d^{2}\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, {\left({\left(a^{2} b + b^{3}\right)} c^{3} - {\left(a^{3} + a b^{2}\right)} c^{2} d + {\left(a^{2} b + b^{3}\right)} c d^{2} - {\left(a^{3} + a b^{2}\right)} d^{3}\right)} f}"," ",0,"1/2*(2*(((A - C)*a*b + B*b^2)*c^2 - ((A - C)*a^2 + (A - C)*b^2)*c*d - (B*a^2 - (A - C)*a*b)*d^2)*f*x + ((C*a^2 - B*a*b + A*b^2)*c^2 + (C*a^2 - B*a*b + A*b^2)*d^2)*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - ((C*a^2 + C*b^2)*c^2 - (B*a^2 + B*b^2)*c*d + (A*a^2 + A*b^2)*d^2)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)))/(((a^2*b + b^3)*c^3 - (a^3 + a*b^2)*c^2*d + (a^2*b + b^3)*c*d^2 - (a^3 + a*b^2)*d^3)*f)","A",0
75,1,1345,0,2.537008," ","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=""fricas"")","-\frac{2 \, {\left(C a^{2} b^{3} - B a b^{4} + A b^{5}\right)} c^{3} - 2 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} c^{2} d + 2 \, {\left(C a^{2} b^{3} - B a b^{4} + A b^{5}\right)} c d^{2} - 2 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} d^{3} - 2 \, {\left({\left({\left(A - C\right)} a^{3} b^{2} + 2 \, B a^{2} b^{3} - {\left(A - C\right)} a b^{4}\right)} c^{3} - {\left(2 \, {\left(A - C\right)} a^{4} b + 3 \, B a^{3} b^{2} + B a b^{4}\right)} c^{2} d + {\left({\left(A - C\right)} a^{5} + 3 \, {\left(A - C\right)} a^{3} b^{2} + 2 \, B a^{2} b^{3}\right)} c d^{2} + {\left(B a^{5} - 2 \, {\left(A - C\right)} a^{4} b - B a^{3} b^{2}\right)} d^{3}\right)} f x + {\left({\left(B a^{3} b^{2} - 2 \, {\left(A - C\right)} a^{2} b^{3} - B a b^{4}\right)} c^{3} + {\left(C a^{5} - 2 \, B a^{4} b + {\left(3 \, A - C\right)} a^{3} b^{2} + A a b^{4}\right)} c^{2} d + {\left(B a^{3} b^{2} - 2 \, {\left(A - C\right)} a^{2} b^{3} - B a b^{4}\right)} c d^{2} + {\left(C a^{5} - 2 \, B a^{4} b + {\left(3 \, A - C\right)} a^{3} b^{2} + A a b^{4}\right)} d^{3} + {\left({\left(B a^{2} b^{3} - 2 \, {\left(A - C\right)} a b^{4} - B b^{5}\right)} c^{3} + {\left(C a^{4} b - 2 \, B a^{3} b^{2} + {\left(3 \, A - C\right)} a^{2} b^{3} + A b^{5}\right)} c^{2} d + {\left(B a^{2} b^{3} - 2 \, {\left(A - C\right)} a b^{4} - B b^{5}\right)} c d^{2} + {\left(C a^{4} b - 2 \, B a^{3} b^{2} + {\left(3 \, A - C\right)} a^{2} b^{3} + A b^{5}\right)} d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left({\left(C a^{5} + 2 \, C a^{3} b^{2} + C a b^{4}\right)} c^{2} d - {\left(B a^{5} + 2 \, B a^{3} b^{2} + B a b^{4}\right)} c d^{2} + {\left(A a^{5} + 2 \, A a^{3} b^{2} + A a b^{4}\right)} d^{3} + {\left({\left(C a^{4} b + 2 \, C a^{2} b^{3} + C b^{5}\right)} c^{2} d - {\left(B a^{4} b + 2 \, B a^{2} b^{3} + B b^{5}\right)} c d^{2} + {\left(A a^{4} b + 2 \, A a^{2} b^{3} + A b^{5}\right)} d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left({\left(C a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} c^{3} - {\left(C a^{4} b - B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{2} d + {\left(C a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} c d^{2} - {\left(C a^{4} b - B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} + {\left({\left({\left(A - C\right)} a^{2} b^{3} + 2 \, B a b^{4} - {\left(A - C\right)} b^{5}\right)} c^{3} - {\left(2 \, {\left(A - C\right)} a^{3} b^{2} + 3 \, B a^{2} b^{3} + B b^{5}\right)} c^{2} d + {\left({\left(A - C\right)} a^{4} b + 3 \, {\left(A - C\right)} a^{2} b^{3} + 2 \, B a b^{4}\right)} c d^{2} + {\left(B a^{4} b - 2 \, {\left(A - C\right)} a^{3} b^{2} - B a^{2} b^{3}\right)} d^{3}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} c^{4} - 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{3} d + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} c^{2} d^{2} - 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c d^{3} + {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{4}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{4} - 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} d + {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} c^{2} d^{2} - 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c d^{3} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{4}\right)} f\right)}}"," ",0,"-1/2*(2*(C*a^2*b^3 - B*a*b^4 + A*b^5)*c^3 - 2*(C*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*c^2*d + 2*(C*a^2*b^3 - B*a*b^4 + A*b^5)*c*d^2 - 2*(C*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*d^3 - 2*(((A - C)*a^3*b^2 + 2*B*a^2*b^3 - (A - C)*a*b^4)*c^3 - (2*(A - C)*a^4*b + 3*B*a^3*b^2 + B*a*b^4)*c^2*d + ((A - C)*a^5 + 3*(A - C)*a^3*b^2 + 2*B*a^2*b^3)*c*d^2 + (B*a^5 - 2*(A - C)*a^4*b - B*a^3*b^2)*d^3)*f*x + ((B*a^3*b^2 - 2*(A - C)*a^2*b^3 - B*a*b^4)*c^3 + (C*a^5 - 2*B*a^4*b + (3*A - C)*a^3*b^2 + A*a*b^4)*c^2*d + (B*a^3*b^2 - 2*(A - C)*a^2*b^3 - B*a*b^4)*c*d^2 + (C*a^5 - 2*B*a^4*b + (3*A - C)*a^3*b^2 + A*a*b^4)*d^3 + ((B*a^2*b^3 - 2*(A - C)*a*b^4 - B*b^5)*c^3 + (C*a^4*b - 2*B*a^3*b^2 + (3*A - C)*a^2*b^3 + A*b^5)*c^2*d + (B*a^2*b^3 - 2*(A - C)*a*b^4 - B*b^5)*c*d^2 + (C*a^4*b - 2*B*a^3*b^2 + (3*A - C)*a^2*b^3 + A*b^5)*d^3)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - ((C*a^5 + 2*C*a^3*b^2 + C*a*b^4)*c^2*d - (B*a^5 + 2*B*a^3*b^2 + B*a*b^4)*c*d^2 + (A*a^5 + 2*A*a^3*b^2 + A*a*b^4)*d^3 + ((C*a^4*b + 2*C*a^2*b^3 + C*b^5)*c^2*d - (B*a^4*b + 2*B*a^2*b^3 + B*b^5)*c*d^2 + (A*a^4*b + 2*A*a^2*b^3 + A*b^5)*d^3)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*((C*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*c^3 - (C*a^4*b - B*a^3*b^2 + A*a^2*b^3)*c^2*d + (C*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*c*d^2 - (C*a^4*b - B*a^3*b^2 + A*a^2*b^3)*d^3 + (((A - C)*a^2*b^3 + 2*B*a*b^4 - (A - C)*b^5)*c^3 - (2*(A - C)*a^3*b^2 + 3*B*a^2*b^3 + B*b^5)*c^2*d + ((A - C)*a^4*b + 3*(A - C)*a^2*b^3 + 2*B*a*b^4)*c*d^2 + (B*a^4*b - 2*(A - C)*a^3*b^2 - B*a^2*b^3)*d^3)*f*x)*tan(f*x + e))/(((a^4*b^3 + 2*a^2*b^5 + b^7)*c^4 - 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^3*d + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*c^2*d^2 - 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c*d^3 + (a^6*b + 2*a^4*b^3 + a^2*b^5)*d^4)*f*tan(f*x + e) + ((a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^4 - 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*c^3*d + (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*c^2*d^2 - 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*c*d^3 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d^4)*f)","B",0
76,1,3643,0,7.175036," ","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=""fricas"")","-\frac{{\left(3 \, C a^{4} b^{4} - 5 \, B a^{3} b^{5} + {\left(7 \, A - 3 \, C\right)} a^{2} b^{6} + B a b^{7} + A b^{8}\right)} c^{4} - 4 \, {\left(2 \, C a^{5} b^{3} - 3 \, B a^{4} b^{4} + {\left(4 \, A - C\right)} a^{3} b^{5} + A a b^{7}\right)} c^{3} d + {\left(5 \, C a^{6} b^{2} - 7 \, B a^{5} b^{3} + {\left(9 \, A + 2 \, C\right)} a^{4} b^{4} - 6 \, B a^{3} b^{5} + {\left(10 \, A - 3 \, C\right)} a^{2} b^{6} + B a b^{7} + A b^{8}\right)} c^{2} d^{2} - 4 \, {\left(2 \, C a^{5} b^{3} - 3 \, B a^{4} b^{4} + {\left(4 \, A - C\right)} a^{3} b^{5} + A a b^{7}\right)} c d^{3} + {\left(5 \, C a^{6} b^{2} - 7 \, B a^{5} b^{3} + {\left(9 \, A - C\right)} a^{4} b^{4} - B a^{3} b^{5} + 3 \, A a^{2} b^{6}\right)} d^{4} - 2 \, {\left({\left({\left(A - C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} - 3 \, {\left(A - C\right)} a^{3} b^{5} - B a^{2} b^{6}\right)} c^{4} - {\left(3 \, {\left(A - C\right)} a^{6} b^{2} + 8 \, B a^{5} b^{3} - 6 \, {\left(A - C\right)} a^{4} b^{4} - {\left(A - C\right)} a^{2} b^{6}\right)} c^{3} d + 3 \, {\left({\left(A - C\right)} a^{7} b + 2 \, B a^{6} b^{2} + 2 \, B a^{4} b^{4} - {\left(A - C\right)} a^{3} b^{5}\right)} c^{2} d^{2} - {\left({\left(A - C\right)} a^{8} + 6 \, {\left(A - C\right)} a^{6} b^{2} + 8 \, B a^{5} b^{3} - 3 \, {\left(A - C\right)} a^{4} b^{4}\right)} c d^{3} - {\left(B a^{8} - 3 \, {\left(A - C\right)} a^{7} b - 3 \, B a^{6} b^{2} + {\left(A - C\right)} a^{5} b^{3}\right)} d^{4}\right)} f x - {\left({\left(C a^{4} b^{4} - 3 \, B a^{3} b^{5} + 5 \, {\left(A - C\right)} a^{2} b^{6} + 3 \, B a b^{7} - A b^{8}\right)} c^{4} - 4 \, {\left(C a^{5} b^{3} - 2 \, B a^{4} b^{4} + {\left(3 \, A - 2 \, C\right)} a^{3} b^{5} + B a^{2} b^{6}\right)} c^{3} d + {\left(3 \, C a^{6} b^{2} - 5 \, B a^{5} b^{3} + {\left(7 \, A - 2 \, C\right)} a^{4} b^{4} - 2 \, B a^{3} b^{5} + {\left(6 \, A - 5 \, C\right)} a^{2} b^{6} + 3 \, B a b^{7} - A b^{8}\right)} c^{2} d^{2} - 4 \, {\left(C a^{5} b^{3} - 2 \, B a^{4} b^{4} + {\left(3 \, A - 2 \, C\right)} a^{3} b^{5} + B a^{2} b^{6}\right)} c d^{3} + {\left(3 \, C a^{6} b^{2} - 5 \, B a^{5} b^{3} + {\left(7 \, A - 3 \, C\right)} a^{4} b^{4} + B a^{3} b^{5} + A a^{2} b^{6}\right)} d^{4} + 2 \, {\left({\left({\left(A - C\right)} a^{3} b^{5} + 3 \, B a^{2} b^{6} - 3 \, {\left(A - C\right)} a b^{7} - B b^{8}\right)} c^{4} - {\left(3 \, {\left(A - C\right)} a^{4} b^{4} + 8 \, B a^{3} b^{5} - 6 \, {\left(A - C\right)} a^{2} b^{6} - {\left(A - C\right)} b^{8}\right)} c^{3} d + 3 \, {\left({\left(A - C\right)} a^{5} b^{3} + 2 \, B a^{4} b^{4} + 2 \, B a^{2} b^{6} - {\left(A - C\right)} a b^{7}\right)} c^{2} d^{2} - {\left({\left(A - C\right)} a^{6} b^{2} + 6 \, {\left(A - C\right)} a^{4} b^{4} + 8 \, B a^{3} b^{5} - 3 \, {\left(A - C\right)} a^{2} b^{6}\right)} c d^{3} - {\left(B a^{6} b^{2} - 3 \, {\left(A - C\right)} a^{5} b^{3} - 3 \, B a^{4} b^{4} + {\left(A - C\right)} a^{3} b^{5}\right)} d^{4}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left({\left(B a^{5} b^{3} - 3 \, {\left(A - C\right)} a^{4} b^{4} - 3 \, B a^{3} b^{5} + {\left(A - C\right)} a^{2} b^{6}\right)} c^{4} - {\left(3 \, B a^{6} b^{2} - 8 \, {\left(A - C\right)} a^{5} b^{3} - 6 \, B a^{4} b^{4} - B a^{2} b^{6}\right)} c^{3} d - {\left(C a^{8} - 3 \, B a^{7} b + 3 \, {\left(2 \, A - C\right)} a^{6} b^{2} + 3 \, {\left(2 \, A - C\right)} a^{4} b^{4} + 3 \, B a^{3} b^{5} + C a^{2} b^{6}\right)} c^{2} d^{2} - {\left(3 \, B a^{6} b^{2} - 8 \, {\left(A - C\right)} a^{5} b^{3} - 6 \, B a^{4} b^{4} - B a^{2} b^{6}\right)} c d^{3} - {\left(C a^{8} - 3 \, B a^{7} b + 3 \, {\left(2 \, A - C\right)} a^{6} b^{2} + B a^{5} b^{3} + 3 \, A a^{4} b^{4} + A a^{2} b^{6}\right)} d^{4} + {\left({\left(B a^{3} b^{5} - 3 \, {\left(A - C\right)} a^{2} b^{6} - 3 \, B a b^{7} + {\left(A - C\right)} b^{8}\right)} c^{4} - {\left(3 \, B a^{4} b^{4} - 8 \, {\left(A - C\right)} a^{3} b^{5} - 6 \, B a^{2} b^{6} - B b^{8}\right)} c^{3} d - {\left(C a^{6} b^{2} - 3 \, B a^{5} b^{3} + 3 \, {\left(2 \, A - C\right)} a^{4} b^{4} + 3 \, {\left(2 \, A - C\right)} a^{2} b^{6} + 3 \, B a b^{7} + C b^{8}\right)} c^{2} d^{2} - {\left(3 \, B a^{4} b^{4} - 8 \, {\left(A - C\right)} a^{3} b^{5} - 6 \, B a^{2} b^{6} - B b^{8}\right)} c d^{3} - {\left(C a^{6} b^{2} - 3 \, B a^{5} b^{3} + 3 \, {\left(2 \, A - C\right)} a^{4} b^{4} + B a^{3} b^{5} + 3 \, A a^{2} b^{6} + A b^{8}\right)} d^{4}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(B a^{4} b^{4} - 3 \, {\left(A - C\right)} a^{3} b^{5} - 3 \, B a^{2} b^{6} + {\left(A - C\right)} a b^{7}\right)} c^{4} - {\left(3 \, B a^{5} b^{3} - 8 \, {\left(A - C\right)} a^{4} b^{4} - 6 \, B a^{3} b^{5} - B a b^{7}\right)} c^{3} d - {\left(C a^{7} b - 3 \, B a^{6} b^{2} + 3 \, {\left(2 \, A - C\right)} a^{5} b^{3} + 3 \, {\left(2 \, A - C\right)} a^{3} b^{5} + 3 \, B a^{2} b^{6} + C a b^{7}\right)} c^{2} d^{2} - {\left(3 \, B a^{5} b^{3} - 8 \, {\left(A - C\right)} a^{4} b^{4} - 6 \, B a^{3} b^{5} - B a b^{7}\right)} c d^{3} - {\left(C a^{7} b - 3 \, B a^{6} b^{2} + 3 \, {\left(2 \, A - C\right)} a^{5} b^{3} + B a^{4} b^{4} + 3 \, A a^{3} b^{5} + A a b^{7}\right)} d^{4}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left({\left(C a^{8} + 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} + C a^{2} b^{6}\right)} c^{2} d^{2} - {\left(B a^{8} + 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} + B a^{2} b^{6}\right)} c d^{3} + {\left(A a^{8} + 3 \, A a^{6} b^{2} + 3 \, A a^{4} b^{4} + A a^{2} b^{6}\right)} d^{4} + {\left({\left(C a^{6} b^{2} + 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} + C b^{8}\right)} c^{2} d^{2} - {\left(B a^{6} b^{2} + 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} + B b^{8}\right)} c d^{3} + {\left(A a^{6} b^{2} + 3 \, A a^{4} b^{4} + 3 \, A a^{2} b^{6} + A b^{8}\right)} d^{4}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(C a^{7} b + 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} + C a b^{7}\right)} c^{2} d^{2} - {\left(B a^{7} b + 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} + B a b^{7}\right)} c d^{3} + {\left(A a^{7} b + 3 \, A a^{5} b^{3} + 3 \, A a^{3} b^{5} + A a b^{7}\right)} d^{4}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left({\left(C a^{5} b^{3} - 2 \, B a^{4} b^{4} + 3 \, {\left(A - C\right)} a^{3} b^{5} + 3 \, B a^{2} b^{6} - {\left(3 \, A - 2 \, C\right)} a b^{7} - B b^{8}\right)} c^{4} - {\left(3 \, C a^{6} b^{2} - 5 \, B a^{5} b^{3} + {\left(7 \, A - 6 \, C\right)} a^{4} b^{4} + 6 \, B a^{3} b^{5} - 3 \, {\left(2 \, A - C\right)} a^{2} b^{6} - B a b^{7} - A b^{8}\right)} c^{3} d + {\left(2 \, C a^{7} b - 3 \, B a^{6} b^{2} + 2 \, {\left(2 \, A - C\right)} a^{5} b^{3} + B a^{4} b^{4} - 2 \, C a^{3} b^{5} + 3 \, B a^{2} b^{6} - 2 \, {\left(2 \, A - C\right)} a b^{7} - B b^{8}\right)} c^{2} d^{2} - {\left(3 \, C a^{6} b^{2} - 5 \, B a^{5} b^{3} + {\left(7 \, A - 6 \, C\right)} a^{4} b^{4} + 6 \, B a^{3} b^{5} - 3 \, {\left(2 \, A - C\right)} a^{2} b^{6} - B a b^{7} - A b^{8}\right)} c d^{3} + {\left(2 \, C a^{7} b - 3 \, B a^{6} b^{2} + {\left(4 \, A - 3 \, C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} - {\left(3 \, A - C\right)} a^{3} b^{5} - A a b^{7}\right)} d^{4} + 2 \, {\left({\left({\left(A - C\right)} a^{4} b^{4} + 3 \, B a^{3} b^{5} - 3 \, {\left(A - C\right)} a^{2} b^{6} - B a b^{7}\right)} c^{4} - {\left(3 \, {\left(A - C\right)} a^{5} b^{3} + 8 \, B a^{4} b^{4} - 6 \, {\left(A - C\right)} a^{3} b^{5} - {\left(A - C\right)} a b^{7}\right)} c^{3} d + 3 \, {\left({\left(A - C\right)} a^{6} b^{2} + 2 \, B a^{5} b^{3} + 2 \, B a^{3} b^{5} - {\left(A - C\right)} a^{2} b^{6}\right)} c^{2} d^{2} - {\left({\left(A - C\right)} a^{7} b + 6 \, {\left(A - C\right)} a^{5} b^{3} + 8 \, B a^{4} b^{4} - 3 \, {\left(A - C\right)} a^{3} b^{5}\right)} c d^{3} - {\left(B a^{7} b - 3 \, {\left(A - C\right)} a^{6} b^{2} - 3 \, B a^{5} b^{3} + {\left(A - C\right)} a^{4} b^{4}\right)} d^{4}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{6} b^{5} + 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + b^{11}\right)} c^{5} - 3 \, {\left(a^{7} b^{4} + 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} + a b^{10}\right)} c^{4} d + {\left(3 \, a^{8} b^{3} + 10 \, a^{6} b^{5} + 12 \, a^{4} b^{7} + 6 \, a^{2} b^{9} + b^{11}\right)} c^{3} d^{2} - {\left(a^{9} b^{2} + 6 \, a^{7} b^{4} + 12 \, a^{5} b^{6} + 10 \, a^{3} b^{8} + 3 \, a b^{10}\right)} c^{2} d^{3} + 3 \, {\left(a^{8} b^{3} + 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} + a^{2} b^{9}\right)} c d^{4} - {\left(a^{9} b^{2} + 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} + a^{3} b^{8}\right)} d^{5}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{7} b^{4} + 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} + a b^{10}\right)} c^{5} - 3 \, {\left(a^{8} b^{3} + 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} + a^{2} b^{9}\right)} c^{4} d + {\left(3 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 12 \, a^{5} b^{6} + 6 \, a^{3} b^{8} + a b^{10}\right)} c^{3} d^{2} - {\left(a^{10} b + 6 \, a^{8} b^{3} + 12 \, a^{6} b^{5} + 10 \, a^{4} b^{7} + 3 \, a^{2} b^{9}\right)} c^{2} d^{3} + 3 \, {\left(a^{9} b^{2} + 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} + a^{3} b^{8}\right)} c d^{4} - {\left(a^{10} b + 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} + a^{4} b^{7}\right)} d^{5}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{8} b^{3} + 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} + a^{2} b^{9}\right)} c^{5} - 3 \, {\left(a^{9} b^{2} + 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} + a^{3} b^{8}\right)} c^{4} d + {\left(3 \, a^{10} b + 10 \, a^{8} b^{3} + 12 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + a^{2} b^{9}\right)} c^{3} d^{2} - {\left(a^{11} + 6 \, a^{9} b^{2} + 12 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 3 \, a^{3} b^{8}\right)} c^{2} d^{3} + 3 \, {\left(a^{10} b + 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} + a^{4} b^{7}\right)} c d^{4} - {\left(a^{11} + 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} + a^{5} b^{6}\right)} d^{5}\right)} f\right)}}"," ",0,"-1/2*((3*C*a^4*b^4 - 5*B*a^3*b^5 + (7*A - 3*C)*a^2*b^6 + B*a*b^7 + A*b^8)*c^4 - 4*(2*C*a^5*b^3 - 3*B*a^4*b^4 + (4*A - C)*a^3*b^5 + A*a*b^7)*c^3*d + (5*C*a^6*b^2 - 7*B*a^5*b^3 + (9*A + 2*C)*a^4*b^4 - 6*B*a^3*b^5 + (10*A - 3*C)*a^2*b^6 + B*a*b^7 + A*b^8)*c^2*d^2 - 4*(2*C*a^5*b^3 - 3*B*a^4*b^4 + (4*A - C)*a^3*b^5 + A*a*b^7)*c*d^3 + (5*C*a^6*b^2 - 7*B*a^5*b^3 + (9*A - C)*a^4*b^4 - B*a^3*b^5 + 3*A*a^2*b^6)*d^4 - 2*(((A - C)*a^5*b^3 + 3*B*a^4*b^4 - 3*(A - C)*a^3*b^5 - B*a^2*b^6)*c^4 - (3*(A - C)*a^6*b^2 + 8*B*a^5*b^3 - 6*(A - C)*a^4*b^4 - (A - C)*a^2*b^6)*c^3*d + 3*((A - C)*a^7*b + 2*B*a^6*b^2 + 2*B*a^4*b^4 - (A - C)*a^3*b^5)*c^2*d^2 - ((A - C)*a^8 + 6*(A - C)*a^6*b^2 + 8*B*a^5*b^3 - 3*(A - C)*a^4*b^4)*c*d^3 - (B*a^8 - 3*(A - C)*a^7*b - 3*B*a^6*b^2 + (A - C)*a^5*b^3)*d^4)*f*x - ((C*a^4*b^4 - 3*B*a^3*b^5 + 5*(A - C)*a^2*b^6 + 3*B*a*b^7 - A*b^8)*c^4 - 4*(C*a^5*b^3 - 2*B*a^4*b^4 + (3*A - 2*C)*a^3*b^5 + B*a^2*b^6)*c^3*d + (3*C*a^6*b^2 - 5*B*a^5*b^3 + (7*A - 2*C)*a^4*b^4 - 2*B*a^3*b^5 + (6*A - 5*C)*a^2*b^6 + 3*B*a*b^7 - A*b^8)*c^2*d^2 - 4*(C*a^5*b^3 - 2*B*a^4*b^4 + (3*A - 2*C)*a^3*b^5 + B*a^2*b^6)*c*d^3 + (3*C*a^6*b^2 - 5*B*a^5*b^3 + (7*A - 3*C)*a^4*b^4 + B*a^3*b^5 + A*a^2*b^6)*d^4 + 2*(((A - C)*a^3*b^5 + 3*B*a^2*b^6 - 3*(A - C)*a*b^7 - B*b^8)*c^4 - (3*(A - C)*a^4*b^4 + 8*B*a^3*b^5 - 6*(A - C)*a^2*b^6 - (A - C)*b^8)*c^3*d + 3*((A - C)*a^5*b^3 + 2*B*a^4*b^4 + 2*B*a^2*b^6 - (A - C)*a*b^7)*c^2*d^2 - ((A - C)*a^6*b^2 + 6*(A - C)*a^4*b^4 + 8*B*a^3*b^5 - 3*(A - C)*a^2*b^6)*c*d^3 - (B*a^6*b^2 - 3*(A - C)*a^5*b^3 - 3*B*a^4*b^4 + (A - C)*a^3*b^5)*d^4)*f*x)*tan(f*x + e)^2 + ((B*a^5*b^3 - 3*(A - C)*a^4*b^4 - 3*B*a^3*b^5 + (A - C)*a^2*b^6)*c^4 - (3*B*a^6*b^2 - 8*(A - C)*a^5*b^3 - 6*B*a^4*b^4 - B*a^2*b^6)*c^3*d - (C*a^8 - 3*B*a^7*b + 3*(2*A - C)*a^6*b^2 + 3*(2*A - C)*a^4*b^4 + 3*B*a^3*b^5 + C*a^2*b^6)*c^2*d^2 - (3*B*a^6*b^2 - 8*(A - C)*a^5*b^3 - 6*B*a^4*b^4 - B*a^2*b^6)*c*d^3 - (C*a^8 - 3*B*a^7*b + 3*(2*A - C)*a^6*b^2 + B*a^5*b^3 + 3*A*a^4*b^4 + A*a^2*b^6)*d^4 + ((B*a^3*b^5 - 3*(A - C)*a^2*b^6 - 3*B*a*b^7 + (A - C)*b^8)*c^4 - (3*B*a^4*b^4 - 8*(A - C)*a^3*b^5 - 6*B*a^2*b^6 - B*b^8)*c^3*d - (C*a^6*b^2 - 3*B*a^5*b^3 + 3*(2*A - C)*a^4*b^4 + 3*(2*A - C)*a^2*b^6 + 3*B*a*b^7 + C*b^8)*c^2*d^2 - (3*B*a^4*b^4 - 8*(A - C)*a^3*b^5 - 6*B*a^2*b^6 - B*b^8)*c*d^3 - (C*a^6*b^2 - 3*B*a^5*b^3 + 3*(2*A - C)*a^4*b^4 + B*a^3*b^5 + 3*A*a^2*b^6 + A*b^8)*d^4)*tan(f*x + e)^2 + 2*((B*a^4*b^4 - 3*(A - C)*a^3*b^5 - 3*B*a^2*b^6 + (A - C)*a*b^7)*c^4 - (3*B*a^5*b^3 - 8*(A - C)*a^4*b^4 - 6*B*a^3*b^5 - B*a*b^7)*c^3*d - (C*a^7*b - 3*B*a^6*b^2 + 3*(2*A - C)*a^5*b^3 + 3*(2*A - C)*a^3*b^5 + 3*B*a^2*b^6 + C*a*b^7)*c^2*d^2 - (3*B*a^5*b^3 - 8*(A - C)*a^4*b^4 - 6*B*a^3*b^5 - B*a*b^7)*c*d^3 - (C*a^7*b - 3*B*a^6*b^2 + 3*(2*A - C)*a^5*b^3 + B*a^4*b^4 + 3*A*a^3*b^5 + A*a*b^7)*d^4)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) + ((C*a^8 + 3*C*a^6*b^2 + 3*C*a^4*b^4 + C*a^2*b^6)*c^2*d^2 - (B*a^8 + 3*B*a^6*b^2 + 3*B*a^4*b^4 + B*a^2*b^6)*c*d^3 + (A*a^8 + 3*A*a^6*b^2 + 3*A*a^4*b^4 + A*a^2*b^6)*d^4 + ((C*a^6*b^2 + 3*C*a^4*b^4 + 3*C*a^2*b^6 + C*b^8)*c^2*d^2 - (B*a^6*b^2 + 3*B*a^4*b^4 + 3*B*a^2*b^6 + B*b^8)*c*d^3 + (A*a^6*b^2 + 3*A*a^4*b^4 + 3*A*a^2*b^6 + A*b^8)*d^4)*tan(f*x + e)^2 + 2*((C*a^7*b + 3*C*a^5*b^3 + 3*C*a^3*b^5 + C*a*b^7)*c^2*d^2 - (B*a^7*b + 3*B*a^5*b^3 + 3*B*a^3*b^5 + B*a*b^7)*c*d^3 + (A*a^7*b + 3*A*a^5*b^3 + 3*A*a^3*b^5 + A*a*b^7)*d^4)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*((C*a^5*b^3 - 2*B*a^4*b^4 + 3*(A - C)*a^3*b^5 + 3*B*a^2*b^6 - (3*A - 2*C)*a*b^7 - B*b^8)*c^4 - (3*C*a^6*b^2 - 5*B*a^5*b^3 + (7*A - 6*C)*a^4*b^4 + 6*B*a^3*b^5 - 3*(2*A - C)*a^2*b^6 - B*a*b^7 - A*b^8)*c^3*d + (2*C*a^7*b - 3*B*a^6*b^2 + 2*(2*A - C)*a^5*b^3 + B*a^4*b^4 - 2*C*a^3*b^5 + 3*B*a^2*b^6 - 2*(2*A - C)*a*b^7 - B*b^8)*c^2*d^2 - (3*C*a^6*b^2 - 5*B*a^5*b^3 + (7*A - 6*C)*a^4*b^4 + 6*B*a^3*b^5 - 3*(2*A - C)*a^2*b^6 - B*a*b^7 - A*b^8)*c*d^3 + (2*C*a^7*b - 3*B*a^6*b^2 + (4*A - 3*C)*a^5*b^3 + 3*B*a^4*b^4 - (3*A - C)*a^3*b^5 - A*a*b^7)*d^4 + 2*(((A - C)*a^4*b^4 + 3*B*a^3*b^5 - 3*(A - C)*a^2*b^6 - B*a*b^7)*c^4 - (3*(A - C)*a^5*b^3 + 8*B*a^4*b^4 - 6*(A - C)*a^3*b^5 - (A - C)*a*b^7)*c^3*d + 3*((A - C)*a^6*b^2 + 2*B*a^5*b^3 + 2*B*a^3*b^5 - (A - C)*a^2*b^6)*c^2*d^2 - ((A - C)*a^7*b + 6*(A - C)*a^5*b^3 + 8*B*a^4*b^4 - 3*(A - C)*a^3*b^5)*c*d^3 - (B*a^7*b - 3*(A - C)*a^6*b^2 - 3*B*a^5*b^3 + (A - C)*a^4*b^4)*d^4)*f*x)*tan(f*x + e))/(((a^6*b^5 + 3*a^4*b^7 + 3*a^2*b^9 + b^11)*c^5 - 3*(a^7*b^4 + 3*a^5*b^6 + 3*a^3*b^8 + a*b^10)*c^4*d + (3*a^8*b^3 + 10*a^6*b^5 + 12*a^4*b^7 + 6*a^2*b^9 + b^11)*c^3*d^2 - (a^9*b^2 + 6*a^7*b^4 + 12*a^5*b^6 + 10*a^3*b^8 + 3*a*b^10)*c^2*d^3 + 3*(a^8*b^3 + 3*a^6*b^5 + 3*a^4*b^7 + a^2*b^9)*c*d^4 - (a^9*b^2 + 3*a^7*b^4 + 3*a^5*b^6 + a^3*b^8)*d^5)*f*tan(f*x + e)^2 + 2*((a^7*b^4 + 3*a^5*b^6 + 3*a^3*b^8 + a*b^10)*c^5 - 3*(a^8*b^3 + 3*a^6*b^5 + 3*a^4*b^7 + a^2*b^9)*c^4*d + (3*a^9*b^2 + 10*a^7*b^4 + 12*a^5*b^6 + 6*a^3*b^8 + a*b^10)*c^3*d^2 - (a^10*b + 6*a^8*b^3 + 12*a^6*b^5 + 10*a^4*b^7 + 3*a^2*b^9)*c^2*d^3 + 3*(a^9*b^2 + 3*a^7*b^4 + 3*a^5*b^6 + a^3*b^8)*c*d^4 - (a^10*b + 3*a^8*b^3 + 3*a^6*b^5 + a^4*b^7)*d^5)*f*tan(f*x + e) + ((a^8*b^3 + 3*a^6*b^5 + 3*a^4*b^7 + a^2*b^9)*c^5 - 3*(a^9*b^2 + 3*a^7*b^4 + 3*a^5*b^6 + a^3*b^8)*c^4*d + (3*a^10*b + 10*a^8*b^3 + 12*a^6*b^5 + 6*a^4*b^7 + a^2*b^9)*c^3*d^2 - (a^11 + 6*a^9*b^2 + 12*a^7*b^4 + 10*a^5*b^6 + 3*a^3*b^8)*c^2*d^3 + 3*(a^10*b + 3*a^8*b^3 + 3*a^6*b^5 + a^4*b^7)*c*d^4 - (a^11 + 3*a^9*b^2 + 3*a^7*b^4 + a^5*b^6)*d^5)*f)","B",0
77,1,1477,0,2.367793," ","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=""fricas"")","\frac{3 \, C b^{3} c^{5} d^{2} - 2 \, A a^{3} d^{7} - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4} d^{3} + 2 \, {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A + C\right)} b^{3}\right)} c^{3} d^{4} - 2 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{5} + {\left(2 \, B a^{3} + 6 \, A a^{2} b + C b^{3}\right)} c d^{6} + {\left(C b^{3} c^{4} d^{3} + 2 \, C b^{3} c^{2} d^{5} + C b^{3} d^{7}\right)} \tan\left(f x + e\right)^{3} + 2 \, {\left({\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c^{3} d^{4} + 2 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c^{2} d^{5} - {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c d^{6}\right)} f x - {\left(3 \, C b^{3} c^{5} d^{2} + 6 \, C b^{3} c^{3} d^{4} + 3 \, C b^{3} c d^{6} - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4} d^{3} - 4 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2} d^{5} - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} d^{7}\right)} \tan\left(f x + e\right)^{2} + {\left(3 \, C b^{3} c^{7} - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{6} d + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A + 5 \, C\right)} b^{3}\right)} c^{5} d^{2} - 4 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4} d^{3} - {\left(B a^{3} + 3 \, {\left(A - 3 \, C\right)} a^{2} b - 9 \, B a b^{2} - 3 \, A b^{3}\right)} c^{3} d^{4} + 2 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} c^{2} d^{5} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{6} + {\left(3 \, C b^{3} c^{6} d - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{5} d^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A + 5 \, C\right)} b^{3}\right)} c^{4} d^{3} - 4 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3} d^{4} - {\left(B a^{3} + 3 \, {\left(A - 3 \, C\right)} a^{2} b - 9 \, B a b^{2} - 3 \, A b^{3}\right)} c^{2} d^{5} + 2 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} c d^{6} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(3 \, C b^{3} c^{7} - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{6} d + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A + 5 \, C\right)} b^{3}\right)} c^{5} d^{2} - 4 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4} d^{3} + {\left(6 \, C a^{2} b + 6 \, B a b^{2} + {\left(2 \, A + C\right)} b^{3}\right)} c^{3} d^{4} - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2} d^{5} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A - C\right)} b^{3}\right)} c d^{6} + {\left(3 \, C b^{3} c^{6} d - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{5} d^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A + 5 \, C\right)} b^{3}\right)} c^{4} d^{3} - 4 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3} d^{4} + {\left(6 \, C a^{2} b + 6 \, B a b^{2} + {\left(2 \, A + C\right)} b^{3}\right)} c^{2} d^{5} - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c d^{6} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A - C\right)} b^{3}\right)} d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(6 \, C b^{3} c^{6} d - C b^{3} d^{7} - 4 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{5} d^{2} + {\left(6 \, C a^{2} b + 6 \, B a b^{2} + {\left(2 \, A + 7 \, C\right)} b^{3}\right)} c^{4} d^{3} - 2 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, {\left(A + 2 \, C\right)} a b^{2} + 2 \, B b^{3}\right)} c^{3} d^{4} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b + C b^{3}\right)} c^{2} d^{5} - 2 \, {\left(A a^{3} + 3 \, C a b^{2} + B b^{3}\right)} c d^{6} - 2 \, {\left({\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c^{2} d^{5} + 2 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c d^{6} - {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} d^{7}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{4} d^{5} + 2 \, c^{2} d^{7} + d^{9}\right)} f \tan\left(f x + e\right) + {\left(c^{5} d^{4} + 2 \, c^{3} d^{6} + c d^{8}\right)} f\right)}}"," ",0,"1/2*(3*C*b^3*c^5*d^2 - 2*A*a^3*d^7 - 2*(3*C*a*b^2 + B*b^3)*c^4*d^3 + 2*(3*C*a^2*b + 3*B*a*b^2 + (A + C)*b^3)*c^3*d^4 - 2*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^5 + (2*B*a^3 + 6*A*a^2*b + C*b^3)*c*d^6 + (C*b^3*c^4*d^3 + 2*C*b^3*c^2*d^5 + C*b^3*d^7)*tan(f*x + e)^3 + 2*(((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c^3*d^4 + 2*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c^2*d^5 - ((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c*d^6)*f*x - (3*C*b^3*c^5*d^2 + 6*C*b^3*c^3*d^4 + 3*C*b^3*c*d^6 - 2*(3*C*a*b^2 + B*b^3)*c^4*d^3 - 4*(3*C*a*b^2 + B*b^3)*c^2*d^5 - 2*(3*C*a*b^2 + B*b^3)*d^7)*tan(f*x + e)^2 + (3*C*b^3*c^7 - 2*(3*C*a*b^2 + B*b^3)*c^6*d + (3*C*a^2*b + 3*B*a*b^2 + (A + 5*C)*b^3)*c^5*d^2 - 4*(3*C*a*b^2 + B*b^3)*c^4*d^3 - (B*a^3 + 3*(A - 3*C)*a^2*b - 9*B*a*b^2 - 3*A*b^3)*c^3*d^4 + 2*((A - C)*a^3 - 3*B*a^2*b - 3*A*a*b^2)*c^2*d^5 + (B*a^3 + 3*A*a^2*b)*c*d^6 + (3*C*b^3*c^6*d - 2*(3*C*a*b^2 + B*b^3)*c^5*d^2 + (3*C*a^2*b + 3*B*a*b^2 + (A + 5*C)*b^3)*c^4*d^3 - 4*(3*C*a*b^2 + B*b^3)*c^3*d^4 - (B*a^3 + 3*(A - 3*C)*a^2*b - 9*B*a*b^2 - 3*A*b^3)*c^2*d^5 + 2*((A - C)*a^3 - 3*B*a^2*b - 3*A*a*b^2)*c*d^6 + (B*a^3 + 3*A*a^2*b)*d^7)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (3*C*b^3*c^7 - 2*(3*C*a*b^2 + B*b^3)*c^6*d + (3*C*a^2*b + 3*B*a*b^2 + (A + 5*C)*b^3)*c^5*d^2 - 4*(3*C*a*b^2 + B*b^3)*c^4*d^3 + (6*C*a^2*b + 6*B*a*b^2 + (2*A + C)*b^3)*c^3*d^4 - 2*(3*C*a*b^2 + B*b^3)*c^2*d^5 + (3*C*a^2*b + 3*B*a*b^2 + (A - C)*b^3)*c*d^6 + (3*C*b^3*c^6*d - 2*(3*C*a*b^2 + B*b^3)*c^5*d^2 + (3*C*a^2*b + 3*B*a*b^2 + (A + 5*C)*b^3)*c^4*d^3 - 4*(3*C*a*b^2 + B*b^3)*c^3*d^4 + (6*C*a^2*b + 6*B*a*b^2 + (2*A + C)*b^3)*c^2*d^5 - 2*(3*C*a*b^2 + B*b^3)*c*d^6 + (3*C*a^2*b + 3*B*a*b^2 + (A - C)*b^3)*d^7)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) - (6*C*b^3*c^6*d - C*b^3*d^7 - 4*(3*C*a*b^2 + B*b^3)*c^5*d^2 + (6*C*a^2*b + 6*B*a*b^2 + (2*A + 7*C)*b^3)*c^4*d^3 - 2*(C*a^3 + 3*B*a^2*b + 3*(A + 2*C)*a*b^2 + 2*B*b^3)*c^3*d^4 + 2*(B*a^3 + 3*A*a^2*b + C*b^3)*c^2*d^5 - 2*(A*a^3 + 3*C*a*b^2 + B*b^3)*c*d^6 - 2*(((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c^2*d^5 + 2*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c*d^6 - ((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*d^7)*f*x)*tan(f*x + e))/((c^4*d^5 + 2*c^2*d^7 + d^9)*f*tan(f*x + e) + (c^5*d^4 + 2*c^3*d^6 + c*d^8)*f)","B",0
78,1,939,0,1.277906," ","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=""fricas"")","-\frac{2 \, C b^{2} c^{4} d^{2} + 2 \, A a^{2} d^{6} - 2 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{3} + 2 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} - 2 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5} - 2 \, {\left({\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c^{3} d^{3} + 2 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{2} d^{4} - {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c d^{5}\right)} f x - 2 \, {\left(C b^{2} c^{4} d^{2} + 2 \, C b^{2} c^{2} d^{4} + C b^{2} d^{6}\right)} \tan\left(f x + e\right)^{2} + {\left(2 \, C b^{2} c^{6} + 4 \, C b^{2} c^{4} d^{2} - {\left(2 \, C a b + B b^{2}\right)} c^{5} d + {\left(B a^{2} + 2 \, {\left(A - 3 \, C\right)} a b - 3 \, B b^{2}\right)} c^{3} d^{3} - 2 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - A b^{2}\right)} c^{2} d^{4} - {\left(B a^{2} + 2 \, A a b\right)} c d^{5} + {\left(2 \, C b^{2} c^{5} d + 4 \, C b^{2} c^{3} d^{3} - {\left(2 \, C a b + B b^{2}\right)} c^{4} d^{2} + {\left(B a^{2} + 2 \, {\left(A - 3 \, C\right)} a b - 3 \, B b^{2}\right)} c^{2} d^{4} - 2 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - A b^{2}\right)} c d^{5} - {\left(B a^{2} + 2 \, A a b\right)} d^{6}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(2 \, C b^{2} c^{6} + 4 \, C b^{2} c^{4} d^{2} + 2 \, C b^{2} c^{2} d^{4} - {\left(2 \, C a b + B b^{2}\right)} c^{5} d - 2 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{3} - {\left(2 \, C a b + B b^{2}\right)} c d^{5} + {\left(2 \, C b^{2} c^{5} d + 4 \, C b^{2} c^{3} d^{3} + 2 \, C b^{2} c d^{5} - {\left(2 \, C a b + B b^{2}\right)} c^{4} d^{2} - 2 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{4} - {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(2 \, C b^{2} c^{5} d - {\left(2 \, C a b + B b^{2}\right)} c^{4} d^{2} + {\left(C a^{2} + 2 \, B a b + {\left(A + 2 \, C\right)} b^{2}\right)} c^{3} d^{3} - {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{4} + {\left(A a^{2} + C b^{2}\right)} c d^{5} + {\left({\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c^{2} d^{4} + 2 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c d^{5} - {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} d^{6}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{4} d^{4} + 2 \, c^{2} d^{6} + d^{8}\right)} f \tan\left(f x + e\right) + {\left(c^{5} d^{3} + 2 \, c^{3} d^{5} + c d^{7}\right)} f\right)}}"," ",0,"-1/2*(2*C*b^2*c^4*d^2 + 2*A*a^2*d^6 - 2*(2*C*a*b + B*b^2)*c^3*d^3 + 2*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 - 2*(B*a^2 + 2*A*a*b)*c*d^5 - 2*(((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c^3*d^3 + 2*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c^2*d^4 - ((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c*d^5)*f*x - 2*(C*b^2*c^4*d^2 + 2*C*b^2*c^2*d^4 + C*b^2*d^6)*tan(f*x + e)^2 + (2*C*b^2*c^6 + 4*C*b^2*c^4*d^2 - (2*C*a*b + B*b^2)*c^5*d + (B*a^2 + 2*(A - 3*C)*a*b - 3*B*b^2)*c^3*d^3 - 2*((A - C)*a^2 - 2*B*a*b - A*b^2)*c^2*d^4 - (B*a^2 + 2*A*a*b)*c*d^5 + (2*C*b^2*c^5*d + 4*C*b^2*c^3*d^3 - (2*C*a*b + B*b^2)*c^4*d^2 + (B*a^2 + 2*(A - 3*C)*a*b - 3*B*b^2)*c^2*d^4 - 2*((A - C)*a^2 - 2*B*a*b - A*b^2)*c*d^5 - (B*a^2 + 2*A*a*b)*d^6)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (2*C*b^2*c^6 + 4*C*b^2*c^4*d^2 + 2*C*b^2*c^2*d^4 - (2*C*a*b + B*b^2)*c^5*d - 2*(2*C*a*b + B*b^2)*c^3*d^3 - (2*C*a*b + B*b^2)*c*d^5 + (2*C*b^2*c^5*d + 4*C*b^2*c^3*d^3 + 2*C*b^2*c*d^5 - (2*C*a*b + B*b^2)*c^4*d^2 - 2*(2*C*a*b + B*b^2)*c^2*d^4 - (2*C*a*b + B*b^2)*d^6)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) - 2*(2*C*b^2*c^5*d - (2*C*a*b + B*b^2)*c^4*d^2 + (C*a^2 + 2*B*a*b + (A + 2*C)*b^2)*c^3*d^3 - (B*a^2 + 2*A*a*b)*c^2*d^4 + (A*a^2 + C*b^2)*c*d^5 + (((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c^2*d^4 + 2*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c*d^5 - ((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*d^6)*f*x)*tan(f*x + e))/((c^4*d^4 + 2*c^2*d^6 + d^8)*f*tan(f*x + e) + (c^5*d^3 + 2*c^3*d^5 + c*d^7)*f)","B",0
79,1,505,0,0.646863," ","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=""fricas"")","\frac{2 \, C b c^{3} d^{2} - 2 \, A a d^{5} - 2 \, {\left(C a + B b\right)} c^{2} d^{3} + 2 \, {\left(B a + A b\right)} c d^{4} + 2 \, {\left({\left({\left(A - C\right)} a - B b\right)} c^{3} d^{2} + 2 \, {\left(B a + {\left(A - C\right)} b\right)} c^{2} d^{3} - {\left({\left(A - C\right)} a - B b\right)} c d^{4}\right)} f x + {\left(C b c^{5} - {\left(B a + {\left(A - 3 \, C\right)} b\right)} c^{3} d^{2} + 2 \, {\left({\left(A - C\right)} a - B b\right)} c^{2} d^{3} + {\left(B a + A b\right)} c d^{4} + {\left(C b c^{4} d - {\left(B a + {\left(A - 3 \, C\right)} b\right)} c^{2} d^{3} + 2 \, {\left({\left(A - C\right)} a - B b\right)} c d^{4} + {\left(B a + A b\right)} d^{5}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(C b c^{5} + 2 \, C b c^{3} d^{2} + C b c d^{4} + {\left(C b c^{4} d + 2 \, C b c^{2} d^{3} + C b d^{5}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(C b c^{4} d - A a c d^{4} - {\left(C a + B b\right)} c^{3} d^{2} + {\left(B a + A b\right)} c^{2} d^{3} - {\left({\left({\left(A - C\right)} a - B b\right)} c^{2} d^{3} + 2 \, {\left(B a + {\left(A - C\right)} b\right)} c d^{4} - {\left({\left(A - C\right)} a - B b\right)} d^{5}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}\right)} f \tan\left(f x + e\right) + {\left(c^{5} d^{2} + 2 \, c^{3} d^{4} + c d^{6}\right)} f\right)}}"," ",0,"1/2*(2*C*b*c^3*d^2 - 2*A*a*d^5 - 2*(C*a + B*b)*c^2*d^3 + 2*(B*a + A*b)*c*d^4 + 2*(((A - C)*a - B*b)*c^3*d^2 + 2*(B*a + (A - C)*b)*c^2*d^3 - ((A - C)*a - B*b)*c*d^4)*f*x + (C*b*c^5 - (B*a + (A - 3*C)*b)*c^3*d^2 + 2*((A - C)*a - B*b)*c^2*d^3 + (B*a + A*b)*c*d^4 + (C*b*c^4*d - (B*a + (A - 3*C)*b)*c^2*d^3 + 2*((A - C)*a - B*b)*c*d^4 + (B*a + A*b)*d^5)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (C*b*c^5 + 2*C*b*c^3*d^2 + C*b*c*d^4 + (C*b*c^4*d + 2*C*b*c^2*d^3 + C*b*d^5)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) - 2*(C*b*c^4*d - A*a*c*d^4 - (C*a + B*b)*c^3*d^2 + (B*a + A*b)*c^2*d^3 - (((A - C)*a - B*b)*c^2*d^3 + 2*(B*a + (A - C)*b)*c*d^4 - ((A - C)*a - B*b)*d^5)*f*x)*tan(f*x + e))/((c^4*d^3 + 2*c^2*d^5 + d^7)*f*tan(f*x + e) + (c^5*d^2 + 2*c^3*d^4 + c*d^6)*f)","A",0
80,1,256,0,0.575473," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, C c^{2} d - 2 \, B c d^{2} + 2 \, A d^{3} - 2 \, {\left({\left(A - C\right)} c^{3} + 2 \, B c^{2} d - {\left(A - C\right)} c d^{2}\right)} f x + {\left(B c^{3} - 2 \, {\left(A - C\right)} c^{2} d - B c d^{2} + {\left(B c^{2} d - 2 \, {\left(A - C\right)} c d^{2} - B d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(C c^{3} - B c^{2} d + A c d^{2} + {\left({\left(A - C\right)} c^{2} d + 2 \, B c d^{2} - {\left(A - C\right)} d^{3}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{4} d + 2 \, c^{2} d^{3} + d^{5}\right)} f \tan\left(f x + e\right) + {\left(c^{5} + 2 \, c^{3} d^{2} + c d^{4}\right)} f\right)}}"," ",0,"-1/2*(2*C*c^2*d - 2*B*c*d^2 + 2*A*d^3 - 2*((A - C)*c^3 + 2*B*c^2*d - (A - C)*c*d^2)*f*x + (B*c^3 - 2*(A - C)*c^2*d - B*c*d^2 + (B*c^2*d - 2*(A - C)*c*d^2 - B*d^3)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*(C*c^3 - B*c^2*d + A*c*d^2 + ((A - C)*c^2*d + 2*B*c*d^2 - (A - C)*d^3)*f*x)*tan(f*x + e))/((c^4*d + 2*c^2*d^3 + d^5)*f*tan(f*x + e) + (c^5 + 2*c^3*d^2 + c*d^4)*f)","A",0
81,1,1275,0,2.707957," ","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=""fricas"")","\frac{2 \, {\left(C a^{2} b + C b^{3}\right)} c^{3} d^{2} - 2 \, {\left(C a^{3} + B a^{2} b + C a b^{2} + B b^{3}\right)} c^{2} d^{3} + 2 \, {\left(B a^{3} + A a^{2} b + B a b^{2} + A b^{3}\right)} c d^{4} - 2 \, {\left(A a^{3} + A a b^{2}\right)} d^{5} + 2 \, {\left({\left({\left(A - C\right)} a b^{2} + B b^{3}\right)} c^{5} - 2 \, {\left({\left(A - C\right)} a^{2} b + {\left(A - C\right)} b^{3}\right)} c^{4} d + {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b + 3 \, {\left(A - C\right)} a b^{2} - B b^{3}\right)} c^{3} d^{2} + 2 \, {\left(B a^{3} + B a b^{2}\right)} c^{2} d^{3} - {\left({\left(A - C\right)} a^{3} + B a^{2} b\right)} c d^{4}\right)} f x + {\left({\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c^{5} + 2 \, {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c^{3} d^{2} + {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c d^{4} + {\left({\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c^{4} d + 2 \, {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c^{2} d^{3} + {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} d^{5}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left({\left(C a^{2} b + C b^{3}\right)} c^{5} - 2 \, {\left(B a^{2} b + B b^{3}\right)} c^{4} d + {\left(B a^{3} + {\left(3 \, A - C\right)} a^{2} b + B a b^{2} + {\left(3 \, A - C\right)} b^{3}\right)} c^{3} d^{2} - 2 \, {\left({\left(A - C\right)} a^{3} + {\left(A - C\right)} a b^{2}\right)} c^{2} d^{3} - {\left(B a^{3} - A a^{2} b + B a b^{2} - A b^{3}\right)} c d^{4} + {\left({\left(C a^{2} b + C b^{3}\right)} c^{4} d - 2 \, {\left(B a^{2} b + B b^{3}\right)} c^{3} d^{2} + {\left(B a^{3} + {\left(3 \, A - C\right)} a^{2} b + B a b^{2} + {\left(3 \, A - C\right)} b^{3}\right)} c^{2} d^{3} - 2 \, {\left({\left(A - C\right)} a^{3} + {\left(A - C\right)} a b^{2}\right)} c d^{4} - {\left(B a^{3} - A a^{2} b + B a b^{2} - A b^{3}\right)} d^{5}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left({\left(C a^{2} b + C b^{3}\right)} c^{4} d - {\left(C a^{3} + B a^{2} b + C a b^{2} + B b^{3}\right)} c^{3} d^{2} + {\left(B a^{3} + A a^{2} b + B a b^{2} + A b^{3}\right)} c^{2} d^{3} - {\left(A a^{3} + A a b^{2}\right)} c d^{4} - {\left({\left({\left(A - C\right)} a b^{2} + B b^{3}\right)} c^{4} d - 2 \, {\left({\left(A - C\right)} a^{2} b + {\left(A - C\right)} b^{3}\right)} c^{3} d^{2} + {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b + 3 \, {\left(A - C\right)} a b^{2} - B b^{3}\right)} c^{2} d^{3} + 2 \, {\left(B a^{3} + B a b^{2}\right)} c d^{4} - {\left({\left(A - C\right)} a^{3} + B a^{2} b\right)} d^{5}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{2} b^{2} + b^{4}\right)} c^{6} d - 2 \, {\left(a^{3} b + a b^{3}\right)} c^{5} d^{2} + {\left(a^{4} + 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{4} d^{3} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{3} d^{4} + {\left(2 \, a^{4} + 3 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{5} - 2 \, {\left(a^{3} b + a b^{3}\right)} c d^{6} + {\left(a^{4} + a^{2} b^{2}\right)} d^{7}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{2} b^{2} + b^{4}\right)} c^{7} - 2 \, {\left(a^{3} b + a b^{3}\right)} c^{6} d + {\left(a^{4} + 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{5} d^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{4} d^{3} + {\left(2 \, a^{4} + 3 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{4} - 2 \, {\left(a^{3} b + a b^{3}\right)} c^{2} d^{5} + {\left(a^{4} + a^{2} b^{2}\right)} c d^{6}\right)} f\right)}}"," ",0,"1/2*(2*(C*a^2*b + C*b^3)*c^3*d^2 - 2*(C*a^3 + B*a^2*b + C*a*b^2 + B*b^3)*c^2*d^3 + 2*(B*a^3 + A*a^2*b + B*a*b^2 + A*b^3)*c*d^4 - 2*(A*a^3 + A*a*b^2)*d^5 + 2*(((A - C)*a*b^2 + B*b^3)*c^5 - 2*((A - C)*a^2*b + (A - C)*b^3)*c^4*d + ((A - C)*a^3 - 3*B*a^2*b + 3*(A - C)*a*b^2 - B*b^3)*c^3*d^2 + 2*(B*a^3 + B*a*b^2)*c^2*d^3 - ((A - C)*a^3 + B*a^2*b)*c*d^4)*f*x + ((C*a^2*b - B*a*b^2 + A*b^3)*c^5 + 2*(C*a^2*b - B*a*b^2 + A*b^3)*c^3*d^2 + (C*a^2*b - B*a*b^2 + A*b^3)*c*d^4 + ((C*a^2*b - B*a*b^2 + A*b^3)*c^4*d + 2*(C*a^2*b - B*a*b^2 + A*b^3)*c^2*d^3 + (C*a^2*b - B*a*b^2 + A*b^3)*d^5)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - ((C*a^2*b + C*b^3)*c^5 - 2*(B*a^2*b + B*b^3)*c^4*d + (B*a^3 + (3*A - C)*a^2*b + B*a*b^2 + (3*A - C)*b^3)*c^3*d^2 - 2*((A - C)*a^3 + (A - C)*a*b^2)*c^2*d^3 - (B*a^3 - A*a^2*b + B*a*b^2 - A*b^3)*c*d^4 + ((C*a^2*b + C*b^3)*c^4*d - 2*(B*a^2*b + B*b^3)*c^3*d^2 + (B*a^3 + (3*A - C)*a^2*b + B*a*b^2 + (3*A - C)*b^3)*c^2*d^3 - 2*((A - C)*a^3 + (A - C)*a*b^2)*c*d^4 - (B*a^3 - A*a^2*b + B*a*b^2 - A*b^3)*d^5)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*((C*a^2*b + C*b^3)*c^4*d - (C*a^3 + B*a^2*b + C*a*b^2 + B*b^3)*c^3*d^2 + (B*a^3 + A*a^2*b + B*a*b^2 + A*b^3)*c^2*d^3 - (A*a^3 + A*a*b^2)*c*d^4 - (((A - C)*a*b^2 + B*b^3)*c^4*d - 2*((A - C)*a^2*b + (A - C)*b^3)*c^3*d^2 + ((A - C)*a^3 - 3*B*a^2*b + 3*(A - C)*a*b^2 - B*b^3)*c^2*d^3 + 2*(B*a^3 + B*a*b^2)*c*d^4 - ((A - C)*a^3 + B*a^2*b)*d^5)*f*x)*tan(f*x + e))/(((a^2*b^2 + b^4)*c^6*d - 2*(a^3*b + a*b^3)*c^5*d^2 + (a^4 + 3*a^2*b^2 + 2*b^4)*c^4*d^3 - 4*(a^3*b + a*b^3)*c^3*d^4 + (2*a^4 + 3*a^2*b^2 + b^4)*c^2*d^5 - 2*(a^3*b + a*b^3)*c*d^6 + (a^4 + a^2*b^2)*d^7)*f*tan(f*x + e) + ((a^2*b^2 + b^4)*c^7 - 2*(a^3*b + a*b^3)*c^6*d + (a^4 + 3*a^2*b^2 + 2*b^4)*c^5*d^2 - 4*(a^3*b + a*b^3)*c^4*d^3 + (2*a^4 + 3*a^2*b^2 + b^4)*c^3*d^4 - 2*(a^3*b + a*b^3)*c^2*d^5 + (a^4 + a^2*b^2)*c*d^6)*f)","B",0
82,1,4174,0,6.550690," ","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=""fricas"")","-\frac{2 \, {\left(C a^{2} b^{4} - B a b^{5} + A b^{6}\right)} c^{6} - 2 \, {\left(C a^{3} b^{3} - B a^{2} b^{4} + A a b^{5}\right)} c^{5} d + 4 \, {\left(C a^{2} b^{4} - B a b^{5} + A b^{6}\right)} c^{4} d^{2} + 2 \, {\left(C a^{5} b + 2 \, B a^{2} b^{4} - {\left(2 \, A - C\right)} a b^{5}\right)} c^{3} d^{3} - 2 \, {\left(C a^{6} + B a^{5} b + 2 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, B a b^{5} - A b^{6}\right)} c^{2} d^{4} + 2 \, {\left(B a^{6} + A a^{5} b + 2 \, B a^{4} b^{2} + {\left(2 \, A - C\right)} a^{3} b^{3} + 2 \, B a^{2} b^{4}\right)} c d^{5} - 2 \, {\left(A a^{6} + 2 \, A a^{4} b^{2} + A a^{2} b^{4}\right)} d^{6} - 2 \, {\left({\left({\left(A - C\right)} a^{3} b^{3} + 2 \, B a^{2} b^{4} - {\left(A - C\right)} a b^{5}\right)} c^{6} - {\left(3 \, {\left(A - C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} + {\left(A - C\right)} a^{2} b^{4} + 2 \, B a b^{5}\right)} c^{5} d + {\left(3 \, {\left(A - C\right)} a^{5} b + 8 \, {\left(A - C\right)} a^{3} b^{3} + 4 \, B a^{2} b^{4} + {\left(A - C\right)} a b^{5}\right)} c^{4} d^{2} - {\left({\left(A - C\right)} a^{6} - 4 \, B a^{5} b + 8 \, {\left(A - C\right)} a^{4} b^{2} + 3 \, {\left(A - C\right)} a^{2} b^{4}\right)} c^{3} d^{3} - {\left(2 \, B a^{6} - {\left(A - C\right)} a^{5} b + 4 \, B a^{4} b^{2} - 3 \, {\left(A - C\right)} a^{3} b^{3}\right)} c^{2} d^{4} + {\left({\left(A - C\right)} a^{6} + 2 \, B a^{5} b - {\left(A - C\right)} a^{4} b^{2}\right)} c d^{5}\right)} f x - 2 \, {\left({\left(C a^{3} b^{3} - B a^{2} b^{4} + A a b^{5}\right)} c^{5} d + {\left(B a^{3} b^{3} - {\left(A - 2 \, C\right)} a^{2} b^{4} + C b^{6}\right)} c^{4} d^{2} - {\left(C a^{5} b + B a^{4} b^{2} + 4 \, B a^{2} b^{4} - {\left(2 \, A - C\right)} a b^{5} + B b^{6}\right)} c^{3} d^{3} + {\left(B a^{5} b + {\left(A - 2 \, C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} + B a b^{5} + A b^{6}\right)} c^{2} d^{4} - {\left(A a^{5} b + {\left(2 \, A - C\right)} a^{3} b^{3} + B a^{2} b^{4}\right)} c d^{5} - {\left(C a^{4} b^{2} - B a^{3} b^{3} + A a^{2} b^{4}\right)} d^{6} + {\left({\left({\left(A - C\right)} a^{2} b^{4} + 2 \, B a b^{5} - {\left(A - C\right)} b^{6}\right)} c^{5} d - {\left(3 \, {\left(A - C\right)} a^{3} b^{3} + 4 \, B a^{2} b^{4} + {\left(A - C\right)} a b^{5} + 2 \, B b^{6}\right)} c^{4} d^{2} + {\left(3 \, {\left(A - C\right)} a^{4} b^{2} + 8 \, {\left(A - C\right)} a^{2} b^{4} + 4 \, B a b^{5} + {\left(A - C\right)} b^{6}\right)} c^{3} d^{3} - {\left({\left(A - C\right)} a^{5} b - 4 \, B a^{4} b^{2} + 8 \, {\left(A - C\right)} a^{3} b^{3} + 3 \, {\left(A - C\right)} a b^{5}\right)} c^{2} d^{4} - {\left(2 \, B a^{5} b - {\left(A - C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} - 3 \, {\left(A - C\right)} a^{2} b^{4}\right)} c d^{5} + {\left({\left(A - C\right)} a^{5} b + 2 \, B a^{4} b^{2} - {\left(A - C\right)} a^{3} b^{3}\right)} d^{6}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left({\left(B a^{3} b^{3} - 2 \, {\left(A - C\right)} a^{2} b^{4} - B a b^{5}\right)} c^{6} + {\left(2 \, C a^{5} b - 3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5}\right)} c^{5} d + 2 \, {\left(B a^{3} b^{3} - 2 \, {\left(A - C\right)} a^{2} b^{4} - B a b^{5}\right)} c^{4} d^{2} + 2 \, {\left(2 \, C a^{5} b - 3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5}\right)} c^{3} d^{3} + {\left(B a^{3} b^{3} - 2 \, {\left(A - C\right)} a^{2} b^{4} - B a b^{5}\right)} c^{2} d^{4} + {\left(2 \, C a^{5} b - 3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5}\right)} c d^{5} + {\left({\left(B a^{2} b^{4} - 2 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c^{5} d + {\left(2 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} - B a b^{5} + 2 \, A b^{6}\right)} c^{4} d^{2} + 2 \, {\left(B a^{2} b^{4} - 2 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c^{3} d^{3} + 2 \, {\left(2 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} - B a b^{5} + 2 \, A b^{6}\right)} c^{2} d^{4} + {\left(B a^{2} b^{4} - 2 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c d^{5} + {\left(2 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} - B a b^{5} + 2 \, A b^{6}\right)} d^{6}\right)} \tan\left(f x + e\right)^{2} + {\left({\left(B a^{2} b^{4} - 2 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c^{6} + 2 \, {\left(C a^{4} b^{2} - B a^{3} b^{3} + {\left(A + C\right)} a^{2} b^{4} - B a b^{5} + A b^{6}\right)} c^{5} d + {\left(2 \, C a^{5} b - 3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, {\left(A - 2 \, C\right)} a b^{5} - 2 \, B b^{6}\right)} c^{4} d^{2} + 4 \, {\left(C a^{4} b^{2} - B a^{3} b^{3} + {\left(A + C\right)} a^{2} b^{4} - B a b^{5} + A b^{6}\right)} c^{3} d^{3} + {\left(4 \, C a^{5} b - 6 \, B a^{4} b^{2} + 8 \, A a^{3} b^{3} - B a^{2} b^{4} + 2 \, {\left(A + C\right)} a b^{5} - B b^{6}\right)} c^{2} d^{4} + 2 \, {\left(C a^{4} b^{2} - B a^{3} b^{3} + {\left(A + C\right)} a^{2} b^{4} - B a b^{5} + A b^{6}\right)} c d^{5} + {\left(2 \, C a^{5} b - 3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{6}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(2 \, {\left(C a^{5} b + 2 \, C a^{3} b^{3} + C a b^{5}\right)} c^{5} d - 3 \, {\left(B a^{5} b + 2 \, B a^{3} b^{3} + B a b^{5}\right)} c^{4} d^{2} + {\left(B a^{6} + 4 \, A a^{5} b + 2 \, B a^{4} b^{2} + 8 \, A a^{3} b^{3} + B a^{2} b^{4} + 4 \, A a b^{5}\right)} c^{3} d^{3} - {\left(2 \, {\left(A - C\right)} a^{6} + B a^{5} b + 4 \, {\left(A - C\right)} a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, {\left(A - C\right)} a^{2} b^{4} + B a b^{5}\right)} c^{2} d^{4} - {\left(B a^{6} - 2 \, A a^{5} b + 2 \, B a^{4} b^{2} - 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, A a b^{5}\right)} c d^{5} + {\left(2 \, {\left(C a^{4} b^{2} + 2 \, C a^{2} b^{4} + C b^{6}\right)} c^{4} d^{2} - 3 \, {\left(B a^{4} b^{2} + 2 \, B a^{2} b^{4} + B b^{6}\right)} c^{3} d^{3} + {\left(B a^{5} b + 4 \, A a^{4} b^{2} + 2 \, B a^{3} b^{3} + 8 \, A a^{2} b^{4} + B a b^{5} + 4 \, A b^{6}\right)} c^{2} d^{4} - {\left(2 \, {\left(A - C\right)} a^{5} b + B a^{4} b^{2} + 4 \, {\left(A - C\right)} a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, {\left(A - C\right)} a b^{5} + B b^{6}\right)} c d^{5} - {\left(B a^{5} b - 2 \, A a^{4} b^{2} + 2 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4} + B a b^{5} - 2 \, A b^{6}\right)} d^{6}\right)} \tan\left(f x + e\right)^{2} + {\left(2 \, {\left(C a^{4} b^{2} + 2 \, C a^{2} b^{4} + C b^{6}\right)} c^{5} d + {\left(2 \, C a^{5} b - 3 \, B a^{4} b^{2} + 4 \, C a^{3} b^{3} - 6 \, B a^{2} b^{4} + 2 \, C a b^{5} - 3 \, B b^{6}\right)} c^{4} d^{2} - 2 \, {\left(B a^{5} b - 2 \, A a^{4} b^{2} + 2 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4} + B a b^{5} - 2 \, A b^{6}\right)} c^{3} d^{3} + {\left(B a^{6} + 2 \, {\left(A + C\right)} a^{5} b + B a^{4} b^{2} + 4 \, {\left(A + C\right)} a^{3} b^{3} - B a^{2} b^{4} + 2 \, {\left(A + C\right)} a b^{5} - B b^{6}\right)} c^{2} d^{4} - 2 \, {\left({\left(A - C\right)} a^{6} + B a^{5} b + {\left(A - 2 \, C\right)} a^{4} b^{2} + 2 \, B a^{3} b^{3} - {\left(A + C\right)} a^{2} b^{4} + B a b^{5} - A b^{6}\right)} c d^{5} - {\left(B a^{6} - 2 \, A a^{5} b + 2 \, B a^{4} b^{2} - 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, A a b^{5}\right)} d^{6}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left({\left(C a^{3} b^{3} - B a^{2} b^{4} + A a b^{5}\right)} c^{6} - {\left(C a^{4} b^{2} - B a^{3} b^{3} + {\left(A + C\right)} a^{2} b^{4} - B a b^{5} + A b^{6}\right)} c^{5} d + {\left(C a^{5} b + 5 \, C a^{3} b^{3} - 3 \, B a^{2} b^{4} + {\left(3 \, A + C\right)} a b^{5}\right)} c^{4} d^{2} - {\left(C a^{6} + B a^{5} b + 5 \, C a^{4} b^{2} + {\left(2 \, A + 5 \, C\right)} a^{2} b^{4} - B a b^{5} + {\left(2 \, A + C\right)} b^{6}\right)} c^{3} d^{3} + {\left(B a^{6} + {\left(A + C\right)} a^{5} b + 3 \, B a^{4} b^{2} + {\left(2 \, A + 5 \, C\right)} a^{3} b^{3} + {\left(4 \, A + C\right)} a b^{5} + B b^{6}\right)} c^{2} d^{4} - {\left(A a^{6} + B a^{5} b + {\left(3 \, A + C\right)} a^{4} b^{2} + B a^{3} b^{3} + {\left(4 \, A + C\right)} a^{2} b^{4} + 2 \, A b^{6}\right)} c d^{5} + {\left(A a^{5} b + {\left(2 \, A + C\right)} a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{6} + {\left({\left({\left(A - C\right)} a^{2} b^{4} + 2 \, B a b^{5} - {\left(A - C\right)} b^{6}\right)} c^{6} - 2 \, {\left({\left(A - C\right)} a^{3} b^{3} + B a^{2} b^{4} + {\left(A - C\right)} a b^{5} + B b^{6}\right)} c^{5} d - {\left(4 \, B a^{3} b^{3} - 7 \, {\left(A - C\right)} a^{2} b^{4} - 2 \, B a b^{5} - {\left(A - C\right)} b^{6}\right)} c^{4} d^{2} + 2 \, {\left({\left(A - C\right)} a^{5} b + 2 \, B a^{4} b^{2} + 2 \, B a^{2} b^{4} - {\left(A - C\right)} a b^{5}\right)} c^{3} d^{3} - {\left({\left(A - C\right)} a^{6} - 2 \, B a^{5} b + 7 \, {\left(A - C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3}\right)} c^{2} d^{4} - 2 \, {\left(B a^{6} - {\left(A - C\right)} a^{5} b + B a^{4} b^{2} - {\left(A - C\right)} a^{3} b^{3}\right)} c d^{5} + {\left({\left(A - C\right)} a^{6} + 2 \, B a^{5} b - {\left(A - C\right)} a^{4} b^{2}\right)} d^{6}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} c^{7} d - 3 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c^{6} d^{2} + {\left(3 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 7 \, a^{2} b^{6} + 2 \, b^{8}\right)} c^{5} d^{3} - {\left(a^{7} b + 8 \, a^{5} b^{3} + 13 \, a^{3} b^{5} + 6 \, a b^{7}\right)} c^{4} d^{4} + {\left(6 \, a^{6} b^{2} + 13 \, a^{4} b^{4} + 8 \, a^{2} b^{6} + b^{8}\right)} c^{3} d^{5} - {\left(2 \, a^{7} b + 7 \, a^{5} b^{3} + 8 \, a^{3} b^{5} + 3 \, a b^{7}\right)} c^{2} d^{6} + 3 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c d^{7} - {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d^{8}\right)} f \tan\left(f x + e\right)^{2} + {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} c^{8} - 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c^{7} d + 2 \, {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} c^{6} d^{2} + 2 \, {\left(a^{7} b - 3 \, a^{3} b^{5} - 2 \, a b^{7}\right)} c^{5} d^{3} - {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} c^{4} d^{4} + 2 \, {\left(2 \, a^{7} b + 3 \, a^{5} b^{3} - a b^{7}\right)} c^{3} d^{5} - 2 \, {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} c^{2} d^{6} + 2 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} c d^{7} - {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d^{8}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c^{8} - 3 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{7} d + {\left(3 \, a^{7} b + 8 \, a^{5} b^{3} + 7 \, a^{3} b^{5} + 2 \, a b^{7}\right)} c^{6} d^{2} - {\left(a^{8} + 8 \, a^{6} b^{2} + 13 \, a^{4} b^{4} + 6 \, a^{2} b^{6}\right)} c^{5} d^{3} + {\left(6 \, a^{7} b + 13 \, a^{5} b^{3} + 8 \, a^{3} b^{5} + a b^{7}\right)} c^{4} d^{4} - {\left(2 \, a^{8} + 7 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 3 \, a^{2} b^{6}\right)} c^{3} d^{5} + 3 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} c^{2} d^{6} - {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} c d^{7}\right)} f\right)}}"," ",0,"-1/2*(2*(C*a^2*b^4 - B*a*b^5 + A*b^6)*c^6 - 2*(C*a^3*b^3 - B*a^2*b^4 + A*a*b^5)*c^5*d + 4*(C*a^2*b^4 - B*a*b^5 + A*b^6)*c^4*d^2 + 2*(C*a^5*b + 2*B*a^2*b^4 - (2*A - C)*a*b^5)*c^3*d^3 - 2*(C*a^6 + B*a^5*b + 2*C*a^4*b^2 + 2*B*a^3*b^3 + 2*B*a*b^5 - A*b^6)*c^2*d^4 + 2*(B*a^6 + A*a^5*b + 2*B*a^4*b^2 + (2*A - C)*a^3*b^3 + 2*B*a^2*b^4)*c*d^5 - 2*(A*a^6 + 2*A*a^4*b^2 + A*a^2*b^4)*d^6 - 2*(((A - C)*a^3*b^3 + 2*B*a^2*b^4 - (A - C)*a*b^5)*c^6 - (3*(A - C)*a^4*b^2 + 4*B*a^3*b^3 + (A - C)*a^2*b^4 + 2*B*a*b^5)*c^5*d + (3*(A - C)*a^5*b + 8*(A - C)*a^3*b^3 + 4*B*a^2*b^4 + (A - C)*a*b^5)*c^4*d^2 - ((A - C)*a^6 - 4*B*a^5*b + 8*(A - C)*a^4*b^2 + 3*(A - C)*a^2*b^4)*c^3*d^3 - (2*B*a^6 - (A - C)*a^5*b + 4*B*a^4*b^2 - 3*(A - C)*a^3*b^3)*c^2*d^4 + ((A - C)*a^6 + 2*B*a^5*b - (A - C)*a^4*b^2)*c*d^5)*f*x - 2*((C*a^3*b^3 - B*a^2*b^4 + A*a*b^5)*c^5*d + (B*a^3*b^3 - (A - 2*C)*a^2*b^4 + C*b^6)*c^4*d^2 - (C*a^5*b + B*a^4*b^2 + 4*B*a^2*b^4 - (2*A - C)*a*b^5 + B*b^6)*c^3*d^3 + (B*a^5*b + (A - 2*C)*a^4*b^2 + 4*B*a^3*b^3 + B*a*b^5 + A*b^6)*c^2*d^4 - (A*a^5*b + (2*A - C)*a^3*b^3 + B*a^2*b^4)*c*d^5 - (C*a^4*b^2 - B*a^3*b^3 + A*a^2*b^4)*d^6 + (((A - C)*a^2*b^4 + 2*B*a*b^5 - (A - C)*b^6)*c^5*d - (3*(A - C)*a^3*b^3 + 4*B*a^2*b^4 + (A - C)*a*b^5 + 2*B*b^6)*c^4*d^2 + (3*(A - C)*a^4*b^2 + 8*(A - C)*a^2*b^4 + 4*B*a*b^5 + (A - C)*b^6)*c^3*d^3 - ((A - C)*a^5*b - 4*B*a^4*b^2 + 8*(A - C)*a^3*b^3 + 3*(A - C)*a*b^5)*c^2*d^4 - (2*B*a^5*b - (A - C)*a^4*b^2 + 4*B*a^3*b^3 - 3*(A - C)*a^2*b^4)*c*d^5 + ((A - C)*a^5*b + 2*B*a^4*b^2 - (A - C)*a^3*b^3)*d^6)*f*x)*tan(f*x + e)^2 + ((B*a^3*b^3 - 2*(A - C)*a^2*b^4 - B*a*b^5)*c^6 + (2*C*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*c^5*d + 2*(B*a^3*b^3 - 2*(A - C)*a^2*b^4 - B*a*b^5)*c^4*d^2 + 2*(2*C*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*c^3*d^3 + (B*a^3*b^3 - 2*(A - C)*a^2*b^4 - B*a*b^5)*c^2*d^4 + (2*C*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*c*d^5 + ((B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c^5*d + (2*C*a^4*b^2 - 3*B*a^3*b^3 + 4*A*a^2*b^4 - B*a*b^5 + 2*A*b^6)*c^4*d^2 + 2*(B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c^3*d^3 + 2*(2*C*a^4*b^2 - 3*B*a^3*b^3 + 4*A*a^2*b^4 - B*a*b^5 + 2*A*b^6)*c^2*d^4 + (B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c*d^5 + (2*C*a^4*b^2 - 3*B*a^3*b^3 + 4*A*a^2*b^4 - B*a*b^5 + 2*A*b^6)*d^6)*tan(f*x + e)^2 + ((B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c^6 + 2*(C*a^4*b^2 - B*a^3*b^3 + (A + C)*a^2*b^4 - B*a*b^5 + A*b^6)*c^5*d + (2*C*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3 + B*a^2*b^4 - 2*(A - 2*C)*a*b^5 - 2*B*b^6)*c^4*d^2 + 4*(C*a^4*b^2 - B*a^3*b^3 + (A + C)*a^2*b^4 - B*a*b^5 + A*b^6)*c^3*d^3 + (4*C*a^5*b - 6*B*a^4*b^2 + 8*A*a^3*b^3 - B*a^2*b^4 + 2*(A + C)*a*b^5 - B*b^6)*c^2*d^4 + 2*(C*a^4*b^2 - B*a^3*b^3 + (A + C)*a^2*b^4 - B*a*b^5 + A*b^6)*c*d^5 + (2*C*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*d^6)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (2*(C*a^5*b + 2*C*a^3*b^3 + C*a*b^5)*c^5*d - 3*(B*a^5*b + 2*B*a^3*b^3 + B*a*b^5)*c^4*d^2 + (B*a^6 + 4*A*a^5*b + 2*B*a^4*b^2 + 8*A*a^3*b^3 + B*a^2*b^4 + 4*A*a*b^5)*c^3*d^3 - (2*(A - C)*a^6 + B*a^5*b + 4*(A - C)*a^4*b^2 + 2*B*a^3*b^3 + 2*(A - C)*a^2*b^4 + B*a*b^5)*c^2*d^4 - (B*a^6 - 2*A*a^5*b + 2*B*a^4*b^2 - 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*c*d^5 + (2*(C*a^4*b^2 + 2*C*a^2*b^4 + C*b^6)*c^4*d^2 - 3*(B*a^4*b^2 + 2*B*a^2*b^4 + B*b^6)*c^3*d^3 + (B*a^5*b + 4*A*a^4*b^2 + 2*B*a^3*b^3 + 8*A*a^2*b^4 + B*a*b^5 + 4*A*b^6)*c^2*d^4 - (2*(A - C)*a^5*b + B*a^4*b^2 + 4*(A - C)*a^3*b^3 + 2*B*a^2*b^4 + 2*(A - C)*a*b^5 + B*b^6)*c*d^5 - (B*a^5*b - 2*A*a^4*b^2 + 2*B*a^3*b^3 - 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*d^6)*tan(f*x + e)^2 + (2*(C*a^4*b^2 + 2*C*a^2*b^4 + C*b^6)*c^5*d + (2*C*a^5*b - 3*B*a^4*b^2 + 4*C*a^3*b^3 - 6*B*a^2*b^4 + 2*C*a*b^5 - 3*B*b^6)*c^4*d^2 - 2*(B*a^5*b - 2*A*a^4*b^2 + 2*B*a^3*b^3 - 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*c^3*d^3 + (B*a^6 + 2*(A + C)*a^5*b + B*a^4*b^2 + 4*(A + C)*a^3*b^3 - B*a^2*b^4 + 2*(A + C)*a*b^5 - B*b^6)*c^2*d^4 - 2*((A - C)*a^6 + B*a^5*b + (A - 2*C)*a^4*b^2 + 2*B*a^3*b^3 - (A + C)*a^2*b^4 + B*a*b^5 - A*b^6)*c*d^5 - (B*a^6 - 2*A*a^5*b + 2*B*a^4*b^2 - 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*d^6)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*((C*a^3*b^3 - B*a^2*b^4 + A*a*b^5)*c^6 - (C*a^4*b^2 - B*a^3*b^3 + (A + C)*a^2*b^4 - B*a*b^5 + A*b^6)*c^5*d + (C*a^5*b + 5*C*a^3*b^3 - 3*B*a^2*b^4 + (3*A + C)*a*b^5)*c^4*d^2 - (C*a^6 + B*a^5*b + 5*C*a^4*b^2 + (2*A + 5*C)*a^2*b^4 - B*a*b^5 + (2*A + C)*b^6)*c^3*d^3 + (B*a^6 + (A + C)*a^5*b + 3*B*a^4*b^2 + (2*A + 5*C)*a^3*b^3 + (4*A + C)*a*b^5 + B*b^6)*c^2*d^4 - (A*a^6 + B*a^5*b + (3*A + C)*a^4*b^2 + B*a^3*b^3 + (4*A + C)*a^2*b^4 + 2*A*b^6)*c*d^5 + (A*a^5*b + (2*A + C)*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*d^6 + (((A - C)*a^2*b^4 + 2*B*a*b^5 - (A - C)*b^6)*c^6 - 2*((A - C)*a^3*b^3 + B*a^2*b^4 + (A - C)*a*b^5 + B*b^6)*c^5*d - (4*B*a^3*b^3 - 7*(A - C)*a^2*b^4 - 2*B*a*b^5 - (A - C)*b^6)*c^4*d^2 + 2*((A - C)*a^5*b + 2*B*a^4*b^2 + 2*B*a^2*b^4 - (A - C)*a*b^5)*c^3*d^3 - ((A - C)*a^6 - 2*B*a^5*b + 7*(A - C)*a^4*b^2 + 4*B*a^3*b^3)*c^2*d^4 - 2*(B*a^6 - (A - C)*a^5*b + B*a^4*b^2 - (A - C)*a^3*b^3)*c*d^5 + ((A - C)*a^6 + 2*B*a^5*b - (A - C)*a^4*b^2)*d^6)*f*x)*tan(f*x + e))/(((a^4*b^4 + 2*a^2*b^6 + b^8)*c^7*d - 3*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^6*d^2 + (3*a^6*b^2 + 8*a^4*b^4 + 7*a^2*b^6 + 2*b^8)*c^5*d^3 - (a^7*b + 8*a^5*b^3 + 13*a^3*b^5 + 6*a*b^7)*c^4*d^4 + (6*a^6*b^2 + 13*a^4*b^4 + 8*a^2*b^6 + b^8)*c^3*d^5 - (2*a^7*b + 7*a^5*b^3 + 8*a^3*b^5 + 3*a*b^7)*c^2*d^6 + 3*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c*d^7 - (a^7*b + 2*a^5*b^3 + a^3*b^5)*d^8)*f*tan(f*x + e)^2 + ((a^4*b^4 + 2*a^2*b^6 + b^8)*c^8 - 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^7*d + 2*(a^4*b^4 + 2*a^2*b^6 + b^8)*c^6*d^2 + 2*(a^7*b - 3*a^3*b^5 - 2*a*b^7)*c^5*d^3 - (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*c^4*d^4 + 2*(2*a^7*b + 3*a^5*b^3 - a*b^7)*c^3*d^5 - 2*(a^8 + 2*a^6*b^2 + a^4*b^4)*c^2*d^6 + 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c*d^7 - (a^8 + 2*a^6*b^2 + a^4*b^4)*d^8)*f*tan(f*x + e) + ((a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^8 - 3*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^7*d + (3*a^7*b + 8*a^5*b^3 + 7*a^3*b^5 + 2*a*b^7)*c^6*d^2 - (a^8 + 8*a^6*b^2 + 13*a^4*b^4 + 6*a^2*b^6)*c^5*d^3 + (6*a^7*b + 13*a^5*b^3 + 8*a^3*b^5 + a*b^7)*c^4*d^4 - (2*a^8 + 7*a^6*b^2 + 8*a^4*b^4 + 3*a^2*b^6)*c^3*d^5 + 3*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c^2*d^6 - (a^8 + 2*a^6*b^2 + a^4*b^4)*c*d^7)*f)","B",0
83,1,9594,0,17.356413," ","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=""fricas"")","-\frac{{\left(3 \, C a^{4} b^{5} - 5 \, B a^{3} b^{6} + {\left(7 \, A - 3 \, C\right)} a^{2} b^{7} + B a b^{8} + A b^{9}\right)} c^{7} - 2 \, {\left(5 \, C a^{5} b^{4} - 7 \, B a^{4} b^{5} + {\left(9 \, A - C\right)} a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8}\right)} c^{6} d + {\left(7 \, C a^{6} b^{3} - 9 \, B a^{5} b^{4} + {\left(11 \, A + 7 \, C\right)} a^{4} b^{5} - 13 \, B a^{3} b^{6} + {\left(19 \, A - 6 \, C\right)} a^{2} b^{7} + 2 \, B a b^{8} + 2 \, A b^{9}\right)} c^{5} d^{2} - 4 \, {\left(5 \, C a^{5} b^{4} - 7 \, B a^{4} b^{5} + {\left(9 \, A - C\right)} a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8}\right)} c^{4} d^{3} - {\left(2 \, C a^{8} b - 8 \, C a^{6} b^{3} + 18 \, B a^{5} b^{4} - {\left(22 \, A - C\right)} a^{4} b^{5} + 11 \, B a^{3} b^{6} - {\left(17 \, A - 5 \, C\right)} a^{2} b^{7} - B a b^{8} - A b^{9}\right)} c^{3} d^{4} + 2 \, {\left(C a^{9} + B a^{8} b + 3 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} - 2 \, C a^{5} b^{4} + 10 \, B a^{4} b^{5} - {\left(9 \, A - 2 \, C\right)} a^{3} b^{6} + 2 \, B a^{2} b^{7} - 3 \, A a b^{8}\right)} c^{2} d^{5} - {\left(2 \, B a^{9} + 2 \, A a^{8} b + 6 \, B a^{7} b^{2} + {\left(6 \, A - 7 \, C\right)} a^{6} b^{3} + 15 \, B a^{5} b^{4} - {\left(5 \, A + C\right)} a^{4} b^{5} + 5 \, B a^{3} b^{6} - 3 \, A a^{2} b^{7}\right)} c d^{6} + 2 \, {\left(A a^{9} + 3 \, A a^{7} b^{2} + 3 \, A a^{5} b^{4} + A a^{3} b^{6}\right)} d^{7} - {\left({\left(C a^{4} b^{5} - 3 \, B a^{3} b^{6} + 5 \, {\left(A - C\right)} a^{2} b^{7} + 3 \, B a b^{8} - A b^{9}\right)} c^{6} d - 2 \, {\left(3 \, C a^{5} b^{4} - 5 \, B a^{4} b^{5} + {\left(7 \, A - 3 \, C\right)} a^{3} b^{6} + B a^{2} b^{7} + A a b^{8}\right)} c^{5} d^{2} + {\left(3 \, C a^{6} b^{3} - 7 \, B a^{5} b^{4} + {\left(9 \, A - 5 \, C\right)} a^{4} b^{5} - 7 \, B a^{3} b^{6} + {\left(13 \, A - 16 \, C\right)} a^{2} b^{7} + 6 \, B a b^{8} - 2 \, {\left(A + C\right)} b^{9}\right)} c^{4} d^{3} + 2 \, {\left(C a^{7} b^{2} + B a^{6} b^{3} - 3 \, C a^{5} b^{4} + 13 \, B a^{4} b^{5} - {\left(14 \, A - 9 \, C\right)} a^{3} b^{6} + B a^{2} b^{7} - {\left(2 \, A - C\right)} a b^{8} + B b^{9}\right)} c^{3} d^{4} - {\left(2 \, B a^{7} b^{2} + 2 \, {\left(A - 5 \, C\right)} a^{6} b^{3} + 20 \, B a^{5} b^{4} - {\left(12 \, A - C\right)} a^{4} b^{5} + 11 \, B a^{3} b^{6} - 5 \, {\left(A - C\right)} a^{2} b^{7} - B a b^{8} + 3 \, A b^{9}\right)} c^{2} d^{5} + 2 \, {\left(A a^{7} b^{2} + 3 \, {\left(A - C\right)} a^{5} b^{4} + 5 \, B a^{4} b^{5} - {\left(4 \, A - 3 \, C\right)} a^{3} b^{6} - B a^{2} b^{7}\right)} c d^{6} + {\left(5 \, C a^{6} b^{3} - 7 \, B a^{5} b^{4} + {\left(9 \, A - C\right)} a^{4} b^{5} - B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} d^{7} + 2 \, {\left({\left({\left(A - C\right)} a^{3} b^{6} + 3 \, B a^{2} b^{7} - 3 \, {\left(A - C\right)} a b^{8} - B b^{9}\right)} c^{6} d - 2 \, {\left(2 \, {\left(A - C\right)} a^{4} b^{5} + 5 \, B a^{3} b^{6} - 3 \, {\left(A - C\right)} a^{2} b^{7} + B a b^{8} - {\left(A - C\right)} b^{9}\right)} c^{5} d^{2} + {\left(6 \, {\left(A - C\right)} a^{5} b^{4} + 10 \, B a^{4} b^{5} + 5 \, {\left(A - C\right)} a^{3} b^{6} + 15 \, B a^{2} b^{7} - 5 \, {\left(A - C\right)} a b^{8} + B b^{9}\right)} c^{4} d^{3} - 4 \, {\left({\left(A - C\right)} a^{6} b^{3} + 5 \, {\left(A - C\right)} a^{4} b^{5} + 5 \, B a^{3} b^{6} + B a b^{8}\right)} c^{3} d^{4} + {\left({\left(A - C\right)} a^{7} b^{2} - 5 \, B a^{6} b^{3} + 15 \, {\left(A - C\right)} a^{5} b^{4} + 5 \, B a^{4} b^{5} + 10 \, {\left(A - C\right)} a^{3} b^{6} + 6 \, B a^{2} b^{7}\right)} c^{2} d^{5} + 2 \, {\left(B a^{7} b^{2} - {\left(A - C\right)} a^{6} b^{3} + 3 \, B a^{5} b^{4} - 5 \, {\left(A - C\right)} a^{4} b^{5} - 2 \, B a^{3} b^{6}\right)} c d^{6} - {\left({\left(A - C\right)} a^{7} b^{2} + 3 \, B a^{6} b^{3} - 3 \, {\left(A - C\right)} a^{5} b^{4} - B a^{4} b^{5}\right)} d^{7}\right)} f x\right)} \tan\left(f x + e\right)^{3} - 2 \, {\left({\left({\left(A - C\right)} a^{5} b^{4} + 3 \, B a^{4} b^{5} - 3 \, {\left(A - C\right)} a^{3} b^{6} - B a^{2} b^{7}\right)} c^{7} - 2 \, {\left(2 \, {\left(A - C\right)} a^{6} b^{3} + 5 \, B a^{5} b^{4} - 3 \, {\left(A - C\right)} a^{4} b^{5} + B a^{3} b^{6} - {\left(A - C\right)} a^{2} b^{7}\right)} c^{6} d + {\left(6 \, {\left(A - C\right)} a^{7} b^{2} + 10 \, B a^{6} b^{3} + 5 \, {\left(A - C\right)} a^{5} b^{4} + 15 \, B a^{4} b^{5} - 5 \, {\left(A - C\right)} a^{3} b^{6} + B a^{2} b^{7}\right)} c^{5} d^{2} - 4 \, {\left({\left(A - C\right)} a^{8} b + 5 \, {\left(A - C\right)} a^{6} b^{3} + 5 \, B a^{5} b^{4} + B a^{3} b^{6}\right)} c^{4} d^{3} + {\left({\left(A - C\right)} a^{9} - 5 \, B a^{8} b + 15 \, {\left(A - C\right)} a^{7} b^{2} + 5 \, B a^{6} b^{3} + 10 \, {\left(A - C\right)} a^{5} b^{4} + 6 \, B a^{4} b^{5}\right)} c^{3} d^{4} + 2 \, {\left(B a^{9} - {\left(A - C\right)} a^{8} b + 3 \, B a^{7} b^{2} - 5 \, {\left(A - C\right)} a^{6} b^{3} - 2 \, B a^{5} b^{4}\right)} c^{2} d^{5} - {\left({\left(A - C\right)} a^{9} + 3 \, B a^{8} b - 3 \, {\left(A - C\right)} a^{7} b^{2} - B a^{6} b^{3}\right)} c d^{6}\right)} f x - {\left({\left(C a^{4} b^{5} - 3 \, B a^{3} b^{6} + 5 \, {\left(A - C\right)} a^{2} b^{7} + 3 \, B a b^{8} - A b^{9}\right)} c^{7} - 2 \, {\left(2 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} + 4 \, A a^{3} b^{6} - 2 \, B a^{2} b^{7} + 2 \, {\left(2 \, A - C\right)} a b^{8} + B b^{9}\right)} c^{6} d - {\left(3 \, C a^{6} b^{3} - 5 \, B a^{5} b^{4} + {\left(7 \, A - 13 \, C\right)} a^{4} b^{5} + 19 \, B a^{3} b^{6} - {\left(25 \, A - 14 \, C\right)} a^{2} b^{7} - 6 \, B a b^{8} - 2 \, A b^{9}\right)} c^{5} d^{2} + 2 \, {\left(C a^{7} b^{2} - 4 \, B a^{6} b^{3} + {\left(5 \, A - 13 \, C\right)} a^{5} b^{4} + 9 \, B a^{4} b^{5} - {\left(11 \, A + 6 \, C\right)} a^{3} b^{6} + 5 \, B a^{2} b^{7} - 2 \, {\left(5 \, A - C\right)} a b^{8} - 2 \, B b^{9}\right)} c^{4} d^{3} + {\left(4 \, C a^{8} b + 4 \, B a^{7} b^{2} + 8 \, C a^{6} b^{3} + 22 \, B a^{5} b^{4} - {\left(14 \, A - 41 \, C\right)} a^{4} b^{5} - 17 \, B a^{3} b^{6} + {\left(35 \, A - 3 \, C\right)} a^{2} b^{7} + 7 \, B a b^{8} + {\left(7 \, A + 2 \, C\right)} b^{9}\right)} c^{3} d^{4} - 2 \, {\left(2 \, B a^{8} b + {\left(2 \, A - 5 \, C\right)} a^{7} b^{2} + 15 \, B a^{6} b^{3} - {\left(4 \, A - 11 \, C\right)} a^{5} b^{4} + {\left(16 \, A + 3 \, C\right)} a^{3} b^{6} + B a^{2} b^{7} + {\left(10 \, A - C\right)} a b^{8} + 2 \, B b^{9}\right)} c^{2} d^{5} + {\left(4 \, A a^{8} b + 2 \, B a^{7} b^{2} + {\left(14 \, A - 3 \, C\right)} a^{6} b^{3} + 11 \, B a^{5} b^{4} + 11 \, {\left(A + C\right)} a^{4} b^{5} - 7 \, B a^{3} b^{6} + {\left(25 \, A - 4 \, C\right)} a^{2} b^{7} + 2 \, B a b^{8} + 6 \, A b^{9}\right)} c d^{6} - 2 \, {\left({\left(A - 3 \, C\right)} a^{7} b^{2} + 4 \, B a^{6} b^{3} - {\left(2 \, A - 3 \, C\right)} a^{5} b^{4} - 3 \, B a^{4} b^{5} + 6 \, A a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8}\right)} d^{7} + 2 \, {\left({\left({\left(A - C\right)} a^{3} b^{6} + 3 \, B a^{2} b^{7} - 3 \, {\left(A - C\right)} a b^{8} - B b^{9}\right)} c^{7} - 2 \, {\left({\left(A - C\right)} a^{4} b^{5} + 2 \, B a^{3} b^{6} + 2 \, B a b^{8} - {\left(A - C\right)} b^{9}\right)} c^{6} d - {\left(2 \, {\left(A - C\right)} a^{5} b^{4} + 10 \, B a^{4} b^{5} - 17 \, {\left(A - C\right)} a^{3} b^{6} - 11 \, B a^{2} b^{7} + {\left(A - C\right)} a b^{8} - B b^{9}\right)} c^{5} d^{2} + 2 \, {\left(4 \, {\left(A - C\right)} a^{6} b^{3} + 10 \, B a^{5} b^{4} - 5 \, {\left(A - C\right)} a^{4} b^{5} + 5 \, B a^{3} b^{6} - 5 \, {\left(A - C\right)} a^{2} b^{7} - B a b^{8}\right)} c^{4} d^{3} - {\left(7 \, {\left(A - C\right)} a^{7} b^{2} + 5 \, B a^{6} b^{3} + 25 \, {\left(A - C\right)} a^{5} b^{4} + 35 \, B a^{4} b^{5} - 10 \, {\left(A - C\right)} a^{3} b^{6} + 2 \, B a^{2} b^{7}\right)} c^{3} d^{4} + 2 \, {\left({\left(A - C\right)} a^{8} b - 4 \, B a^{7} b^{2} + 14 \, {\left(A - C\right)} a^{6} b^{3} + 8 \, B a^{5} b^{4} + 5 \, {\left(A - C\right)} a^{4} b^{5} + 4 \, B a^{3} b^{6}\right)} c^{2} d^{5} + {\left(4 \, B a^{8} b - 5 \, {\left(A - C\right)} a^{7} b^{2} + 9 \, B a^{6} b^{3} - 17 \, {\left(A - C\right)} a^{5} b^{4} - 7 \, B a^{4} b^{5}\right)} c d^{6} - 2 \, {\left({\left(A - C\right)} a^{8} b + 3 \, B a^{7} b^{2} - 3 \, {\left(A - C\right)} a^{6} b^{3} - B a^{5} b^{4}\right)} d^{7}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left({\left(B a^{5} b^{4} - 3 \, {\left(A - C\right)} a^{4} b^{5} - 3 \, B a^{3} b^{6} + {\left(A - C\right)} a^{2} b^{7}\right)} c^{7} - 2 \, {\left(2 \, B a^{6} b^{3} - 5 \, {\left(A - C\right)} a^{5} b^{4} - 3 \, B a^{4} b^{5} - {\left(A - C\right)} a^{3} b^{6} - B a^{2} b^{7}\right)} c^{6} d - {\left(3 \, C a^{8} b - 6 \, B a^{7} b^{2} + {\left(10 \, A - C\right)} a^{6} b^{3} - 5 \, B a^{5} b^{4} + 3 \, {\left(5 \, A - 2 \, C\right)} a^{4} b^{5} + 5 \, B a^{3} b^{6} + {\left(A + 2 \, C\right)} a^{2} b^{7}\right)} c^{5} d^{2} - 4 \, {\left(2 \, B a^{6} b^{3} - 5 \, {\left(A - C\right)} a^{5} b^{4} - 3 \, B a^{4} b^{5} - {\left(A - C\right)} a^{3} b^{6} - B a^{2} b^{7}\right)} c^{4} d^{3} - {\left(6 \, C a^{8} b - 12 \, B a^{7} b^{2} + 2 \, {\left(10 \, A - C\right)} a^{6} b^{3} - 7 \, B a^{5} b^{4} + 3 \, {\left(7 \, A - C\right)} a^{4} b^{5} + B a^{3} b^{6} + {\left(5 \, A + C\right)} a^{2} b^{7}\right)} c^{3} d^{4} - 2 \, {\left(2 \, B a^{6} b^{3} - 5 \, {\left(A - C\right)} a^{5} b^{4} - 3 \, B a^{4} b^{5} - {\left(A - C\right)} a^{3} b^{6} - B a^{2} b^{7}\right)} c^{2} d^{5} - {\left(3 \, C a^{8} b - 6 \, B a^{7} b^{2} + {\left(10 \, A - C\right)} a^{6} b^{3} - 3 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} - B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} c d^{6} + {\left({\left(B a^{3} b^{6} - 3 \, {\left(A - C\right)} a^{2} b^{7} - 3 \, B a b^{8} + {\left(A - C\right)} b^{9}\right)} c^{6} d - 2 \, {\left(2 \, B a^{4} b^{5} - 5 \, {\left(A - C\right)} a^{3} b^{6} - 3 \, B a^{2} b^{7} - {\left(A - C\right)} a b^{8} - B b^{9}\right)} c^{5} d^{2} - {\left(3 \, C a^{6} b^{3} - 6 \, B a^{5} b^{4} + {\left(10 \, A - C\right)} a^{4} b^{5} - 5 \, B a^{3} b^{6} + 3 \, {\left(5 \, A - 2 \, C\right)} a^{2} b^{7} + 5 \, B a b^{8} + {\left(A + 2 \, C\right)} b^{9}\right)} c^{4} d^{3} - 4 \, {\left(2 \, B a^{4} b^{5} - 5 \, {\left(A - C\right)} a^{3} b^{6} - 3 \, B a^{2} b^{7} - {\left(A - C\right)} a b^{8} - B b^{9}\right)} c^{3} d^{4} - {\left(6 \, C a^{6} b^{3} - 12 \, B a^{5} b^{4} + 2 \, {\left(10 \, A - C\right)} a^{4} b^{5} - 7 \, B a^{3} b^{6} + 3 \, {\left(7 \, A - C\right)} a^{2} b^{7} + B a b^{8} + {\left(5 \, A + C\right)} b^{9}\right)} c^{2} d^{5} - 2 \, {\left(2 \, B a^{4} b^{5} - 5 \, {\left(A - C\right)} a^{3} b^{6} - 3 \, B a^{2} b^{7} - {\left(A - C\right)} a b^{8} - B b^{9}\right)} c d^{6} - {\left(3 \, C a^{6} b^{3} - 6 \, B a^{5} b^{4} + {\left(10 \, A - C\right)} a^{4} b^{5} - 3 \, B a^{3} b^{6} + 9 \, A a^{2} b^{7} - B a b^{8} + 3 \, A b^{9}\right)} d^{7}\right)} \tan\left(f x + e\right)^{3} + {\left({\left(B a^{3} b^{6} - 3 \, {\left(A - C\right)} a^{2} b^{7} - 3 \, B a b^{8} + {\left(A - C\right)} b^{9}\right)} c^{7} - 2 \, {\left(B a^{4} b^{5} - 2 \, {\left(A - C\right)} a^{3} b^{6} - 2 \, {\left(A - C\right)} a b^{8} - B b^{9}\right)} c^{6} d - {\left(3 \, C a^{6} b^{3} + 2 \, B a^{5} b^{4} - {\left(10 \, A - 19 \, C\right)} a^{4} b^{5} - 17 \, B a^{3} b^{6} + {\left(11 \, A - 2 \, C\right)} a^{2} b^{7} + B a b^{8} + {\left(A + 2 \, C\right)} b^{9}\right)} c^{5} d^{2} - 2 \, {\left(3 \, C a^{7} b^{2} - 6 \, B a^{6} b^{3} + {\left(10 \, A - C\right)} a^{5} b^{4} - B a^{4} b^{5} + {\left(5 \, A + 4 \, C\right)} a^{3} b^{6} - B a^{2} b^{7} - {\left(A - 4 \, C\right)} a b^{8} - 2 \, B b^{9}\right)} c^{4} d^{3} - {\left(6 \, C a^{6} b^{3} + 4 \, B a^{5} b^{4} - 2 \, {\left(10 \, A - 19 \, C\right)} a^{4} b^{5} - 31 \, B a^{3} b^{6} + {\left(13 \, A + 5 \, C\right)} a^{2} b^{7} - 7 \, B a b^{8} + {\left(5 \, A + C\right)} b^{9}\right)} c^{3} d^{4} - 2 \, {\left(6 \, C a^{7} b^{2} - 12 \, B a^{6} b^{3} + 2 \, {\left(10 \, A - C\right)} a^{5} b^{4} - 5 \, B a^{4} b^{5} + 2 \, {\left(8 \, A + C\right)} a^{3} b^{6} - 2 \, B a^{2} b^{7} + 2 \, {\left(2 \, A + C\right)} a b^{8} - B b^{9}\right)} c^{2} d^{5} - {\left(3 \, C a^{6} b^{3} + 2 \, B a^{5} b^{4} - {\left(10 \, A - 19 \, C\right)} a^{4} b^{5} - 15 \, B a^{3} b^{6} + {\left(5 \, A + 4 \, C\right)} a^{2} b^{7} - 5 \, B a b^{8} + 3 \, A b^{9}\right)} c d^{6} - 2 \, {\left(3 \, C a^{7} b^{2} - 6 \, B a^{6} b^{3} + {\left(10 \, A - C\right)} a^{5} b^{4} - 3 \, B a^{4} b^{5} + 9 \, A a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8}\right)} d^{7}\right)} \tan\left(f x + e\right)^{2} + {\left(2 \, {\left(B a^{4} b^{5} - 3 \, {\left(A - C\right)} a^{3} b^{6} - 3 \, B a^{2} b^{7} + {\left(A - C\right)} a b^{8}\right)} c^{7} - {\left(7 \, B a^{5} b^{4} - 17 \, {\left(A - C\right)} a^{4} b^{5} - 9 \, B a^{3} b^{6} - 5 \, {\left(A - C\right)} a^{2} b^{7} - 4 \, B a b^{8}\right)} c^{6} d - 2 \, {\left(3 \, C a^{7} b^{2} - 4 \, B a^{6} b^{3} + {\left(5 \, A + 4 \, C\right)} a^{5} b^{4} - 8 \, B a^{4} b^{5} + {\left(14 \, A - 5 \, C\right)} a^{3} b^{6} + 4 \, B a^{2} b^{7} + {\left(A + 2 \, C\right)} a b^{8}\right)} c^{5} d^{2} - {\left(3 \, C a^{8} b - 6 \, B a^{7} b^{2} + {\left(10 \, A - C\right)} a^{6} b^{3} + 11 \, B a^{5} b^{4} - {\left(25 \, A - 34 \, C\right)} a^{4} b^{5} - 19 \, B a^{3} b^{6} - {\left(7 \, A - 10 \, C\right)} a^{2} b^{7} - 8 \, B a b^{8}\right)} c^{4} d^{3} - 2 \, {\left(6 \, C a^{7} b^{2} - 8 \, B a^{6} b^{3} + 2 \, {\left(5 \, A + 4 \, C\right)} a^{5} b^{4} - 13 \, B a^{4} b^{5} + {\left(19 \, A - C\right)} a^{3} b^{6} - B a^{2} b^{7} + {\left(5 \, A + C\right)} a b^{8}\right)} c^{3} d^{4} - {\left(6 \, C a^{8} b - 12 \, B a^{7} b^{2} + 2 \, {\left(10 \, A - C\right)} a^{6} b^{3} + B a^{5} b^{4} + {\left(A + 17 \, C\right)} a^{4} b^{5} - 11 \, B a^{3} b^{6} + {\left(A + 5 \, C\right)} a^{2} b^{7} - 4 \, B a b^{8}\right)} c^{2} d^{5} - 2 \, {\left(3 \, C a^{7} b^{2} - 4 \, B a^{6} b^{3} + {\left(5 \, A + 4 \, C\right)} a^{5} b^{4} - 6 \, B a^{4} b^{5} + {\left(8 \, A + C\right)} a^{3} b^{6} - 2 \, B a^{2} b^{7} + 3 \, A a b^{8}\right)} c d^{6} - {\left(3 \, C a^{8} b - 6 \, B a^{7} b^{2} + {\left(10 \, A - C\right)} a^{6} b^{3} - 3 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} - B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(3 \, {\left(C a^{8} b + 3 \, C a^{6} b^{3} + 3 \, C a^{4} b^{5} + C a^{2} b^{7}\right)} c^{5} d^{2} - 4 \, {\left(B a^{8} b + 3 \, B a^{6} b^{3} + 3 \, B a^{4} b^{5} + B a^{2} b^{7}\right)} c^{4} d^{3} + {\left(B a^{9} + {\left(5 \, A + C\right)} a^{8} b + 3 \, B a^{7} b^{2} + 3 \, {\left(5 \, A + C\right)} a^{6} b^{3} + 3 \, B a^{5} b^{4} + 3 \, {\left(5 \, A + C\right)} a^{4} b^{5} + B a^{3} b^{6} + {\left(5 \, A + C\right)} a^{2} b^{7}\right)} c^{3} d^{4} - 2 \, {\left({\left(A - C\right)} a^{9} + B a^{8} b + 3 \, {\left(A - C\right)} a^{7} b^{2} + 3 \, B a^{6} b^{3} + 3 \, {\left(A - C\right)} a^{5} b^{4} + 3 \, B a^{4} b^{5} + {\left(A - C\right)} a^{3} b^{6} + B a^{2} b^{7}\right)} c^{2} d^{5} - {\left(B a^{9} - 3 \, A a^{8} b + 3 \, B a^{7} b^{2} - 9 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} + B a^{3} b^{6} - 3 \, A a^{2} b^{7}\right)} c d^{6} + {\left(3 \, {\left(C a^{6} b^{3} + 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} + C b^{9}\right)} c^{4} d^{3} - 4 \, {\left(B a^{6} b^{3} + 3 \, B a^{4} b^{5} + 3 \, B a^{2} b^{7} + B b^{9}\right)} c^{3} d^{4} + {\left(B a^{7} b^{2} + {\left(5 \, A + C\right)} a^{6} b^{3} + 3 \, B a^{5} b^{4} + 3 \, {\left(5 \, A + C\right)} a^{4} b^{5} + 3 \, B a^{3} b^{6} + 3 \, {\left(5 \, A + C\right)} a^{2} b^{7} + B a b^{8} + {\left(5 \, A + C\right)} b^{9}\right)} c^{2} d^{5} - 2 \, {\left({\left(A - C\right)} a^{7} b^{2} + B a^{6} b^{3} + 3 \, {\left(A - C\right)} a^{5} b^{4} + 3 \, B a^{4} b^{5} + 3 \, {\left(A - C\right)} a^{3} b^{6} + 3 \, B a^{2} b^{7} + {\left(A - C\right)} a b^{8} + B b^{9}\right)} c d^{6} - {\left(B a^{7} b^{2} - 3 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} + B a b^{8} - 3 \, A b^{9}\right)} d^{7}\right)} \tan\left(f x + e\right)^{3} + {\left(3 \, {\left(C a^{6} b^{3} + 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} + C b^{9}\right)} c^{5} d^{2} + 2 \, {\left(3 \, C a^{7} b^{2} - 2 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 6 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 6 \, B a^{2} b^{7} + 3 \, C a b^{8} - 2 \, B b^{9}\right)} c^{4} d^{3} - {\left(7 \, B a^{7} b^{2} - {\left(5 \, A + C\right)} a^{6} b^{3} + 21 \, B a^{5} b^{4} - 3 \, {\left(5 \, A + C\right)} a^{4} b^{5} + 21 \, B a^{3} b^{6} - 3 \, {\left(5 \, A + C\right)} a^{2} b^{7} + 7 \, B a b^{8} - {\left(5 \, A + C\right)} b^{9}\right)} c^{3} d^{4} + 2 \, {\left(B a^{8} b + 2 \, {\left(2 \, A + C\right)} a^{7} b^{2} + 2 \, B a^{6} b^{3} + 6 \, {\left(2 \, A + C\right)} a^{5} b^{4} + 6 \, {\left(2 \, A + C\right)} a^{3} b^{6} - 2 \, B a^{2} b^{7} + 2 \, {\left(2 \, A + C\right)} a b^{8} - B b^{9}\right)} c^{2} d^{5} - {\left(4 \, {\left(A - C\right)} a^{8} b + 5 \, B a^{7} b^{2} + 3 \, {\left(3 \, A - 4 \, C\right)} a^{6} b^{3} + 15 \, B a^{5} b^{4} + 3 \, {\left(A - 4 \, C\right)} a^{4} b^{5} + 15 \, B a^{3} b^{6} - {\left(5 \, A + 4 \, C\right)} a^{2} b^{7} + 5 \, B a b^{8} - 3 \, A b^{9}\right)} c d^{6} - 2 \, {\left(B a^{8} b - 3 \, A a^{7} b^{2} + 3 \, B a^{6} b^{3} - 9 \, A a^{5} b^{4} + 3 \, B a^{4} b^{5} - 9 \, A a^{3} b^{6} + B a^{2} b^{7} - 3 \, A a b^{8}\right)} d^{7}\right)} \tan\left(f x + e\right)^{2} + {\left(6 \, {\left(C a^{7} b^{2} + 3 \, C a^{5} b^{4} + 3 \, C a^{3} b^{6} + C a b^{8}\right)} c^{5} d^{2} + {\left(3 \, C a^{8} b - 8 \, B a^{7} b^{2} + 9 \, C a^{6} b^{3} - 24 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 24 \, B a^{3} b^{6} + 3 \, C a^{2} b^{7} - 8 \, B a b^{8}\right)} c^{4} d^{3} - 2 \, {\left(B a^{8} b - {\left(5 \, A + C\right)} a^{7} b^{2} + 3 \, B a^{6} b^{3} - 3 \, {\left(5 \, A + C\right)} a^{5} b^{4} + 3 \, B a^{4} b^{5} - 3 \, {\left(5 \, A + C\right)} a^{3} b^{6} + B a^{2} b^{7} - {\left(5 \, A + C\right)} a b^{8}\right)} c^{3} d^{4} + {\left(B a^{9} + {\left(A + 5 \, C\right)} a^{8} b - B a^{7} b^{2} + 3 \, {\left(A + 5 \, C\right)} a^{6} b^{3} - 9 \, B a^{5} b^{4} + 3 \, {\left(A + 5 \, C\right)} a^{4} b^{5} - 11 \, B a^{3} b^{6} + {\left(A + 5 \, C\right)} a^{2} b^{7} - 4 \, B a b^{8}\right)} c^{2} d^{5} - 2 \, {\left({\left(A - C\right)} a^{9} + 2 \, B a^{8} b - 3 \, C a^{7} b^{2} + 6 \, B a^{6} b^{3} - 3 \, {\left(2 \, A + C\right)} a^{5} b^{4} + 6 \, B a^{4} b^{5} - {\left(8 \, A + C\right)} a^{3} b^{6} + 2 \, B a^{2} b^{7} - 3 \, A a b^{8}\right)} c d^{6} - {\left(B a^{9} - 3 \, A a^{8} b + 3 \, B a^{7} b^{2} - 9 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} + B a^{3} b^{6} - 3 \, A a^{2} b^{7}\right)} d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(2 \, {\left(C a^{5} b^{4} - 2 \, B a^{4} b^{5} + 3 \, {\left(A - C\right)} a^{3} b^{6} + 3 \, B a^{2} b^{7} - {\left(3 \, A - 2 \, C\right)} a b^{8} - B b^{9}\right)} c^{7} - {\left(8 \, C a^{6} b^{3} - 12 \, B a^{5} b^{4} + {\left(16 \, A - 9 \, C\right)} a^{4} b^{5} + 7 \, B a^{3} b^{6} - {\left(5 \, A - C\right)} a^{2} b^{7} + B a b^{8} - 3 \, A b^{9}\right)} c^{6} d + 2 \, {\left(3 \, C a^{7} b^{2} - 4 \, B a^{6} b^{3} + {\left(5 \, A + 4 \, C\right)} a^{5} b^{4} - 8 \, B a^{4} b^{5} + {\left(12 \, A - 7 \, C\right)} a^{3} b^{6} + 6 \, B a^{2} b^{7} - {\left(5 \, A - 4 \, C\right)} a b^{8} - 2 \, B b^{9}\right)} c^{5} d^{2} - {\left(2 \, C a^{8} b + 29 \, C a^{6} b^{3} - 33 \, B a^{5} b^{4} + {\left(43 \, A - 11 \, C\right)} a^{4} b^{5} + 11 \, B a^{3} b^{6} - {\left(5 \, A - 4 \, C\right)} a^{2} b^{7} + 2 \, B a b^{8} - 6 \, A b^{9}\right)} c^{4} d^{3} + 2 \, {\left(C a^{9} + B a^{8} b + 11 \, C a^{7} b^{2} - 5 \, B a^{6} b^{3} + 2 \, {\left(5 \, A + 7 \, C\right)} a^{5} b^{4} - 7 \, B a^{4} b^{5} + {\left(15 \, A + 2 \, C\right)} a^{3} b^{6} + 4 \, B a^{2} b^{7} - {\left(A - 4 \, C\right)} a b^{8} - B b^{9}\right)} c^{3} d^{4} - {\left(2 \, B a^{9} + 2 \, {\left(A + 2 \, C\right)} a^{8} b + 10 \, B a^{7} b^{2} + 2 \, {\left(3 \, A + 17 \, C\right)} a^{6} b^{3} - 12 \, B a^{5} b^{4} + {\left(44 \, A + 5 \, C\right)} a^{4} b^{5} + 15 \, B a^{3} b^{6} + {\left(7 \, A + 5 \, C\right)} a^{2} b^{7} + 5 \, B a b^{8} - 3 \, A b^{9}\right)} c^{2} d^{5} + 2 \, {\left(A a^{9} + 2 \, B a^{8} b + {\left(5 \, A + 3 \, C\right)} a^{7} b^{2} + 2 \, B a^{6} b^{3} + 2 \, {\left(7 \, A + C\right)} a^{5} b^{4} + 2 \, B a^{4} b^{5} + {\left(13 \, A - C\right)} a^{3} b^{6} + 2 \, B a^{2} b^{7} + 3 \, A a b^{8}\right)} c d^{6} - {\left(4 \, A a^{8} b + {\left(12 \, A + 7 \, C\right)} a^{6} b^{3} - 9 \, B a^{5} b^{4} + {\left(23 \, A + C\right)} a^{4} b^{5} - 3 \, B a^{3} b^{6} + 9 \, A a^{2} b^{7}\right)} d^{7} + 2 \, {\left(2 \, {\left({\left(A - C\right)} a^{4} b^{5} + 3 \, B a^{3} b^{6} - 3 \, {\left(A - C\right)} a^{2} b^{7} - B a b^{8}\right)} c^{7} - {\left(7 \, {\left(A - C\right)} a^{5} b^{4} + 17 \, B a^{4} b^{5} - 9 \, {\left(A - C\right)} a^{3} b^{6} + 5 \, B a^{2} b^{7} - 4 \, {\left(A - C\right)} a b^{8}\right)} c^{6} d + 2 \, {\left(4 \, {\left(A - C\right)} a^{6} b^{3} + 5 \, B a^{5} b^{4} + 8 \, {\left(A - C\right)} a^{4} b^{5} + 14 \, B a^{3} b^{6} - 4 \, {\left(A - C\right)} a^{2} b^{7} + B a b^{8}\right)} c^{5} d^{2} - {\left(2 \, {\left(A - C\right)} a^{7} b^{2} - 10 \, B a^{6} b^{3} + 35 \, {\left(A - C\right)} a^{5} b^{4} + 25 \, B a^{4} b^{5} + 5 \, {\left(A - C\right)} a^{3} b^{6} + 7 \, B a^{2} b^{7}\right)} c^{4} d^{3} - 2 \, {\left({\left(A - C\right)} a^{8} b + 5 \, B a^{7} b^{2} - 5 \, {\left(A - C\right)} a^{6} b^{3} + 5 \, B a^{5} b^{4} - 10 \, {\left(A - C\right)} a^{4} b^{5} - 4 \, B a^{3} b^{6}\right)} c^{3} d^{4} + {\left({\left(A - C\right)} a^{9} - B a^{8} b + 11 \, {\left(A - C\right)} a^{7} b^{2} + 17 \, B a^{6} b^{3} - 10 \, {\left(A - C\right)} a^{5} b^{4} - 2 \, B a^{4} b^{5}\right)} c^{2} d^{5} + 2 \, {\left(B a^{9} - 2 \, {\left(A - C\right)} a^{8} b - 2 \, {\left(A - C\right)} a^{6} b^{3} - B a^{5} b^{4}\right)} c d^{6} - {\left({\left(A - C\right)} a^{9} + 3 \, B a^{8} b - 3 \, {\left(A - C\right)} a^{7} b^{2} - B a^{6} b^{3}\right)} d^{7}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{6} b^{6} + 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} + b^{12}\right)} c^{8} d - 4 \, {\left(a^{7} b^{5} + 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} + a b^{11}\right)} c^{7} d^{2} + 2 \, {\left(3 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 12 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} c^{6} d^{3} - 4 \, {\left(a^{9} b^{3} + 5 \, a^{7} b^{5} + 9 \, a^{5} b^{7} + 7 \, a^{3} b^{9} + 2 \, a b^{11}\right)} c^{5} d^{4} + {\left(a^{10} b^{2} + 15 \, a^{8} b^{4} + 40 \, a^{6} b^{6} + 40 \, a^{4} b^{8} + 15 \, a^{2} b^{10} + b^{12}\right)} c^{4} d^{5} - 4 \, {\left(2 \, a^{9} b^{3} + 7 \, a^{7} b^{5} + 9 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} c^{3} d^{6} + 2 \, {\left(a^{10} b^{2} + 6 \, a^{8} b^{4} + 12 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 3 \, a^{2} b^{10}\right)} c^{2} d^{7} - 4 \, {\left(a^{9} b^{3} + 3 \, a^{7} b^{5} + 3 \, a^{5} b^{7} + a^{3} b^{9}\right)} c d^{8} + {\left(a^{10} b^{2} + 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} + a^{4} b^{8}\right)} d^{9}\right)} f \tan\left(f x + e\right)^{3} + {\left({\left(a^{6} b^{6} + 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} + b^{12}\right)} c^{9} - 2 \, {\left(a^{7} b^{5} + 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} + a b^{11}\right)} c^{8} d - 2 \, {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} - 2 \, a^{2} b^{10} - b^{12}\right)} c^{7} d^{2} + 4 \, {\left(2 \, a^{9} b^{3} + 5 \, a^{7} b^{5} + 3 \, a^{5} b^{7} - a^{3} b^{9} - a b^{11}\right)} c^{6} d^{3} - {\left(7 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 32 \, a^{6} b^{6} + 16 \, a^{4} b^{8} + a^{2} b^{10} - b^{12}\right)} c^{5} d^{4} + 2 \, {\left(a^{11} b + 11 \, a^{9} b^{3} + 26 \, a^{7} b^{5} + 22 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} c^{4} d^{5} - 2 \, {\left(7 \, a^{10} b^{2} + 22 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{3} d^{6} + 4 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 9 \, a^{7} b^{5} + 7 \, a^{5} b^{7} + 2 \, a^{3} b^{9}\right)} c^{2} d^{7} - 7 \, {\left(a^{10} b^{2} + 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} + a^{4} b^{8}\right)} c d^{8} + 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} d^{9}\right)} f \tan\left(f x + e\right)^{2} + {\left(2 \, {\left(a^{7} b^{5} + 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} + a b^{11}\right)} c^{9} - 7 \, {\left(a^{8} b^{4} + 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{8} d + 4 \, {\left(2 \, a^{9} b^{3} + 7 \, a^{7} b^{5} + 9 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} c^{7} d^{2} - 2 \, {\left(a^{10} b^{2} + 10 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 22 \, a^{4} b^{8} + 7 \, a^{2} b^{10}\right)} c^{6} d^{3} - 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} - 22 \, a^{7} b^{5} - 26 \, a^{5} b^{7} - 11 \, a^{3} b^{9} - a b^{11}\right)} c^{5} d^{4} + {\left(a^{12} - a^{10} b^{2} - 16 \, a^{8} b^{4} - 32 \, a^{6} b^{6} - 25 \, a^{4} b^{8} - 7 \, a^{2} b^{10}\right)} c^{4} d^{5} - 4 \, {\left(a^{11} b + a^{9} b^{3} - 3 \, a^{7} b^{5} - 5 \, a^{5} b^{7} - 2 \, a^{3} b^{9}\right)} c^{3} d^{6} + 2 \, {\left(a^{12} + 2 \, a^{10} b^{2} - 2 \, a^{6} b^{6} - a^{4} b^{8}\right)} c^{2} d^{7} - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} c d^{8} + {\left(a^{12} + 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} + a^{6} b^{6}\right)} d^{9}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{8} b^{4} + 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{9} - 4 \, {\left(a^{9} b^{3} + 3 \, a^{7} b^{5} + 3 \, a^{5} b^{7} + a^{3} b^{9}\right)} c^{8} d + 2 \, {\left(3 \, a^{10} b^{2} + 10 \, a^{8} b^{4} + 12 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{7} d^{2} - 4 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 9 \, a^{7} b^{5} + 7 \, a^{5} b^{7} + 2 \, a^{3} b^{9}\right)} c^{6} d^{3} + {\left(a^{12} + 15 \, a^{10} b^{2} + 40 \, a^{8} b^{4} + 40 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{5} d^{4} - 4 \, {\left(2 \, a^{11} b + 7 \, a^{9} b^{3} + 9 \, a^{7} b^{5} + 5 \, a^{5} b^{7} + a^{3} b^{9}\right)} c^{4} d^{5} + 2 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 12 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 3 \, a^{4} b^{8}\right)} c^{3} d^{6} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} c^{2} d^{7} + {\left(a^{12} + 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} + a^{6} b^{6}\right)} c d^{8}\right)} f\right)}}"," ",0,"-1/2*((3*C*a^4*b^5 - 5*B*a^3*b^6 + (7*A - 3*C)*a^2*b^7 + B*a*b^8 + A*b^9)*c^7 - 2*(5*C*a^5*b^4 - 7*B*a^4*b^5 + (9*A - C)*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8)*c^6*d + (7*C*a^6*b^3 - 9*B*a^5*b^4 + (11*A + 7*C)*a^4*b^5 - 13*B*a^3*b^6 + (19*A - 6*C)*a^2*b^7 + 2*B*a*b^8 + 2*A*b^9)*c^5*d^2 - 4*(5*C*a^5*b^4 - 7*B*a^4*b^5 + (9*A - C)*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8)*c^4*d^3 - (2*C*a^8*b - 8*C*a^6*b^3 + 18*B*a^5*b^4 - (22*A - C)*a^4*b^5 + 11*B*a^3*b^6 - (17*A - 5*C)*a^2*b^7 - B*a*b^8 - A*b^9)*c^3*d^4 + 2*(C*a^9 + B*a^8*b + 3*C*a^7*b^2 + 3*B*a^6*b^3 - 2*C*a^5*b^4 + 10*B*a^4*b^5 - (9*A - 2*C)*a^3*b^6 + 2*B*a^2*b^7 - 3*A*a*b^8)*c^2*d^5 - (2*B*a^9 + 2*A*a^8*b + 6*B*a^7*b^2 + (6*A - 7*C)*a^6*b^3 + 15*B*a^5*b^4 - (5*A + C)*a^4*b^5 + 5*B*a^3*b^6 - 3*A*a^2*b^7)*c*d^6 + 2*(A*a^9 + 3*A*a^7*b^2 + 3*A*a^5*b^4 + A*a^3*b^6)*d^7 - ((C*a^4*b^5 - 3*B*a^3*b^6 + 5*(A - C)*a^2*b^7 + 3*B*a*b^8 - A*b^9)*c^6*d - 2*(3*C*a^5*b^4 - 5*B*a^4*b^5 + (7*A - 3*C)*a^3*b^6 + B*a^2*b^7 + A*a*b^8)*c^5*d^2 + (3*C*a^6*b^3 - 7*B*a^5*b^4 + (9*A - 5*C)*a^4*b^5 - 7*B*a^3*b^6 + (13*A - 16*C)*a^2*b^7 + 6*B*a*b^8 - 2*(A + C)*b^9)*c^4*d^3 + 2*(C*a^7*b^2 + B*a^6*b^3 - 3*C*a^5*b^4 + 13*B*a^4*b^5 - (14*A - 9*C)*a^3*b^6 + B*a^2*b^7 - (2*A - C)*a*b^8 + B*b^9)*c^3*d^4 - (2*B*a^7*b^2 + 2*(A - 5*C)*a^6*b^3 + 20*B*a^5*b^4 - (12*A - C)*a^4*b^5 + 11*B*a^3*b^6 - 5*(A - C)*a^2*b^7 - B*a*b^8 + 3*A*b^9)*c^2*d^5 + 2*(A*a^7*b^2 + 3*(A - C)*a^5*b^4 + 5*B*a^4*b^5 - (4*A - 3*C)*a^3*b^6 - B*a^2*b^7)*c*d^6 + (5*C*a^6*b^3 - 7*B*a^5*b^4 + (9*A - C)*a^4*b^5 - B*a^3*b^6 + 3*A*a^2*b^7)*d^7 + 2*(((A - C)*a^3*b^6 + 3*B*a^2*b^7 - 3*(A - C)*a*b^8 - B*b^9)*c^6*d - 2*(2*(A - C)*a^4*b^5 + 5*B*a^3*b^6 - 3*(A - C)*a^2*b^7 + B*a*b^8 - (A - C)*b^9)*c^5*d^2 + (6*(A - C)*a^5*b^4 + 10*B*a^4*b^5 + 5*(A - C)*a^3*b^6 + 15*B*a^2*b^7 - 5*(A - C)*a*b^8 + B*b^9)*c^4*d^3 - 4*((A - C)*a^6*b^3 + 5*(A - C)*a^4*b^5 + 5*B*a^3*b^6 + B*a*b^8)*c^3*d^4 + ((A - C)*a^7*b^2 - 5*B*a^6*b^3 + 15*(A - C)*a^5*b^4 + 5*B*a^4*b^5 + 10*(A - C)*a^3*b^6 + 6*B*a^2*b^7)*c^2*d^5 + 2*(B*a^7*b^2 - (A - C)*a^6*b^3 + 3*B*a^5*b^4 - 5*(A - C)*a^4*b^5 - 2*B*a^3*b^6)*c*d^6 - ((A - C)*a^7*b^2 + 3*B*a^6*b^3 - 3*(A - C)*a^5*b^4 - B*a^4*b^5)*d^7)*f*x)*tan(f*x + e)^3 - 2*(((A - C)*a^5*b^4 + 3*B*a^4*b^5 - 3*(A - C)*a^3*b^6 - B*a^2*b^7)*c^7 - 2*(2*(A - C)*a^6*b^3 + 5*B*a^5*b^4 - 3*(A - C)*a^4*b^5 + B*a^3*b^6 - (A - C)*a^2*b^7)*c^6*d + (6*(A - C)*a^7*b^2 + 10*B*a^6*b^3 + 5*(A - C)*a^5*b^4 + 15*B*a^4*b^5 - 5*(A - C)*a^3*b^6 + B*a^2*b^7)*c^5*d^2 - 4*((A - C)*a^8*b + 5*(A - C)*a^6*b^3 + 5*B*a^5*b^4 + B*a^3*b^6)*c^4*d^3 + ((A - C)*a^9 - 5*B*a^8*b + 15*(A - C)*a^7*b^2 + 5*B*a^6*b^3 + 10*(A - C)*a^5*b^4 + 6*B*a^4*b^5)*c^3*d^4 + 2*(B*a^9 - (A - C)*a^8*b + 3*B*a^7*b^2 - 5*(A - C)*a^6*b^3 - 2*B*a^5*b^4)*c^2*d^5 - ((A - C)*a^9 + 3*B*a^8*b - 3*(A - C)*a^7*b^2 - B*a^6*b^3)*c*d^6)*f*x - ((C*a^4*b^5 - 3*B*a^3*b^6 + 5*(A - C)*a^2*b^7 + 3*B*a*b^8 - A*b^9)*c^7 - 2*(2*C*a^5*b^4 - 3*B*a^4*b^5 + 4*A*a^3*b^6 - 2*B*a^2*b^7 + 2*(2*A - C)*a*b^8 + B*b^9)*c^6*d - (3*C*a^6*b^3 - 5*B*a^5*b^4 + (7*A - 13*C)*a^4*b^5 + 19*B*a^3*b^6 - (25*A - 14*C)*a^2*b^7 - 6*B*a*b^8 - 2*A*b^9)*c^5*d^2 + 2*(C*a^7*b^2 - 4*B*a^6*b^3 + (5*A - 13*C)*a^5*b^4 + 9*B*a^4*b^5 - (11*A + 6*C)*a^3*b^6 + 5*B*a^2*b^7 - 2*(5*A - C)*a*b^8 - 2*B*b^9)*c^4*d^3 + (4*C*a^8*b + 4*B*a^7*b^2 + 8*C*a^6*b^3 + 22*B*a^5*b^4 - (14*A - 41*C)*a^4*b^5 - 17*B*a^3*b^6 + (35*A - 3*C)*a^2*b^7 + 7*B*a*b^8 + (7*A + 2*C)*b^9)*c^3*d^4 - 2*(2*B*a^8*b + (2*A - 5*C)*a^7*b^2 + 15*B*a^6*b^3 - (4*A - 11*C)*a^5*b^4 + (16*A + 3*C)*a^3*b^6 + B*a^2*b^7 + (10*A - C)*a*b^8 + 2*B*b^9)*c^2*d^5 + (4*A*a^8*b + 2*B*a^7*b^2 + (14*A - 3*C)*a^6*b^3 + 11*B*a^5*b^4 + 11*(A + C)*a^4*b^5 - 7*B*a^3*b^6 + (25*A - 4*C)*a^2*b^7 + 2*B*a*b^8 + 6*A*b^9)*c*d^6 - 2*((A - 3*C)*a^7*b^2 + 4*B*a^6*b^3 - (2*A - 3*C)*a^5*b^4 - 3*B*a^4*b^5 + 6*A*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8)*d^7 + 2*(((A - C)*a^3*b^6 + 3*B*a^2*b^7 - 3*(A - C)*a*b^8 - B*b^9)*c^7 - 2*((A - C)*a^4*b^5 + 2*B*a^3*b^6 + 2*B*a*b^8 - (A - C)*b^9)*c^6*d - (2*(A - C)*a^5*b^4 + 10*B*a^4*b^5 - 17*(A - C)*a^3*b^6 - 11*B*a^2*b^7 + (A - C)*a*b^8 - B*b^9)*c^5*d^2 + 2*(4*(A - C)*a^6*b^3 + 10*B*a^5*b^4 - 5*(A - C)*a^4*b^5 + 5*B*a^3*b^6 - 5*(A - C)*a^2*b^7 - B*a*b^8)*c^4*d^3 - (7*(A - C)*a^7*b^2 + 5*B*a^6*b^3 + 25*(A - C)*a^5*b^4 + 35*B*a^4*b^5 - 10*(A - C)*a^3*b^6 + 2*B*a^2*b^7)*c^3*d^4 + 2*((A - C)*a^8*b - 4*B*a^7*b^2 + 14*(A - C)*a^6*b^3 + 8*B*a^5*b^4 + 5*(A - C)*a^4*b^5 + 4*B*a^3*b^6)*c^2*d^5 + (4*B*a^8*b - 5*(A - C)*a^7*b^2 + 9*B*a^6*b^3 - 17*(A - C)*a^5*b^4 - 7*B*a^4*b^5)*c*d^6 - 2*((A - C)*a^8*b + 3*B*a^7*b^2 - 3*(A - C)*a^6*b^3 - B*a^5*b^4)*d^7)*f*x)*tan(f*x + e)^2 + ((B*a^5*b^4 - 3*(A - C)*a^4*b^5 - 3*B*a^3*b^6 + (A - C)*a^2*b^7)*c^7 - 2*(2*B*a^6*b^3 - 5*(A - C)*a^5*b^4 - 3*B*a^4*b^5 - (A - C)*a^3*b^6 - B*a^2*b^7)*c^6*d - (3*C*a^8*b - 6*B*a^7*b^2 + (10*A - C)*a^6*b^3 - 5*B*a^5*b^4 + 3*(5*A - 2*C)*a^4*b^5 + 5*B*a^3*b^6 + (A + 2*C)*a^2*b^7)*c^5*d^2 - 4*(2*B*a^6*b^3 - 5*(A - C)*a^5*b^4 - 3*B*a^4*b^5 - (A - C)*a^3*b^6 - B*a^2*b^7)*c^4*d^3 - (6*C*a^8*b - 12*B*a^7*b^2 + 2*(10*A - C)*a^6*b^3 - 7*B*a^5*b^4 + 3*(7*A - C)*a^4*b^5 + B*a^3*b^6 + (5*A + C)*a^2*b^7)*c^3*d^4 - 2*(2*B*a^6*b^3 - 5*(A - C)*a^5*b^4 - 3*B*a^4*b^5 - (A - C)*a^3*b^6 - B*a^2*b^7)*c^2*d^5 - (3*C*a^8*b - 6*B*a^7*b^2 + (10*A - C)*a^6*b^3 - 3*B*a^5*b^4 + 9*A*a^4*b^5 - B*a^3*b^6 + 3*A*a^2*b^7)*c*d^6 + ((B*a^3*b^6 - 3*(A - C)*a^2*b^7 - 3*B*a*b^8 + (A - C)*b^9)*c^6*d - 2*(2*B*a^4*b^5 - 5*(A - C)*a^3*b^6 - 3*B*a^2*b^7 - (A - C)*a*b^8 - B*b^9)*c^5*d^2 - (3*C*a^6*b^3 - 6*B*a^5*b^4 + (10*A - C)*a^4*b^5 - 5*B*a^3*b^6 + 3*(5*A - 2*C)*a^2*b^7 + 5*B*a*b^8 + (A + 2*C)*b^9)*c^4*d^3 - 4*(2*B*a^4*b^5 - 5*(A - C)*a^3*b^6 - 3*B*a^2*b^7 - (A - C)*a*b^8 - B*b^9)*c^3*d^4 - (6*C*a^6*b^3 - 12*B*a^5*b^4 + 2*(10*A - C)*a^4*b^5 - 7*B*a^3*b^6 + 3*(7*A - C)*a^2*b^7 + B*a*b^8 + (5*A + C)*b^9)*c^2*d^5 - 2*(2*B*a^4*b^5 - 5*(A - C)*a^3*b^6 - 3*B*a^2*b^7 - (A - C)*a*b^8 - B*b^9)*c*d^6 - (3*C*a^6*b^3 - 6*B*a^5*b^4 + (10*A - C)*a^4*b^5 - 3*B*a^3*b^6 + 9*A*a^2*b^7 - B*a*b^8 + 3*A*b^9)*d^7)*tan(f*x + e)^3 + ((B*a^3*b^6 - 3*(A - C)*a^2*b^7 - 3*B*a*b^8 + (A - C)*b^9)*c^7 - 2*(B*a^4*b^5 - 2*(A - C)*a^3*b^6 - 2*(A - C)*a*b^8 - B*b^9)*c^6*d - (3*C*a^6*b^3 + 2*B*a^5*b^4 - (10*A - 19*C)*a^4*b^5 - 17*B*a^3*b^6 + (11*A - 2*C)*a^2*b^7 + B*a*b^8 + (A + 2*C)*b^9)*c^5*d^2 - 2*(3*C*a^7*b^2 - 6*B*a^6*b^3 + (10*A - C)*a^5*b^4 - B*a^4*b^5 + (5*A + 4*C)*a^3*b^6 - B*a^2*b^7 - (A - 4*C)*a*b^8 - 2*B*b^9)*c^4*d^3 - (6*C*a^6*b^3 + 4*B*a^5*b^4 - 2*(10*A - 19*C)*a^4*b^5 - 31*B*a^3*b^6 + (13*A + 5*C)*a^2*b^7 - 7*B*a*b^8 + (5*A + C)*b^9)*c^3*d^4 - 2*(6*C*a^7*b^2 - 12*B*a^6*b^3 + 2*(10*A - C)*a^5*b^4 - 5*B*a^4*b^5 + 2*(8*A + C)*a^3*b^6 - 2*B*a^2*b^7 + 2*(2*A + C)*a*b^8 - B*b^9)*c^2*d^5 - (3*C*a^6*b^3 + 2*B*a^5*b^4 - (10*A - 19*C)*a^4*b^5 - 15*B*a^3*b^6 + (5*A + 4*C)*a^2*b^7 - 5*B*a*b^8 + 3*A*b^9)*c*d^6 - 2*(3*C*a^7*b^2 - 6*B*a^6*b^3 + (10*A - C)*a^5*b^4 - 3*B*a^4*b^5 + 9*A*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8)*d^7)*tan(f*x + e)^2 + (2*(B*a^4*b^5 - 3*(A - C)*a^3*b^6 - 3*B*a^2*b^7 + (A - C)*a*b^8)*c^7 - (7*B*a^5*b^4 - 17*(A - C)*a^4*b^5 - 9*B*a^3*b^6 - 5*(A - C)*a^2*b^7 - 4*B*a*b^8)*c^6*d - 2*(3*C*a^7*b^2 - 4*B*a^6*b^3 + (5*A + 4*C)*a^5*b^4 - 8*B*a^4*b^5 + (14*A - 5*C)*a^3*b^6 + 4*B*a^2*b^7 + (A + 2*C)*a*b^8)*c^5*d^2 - (3*C*a^8*b - 6*B*a^7*b^2 + (10*A - C)*a^6*b^3 + 11*B*a^5*b^4 - (25*A - 34*C)*a^4*b^5 - 19*B*a^3*b^6 - (7*A - 10*C)*a^2*b^7 - 8*B*a*b^8)*c^4*d^3 - 2*(6*C*a^7*b^2 - 8*B*a^6*b^3 + 2*(5*A + 4*C)*a^5*b^4 - 13*B*a^4*b^5 + (19*A - C)*a^3*b^6 - B*a^2*b^7 + (5*A + C)*a*b^8)*c^3*d^4 - (6*C*a^8*b - 12*B*a^7*b^2 + 2*(10*A - C)*a^6*b^3 + B*a^5*b^4 + (A + 17*C)*a^4*b^5 - 11*B*a^3*b^6 + (A + 5*C)*a^2*b^7 - 4*B*a*b^8)*c^2*d^5 - 2*(3*C*a^7*b^2 - 4*B*a^6*b^3 + (5*A + 4*C)*a^5*b^4 - 6*B*a^4*b^5 + (8*A + C)*a^3*b^6 - 2*B*a^2*b^7 + 3*A*a*b^8)*c*d^6 - (3*C*a^8*b - 6*B*a^7*b^2 + (10*A - C)*a^6*b^3 - 3*B*a^5*b^4 + 9*A*a^4*b^5 - B*a^3*b^6 + 3*A*a^2*b^7)*d^7)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) + (3*(C*a^8*b + 3*C*a^6*b^3 + 3*C*a^4*b^5 + C*a^2*b^7)*c^5*d^2 - 4*(B*a^8*b + 3*B*a^6*b^3 + 3*B*a^4*b^5 + B*a^2*b^7)*c^4*d^3 + (B*a^9 + (5*A + C)*a^8*b + 3*B*a^7*b^2 + 3*(5*A + C)*a^6*b^3 + 3*B*a^5*b^4 + 3*(5*A + C)*a^4*b^5 + B*a^3*b^6 + (5*A + C)*a^2*b^7)*c^3*d^4 - 2*((A - C)*a^9 + B*a^8*b + 3*(A - C)*a^7*b^2 + 3*B*a^6*b^3 + 3*(A - C)*a^5*b^4 + 3*B*a^4*b^5 + (A - C)*a^3*b^6 + B*a^2*b^7)*c^2*d^5 - (B*a^9 - 3*A*a^8*b + 3*B*a^7*b^2 - 9*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 + B*a^3*b^6 - 3*A*a^2*b^7)*c*d^6 + (3*(C*a^6*b^3 + 3*C*a^4*b^5 + 3*C*a^2*b^7 + C*b^9)*c^4*d^3 - 4*(B*a^6*b^3 + 3*B*a^4*b^5 + 3*B*a^2*b^7 + B*b^9)*c^3*d^4 + (B*a^7*b^2 + (5*A + C)*a^6*b^3 + 3*B*a^5*b^4 + 3*(5*A + C)*a^4*b^5 + 3*B*a^3*b^6 + 3*(5*A + C)*a^2*b^7 + B*a*b^8 + (5*A + C)*b^9)*c^2*d^5 - 2*((A - C)*a^7*b^2 + B*a^6*b^3 + 3*(A - C)*a^5*b^4 + 3*B*a^4*b^5 + 3*(A - C)*a^3*b^6 + 3*B*a^2*b^7 + (A - C)*a*b^8 + B*b^9)*c*d^6 - (B*a^7*b^2 - 3*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7 + B*a*b^8 - 3*A*b^9)*d^7)*tan(f*x + e)^3 + (3*(C*a^6*b^3 + 3*C*a^4*b^5 + 3*C*a^2*b^7 + C*b^9)*c^5*d^2 + 2*(3*C*a^7*b^2 - 2*B*a^6*b^3 + 9*C*a^5*b^4 - 6*B*a^4*b^5 + 9*C*a^3*b^6 - 6*B*a^2*b^7 + 3*C*a*b^8 - 2*B*b^9)*c^4*d^3 - (7*B*a^7*b^2 - (5*A + C)*a^6*b^3 + 21*B*a^5*b^4 - 3*(5*A + C)*a^4*b^5 + 21*B*a^3*b^6 - 3*(5*A + C)*a^2*b^7 + 7*B*a*b^8 - (5*A + C)*b^9)*c^3*d^4 + 2*(B*a^8*b + 2*(2*A + C)*a^7*b^2 + 2*B*a^6*b^3 + 6*(2*A + C)*a^5*b^4 + 6*(2*A + C)*a^3*b^6 - 2*B*a^2*b^7 + 2*(2*A + C)*a*b^8 - B*b^9)*c^2*d^5 - (4*(A - C)*a^8*b + 5*B*a^7*b^2 + 3*(3*A - 4*C)*a^6*b^3 + 15*B*a^5*b^4 + 3*(A - 4*C)*a^4*b^5 + 15*B*a^3*b^6 - (5*A + 4*C)*a^2*b^7 + 5*B*a*b^8 - 3*A*b^9)*c*d^6 - 2*(B*a^8*b - 3*A*a^7*b^2 + 3*B*a^6*b^3 - 9*A*a^5*b^4 + 3*B*a^4*b^5 - 9*A*a^3*b^6 + B*a^2*b^7 - 3*A*a*b^8)*d^7)*tan(f*x + e)^2 + (6*(C*a^7*b^2 + 3*C*a^5*b^4 + 3*C*a^3*b^6 + C*a*b^8)*c^5*d^2 + (3*C*a^8*b - 8*B*a^7*b^2 + 9*C*a^6*b^3 - 24*B*a^5*b^4 + 9*C*a^4*b^5 - 24*B*a^3*b^6 + 3*C*a^2*b^7 - 8*B*a*b^8)*c^4*d^3 - 2*(B*a^8*b - (5*A + C)*a^7*b^2 + 3*B*a^6*b^3 - 3*(5*A + C)*a^5*b^4 + 3*B*a^4*b^5 - 3*(5*A + C)*a^3*b^6 + B*a^2*b^7 - (5*A + C)*a*b^8)*c^3*d^4 + (B*a^9 + (A + 5*C)*a^8*b - B*a^7*b^2 + 3*(A + 5*C)*a^6*b^3 - 9*B*a^5*b^4 + 3*(A + 5*C)*a^4*b^5 - 11*B*a^3*b^6 + (A + 5*C)*a^2*b^7 - 4*B*a*b^8)*c^2*d^5 - 2*((A - C)*a^9 + 2*B*a^8*b - 3*C*a^7*b^2 + 6*B*a^6*b^3 - 3*(2*A + C)*a^5*b^4 + 6*B*a^4*b^5 - (8*A + C)*a^3*b^6 + 2*B*a^2*b^7 - 3*A*a*b^8)*c*d^6 - (B*a^9 - 3*A*a^8*b + 3*B*a^7*b^2 - 9*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 + B*a^3*b^6 - 3*A*a^2*b^7)*d^7)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (2*(C*a^5*b^4 - 2*B*a^4*b^5 + 3*(A - C)*a^3*b^6 + 3*B*a^2*b^7 - (3*A - 2*C)*a*b^8 - B*b^9)*c^7 - (8*C*a^6*b^3 - 12*B*a^5*b^4 + (16*A - 9*C)*a^4*b^5 + 7*B*a^3*b^6 - (5*A - C)*a^2*b^7 + B*a*b^8 - 3*A*b^9)*c^6*d + 2*(3*C*a^7*b^2 - 4*B*a^6*b^3 + (5*A + 4*C)*a^5*b^4 - 8*B*a^4*b^5 + (12*A - 7*C)*a^3*b^6 + 6*B*a^2*b^7 - (5*A - 4*C)*a*b^8 - 2*B*b^9)*c^5*d^2 - (2*C*a^8*b + 29*C*a^6*b^3 - 33*B*a^5*b^4 + (43*A - 11*C)*a^4*b^5 + 11*B*a^3*b^6 - (5*A - 4*C)*a^2*b^7 + 2*B*a*b^8 - 6*A*b^9)*c^4*d^3 + 2*(C*a^9 + B*a^8*b + 11*C*a^7*b^2 - 5*B*a^6*b^3 + 2*(5*A + 7*C)*a^5*b^4 - 7*B*a^4*b^5 + (15*A + 2*C)*a^3*b^6 + 4*B*a^2*b^7 - (A - 4*C)*a*b^8 - B*b^9)*c^3*d^4 - (2*B*a^9 + 2*(A + 2*C)*a^8*b + 10*B*a^7*b^2 + 2*(3*A + 17*C)*a^6*b^3 - 12*B*a^5*b^4 + (44*A + 5*C)*a^4*b^5 + 15*B*a^3*b^6 + (7*A + 5*C)*a^2*b^7 + 5*B*a*b^8 - 3*A*b^9)*c^2*d^5 + 2*(A*a^9 + 2*B*a^8*b + (5*A + 3*C)*a^7*b^2 + 2*B*a^6*b^3 + 2*(7*A + C)*a^5*b^4 + 2*B*a^4*b^5 + (13*A - C)*a^3*b^6 + 2*B*a^2*b^7 + 3*A*a*b^8)*c*d^6 - (4*A*a^8*b + (12*A + 7*C)*a^6*b^3 - 9*B*a^5*b^4 + (23*A + C)*a^4*b^5 - 3*B*a^3*b^6 + 9*A*a^2*b^7)*d^7 + 2*(2*((A - C)*a^4*b^5 + 3*B*a^3*b^6 - 3*(A - C)*a^2*b^7 - B*a*b^8)*c^7 - (7*(A - C)*a^5*b^4 + 17*B*a^4*b^5 - 9*(A - C)*a^3*b^6 + 5*B*a^2*b^7 - 4*(A - C)*a*b^8)*c^6*d + 2*(4*(A - C)*a^6*b^3 + 5*B*a^5*b^4 + 8*(A - C)*a^4*b^5 + 14*B*a^3*b^6 - 4*(A - C)*a^2*b^7 + B*a*b^8)*c^5*d^2 - (2*(A - C)*a^7*b^2 - 10*B*a^6*b^3 + 35*(A - C)*a^5*b^4 + 25*B*a^4*b^5 + 5*(A - C)*a^3*b^6 + 7*B*a^2*b^7)*c^4*d^3 - 2*((A - C)*a^8*b + 5*B*a^7*b^2 - 5*(A - C)*a^6*b^3 + 5*B*a^5*b^4 - 10*(A - C)*a^4*b^5 - 4*B*a^3*b^6)*c^3*d^4 + ((A - C)*a^9 - B*a^8*b + 11*(A - C)*a^7*b^2 + 17*B*a^6*b^3 - 10*(A - C)*a^5*b^4 - 2*B*a^4*b^5)*c^2*d^5 + 2*(B*a^9 - 2*(A - C)*a^8*b - 2*(A - C)*a^6*b^3 - B*a^5*b^4)*c*d^6 - ((A - C)*a^9 + 3*B*a^8*b - 3*(A - C)*a^7*b^2 - B*a^6*b^3)*d^7)*f*x)*tan(f*x + e))/(((a^6*b^6 + 3*a^4*b^8 + 3*a^2*b^10 + b^12)*c^8*d - 4*(a^7*b^5 + 3*a^5*b^7 + 3*a^3*b^9 + a*b^11)*c^7*d^2 + 2*(3*a^8*b^4 + 10*a^6*b^6 + 12*a^4*b^8 + 6*a^2*b^10 + b^12)*c^6*d^3 - 4*(a^9*b^3 + 5*a^7*b^5 + 9*a^5*b^7 + 7*a^3*b^9 + 2*a*b^11)*c^5*d^4 + (a^10*b^2 + 15*a^8*b^4 + 40*a^6*b^6 + 40*a^4*b^8 + 15*a^2*b^10 + b^12)*c^4*d^5 - 4*(2*a^9*b^3 + 7*a^7*b^5 + 9*a^5*b^7 + 5*a^3*b^9 + a*b^11)*c^3*d^6 + 2*(a^10*b^2 + 6*a^8*b^4 + 12*a^6*b^6 + 10*a^4*b^8 + 3*a^2*b^10)*c^2*d^7 - 4*(a^9*b^3 + 3*a^7*b^5 + 3*a^5*b^7 + a^3*b^9)*c*d^8 + (a^10*b^2 + 3*a^8*b^4 + 3*a^6*b^6 + a^4*b^8)*d^9)*f*tan(f*x + e)^3 + ((a^6*b^6 + 3*a^4*b^8 + 3*a^2*b^10 + b^12)*c^9 - 2*(a^7*b^5 + 3*a^5*b^7 + 3*a^3*b^9 + a*b^11)*c^8*d - 2*(a^8*b^4 + 2*a^6*b^6 - 2*a^2*b^10 - b^12)*c^7*d^2 + 4*(2*a^9*b^3 + 5*a^7*b^5 + 3*a^5*b^7 - a^3*b^9 - a*b^11)*c^6*d^3 - (7*a^10*b^2 + 25*a^8*b^4 + 32*a^6*b^6 + 16*a^4*b^8 + a^2*b^10 - b^12)*c^5*d^4 + 2*(a^11*b + 11*a^9*b^3 + 26*a^7*b^5 + 22*a^5*b^7 + 5*a^3*b^9 - a*b^11)*c^4*d^5 - 2*(7*a^10*b^2 + 22*a^8*b^4 + 24*a^6*b^6 + 10*a^4*b^8 + a^2*b^10)*c^3*d^6 + 4*(a^11*b + 5*a^9*b^3 + 9*a^7*b^5 + 7*a^5*b^7 + 2*a^3*b^9)*c^2*d^7 - 7*(a^10*b^2 + 3*a^8*b^4 + 3*a^6*b^6 + a^4*b^8)*c*d^8 + 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*d^9)*f*tan(f*x + e)^2 + (2*(a^7*b^5 + 3*a^5*b^7 + 3*a^3*b^9 + a*b^11)*c^9 - 7*(a^8*b^4 + 3*a^6*b^6 + 3*a^4*b^8 + a^2*b^10)*c^8*d + 4*(2*a^9*b^3 + 7*a^7*b^5 + 9*a^5*b^7 + 5*a^3*b^9 + a*b^11)*c^7*d^2 - 2*(a^10*b^2 + 10*a^8*b^4 + 24*a^6*b^6 + 22*a^4*b^8 + 7*a^2*b^10)*c^6*d^3 - 2*(a^11*b - 5*a^9*b^3 - 22*a^7*b^5 - 26*a^5*b^7 - 11*a^3*b^9 - a*b^11)*c^5*d^4 + (a^12 - a^10*b^2 - 16*a^8*b^4 - 32*a^6*b^6 - 25*a^4*b^8 - 7*a^2*b^10)*c^4*d^5 - 4*(a^11*b + a^9*b^3 - 3*a^7*b^5 - 5*a^5*b^7 - 2*a^3*b^9)*c^3*d^6 + 2*(a^12 + 2*a^10*b^2 - 2*a^6*b^6 - a^4*b^8)*c^2*d^7 - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*c*d^8 + (a^12 + 3*a^10*b^2 + 3*a^8*b^4 + a^6*b^6)*d^9)*f*tan(f*x + e) + ((a^8*b^4 + 3*a^6*b^6 + 3*a^4*b^8 + a^2*b^10)*c^9 - 4*(a^9*b^3 + 3*a^7*b^5 + 3*a^5*b^7 + a^3*b^9)*c^8*d + 2*(3*a^10*b^2 + 10*a^8*b^4 + 12*a^6*b^6 + 6*a^4*b^8 + a^2*b^10)*c^7*d^2 - 4*(a^11*b + 5*a^9*b^3 + 9*a^7*b^5 + 7*a^5*b^7 + 2*a^3*b^9)*c^6*d^3 + (a^12 + 15*a^10*b^2 + 40*a^8*b^4 + 40*a^6*b^6 + 15*a^4*b^8 + a^2*b^10)*c^5*d^4 - 4*(2*a^11*b + 7*a^9*b^3 + 9*a^7*b^5 + 5*a^5*b^7 + a^3*b^9)*c^4*d^5 + 2*(a^12 + 6*a^10*b^2 + 12*a^8*b^4 + 10*a^6*b^6 + 3*a^4*b^8)*c^3*d^6 - 4*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*c^2*d^7 + (a^12 + 3*a^10*b^2 + 3*a^8*b^4 + a^6*b^6)*c*d^8)*f)","B",0
84,1,2490,0,2.647152," ","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=""fricas"")","-\frac{3 \, C b^{3} c^{7} d^{2} + A a^{3} d^{9} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{6} d^{3} - {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A - 9 \, C\right)} b^{3}\right)} c^{5} d^{4} + {\left(3 \, C a^{3} + 9 \, B a^{2} b + 3 \, {\left(3 \, A - 7 \, C\right)} a b^{2} - 7 \, B b^{3}\right)} c^{4} d^{5} - 5 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} c^{3} d^{6} + {\left({\left(7 \, A - 3 \, C\right)} a^{3} - 9 \, B a^{2} b - 9 \, A a b^{2}\right)} c^{2} d^{7} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{8} - 2 \, {\left(C b^{3} c^{6} d^{3} + 3 \, C b^{3} c^{4} d^{5} + 3 \, C b^{3} c^{2} d^{7} + C b^{3} d^{9}\right)} \tan\left(f x + e\right)^{3} - 2 \, {\left({\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c^{5} d^{4} + 3 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c^{4} d^{5} - 3 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c^{3} d^{6} - {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c^{2} d^{7}\right)} f x - {\left(9 \, C b^{3} c^{7} d^{2} - A a^{3} d^{9} - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{6} d^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A + 23 \, C\right)} b^{3}\right)} c^{5} d^{4} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, {\left(A - 9 \, C\right)} a b^{2} - 9 \, B b^{3}\right)} c^{4} d^{5} - {\left(3 \, B a^{3} + 3 \, {\left(3 \, A - 7 \, C\right)} a^{2} b - 21 \, B a b^{2} - {\left(7 \, A + 12 \, C\right)} b^{3}\right)} c^{3} d^{6} + 5 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} c^{2} d^{7} + {\left(3 \, B a^{3} + 9 \, A a^{2} b + 4 \, C b^{3}\right)} c d^{8} + 2 \, {\left({\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c^{3} d^{6} + 3 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c^{2} d^{7} - 3 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c d^{8} - {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} d^{9}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left(3 \, C b^{3} c^{9} + 9 \, C b^{3} c^{7} d^{2} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{8} d - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{6} d^{3} + {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - 10 \, C\right)} b^{3}\right)} c^{5} d^{4} - 3 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - 2 \, C\right)} a b^{2} + 2 \, B b^{3}\right)} c^{4} d^{5} - 3 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} c^{3} d^{6} + {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} c^{2} d^{7} + {\left(3 \, C b^{3} c^{7} d^{2} + 9 \, C b^{3} c^{5} d^{4} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{6} d^{3} - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4} d^{5} + {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - 10 \, C\right)} b^{3}\right)} c^{3} d^{6} - 3 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - 2 \, C\right)} a b^{2} + 2 \, B b^{3}\right)} c^{2} d^{7} - 3 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} c d^{8} + {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} d^{9}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(3 \, C b^{3} c^{8} d + 9 \, C b^{3} c^{6} d^{3} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{7} d^{2} - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{5} d^{4} + {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - 10 \, C\right)} b^{3}\right)} c^{4} d^{5} - 3 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - 2 \, C\right)} a b^{2} + 2 \, B b^{3}\right)} c^{3} d^{6} - 3 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} c^{2} d^{7} + {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} c d^{8}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(3 \, C b^{3} c^{9} + 9 \, C b^{3} c^{7} d^{2} + 9 \, C b^{3} c^{5} d^{4} + 3 \, C b^{3} c^{3} d^{6} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{8} d - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{6} d^{3} - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4} d^{5} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2} d^{7} + {\left(3 \, C b^{3} c^{7} d^{2} + 9 \, C b^{3} c^{5} d^{4} + 9 \, C b^{3} c^{3} d^{6} + 3 \, C b^{3} c d^{8} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{6} d^{3} - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4} d^{5} - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2} d^{7} - {\left(3 \, C a b^{2} + B b^{3}\right)} d^{9}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(3 \, C b^{3} c^{8} d + 9 \, C b^{3} c^{6} d^{3} + 9 \, C b^{3} c^{4} d^{5} + 3 \, C b^{3} c^{2} d^{7} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{7} d^{2} - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{5} d^{4} - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3} d^{6} - {\left(3 \, C a b^{2} + B b^{3}\right)} c d^{8}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(3 \, C b^{3} c^{8} d + 6 \, C b^{3} c^{6} d^{3} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{7} d^{2} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, {\left(A - 3 \, C\right)} a b^{2} - 3 \, B b^{3}\right)} c^{5} d^{4} - {\left(2 \, B a^{3} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{2} b - 9 \, B a b^{2} - {\left(3 \, A - 2 \, C\right)} b^{3}\right)} c^{4} d^{5} + {\left(3 \, {\left(A - C\right)} a^{3} - 9 \, B a^{2} b - 3 \, {\left(3 \, A - 4 \, C\right)} a b^{2} + 4 \, B b^{3}\right)} c^{3} d^{6} + {\left(3 \, B a^{3} + 9 \, {\left(A - C\right)} a^{2} b - 9 \, B a b^{2} - {\left(3 \, A - C\right)} b^{3}\right)} c^{2} d^{7} - {\left({\left(3 \, A - 2 \, C\right)} a^{3} - 6 \, B a^{2} b - 6 \, A a b^{2}\right)} c d^{8} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{9} + 2 \, {\left({\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c^{4} d^{5} + 3 \, {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c^{3} d^{6} - 3 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, {\left(A - C\right)} a b^{2} + B b^{3}\right)} c^{2} d^{7} - {\left(B a^{3} + 3 \, {\left(A - C\right)} a^{2} b - 3 \, B a b^{2} - {\left(A - C\right)} b^{3}\right)} c d^{8}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{6} d^{6} + 3 \, c^{4} d^{8} + 3 \, c^{2} d^{10} + d^{12}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{7} d^{5} + 3 \, c^{5} d^{7} + 3 \, c^{3} d^{9} + c d^{11}\right)} f \tan\left(f x + e\right) + {\left(c^{8} d^{4} + 3 \, c^{6} d^{6} + 3 \, c^{4} d^{8} + c^{2} d^{10}\right)} f\right)}}"," ",0,"-1/2*(3*C*b^3*c^7*d^2 + A*a^3*d^9 - (3*C*a*b^2 + B*b^3)*c^6*d^3 - (3*C*a^2*b + 3*B*a*b^2 + (A - 9*C)*b^3)*c^5*d^4 + (3*C*a^3 + 9*B*a^2*b + 3*(3*A - 7*C)*a*b^2 - 7*B*b^3)*c^4*d^5 - 5*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - A*b^3)*c^3*d^6 + ((7*A - 3*C)*a^3 - 9*B*a^2*b - 9*A*a*b^2)*c^2*d^7 + (B*a^3 + 3*A*a^2*b)*c*d^8 - 2*(C*b^3*c^6*d^3 + 3*C*b^3*c^4*d^5 + 3*C*b^3*c^2*d^7 + C*b^3*d^9)*tan(f*x + e)^3 - 2*(((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c^5*d^4 + 3*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c^4*d^5 - 3*((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c^3*d^6 - (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c^2*d^7)*f*x - (9*C*b^3*c^7*d^2 - A*a^3*d^9 - 3*(3*C*a*b^2 + B*b^3)*c^6*d^3 + (3*C*a^2*b + 3*B*a*b^2 + (A + 23*C)*b^3)*c^5*d^4 + (C*a^3 + 3*B*a^2*b + 3*(A - 9*C)*a*b^2 - 9*B*b^3)*c^4*d^5 - (3*B*a^3 + 3*(3*A - 7*C)*a^2*b - 21*B*a*b^2 - (7*A + 12*C)*b^3)*c^3*d^6 + 5*((A - C)*a^3 - 3*B*a^2*b - 3*A*a*b^2)*c^2*d^7 + (3*B*a^3 + 9*A*a^2*b + 4*C*b^3)*c*d^8 + 2*(((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c^3*d^6 + 3*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c^2*d^7 - 3*((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c*d^8 - (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*d^9)*f*x)*tan(f*x + e)^2 + (3*C*b^3*c^9 + 9*C*b^3*c^7*d^2 - (3*C*a*b^2 + B*b^3)*c^8*d - 3*(3*C*a*b^2 + B*b^3)*c^6*d^3 + (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - 10*C)*b^3)*c^5*d^4 - 3*((A - C)*a^3 - 3*B*a^2*b - 3*(A - 2*C)*a*b^2 + 2*B*b^3)*c^4*d^5 - 3*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - A*b^3)*c^3*d^6 + ((A - C)*a^3 - 3*B*a^2*b - 3*A*a*b^2)*c^2*d^7 + (3*C*b^3*c^7*d^2 + 9*C*b^3*c^5*d^4 - (3*C*a*b^2 + B*b^3)*c^6*d^3 - 3*(3*C*a*b^2 + B*b^3)*c^4*d^5 + (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - 10*C)*b^3)*c^3*d^6 - 3*((A - C)*a^3 - 3*B*a^2*b - 3*(A - 2*C)*a*b^2 + 2*B*b^3)*c^2*d^7 - 3*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - A*b^3)*c*d^8 + ((A - C)*a^3 - 3*B*a^2*b - 3*A*a*b^2)*d^9)*tan(f*x + e)^2 + 2*(3*C*b^3*c^8*d + 9*C*b^3*c^6*d^3 - (3*C*a*b^2 + B*b^3)*c^7*d^2 - 3*(3*C*a*b^2 + B*b^3)*c^5*d^4 + (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - 10*C)*b^3)*c^4*d^5 - 3*((A - C)*a^3 - 3*B*a^2*b - 3*(A - 2*C)*a*b^2 + 2*B*b^3)*c^3*d^6 - 3*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - A*b^3)*c^2*d^7 + ((A - C)*a^3 - 3*B*a^2*b - 3*A*a*b^2)*c*d^8)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (3*C*b^3*c^9 + 9*C*b^3*c^7*d^2 + 9*C*b^3*c^5*d^4 + 3*C*b^3*c^3*d^6 - (3*C*a*b^2 + B*b^3)*c^8*d - 3*(3*C*a*b^2 + B*b^3)*c^6*d^3 - 3*(3*C*a*b^2 + B*b^3)*c^4*d^5 - (3*C*a*b^2 + B*b^3)*c^2*d^7 + (3*C*b^3*c^7*d^2 + 9*C*b^3*c^5*d^4 + 9*C*b^3*c^3*d^6 + 3*C*b^3*c*d^8 - (3*C*a*b^2 + B*b^3)*c^6*d^3 - 3*(3*C*a*b^2 + B*b^3)*c^4*d^5 - 3*(3*C*a*b^2 + B*b^3)*c^2*d^7 - (3*C*a*b^2 + B*b^3)*d^9)*tan(f*x + e)^2 + 2*(3*C*b^3*c^8*d + 9*C*b^3*c^6*d^3 + 9*C*b^3*c^4*d^5 + 3*C*b^3*c^2*d^7 - (3*C*a*b^2 + B*b^3)*c^7*d^2 - 3*(3*C*a*b^2 + B*b^3)*c^5*d^4 - 3*(3*C*a*b^2 + B*b^3)*c^3*d^6 - (3*C*a*b^2 + B*b^3)*c*d^8)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) - 2*(3*C*b^3*c^8*d + 6*C*b^3*c^6*d^3 - (3*C*a*b^2 + B*b^3)*c^7*d^2 + (C*a^3 + 3*B*a^2*b + 3*(A - 3*C)*a*b^2 - 3*B*b^3)*c^5*d^4 - (2*B*a^3 + 3*(2*A - 3*C)*a^2*b - 9*B*a*b^2 - (3*A - 2*C)*b^3)*c^4*d^5 + (3*(A - C)*a^3 - 9*B*a^2*b - 3*(3*A - 4*C)*a*b^2 + 4*B*b^3)*c^3*d^6 + (3*B*a^3 + 9*(A - C)*a^2*b - 9*B*a*b^2 - (3*A - C)*b^3)*c^2*d^7 - ((3*A - 2*C)*a^3 - 6*B*a^2*b - 6*A*a*b^2)*c*d^8 - (B*a^3 + 3*A*a^2*b)*d^9 + 2*(((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c^4*d^5 + 3*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c^3*d^6 - 3*((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c^2*d^7 - (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c*d^8)*f*x)*tan(f*x + e))/((c^6*d^6 + 3*c^4*d^8 + 3*c^2*d^10 + d^12)*f*tan(f*x + e)^2 + 2*(c^7*d^5 + 3*c^5*d^7 + 3*c^3*d^9 + c*d^11)*f*tan(f*x + e) + (c^8*d^4 + 3*c^6*d^6 + 3*c^4*d^8 + c^2*d^10)*f)","B",0
85,1,1618,0,1.230811," ","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=""fricas"")","\frac{C b^{2} c^{6} d^{2} - A a^{2} d^{8} + {\left(2 \, C a b + B b^{2}\right)} c^{5} d^{3} - {\left(3 \, C a^{2} + 6 \, B a b + {\left(3 \, A - 7 \, C\right)} b^{2}\right)} c^{4} d^{4} + 5 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{3} d^{5} - {\left({\left(7 \, A - 3 \, C\right)} a^{2} - 6 \, B a b - 3 \, A b^{2}\right)} c^{2} d^{6} - {\left(B a^{2} + 2 \, A a b\right)} c d^{7} + 2 \, {\left({\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c^{5} d^{3} + 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{4} d^{4} - 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c^{3} d^{5} - {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{2} d^{6}\right)} f x - {\left(3 \, C b^{2} c^{6} d^{2} + A a^{2} d^{8} - {\left(2 \, C a b + B b^{2}\right)} c^{5} d^{3} - {\left(C a^{2} + 2 \, B a b + {\left(A - 9 \, C\right)} b^{2}\right)} c^{4} d^{4} + {\left(3 \, B a^{2} + 2 \, {\left(3 \, A - 7 \, C\right)} a b - 7 \, B b^{2}\right)} c^{3} d^{5} - 5 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - A b^{2}\right)} c^{2} d^{6} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{7} - 2 \, {\left({\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c^{3} d^{5} + 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{2} d^{6} - 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c d^{7} - {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} d^{8}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left(C b^{2} c^{8} + 3 \, C b^{2} c^{6} d^{2} - {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{5} d^{3} + 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - 2 \, C\right)} b^{2}\right)} c^{4} d^{4} + 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{3} d^{5} - {\left({\left(A - C\right)} a^{2} - 2 \, B a b - A b^{2}\right)} c^{2} d^{6} + {\left(C b^{2} c^{6} d^{2} + 3 \, C b^{2} c^{4} d^{4} - {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{3} d^{5} + 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - 2 \, C\right)} b^{2}\right)} c^{2} d^{6} + 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c d^{7} - {\left({\left(A - C\right)} a^{2} - 2 \, B a b - A b^{2}\right)} d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(C b^{2} c^{7} d + 3 \, C b^{2} c^{5} d^{3} - {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{4} d^{4} + 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - 2 \, C\right)} b^{2}\right)} c^{3} d^{5} + 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{2} d^{6} - {\left({\left(A - C\right)} a^{2} - 2 \, B a b - A b^{2}\right)} c d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(C b^{2} c^{8} + 3 \, C b^{2} c^{6} d^{2} + 3 \, C b^{2} c^{4} d^{4} + C b^{2} c^{2} d^{6} + {\left(C b^{2} c^{6} d^{2} + 3 \, C b^{2} c^{4} d^{4} + 3 \, C b^{2} c^{2} d^{6} + C b^{2} d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(C b^{2} c^{7} d + 3 \, C b^{2} c^{5} d^{3} + 3 \, C b^{2} c^{3} d^{5} + C b^{2} c d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(C b^{2} c^{7} d - {\left(C a^{2} + 2 \, B a b + {\left(A - 3 \, C\right)} b^{2}\right)} c^{5} d^{3} + {\left(2 \, B a^{2} + 2 \, {\left(2 \, A - 3 \, C\right)} a b - 3 \, B b^{2}\right)} c^{4} d^{4} - {\left(3 \, {\left(A - C\right)} a^{2} - 6 \, B a b - {\left(3 \, A - 4 \, C\right)} b^{2}\right)} c^{3} d^{5} - 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{2} d^{6} + {\left({\left(3 \, A - 2 \, C\right)} a^{2} - 4 \, B a b - 2 \, A b^{2}\right)} c d^{7} + {\left(B a^{2} + 2 \, A a b\right)} d^{8} - 2 \, {\left({\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c^{4} d^{4} + 3 \, {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{3} d^{5} - 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - C\right)} b^{2}\right)} c^{2} d^{6} - {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c d^{7}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{6} d^{5} + 3 \, c^{4} d^{7} + 3 \, c^{2} d^{9} + d^{11}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{7} d^{4} + 3 \, c^{5} d^{6} + 3 \, c^{3} d^{8} + c d^{10}\right)} f \tan\left(f x + e\right) + {\left(c^{8} d^{3} + 3 \, c^{6} d^{5} + 3 \, c^{4} d^{7} + c^{2} d^{9}\right)} f\right)}}"," ",0,"1/2*(C*b^2*c^6*d^2 - A*a^2*d^8 + (2*C*a*b + B*b^2)*c^5*d^3 - (3*C*a^2 + 6*B*a*b + (3*A - 7*C)*b^2)*c^4*d^4 + 5*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c^3*d^5 - ((7*A - 3*C)*a^2 - 6*B*a*b - 3*A*b^2)*c^2*d^6 - (B*a^2 + 2*A*a*b)*c*d^7 + 2*(((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c^5*d^3 + 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c^4*d^4 - 3*((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c^3*d^5 - (B*a^2 + 2*(A - C)*a*b - B*b^2)*c^2*d^6)*f*x - (3*C*b^2*c^6*d^2 + A*a^2*d^8 - (2*C*a*b + B*b^2)*c^5*d^3 - (C*a^2 + 2*B*a*b + (A - 9*C)*b^2)*c^4*d^4 + (3*B*a^2 + 2*(3*A - 7*C)*a*b - 7*B*b^2)*c^3*d^5 - 5*((A - C)*a^2 - 2*B*a*b - A*b^2)*c^2*d^6 - 3*(B*a^2 + 2*A*a*b)*c*d^7 - 2*(((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c^3*d^5 + 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c^2*d^6 - 3*((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c*d^7 - (B*a^2 + 2*(A - C)*a*b - B*b^2)*d^8)*f*x)*tan(f*x + e)^2 + (C*b^2*c^8 + 3*C*b^2*c^6*d^2 - (B*a^2 + 2*(A - C)*a*b - B*b^2)*c^5*d^3 + 3*((A - C)*a^2 - 2*B*a*b - (A - 2*C)*b^2)*c^4*d^4 + 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c^3*d^5 - ((A - C)*a^2 - 2*B*a*b - A*b^2)*c^2*d^6 + (C*b^2*c^6*d^2 + 3*C*b^2*c^4*d^4 - (B*a^2 + 2*(A - C)*a*b - B*b^2)*c^3*d^5 + 3*((A - C)*a^2 - 2*B*a*b - (A - 2*C)*b^2)*c^2*d^6 + 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c*d^7 - ((A - C)*a^2 - 2*B*a*b - A*b^2)*d^8)*tan(f*x + e)^2 + 2*(C*b^2*c^7*d + 3*C*b^2*c^5*d^3 - (B*a^2 + 2*(A - C)*a*b - B*b^2)*c^4*d^4 + 3*((A - C)*a^2 - 2*B*a*b - (A - 2*C)*b^2)*c^3*d^5 + 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c^2*d^6 - ((A - C)*a^2 - 2*B*a*b - A*b^2)*c*d^7)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (C*b^2*c^8 + 3*C*b^2*c^6*d^2 + 3*C*b^2*c^4*d^4 + C*b^2*c^2*d^6 + (C*b^2*c^6*d^2 + 3*C*b^2*c^4*d^4 + 3*C*b^2*c^2*d^6 + C*b^2*d^8)*tan(f*x + e)^2 + 2*(C*b^2*c^7*d + 3*C*b^2*c^5*d^3 + 3*C*b^2*c^3*d^5 + C*b^2*c*d^7)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) - 2*(C*b^2*c^7*d - (C*a^2 + 2*B*a*b + (A - 3*C)*b^2)*c^5*d^3 + (2*B*a^2 + 2*(2*A - 3*C)*a*b - 3*B*b^2)*c^4*d^4 - (3*(A - C)*a^2 - 6*B*a*b - (3*A - 4*C)*b^2)*c^3*d^5 - 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c^2*d^6 + ((3*A - 2*C)*a^2 - 4*B*a*b - 2*A*b^2)*c*d^7 + (B*a^2 + 2*A*a*b)*d^8 - 2*(((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c^4*d^4 + 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c^3*d^5 - 3*((A - C)*a^2 - 2*B*a*b - (A - C)*b^2)*c^2*d^6 - (B*a^2 + 2*(A - C)*a*b - B*b^2)*c*d^7)*f*x)*tan(f*x + e))/((c^6*d^5 + 3*c^4*d^7 + 3*c^2*d^9 + d^11)*f*tan(f*x + e)^2 + 2*(c^7*d^4 + 3*c^5*d^6 + 3*c^3*d^8 + c*d^10)*f*tan(f*x + e) + (c^8*d^3 + 3*c^6*d^5 + 3*c^4*d^7 + c^2*d^9)*f)","B",0
86,1,897,0,0.537317," ","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=""fricas"")","\frac{C b c^{5} - A a d^{5} - 3 \, {\left(C a + B b\right)} c^{4} d + 5 \, {\left(B a + {\left(A - C\right)} b\right)} c^{3} d^{2} - {\left({\left(7 \, A - 3 \, C\right)} a - 3 \, B b\right)} c^{2} d^{3} - {\left(B a + A b\right)} c d^{4} + 2 \, {\left({\left({\left(A - C\right)} a - B b\right)} c^{5} + 3 \, {\left(B a + {\left(A - C\right)} b\right)} c^{4} d - 3 \, {\left({\left(A - C\right)} a - B b\right)} c^{3} d^{2} - {\left(B a + {\left(A - C\right)} b\right)} c^{2} d^{3}\right)} f x + {\left(C b c^{5} - A a d^{5} + {\left(C a + B b\right)} c^{4} d - {\left(3 \, B a + {\left(3 \, A - 7 \, C\right)} b\right)} c^{3} d^{2} + 5 \, {\left({\left(A - C\right)} a - B b\right)} c^{2} d^{3} + 3 \, {\left(B a + A b\right)} c d^{4} + 2 \, {\left({\left({\left(A - C\right)} a - B b\right)} c^{3} d^{2} + 3 \, {\left(B a + {\left(A - C\right)} b\right)} c^{2} d^{3} - 3 \, {\left({\left(A - C\right)} a - B b\right)} c d^{4} - {\left(B a + {\left(A - C\right)} b\right)} d^{5}\right)} f x\right)} \tan\left(f x + e\right)^{2} - {\left({\left(B a + {\left(A - C\right)} b\right)} c^{5} - 3 \, {\left({\left(A - C\right)} a - B b\right)} c^{4} d - 3 \, {\left(B a + {\left(A - C\right)} b\right)} c^{3} d^{2} + {\left({\left(A - C\right)} a - B b\right)} c^{2} d^{3} + {\left({\left(B a + {\left(A - C\right)} b\right)} c^{3} d^{2} - 3 \, {\left({\left(A - C\right)} a - B b\right)} c^{2} d^{3} - 3 \, {\left(B a + {\left(A - C\right)} b\right)} c d^{4} + {\left({\left(A - C\right)} a - B b\right)} d^{5}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(B a + {\left(A - C\right)} b\right)} c^{4} d - 3 \, {\left({\left(A - C\right)} a - B b\right)} c^{3} d^{2} - 3 \, {\left(B a + {\left(A - C\right)} b\right)} c^{2} d^{3} + {\left({\left(A - C\right)} a - B b\right)} c d^{4}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left({\left(C a + B b\right)} c^{5} - {\left(2 \, B a + {\left(2 \, A - 3 \, C\right)} b\right)} c^{4} d + 3 \, {\left({\left(A - C\right)} a - B b\right)} c^{3} d^{2} + 3 \, {\left(B a + {\left(A - C\right)} b\right)} c^{2} d^{3} - {\left({\left(3 \, A - 2 \, C\right)} a - 2 \, B b\right)} c d^{4} - {\left(B a + A b\right)} d^{5} + 2 \, {\left({\left({\left(A - C\right)} a - B b\right)} c^{4} d + 3 \, {\left(B a + {\left(A - C\right)} b\right)} c^{3} d^{2} - 3 \, {\left({\left(A - C\right)} a - B b\right)} c^{2} d^{3} - {\left(B a + {\left(A - C\right)} b\right)} c d^{4}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{6} d^{2} + 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} + d^{8}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{7} d + 3 \, c^{5} d^{3} + 3 \, c^{3} d^{5} + c d^{7}\right)} f \tan\left(f x + e\right) + {\left(c^{8} + 3 \, c^{6} d^{2} + 3 \, c^{4} d^{4} + c^{2} d^{6}\right)} f\right)}}"," ",0,"1/2*(C*b*c^5 - A*a*d^5 - 3*(C*a + B*b)*c^4*d + 5*(B*a + (A - C)*b)*c^3*d^2 - ((7*A - 3*C)*a - 3*B*b)*c^2*d^3 - (B*a + A*b)*c*d^4 + 2*(((A - C)*a - B*b)*c^5 + 3*(B*a + (A - C)*b)*c^4*d - 3*((A - C)*a - B*b)*c^3*d^2 - (B*a + (A - C)*b)*c^2*d^3)*f*x + (C*b*c^5 - A*a*d^5 + (C*a + B*b)*c^4*d - (3*B*a + (3*A - 7*C)*b)*c^3*d^2 + 5*((A - C)*a - B*b)*c^2*d^3 + 3*(B*a + A*b)*c*d^4 + 2*(((A - C)*a - B*b)*c^3*d^2 + 3*(B*a + (A - C)*b)*c^2*d^3 - 3*((A - C)*a - B*b)*c*d^4 - (B*a + (A - C)*b)*d^5)*f*x)*tan(f*x + e)^2 - ((B*a + (A - C)*b)*c^5 - 3*((A - C)*a - B*b)*c^4*d - 3*(B*a + (A - C)*b)*c^3*d^2 + ((A - C)*a - B*b)*c^2*d^3 + ((B*a + (A - C)*b)*c^3*d^2 - 3*((A - C)*a - B*b)*c^2*d^3 - 3*(B*a + (A - C)*b)*c*d^4 + ((A - C)*a - B*b)*d^5)*tan(f*x + e)^2 + 2*((B*a + (A - C)*b)*c^4*d - 3*((A - C)*a - B*b)*c^3*d^2 - 3*(B*a + (A - C)*b)*c^2*d^3 + ((A - C)*a - B*b)*c*d^4)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) + 2*((C*a + B*b)*c^5 - (2*B*a + (2*A - 3*C)*b)*c^4*d + 3*((A - C)*a - B*b)*c^3*d^2 + 3*(B*a + (A - C)*b)*c^2*d^3 - ((3*A - 2*C)*a - 2*B*b)*c*d^4 - (B*a + A*b)*d^5 + 2*(((A - C)*a - B*b)*c^4*d + 3*(B*a + (A - C)*b)*c^3*d^2 - 3*((A - C)*a - B*b)*c^2*d^3 - (B*a + (A - C)*b)*c*d^4)*f*x)*tan(f*x + e))/((c^6*d^2 + 3*c^4*d^4 + 3*c^2*d^6 + d^8)*f*tan(f*x + e)^2 + 2*(c^7*d + 3*c^5*d^3 + 3*c^3*d^5 + c*d^7)*f*tan(f*x + e) + (c^8 + 3*c^6*d^2 + 3*c^4*d^4 + c^2*d^6)*f)","B",0
87,1,566,0,0.717406," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{3 \, C c^{4} d - 5 \, B c^{3} d^{2} + {\left(7 \, A - 3 \, C\right)} c^{2} d^{3} + B c d^{4} + A d^{5} - 2 \, {\left({\left(A - C\right)} c^{5} + 3 \, B c^{4} d - 3 \, {\left(A - C\right)} c^{3} d^{2} - B c^{2} d^{3}\right)} f x - {\left(C c^{4} d - 3 \, B c^{3} d^{2} + 5 \, {\left(A - C\right)} c^{2} d^{3} + 3 \, B c d^{4} - A d^{5} + 2 \, {\left({\left(A - C\right)} c^{3} d^{2} + 3 \, B c^{2} d^{3} - 3 \, {\left(A - C\right)} c d^{4} - B d^{5}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left(B c^{5} - 3 \, {\left(A - C\right)} c^{4} d - 3 \, B c^{3} d^{2} + {\left(A - C\right)} c^{2} d^{3} + {\left(B c^{3} d^{2} - 3 \, {\left(A - C\right)} c^{2} d^{3} - 3 \, B c d^{4} + {\left(A - C\right)} d^{5}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(B c^{4} d - 3 \, {\left(A - C\right)} c^{3} d^{2} - 3 \, B c^{2} d^{3} + {\left(A - C\right)} c d^{4}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(C c^{5} - 2 \, B c^{4} d + 3 \, {\left(A - C\right)} c^{3} d^{2} + 3 \, B c^{2} d^{3} - {\left(3 \, A - 2 \, C\right)} c d^{4} - B d^{5} + 2 \, {\left({\left(A - C\right)} c^{4} d + 3 \, B c^{3} d^{2} - 3 \, {\left(A - C\right)} c^{2} d^{3} - B c d^{4}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{6} d^{2} + 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} + d^{8}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{7} d + 3 \, c^{5} d^{3} + 3 \, c^{3} d^{5} + c d^{7}\right)} f \tan\left(f x + e\right) + {\left(c^{8} + 3 \, c^{6} d^{2} + 3 \, c^{4} d^{4} + c^{2} d^{6}\right)} f\right)}}"," ",0,"-1/2*(3*C*c^4*d - 5*B*c^3*d^2 + (7*A - 3*C)*c^2*d^3 + B*c*d^4 + A*d^5 - 2*((A - C)*c^5 + 3*B*c^4*d - 3*(A - C)*c^3*d^2 - B*c^2*d^3)*f*x - (C*c^4*d - 3*B*c^3*d^2 + 5*(A - C)*c^2*d^3 + 3*B*c*d^4 - A*d^5 + 2*((A - C)*c^3*d^2 + 3*B*c^2*d^3 - 3*(A - C)*c*d^4 - B*d^5)*f*x)*tan(f*x + e)^2 + (B*c^5 - 3*(A - C)*c^4*d - 3*B*c^3*d^2 + (A - C)*c^2*d^3 + (B*c^3*d^2 - 3*(A - C)*c^2*d^3 - 3*B*c*d^4 + (A - C)*d^5)*tan(f*x + e)^2 + 2*(B*c^4*d - 3*(A - C)*c^3*d^2 - 3*B*c^2*d^3 + (A - C)*c*d^4)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*(C*c^5 - 2*B*c^4*d + 3*(A - C)*c^3*d^2 + 3*B*c^2*d^3 - (3*A - 2*C)*c*d^4 - B*d^5 + 2*((A - C)*c^4*d + 3*B*c^3*d^2 - 3*(A - C)*c^2*d^3 - B*c*d^4)*f*x)*tan(f*x + e))/((c^6*d^2 + 3*c^4*d^4 + 3*c^2*d^6 + d^8)*f*tan(f*x + e)^2 + 2*(c^7*d + 3*c^5*d^3 + 3*c^3*d^5 + c*d^7)*f*tan(f*x + e) + (c^8 + 3*c^6*d^2 + 3*c^4*d^4 + c^2*d^6)*f)","B",0
88,1,3496,0,6.767227," ","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=""fricas"")","\frac{5 \, {\left(C a^{2} b^{2} + C b^{4}\right)} c^{6} d^{2} - {\left(8 \, C a^{3} b + 7 \, B a^{2} b^{2} + 8 \, C a b^{3} + 7 \, B b^{4}\right)} c^{5} d^{3} + {\left(3 \, C a^{4} + 12 \, B a^{3} b + {\left(9 \, A + 2 \, C\right)} a^{2} b^{2} + 12 \, B a b^{3} + {\left(9 \, A - C\right)} b^{4}\right)} c^{4} d^{4} - {\left(5 \, B a^{4} + 4 \, {\left(4 \, A - C\right)} a^{3} b + 6 \, B a^{2} b^{2} + 4 \, {\left(4 \, A - C\right)} a b^{3} + B b^{4}\right)} c^{3} d^{5} + {\left({\left(7 \, A - 3 \, C\right)} a^{4} + {\left(10 \, A - 3 \, C\right)} a^{2} b^{2} + 3 \, A b^{4}\right)} c^{2} d^{6} + {\left(B a^{4} - 4 \, A a^{3} b + B a^{2} b^{2} - 4 \, A a b^{3}\right)} c d^{7} + {\left(A a^{4} + A a^{2} b^{2}\right)} d^{8} + 2 \, {\left({\left({\left(A - C\right)} a b^{3} + B b^{4}\right)} c^{8} - 3 \, {\left({\left(A - C\right)} a^{2} b^{2} + {\left(A - C\right)} b^{4}\right)} c^{7} d + 3 \, {\left({\left(A - C\right)} a^{3} b - 2 \, B a^{2} b^{2} + 2 \, {\left(A - C\right)} a b^{3} - B b^{4}\right)} c^{6} d^{2} - {\left({\left(A - C\right)} a^{4} - 8 \, B a^{3} b - 8 \, B a b^{3} - {\left(A - C\right)} b^{4}\right)} c^{5} d^{3} - 3 \, {\left(B a^{4} + 2 \, {\left(A - C\right)} a^{3} b + 2 \, B a^{2} b^{2} + {\left(A - C\right)} a b^{3}\right)} c^{4} d^{4} + 3 \, {\left({\left(A - C\right)} a^{4} + {\left(A - C\right)} a^{2} b^{2}\right)} c^{3} d^{5} + {\left(B a^{4} - {\left(A - C\right)} a^{3} b\right)} c^{2} d^{6}\right)} f x - {\left(3 \, {\left(C a^{2} b^{2} + C b^{4}\right)} c^{6} d^{2} - {\left(4 \, C a^{3} b + 5 \, B a^{2} b^{2} + 4 \, C a b^{3} + 5 \, B b^{4}\right)} c^{5} d^{3} + {\left(C a^{4} + 8 \, B a^{3} b + {\left(7 \, A - 2 \, C\right)} a^{2} b^{2} + 8 \, B a b^{3} + {\left(7 \, A - 3 \, C\right)} b^{4}\right)} c^{4} d^{4} - {\left(3 \, B a^{4} + 4 \, {\left(3 \, A - 2 \, C\right)} a^{3} b + 2 \, B a^{2} b^{2} + 4 \, {\left(3 \, A - 2 \, C\right)} a b^{3} - B b^{4}\right)} c^{3} d^{5} + {\left(5 \, {\left(A - C\right)} a^{4} - 4 \, B a^{3} b + {\left(6 \, A - 5 \, C\right)} a^{2} b^{2} - 4 \, B a b^{3} + A b^{4}\right)} c^{2} d^{6} + 3 \, {\left(B a^{4} + B a^{2} b^{2}\right)} c d^{7} - {\left(A a^{4} + A a^{2} b^{2}\right)} d^{8} - 2 \, {\left({\left({\left(A - C\right)} a b^{3} + B b^{4}\right)} c^{6} d^{2} - 3 \, {\left({\left(A - C\right)} a^{2} b^{2} + {\left(A - C\right)} b^{4}\right)} c^{5} d^{3} + 3 \, {\left({\left(A - C\right)} a^{3} b - 2 \, B a^{2} b^{2} + 2 \, {\left(A - C\right)} a b^{3} - B b^{4}\right)} c^{4} d^{4} - {\left({\left(A - C\right)} a^{4} - 8 \, B a^{3} b - 8 \, B a b^{3} - {\left(A - C\right)} b^{4}\right)} c^{3} d^{5} - 3 \, {\left(B a^{4} + 2 \, {\left(A - C\right)} a^{3} b + 2 \, B a^{2} b^{2} + {\left(A - C\right)} a b^{3}\right)} c^{2} d^{6} + 3 \, {\left({\left(A - C\right)} a^{4} + {\left(A - C\right)} a^{2} b^{2}\right)} c d^{7} + {\left(B a^{4} - {\left(A - C\right)} a^{3} b\right)} d^{8}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left({\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{8} + 3 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{6} d^{2} + 3 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{4} d^{4} + {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{2} d^{6} + {\left({\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{6} d^{2} + 3 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{4} d^{4} + 3 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{2} d^{6} + {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{7} d + 3 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{5} d^{3} + 3 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{3} d^{5} + {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left({\left(C a^{2} b^{2} + C b^{4}\right)} c^{8} - 3 \, {\left(B a^{2} b^{2} + B b^{4}\right)} c^{7} d + 3 \, {\left(B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} + B a b^{3} + {\left(2 \, A - C\right)} b^{4}\right)} c^{6} d^{2} - {\left(B a^{4} + 8 \, {\left(A - C\right)} a^{3} b + 8 \, {\left(A - C\right)} a b^{3} - B b^{4}\right)} c^{5} d^{3} + 3 \, {\left({\left(A - C\right)} a^{4} - 2 \, B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} - 2 \, B a b^{3} + A b^{4}\right)} c^{4} d^{4} + 3 \, {\left(B a^{4} + B a^{2} b^{2}\right)} c^{3} d^{5} - {\left({\left(A - C\right)} a^{4} + B a^{3} b - C a^{2} b^{2} + B a b^{3} - A b^{4}\right)} c^{2} d^{6} + {\left({\left(C a^{2} b^{2} + C b^{4}\right)} c^{6} d^{2} - 3 \, {\left(B a^{2} b^{2} + B b^{4}\right)} c^{5} d^{3} + 3 \, {\left(B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} + B a b^{3} + {\left(2 \, A - C\right)} b^{4}\right)} c^{4} d^{4} - {\left(B a^{4} + 8 \, {\left(A - C\right)} a^{3} b + 8 \, {\left(A - C\right)} a b^{3} - B b^{4}\right)} c^{3} d^{5} + 3 \, {\left({\left(A - C\right)} a^{4} - 2 \, B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} - 2 \, B a b^{3} + A b^{4}\right)} c^{2} d^{6} + 3 \, {\left(B a^{4} + B a^{2} b^{2}\right)} c d^{7} - {\left({\left(A - C\right)} a^{4} + B a^{3} b - C a^{2} b^{2} + B a b^{3} - A b^{4}\right)} d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(C a^{2} b^{2} + C b^{4}\right)} c^{7} d - 3 \, {\left(B a^{2} b^{2} + B b^{4}\right)} c^{6} d^{2} + 3 \, {\left(B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} + B a b^{3} + {\left(2 \, A - C\right)} b^{4}\right)} c^{5} d^{3} - {\left(B a^{4} + 8 \, {\left(A - C\right)} a^{3} b + 8 \, {\left(A - C\right)} a b^{3} - B b^{4}\right)} c^{4} d^{4} + 3 \, {\left({\left(A - C\right)} a^{4} - 2 \, B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} - 2 \, B a b^{3} + A b^{4}\right)} c^{3} d^{5} + 3 \, {\left(B a^{4} + B a^{2} b^{2}\right)} c^{2} d^{6} - {\left({\left(A - C\right)} a^{4} + B a^{3} b - C a^{2} b^{2} + B a b^{3} - A b^{4}\right)} c d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(2 \, {\left(C a^{2} b^{2} + C b^{4}\right)} c^{7} d - 3 \, {\left(C a^{3} b + B a^{2} b^{2} + C a b^{3} + B b^{4}\right)} c^{6} d^{2} + {\left(C a^{4} + 5 \, B a^{3} b + 2 \, {\left(2 \, A - C\right)} a^{2} b^{2} + 5 \, B a b^{3} + {\left(4 \, A - 3 \, C\right)} b^{4}\right)} c^{5} d^{3} - {\left(2 \, B a^{4} + {\left(7 \, A - 6 \, C\right)} a^{3} b - B a^{2} b^{2} + {\left(7 \, A - 6 \, C\right)} a b^{3} - 3 \, B b^{4}\right)} c^{4} d^{4} + {\left(3 \, {\left(A - C\right)} a^{4} - 6 \, B a^{3} b - 2 \, C a^{2} b^{2} - 6 \, B a b^{3} - {\left(3 \, A - C\right)} b^{4}\right)} c^{3} d^{5} + 3 \, {\left(B a^{4} + {\left(2 \, A - C\right)} a^{3} b + B a^{2} b^{2} + {\left(2 \, A - C\right)} a b^{3}\right)} c^{2} d^{6} - {\left({\left(3 \, A - 2 \, C\right)} a^{4} - B a^{3} b + 2 \, {\left(2 \, A - C\right)} a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c d^{7} - {\left(B a^{4} - A a^{3} b + B a^{2} b^{2} - A a b^{3}\right)} d^{8} - 2 \, {\left({\left({\left(A - C\right)} a b^{3} + B b^{4}\right)} c^{7} d - 3 \, {\left({\left(A - C\right)} a^{2} b^{2} + {\left(A - C\right)} b^{4}\right)} c^{6} d^{2} + 3 \, {\left({\left(A - C\right)} a^{3} b - 2 \, B a^{2} b^{2} + 2 \, {\left(A - C\right)} a b^{3} - B b^{4}\right)} c^{5} d^{3} - {\left({\left(A - C\right)} a^{4} - 8 \, B a^{3} b - 8 \, B a b^{3} - {\left(A - C\right)} b^{4}\right)} c^{4} d^{4} - 3 \, {\left(B a^{4} + 2 \, {\left(A - C\right)} a^{3} b + 2 \, B a^{2} b^{2} + {\left(A - C\right)} a b^{3}\right)} c^{3} d^{5} + 3 \, {\left({\left(A - C\right)} a^{4} + {\left(A - C\right)} a^{2} b^{2}\right)} c^{2} d^{6} + {\left(B a^{4} - {\left(A - C\right)} a^{3} b\right)} c d^{7}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{2} b^{3} + b^{5}\right)} c^{9} d^{2} - 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{8} d^{3} + 3 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{7} d^{4} - {\left(a^{5} + 10 \, a^{3} b^{2} + 9 \, a b^{4}\right)} c^{6} d^{5} + 3 \, {\left(3 \, a^{4} b + 4 \, a^{2} b^{3} + b^{5}\right)} c^{5} d^{6} - 3 \, {\left(a^{5} + 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{4} d^{7} + {\left(9 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} c^{3} d^{8} - 3 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c^{2} d^{9} + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} c d^{10} - {\left(a^{5} + a^{3} b^{2}\right)} d^{11}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b^{3} + b^{5}\right)} c^{10} d - 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{9} d^{2} + 3 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{8} d^{3} - {\left(a^{5} + 10 \, a^{3} b^{2} + 9 \, a b^{4}\right)} c^{7} d^{4} + 3 \, {\left(3 \, a^{4} b + 4 \, a^{2} b^{3} + b^{5}\right)} c^{6} d^{5} - 3 \, {\left(a^{5} + 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{5} d^{6} + {\left(9 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} c^{4} d^{7} - 3 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c^{3} d^{8} + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} c^{2} d^{9} - {\left(a^{5} + a^{3} b^{2}\right)} c d^{10}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{2} b^{3} + b^{5}\right)} c^{11} - 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{10} d + 3 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{9} d^{2} - {\left(a^{5} + 10 \, a^{3} b^{2} + 9 \, a b^{4}\right)} c^{8} d^{3} + 3 \, {\left(3 \, a^{4} b + 4 \, a^{2} b^{3} + b^{5}\right)} c^{7} d^{4} - 3 \, {\left(a^{5} + 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{6} d^{5} + {\left(9 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} c^{5} d^{6} - 3 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c^{4} d^{7} + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} c^{3} d^{8} - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} d^{9}\right)} f\right)}}"," ",0,"1/2*(5*(C*a^2*b^2 + C*b^4)*c^6*d^2 - (8*C*a^3*b + 7*B*a^2*b^2 + 8*C*a*b^3 + 7*B*b^4)*c^5*d^3 + (3*C*a^4 + 12*B*a^3*b + (9*A + 2*C)*a^2*b^2 + 12*B*a*b^3 + (9*A - C)*b^4)*c^4*d^4 - (5*B*a^4 + 4*(4*A - C)*a^3*b + 6*B*a^2*b^2 + 4*(4*A - C)*a*b^3 + B*b^4)*c^3*d^5 + ((7*A - 3*C)*a^4 + (10*A - 3*C)*a^2*b^2 + 3*A*b^4)*c^2*d^6 + (B*a^4 - 4*A*a^3*b + B*a^2*b^2 - 4*A*a*b^3)*c*d^7 + (A*a^4 + A*a^2*b^2)*d^8 + 2*(((A - C)*a*b^3 + B*b^4)*c^8 - 3*((A - C)*a^2*b^2 + (A - C)*b^4)*c^7*d + 3*((A - C)*a^3*b - 2*B*a^2*b^2 + 2*(A - C)*a*b^3 - B*b^4)*c^6*d^2 - ((A - C)*a^4 - 8*B*a^3*b - 8*B*a*b^3 - (A - C)*b^4)*c^5*d^3 - 3*(B*a^4 + 2*(A - C)*a^3*b + 2*B*a^2*b^2 + (A - C)*a*b^3)*c^4*d^4 + 3*((A - C)*a^4 + (A - C)*a^2*b^2)*c^3*d^5 + (B*a^4 - (A - C)*a^3*b)*c^2*d^6)*f*x - (3*(C*a^2*b^2 + C*b^4)*c^6*d^2 - (4*C*a^3*b + 5*B*a^2*b^2 + 4*C*a*b^3 + 5*B*b^4)*c^5*d^3 + (C*a^4 + 8*B*a^3*b + (7*A - 2*C)*a^2*b^2 + 8*B*a*b^3 + (7*A - 3*C)*b^4)*c^4*d^4 - (3*B*a^4 + 4*(3*A - 2*C)*a^3*b + 2*B*a^2*b^2 + 4*(3*A - 2*C)*a*b^3 - B*b^4)*c^3*d^5 + (5*(A - C)*a^4 - 4*B*a^3*b + (6*A - 5*C)*a^2*b^2 - 4*B*a*b^3 + A*b^4)*c^2*d^6 + 3*(B*a^4 + B*a^2*b^2)*c*d^7 - (A*a^4 + A*a^2*b^2)*d^8 - 2*(((A - C)*a*b^3 + B*b^4)*c^6*d^2 - 3*((A - C)*a^2*b^2 + (A - C)*b^4)*c^5*d^3 + 3*((A - C)*a^3*b - 2*B*a^2*b^2 + 2*(A - C)*a*b^3 - B*b^4)*c^4*d^4 - ((A - C)*a^4 - 8*B*a^3*b - 8*B*a*b^3 - (A - C)*b^4)*c^3*d^5 - 3*(B*a^4 + 2*(A - C)*a^3*b + 2*B*a^2*b^2 + (A - C)*a*b^3)*c^2*d^6 + 3*((A - C)*a^4 + (A - C)*a^2*b^2)*c*d^7 + (B*a^4 - (A - C)*a^3*b)*d^8)*f*x)*tan(f*x + e)^2 + ((C*a^2*b^2 - B*a*b^3 + A*b^4)*c^8 + 3*(C*a^2*b^2 - B*a*b^3 + A*b^4)*c^6*d^2 + 3*(C*a^2*b^2 - B*a*b^3 + A*b^4)*c^4*d^4 + (C*a^2*b^2 - B*a*b^3 + A*b^4)*c^2*d^6 + ((C*a^2*b^2 - B*a*b^3 + A*b^4)*c^6*d^2 + 3*(C*a^2*b^2 - B*a*b^3 + A*b^4)*c^4*d^4 + 3*(C*a^2*b^2 - B*a*b^3 + A*b^4)*c^2*d^6 + (C*a^2*b^2 - B*a*b^3 + A*b^4)*d^8)*tan(f*x + e)^2 + 2*((C*a^2*b^2 - B*a*b^3 + A*b^4)*c^7*d + 3*(C*a^2*b^2 - B*a*b^3 + A*b^4)*c^5*d^3 + 3*(C*a^2*b^2 - B*a*b^3 + A*b^4)*c^3*d^5 + (C*a^2*b^2 - B*a*b^3 + A*b^4)*c*d^7)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - ((C*a^2*b^2 + C*b^4)*c^8 - 3*(B*a^2*b^2 + B*b^4)*c^7*d + 3*(B*a^3*b + (2*A - C)*a^2*b^2 + B*a*b^3 + (2*A - C)*b^4)*c^6*d^2 - (B*a^4 + 8*(A - C)*a^3*b + 8*(A - C)*a*b^3 - B*b^4)*c^5*d^3 + 3*((A - C)*a^4 - 2*B*a^3*b + (2*A - C)*a^2*b^2 - 2*B*a*b^3 + A*b^4)*c^4*d^4 + 3*(B*a^4 + B*a^2*b^2)*c^3*d^5 - ((A - C)*a^4 + B*a^3*b - C*a^2*b^2 + B*a*b^3 - A*b^4)*c^2*d^6 + ((C*a^2*b^2 + C*b^4)*c^6*d^2 - 3*(B*a^2*b^2 + B*b^4)*c^5*d^3 + 3*(B*a^3*b + (2*A - C)*a^2*b^2 + B*a*b^3 + (2*A - C)*b^4)*c^4*d^4 - (B*a^4 + 8*(A - C)*a^3*b + 8*(A - C)*a*b^3 - B*b^4)*c^3*d^5 + 3*((A - C)*a^4 - 2*B*a^3*b + (2*A - C)*a^2*b^2 - 2*B*a*b^3 + A*b^4)*c^2*d^6 + 3*(B*a^4 + B*a^2*b^2)*c*d^7 - ((A - C)*a^4 + B*a^3*b - C*a^2*b^2 + B*a*b^3 - A*b^4)*d^8)*tan(f*x + e)^2 + 2*((C*a^2*b^2 + C*b^4)*c^7*d - 3*(B*a^2*b^2 + B*b^4)*c^6*d^2 + 3*(B*a^3*b + (2*A - C)*a^2*b^2 + B*a*b^3 + (2*A - C)*b^4)*c^5*d^3 - (B*a^4 + 8*(A - C)*a^3*b + 8*(A - C)*a*b^3 - B*b^4)*c^4*d^4 + 3*((A - C)*a^4 - 2*B*a^3*b + (2*A - C)*a^2*b^2 - 2*B*a*b^3 + A*b^4)*c^3*d^5 + 3*(B*a^4 + B*a^2*b^2)*c^2*d^6 - ((A - C)*a^4 + B*a^3*b - C*a^2*b^2 + B*a*b^3 - A*b^4)*c*d^7)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*(2*(C*a^2*b^2 + C*b^4)*c^7*d - 3*(C*a^3*b + B*a^2*b^2 + C*a*b^3 + B*b^4)*c^6*d^2 + (C*a^4 + 5*B*a^3*b + 2*(2*A - C)*a^2*b^2 + 5*B*a*b^3 + (4*A - 3*C)*b^4)*c^5*d^3 - (2*B*a^4 + (7*A - 6*C)*a^3*b - B*a^2*b^2 + (7*A - 6*C)*a*b^3 - 3*B*b^4)*c^4*d^4 + (3*(A - C)*a^4 - 6*B*a^3*b - 2*C*a^2*b^2 - 6*B*a*b^3 - (3*A - C)*b^4)*c^3*d^5 + 3*(B*a^4 + (2*A - C)*a^3*b + B*a^2*b^2 + (2*A - C)*a*b^3)*c^2*d^6 - ((3*A - 2*C)*a^4 - B*a^3*b + 2*(2*A - C)*a^2*b^2 - B*a*b^3 + A*b^4)*c*d^7 - (B*a^4 - A*a^3*b + B*a^2*b^2 - A*a*b^3)*d^8 - 2*(((A - C)*a*b^3 + B*b^4)*c^7*d - 3*((A - C)*a^2*b^2 + (A - C)*b^4)*c^6*d^2 + 3*((A - C)*a^3*b - 2*B*a^2*b^2 + 2*(A - C)*a*b^3 - B*b^4)*c^5*d^3 - ((A - C)*a^4 - 8*B*a^3*b - 8*B*a*b^3 - (A - C)*b^4)*c^4*d^4 - 3*(B*a^4 + 2*(A - C)*a^3*b + 2*B*a^2*b^2 + (A - C)*a*b^3)*c^3*d^5 + 3*((A - C)*a^4 + (A - C)*a^2*b^2)*c^2*d^6 + (B*a^4 - (A - C)*a^3*b)*c*d^7)*f*x)*tan(f*x + e))/(((a^2*b^3 + b^5)*c^9*d^2 - 3*(a^3*b^2 + a*b^4)*c^8*d^3 + 3*(a^4*b + 2*a^2*b^3 + b^5)*c^7*d^4 - (a^5 + 10*a^3*b^2 + 9*a*b^4)*c^6*d^5 + 3*(3*a^4*b + 4*a^2*b^3 + b^5)*c^5*d^6 - 3*(a^5 + 4*a^3*b^2 + 3*a*b^4)*c^4*d^7 + (9*a^4*b + 10*a^2*b^3 + b^5)*c^3*d^8 - 3*(a^5 + 2*a^3*b^2 + a*b^4)*c^2*d^9 + 3*(a^4*b + a^2*b^3)*c*d^10 - (a^5 + a^3*b^2)*d^11)*f*tan(f*x + e)^2 + 2*((a^2*b^3 + b^5)*c^10*d - 3*(a^3*b^2 + a*b^4)*c^9*d^2 + 3*(a^4*b + 2*a^2*b^3 + b^5)*c^8*d^3 - (a^5 + 10*a^3*b^2 + 9*a*b^4)*c^7*d^4 + 3*(3*a^4*b + 4*a^2*b^3 + b^5)*c^6*d^5 - 3*(a^5 + 4*a^3*b^2 + 3*a*b^4)*c^5*d^6 + (9*a^4*b + 10*a^2*b^3 + b^5)*c^4*d^7 - 3*(a^5 + 2*a^3*b^2 + a*b^4)*c^3*d^8 + 3*(a^4*b + a^2*b^3)*c^2*d^9 - (a^5 + a^3*b^2)*c*d^10)*f*tan(f*x + e) + ((a^2*b^3 + b^5)*c^11 - 3*(a^3*b^2 + a*b^4)*c^10*d + 3*(a^4*b + 2*a^2*b^3 + b^5)*c^9*d^2 - (a^5 + 10*a^3*b^2 + 9*a*b^4)*c^8*d^3 + 3*(3*a^4*b + 4*a^2*b^3 + b^5)*c^7*d^4 - 3*(a^5 + 4*a^3*b^2 + 3*a*b^4)*c^6*d^5 + (9*a^4*b + 10*a^2*b^3 + b^5)*c^5*d^6 - 3*(a^5 + 2*a^3*b^2 + a*b^4)*c^4*d^7 + 3*(a^4*b + a^2*b^3)*c^3*d^8 - (a^5 + a^3*b^2)*c^2*d^9)*f)","B",0
89,1,9567,0,20.866587," ","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=""fricas"")","-\frac{2 \, {\left(C a^{2} b^{5} - B a b^{6} + A b^{7}\right)} c^{9} - 2 \, {\left(C a^{3} b^{4} - B a^{2} b^{5} + A a b^{6}\right)} c^{8} d + 6 \, {\left(C a^{2} b^{5} - B a b^{6} + A b^{7}\right)} c^{7} d^{2} + {\left(7 \, C a^{5} b^{2} + 8 \, C a^{3} b^{4} + 6 \, B a^{2} b^{5} - {\left(6 \, A - 7 \, C\right)} a b^{6}\right)} c^{6} d^{3} - {\left(10 \, C a^{6} b + 9 \, B a^{5} b^{2} + 20 \, C a^{4} b^{3} + 18 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} + 15 \, B a b^{6} - 6 \, A b^{7}\right)} c^{5} d^{4} + {\left(3 \, C a^{7} + 14 \, B a^{6} b + {\left(11 \, A + 7 \, C\right)} a^{5} b^{2} + 28 \, B a^{4} b^{3} + {\left(22 \, A - C\right)} a^{3} b^{4} + 20 \, B a^{2} b^{5} + {\left(5 \, A + C\right)} a b^{6}\right)} c^{4} d^{5} - {\left(5 \, B a^{7} + 2 \, {\left(9 \, A - C\right)} a^{6} b + 13 \, B a^{5} b^{2} + 4 \, {\left(9 \, A - C\right)} a^{4} b^{3} + 11 \, B a^{3} b^{4} + 2 \, {\left(9 \, A - 2 \, C\right)} a^{2} b^{5} + 5 \, B a b^{6} - 2 \, A b^{7}\right)} c^{3} d^{6} + {\left({\left(7 \, A - 3 \, C\right)} a^{7} + 2 \, B a^{6} b + {\left(19 \, A - 6 \, C\right)} a^{5} b^{2} + 4 \, B a^{4} b^{3} + {\left(17 \, A - 5 \, C\right)} a^{3} b^{4} + 4 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} c^{2} d^{7} + {\left(B a^{7} - 6 \, A a^{6} b + 2 \, B a^{5} b^{2} - 12 \, A a^{4} b^{3} + B a^{3} b^{4} - 6 \, A a^{2} b^{5}\right)} c d^{8} + {\left(A a^{7} + 2 \, A a^{5} b^{2} + A a^{3} b^{4}\right)} d^{9} - {\left(2 \, {\left(C a^{3} b^{4} - B a^{2} b^{5} + A a b^{6}\right)} c^{7} d^{2} + {\left(3 \, C a^{4} b^{3} + 2 \, B a^{3} b^{4} - 2 \, {\left(A - 5 \, C\right)} a^{2} b^{5} + 5 \, C b^{7}\right)} c^{6} d^{3} - {\left(6 \, C a^{5} b^{2} + 7 \, B a^{4} b^{3} + 6 \, C a^{3} b^{4} + 20 \, B a^{2} b^{5} - 6 \, {\left(A - C\right)} a b^{6} + 7 \, B b^{7}\right)} c^{5} d^{4} + {\left(C a^{6} b + 10 \, B a^{5} b^{2} + {\left(9 \, A - 5 \, C\right)} a^{4} b^{3} + 26 \, B a^{3} b^{4} + {\left(12 \, A - C\right)} a^{2} b^{5} + 10 \, B a b^{6} + {\left(9 \, A - C\right)} b^{7}\right)} c^{4} d^{5} - {\left(3 \, B a^{6} b + 2 \, {\left(7 \, A - 3 \, C\right)} a^{5} b^{2} + 7 \, B a^{4} b^{3} + 2 \, {\left(14 \, A - 9 \, C\right)} a^{3} b^{4} + 11 \, B a^{2} b^{5} + 2 \, {\left(4 \, A - 3 \, C\right)} a b^{6} + B b^{7}\right)} c^{3} d^{6} + {\left(5 \, {\left(A - C\right)} a^{6} b - 2 \, B a^{5} b^{2} + {\left(13 \, A - 16 \, C\right)} a^{4} b^{3} + 2 \, B a^{3} b^{4} + 5 \, {\left(A - C\right)} a^{2} b^{5} - 2 \, B a b^{6} + 3 \, A b^{7}\right)} c^{2} d^{7} + {\left(3 \, B a^{6} b - 2 \, A a^{5} b^{2} + 6 \, B a^{4} b^{3} - 2 \, {\left(2 \, A - C\right)} a^{3} b^{4} + B a^{2} b^{5}\right)} c d^{8} - {\left(A a^{6} b + 2 \, {\left(A + C\right)} a^{4} b^{3} - 2 \, B a^{3} b^{4} + 3 \, A a^{2} b^{5}\right)} d^{9} + 2 \, {\left({\left({\left(A - C\right)} a^{2} b^{5} + 2 \, B a b^{6} - {\left(A - C\right)} b^{7}\right)} c^{7} d^{2} - {\left(4 \, {\left(A - C\right)} a^{3} b^{4} + 5 \, B a^{2} b^{5} + 2 \, {\left(A - C\right)} a b^{6} + 3 \, B b^{7}\right)} c^{6} d^{3} + 3 \, {\left(2 \, {\left(A - C\right)} a^{4} b^{3} + 5 \, {\left(A - C\right)} a^{2} b^{5} + 2 \, B a b^{6} + {\left(A - C\right)} b^{7}\right)} c^{5} d^{4} - {\left(4 \, {\left(A - C\right)} a^{5} b^{2} - 10 \, B a^{4} b^{3} + 20 \, {\left(A - C\right)} a^{3} b^{4} - 5 \, B a^{2} b^{5} + 10 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c^{4} d^{5} + {\left({\left(A - C\right)} a^{6} b - 10 \, B a^{5} b^{2} + 5 \, {\left(A - C\right)} a^{4} b^{3} - 20 \, B a^{3} b^{4} + 10 \, {\left(A - C\right)} a^{2} b^{5} - 4 \, B a b^{6}\right)} c^{3} d^{6} + 3 \, {\left(B a^{6} b + 2 \, {\left(A - C\right)} a^{5} b^{2} + 5 \, B a^{4} b^{3} + 2 \, B a^{2} b^{5}\right)} c^{2} d^{7} - {\left(3 \, {\left(A - C\right)} a^{6} b + 2 \, B a^{5} b^{2} + 5 \, {\left(A - C\right)} a^{4} b^{3} + 4 \, B a^{3} b^{4}\right)} c d^{8} - {\left(B a^{6} b - 2 \, {\left(A - C\right)} a^{5} b^{2} - B a^{4} b^{3}\right)} d^{9}\right)} f x\right)} \tan\left(f x + e\right)^{3} - 2 \, {\left({\left({\left(A - C\right)} a^{3} b^{4} + 2 \, B a^{2} b^{5} - {\left(A - C\right)} a b^{6}\right)} c^{9} - {\left(4 \, {\left(A - C\right)} a^{4} b^{3} + 5 \, B a^{3} b^{4} + 2 \, {\left(A - C\right)} a^{2} b^{5} + 3 \, B a b^{6}\right)} c^{8} d + 3 \, {\left(2 \, {\left(A - C\right)} a^{5} b^{2} + 5 \, {\left(A - C\right)} a^{3} b^{4} + 2 \, B a^{2} b^{5} + {\left(A - C\right)} a b^{6}\right)} c^{7} d^{2} - {\left(4 \, {\left(A - C\right)} a^{6} b - 10 \, B a^{5} b^{2} + 20 \, {\left(A - C\right)} a^{4} b^{3} - 5 \, B a^{3} b^{4} + 10 \, {\left(A - C\right)} a^{2} b^{5} - B a b^{6}\right)} c^{6} d^{3} + {\left({\left(A - C\right)} a^{7} - 10 \, B a^{6} b + 5 \, {\left(A - C\right)} a^{5} b^{2} - 20 \, B a^{4} b^{3} + 10 \, {\left(A - C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5}\right)} c^{5} d^{4} + 3 \, {\left(B a^{7} + 2 \, {\left(A - C\right)} a^{6} b + 5 \, B a^{5} b^{2} + 2 \, B a^{3} b^{4}\right)} c^{4} d^{5} - {\left(3 \, {\left(A - C\right)} a^{7} + 2 \, B a^{6} b + 5 \, {\left(A - C\right)} a^{5} b^{2} + 4 \, B a^{4} b^{3}\right)} c^{3} d^{6} - {\left(B a^{7} - 2 \, {\left(A - C\right)} a^{6} b - B a^{5} b^{2}\right)} c^{2} d^{7}\right)} f x - {\left(4 \, {\left(C a^{3} b^{4} - B a^{2} b^{5} + A a b^{6}\right)} c^{8} d + 2 \, {\left(C a^{4} b^{3} + 2 \, B a^{3} b^{4} - {\left(2 \, A - 5 \, C\right)} a^{2} b^{5} + B a b^{6} - {\left(A - 3 \, C\right)} b^{7}\right)} c^{7} d^{2} - {\left(3 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3} - 8 \, C a^{3} b^{4} + 30 \, B a^{2} b^{5} - {\left(14 \, A - 3 \, C\right)} a b^{6} + 8 \, B b^{7}\right)} c^{6} d^{3} - {\left(4 \, C a^{6} b - 5 \, B a^{5} b^{2} - 2 \, {\left(5 \, A - 13 \, C\right)} a^{4} b^{3} - 22 \, B a^{3} b^{4} - 2 \, {\left(4 \, A - 11 \, C\right)} a^{2} b^{5} - 11 \, B a b^{6} - 2 \, {\left(2 \, A - 3 \, C\right)} b^{7}\right)} c^{5} d^{4} + {\left(C a^{7} + 6 \, B a^{6} b - {\left(7 \, A - 13 \, C\right)} a^{5} b^{2} + 18 \, B a^{4} b^{3} - {\left(14 \, A - 41 \, C\right)} a^{3} b^{4} + 11 \, {\left(A + C\right)} a b^{6} + 6 \, B b^{7}\right)} c^{4} d^{5} - {\left(3 \, B a^{7} + 8 \, A a^{6} b + 19 \, B a^{5} b^{2} + 2 \, {\left(11 \, A + 6 \, C\right)} a^{4} b^{3} + 17 \, B a^{3} b^{4} + 2 \, {\left(16 \, A + 3 \, C\right)} a^{2} b^{5} + 7 \, B a b^{6} + 12 \, A b^{7}\right)} c^{3} d^{6} + {\left(5 \, {\left(A - C\right)} a^{7} + 4 \, B a^{6} b + {\left(25 \, A - 14 \, C\right)} a^{5} b^{2} + 10 \, B a^{4} b^{3} + {\left(35 \, A - 3 \, C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + {\left(25 \, A - 4 \, C\right)} a b^{6} + 2 \, B b^{7}\right)} c^{2} d^{7} + {\left(3 \, B a^{7} - 4 \, {\left(2 \, A - C\right)} a^{6} b + 6 \, B a^{5} b^{2} - 4 \, {\left(5 \, A - C\right)} a^{4} b^{3} + 7 \, B a^{3} b^{4} - 2 \, {\left(10 \, A - C\right)} a^{2} b^{5} + 2 \, B a b^{6} - 6 \, A b^{7}\right)} c d^{8} - {\left(A a^{7} + 2 \, B a^{6} b - 2 \, A a^{5} b^{2} + 4 \, B a^{4} b^{3} - {\left(7 \, A + 2 \, C\right)} a^{3} b^{4} + 4 \, B a^{2} b^{5} - 6 \, A a b^{6}\right)} d^{9} + 2 \, {\left(2 \, {\left({\left(A - C\right)} a^{2} b^{5} + 2 \, B a b^{6} - {\left(A - C\right)} b^{7}\right)} c^{8} d - {\left(7 \, {\left(A - C\right)} a^{3} b^{4} + 8 \, B a^{2} b^{5} + 5 \, {\left(A - C\right)} a b^{6} + 6 \, B b^{7}\right)} c^{7} d^{2} + {\left(8 \, {\left(A - C\right)} a^{4} b^{3} - 5 \, B a^{3} b^{4} + 28 \, {\left(A - C\right)} a^{2} b^{5} + 9 \, B a b^{6} + 6 \, {\left(A - C\right)} b^{7}\right)} c^{6} d^{3} - {\left(2 \, {\left(A - C\right)} a^{5} b^{2} - 20 \, B a^{4} b^{3} + 25 \, {\left(A - C\right)} a^{3} b^{4} - 16 \, B a^{2} b^{5} + 17 \, {\left(A - C\right)} a b^{6} - 2 \, B b^{7}\right)} c^{5} d^{4} - {\left(2 \, {\left(A - C\right)} a^{6} b + 10 \, B a^{5} b^{2} + 10 \, {\left(A - C\right)} a^{4} b^{3} + 35 \, B a^{3} b^{4} - 10 \, {\left(A - C\right)} a^{2} b^{5} + 7 \, B a b^{6}\right)} c^{4} d^{5} + {\left({\left(A - C\right)} a^{7} - 4 \, B a^{6} b + 17 \, {\left(A - C\right)} a^{5} b^{2} + 10 \, B a^{4} b^{3} + 10 \, {\left(A - C\right)} a^{3} b^{4} + 8 \, B a^{2} b^{5}\right)} c^{3} d^{6} + {\left(3 \, B a^{7} + 11 \, B a^{5} b^{2} - 10 \, {\left(A - C\right)} a^{4} b^{3} - 2 \, B a^{3} b^{4}\right)} c^{2} d^{7} - {\left(3 \, {\left(A - C\right)} a^{7} + 4 \, B a^{6} b + {\left(A - C\right)} a^{5} b^{2} + 2 \, B a^{4} b^{3}\right)} c d^{8} - {\left(B a^{7} - 2 \, {\left(A - C\right)} a^{6} b - B a^{5} b^{2}\right)} d^{9}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left({\left(B a^{3} b^{4} - 2 \, {\left(A - C\right)} a^{2} b^{5} - B a b^{6}\right)} c^{9} + {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A + C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} c^{8} d + 3 \, {\left(B a^{3} b^{4} - 2 \, {\left(A - C\right)} a^{2} b^{5} - B a b^{6}\right)} c^{7} d^{2} + 3 \, {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A + C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} c^{6} d^{3} + 3 \, {\left(B a^{3} b^{4} - 2 \, {\left(A - C\right)} a^{2} b^{5} - B a b^{6}\right)} c^{5} d^{4} + 3 \, {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A + C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} c^{4} d^{5} + {\left(B a^{3} b^{4} - 2 \, {\left(A - C\right)} a^{2} b^{5} - B a b^{6}\right)} c^{3} d^{6} + {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A + C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} c^{2} d^{7} + {\left({\left(B a^{2} b^{5} - 2 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c^{7} d^{2} + {\left(3 \, C a^{4} b^{3} - 4 \, B a^{3} b^{4} + {\left(5 \, A + C\right)} a^{2} b^{5} - 2 \, B a b^{6} + 3 \, A b^{7}\right)} c^{6} d^{3} + 3 \, {\left(B a^{2} b^{5} - 2 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c^{5} d^{4} + 3 \, {\left(3 \, C a^{4} b^{3} - 4 \, B a^{3} b^{4} + {\left(5 \, A + C\right)} a^{2} b^{5} - 2 \, B a b^{6} + 3 \, A b^{7}\right)} c^{4} d^{5} + 3 \, {\left(B a^{2} b^{5} - 2 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c^{3} d^{6} + 3 \, {\left(3 \, C a^{4} b^{3} - 4 \, B a^{3} b^{4} + {\left(5 \, A + C\right)} a^{2} b^{5} - 2 \, B a b^{6} + 3 \, A b^{7}\right)} c^{2} d^{7} + {\left(B a^{2} b^{5} - 2 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c d^{8} + {\left(3 \, C a^{4} b^{3} - 4 \, B a^{3} b^{4} + {\left(5 \, A + C\right)} a^{2} b^{5} - 2 \, B a b^{6} + 3 \, A b^{7}\right)} d^{9}\right)} \tan\left(f x + e\right)^{3} + {\left(2 \, {\left(B a^{2} b^{5} - 2 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c^{8} d + {\left(6 \, C a^{4} b^{3} - 7 \, B a^{3} b^{4} + 4 \, {\left(2 \, A + C\right)} a^{2} b^{5} - 5 \, B a b^{6} + 6 \, A b^{7}\right)} c^{7} d^{2} + {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A + C\right)} a^{3} b^{4} + 4 \, B a^{2} b^{5} - 3 \, {\left(3 \, A - 4 \, C\right)} a b^{6} - 6 \, B b^{7}\right)} c^{6} d^{3} + 3 \, {\left(6 \, C a^{4} b^{3} - 7 \, B a^{3} b^{4} + 4 \, {\left(2 \, A + C\right)} a^{2} b^{5} - 5 \, B a b^{6} + 6 \, A b^{7}\right)} c^{5} d^{4} + 3 \, {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A + C\right)} a^{3} b^{4} - {\left(A - 4 \, C\right)} a b^{6} - 2 \, B b^{7}\right)} c^{4} d^{5} + 3 \, {\left(6 \, C a^{4} b^{3} - 7 \, B a^{3} b^{4} + 4 \, {\left(2 \, A + C\right)} a^{2} b^{5} - 5 \, B a b^{6} + 6 \, A b^{7}\right)} c^{3} d^{6} + {\left(9 \, C a^{5} b^{2} - 12 \, B a^{4} b^{3} + 3 \, {\left(5 \, A + C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + {\left(5 \, A + 4 \, C\right)} a b^{6} - 2 \, B b^{7}\right)} c^{2} d^{7} + {\left(6 \, C a^{4} b^{3} - 7 \, B a^{3} b^{4} + 4 \, {\left(2 \, A + C\right)} a^{2} b^{5} - 5 \, B a b^{6} + 6 \, A b^{7}\right)} c d^{8} + {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A + C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} d^{9}\right)} \tan\left(f x + e\right)^{2} + {\left({\left(B a^{2} b^{5} - 2 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c^{9} + {\left(3 \, C a^{4} b^{3} - 2 \, B a^{3} b^{4} + {\left(A + 5 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 3 \, A b^{7}\right)} c^{8} d + {\left(6 \, C a^{5} b^{2} - 8 \, B a^{4} b^{3} + 2 \, {\left(5 \, A + C\right)} a^{3} b^{4} - B a^{2} b^{5} + 6 \, C a b^{6} - 3 \, B b^{7}\right)} c^{7} d^{2} + 3 \, {\left(3 \, C a^{4} b^{3} - 2 \, B a^{3} b^{4} + {\left(A + 5 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 3 \, A b^{7}\right)} c^{6} d^{3} + 3 \, {\left(6 \, C a^{5} b^{2} - 8 \, B a^{4} b^{3} + 2 \, {\left(5 \, A + C\right)} a^{3} b^{4} - 3 \, B a^{2} b^{5} + 2 \, {\left(2 \, A + C\right)} a b^{6} - B b^{7}\right)} c^{5} d^{4} + 3 \, {\left(3 \, C a^{4} b^{3} - 2 \, B a^{3} b^{4} + {\left(A + 5 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 3 \, A b^{7}\right)} c^{4} d^{5} + {\left(18 \, C a^{5} b^{2} - 24 \, B a^{4} b^{3} + 6 \, {\left(5 \, A + C\right)} a^{3} b^{4} - 11 \, B a^{2} b^{5} + 2 \, {\left(8 \, A + C\right)} a b^{6} - B b^{7}\right)} c^{3} d^{6} + {\left(3 \, C a^{4} b^{3} - 2 \, B a^{3} b^{4} + {\left(A + 5 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 3 \, A b^{7}\right)} c^{2} d^{7} + 2 \, {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A + C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} c d^{8}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(3 \, {\left(C a^{5} b^{2} + 2 \, C a^{3} b^{4} + C a b^{6}\right)} c^{8} d - 6 \, {\left(B a^{5} b^{2} + 2 \, B a^{3} b^{4} + B a b^{6}\right)} c^{7} d^{2} + {\left(4 \, B a^{6} b + {\left(10 \, A - C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} + 2 \, {\left(10 \, A - C\right)} a^{3} b^{4} + 4 \, B a^{2} b^{5} + {\left(10 \, A - C\right)} a b^{6}\right)} c^{6} d^{3} - {\left(B a^{7} + 10 \, {\left(A - C\right)} a^{6} b + 5 \, B a^{5} b^{2} + 20 \, {\left(A - C\right)} a^{4} b^{3} + 7 \, B a^{3} b^{4} + 10 \, {\left(A - C\right)} a^{2} b^{5} + 3 \, B a b^{6}\right)} c^{5} d^{4} + 3 \, {\left({\left(A - C\right)} a^{7} - 2 \, B a^{6} b + {\left(5 \, A - 2 \, C\right)} a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(7 \, A - C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} c^{4} d^{5} + {\left(3 \, B a^{7} - 2 \, {\left(A - C\right)} a^{6} b + 5 \, B a^{5} b^{2} - 4 \, {\left(A - C\right)} a^{4} b^{3} + B a^{3} b^{4} - 2 \, {\left(A - C\right)} a^{2} b^{5} - B a b^{6}\right)} c^{3} d^{6} - {\left({\left(A - C\right)} a^{7} + 2 \, B a^{6} b - {\left(A + 2 \, C\right)} a^{5} b^{2} + 4 \, B a^{4} b^{3} - {\left(5 \, A + C\right)} a^{3} b^{4} + 2 \, B a^{2} b^{5} - 3 \, A a b^{6}\right)} c^{2} d^{7} + {\left(3 \, {\left(C a^{4} b^{3} + 2 \, C a^{2} b^{5} + C b^{7}\right)} c^{6} d^{3} - 6 \, {\left(B a^{4} b^{3} + 2 \, B a^{2} b^{5} + B b^{7}\right)} c^{5} d^{4} + {\left(4 \, B a^{5} b^{2} + {\left(10 \, A - C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} + 2 \, {\left(10 \, A - C\right)} a^{2} b^{5} + 4 \, B a b^{6} + {\left(10 \, A - C\right)} b^{7}\right)} c^{4} d^{5} - {\left(B a^{6} b + 10 \, {\left(A - C\right)} a^{5} b^{2} + 5 \, B a^{4} b^{3} + 20 \, {\left(A - C\right)} a^{3} b^{4} + 7 \, B a^{2} b^{5} + 10 \, {\left(A - C\right)} a b^{6} + 3 \, B b^{7}\right)} c^{3} d^{6} + 3 \, {\left({\left(A - C\right)} a^{6} b - 2 \, B a^{5} b^{2} + {\left(5 \, A - 2 \, C\right)} a^{4} b^{3} - 4 \, B a^{3} b^{4} + {\left(7 \, A - C\right)} a^{2} b^{5} - 2 \, B a b^{6} + 3 \, A b^{7}\right)} c^{2} d^{7} + {\left(3 \, B a^{6} b - 2 \, {\left(A - C\right)} a^{5} b^{2} + 5 \, B a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{3} b^{4} + B a^{2} b^{5} - 2 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c d^{8} - {\left({\left(A - C\right)} a^{6} b + 2 \, B a^{5} b^{2} - {\left(A + 2 \, C\right)} a^{4} b^{3} + 4 \, B a^{3} b^{4} - {\left(5 \, A + C\right)} a^{2} b^{5} + 2 \, B a b^{6} - 3 \, A b^{7}\right)} d^{9}\right)} \tan\left(f x + e\right)^{3} + {\left(6 \, {\left(C a^{4} b^{3} + 2 \, C a^{2} b^{5} + C b^{7}\right)} c^{7} d^{2} + 3 \, {\left(C a^{5} b^{2} - 4 \, B a^{4} b^{3} + 2 \, C a^{3} b^{4} - 8 \, B a^{2} b^{5} + C a b^{6} - 4 \, B b^{7}\right)} c^{6} d^{3} + 2 \, {\left(B a^{5} b^{2} + {\left(10 \, A - C\right)} a^{4} b^{3} + 2 \, B a^{3} b^{4} + 2 \, {\left(10 \, A - C\right)} a^{2} b^{5} + B a b^{6} + {\left(10 \, A - C\right)} b^{7}\right)} c^{5} d^{4} + {\left(2 \, B a^{6} b - {\left(10 \, A - 19 \, C\right)} a^{5} b^{2} - 2 \, B a^{4} b^{3} - 2 \, {\left(10 \, A - 19 \, C\right)} a^{3} b^{4} - 10 \, B a^{2} b^{5} - {\left(10 \, A - 19 \, C\right)} a b^{6} - 6 \, B b^{7}\right)} c^{4} d^{5} - {\left(B a^{7} + 4 \, {\left(A - C\right)} a^{6} b + 17 \, B a^{5} b^{2} - 2 \, {\left(5 \, A + 4 \, C\right)} a^{4} b^{3} + 31 \, B a^{3} b^{4} - 4 \, {\left(8 \, A + C\right)} a^{2} b^{5} + 15 \, B a b^{6} - 18 \, A b^{7}\right)} c^{3} d^{6} + {\left(3 \, {\left(A - C\right)} a^{7} + {\left(11 \, A - 2 \, C\right)} a^{5} b^{2} - 2 \, B a^{4} b^{3} + {\left(13 \, A + 5 \, C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + {\left(5 \, A + 4 \, C\right)} a b^{6} - 2 \, B b^{7}\right)} c^{2} d^{7} + {\left(3 \, B a^{7} - 4 \, {\left(A - C\right)} a^{6} b + B a^{5} b^{2} - 2 \, {\left(A - 4 \, C\right)} a^{4} b^{3} - 7 \, B a^{3} b^{4} + 4 \, {\left(2 \, A + C\right)} a^{2} b^{5} - 5 \, B a b^{6} + 6 \, A b^{7}\right)} c d^{8} - {\left({\left(A - C\right)} a^{7} + 2 \, B a^{6} b - {\left(A + 2 \, C\right)} a^{5} b^{2} + 4 \, B a^{4} b^{3} - {\left(5 \, A + C\right)} a^{3} b^{4} + 2 \, B a^{2} b^{5} - 3 \, A a b^{6}\right)} d^{9}\right)} \tan\left(f x + e\right)^{2} + {\left(3 \, {\left(C a^{4} b^{3} + 2 \, C a^{2} b^{5} + C b^{7}\right)} c^{8} d + 6 \, {\left(C a^{5} b^{2} - B a^{4} b^{3} + 2 \, C a^{3} b^{4} - 2 \, B a^{2} b^{5} + C a b^{6} - B b^{7}\right)} c^{7} d^{2} - {\left(8 \, B a^{5} b^{2} - {\left(10 \, A - C\right)} a^{4} b^{3} + 16 \, B a^{3} b^{4} - 2 \, {\left(10 \, A - C\right)} a^{2} b^{5} + 8 \, B a b^{6} - {\left(10 \, A - C\right)} b^{7}\right)} c^{6} d^{3} + {\left(7 \, B a^{6} b + 2 \, {\left(5 \, A + 4 \, C\right)} a^{5} b^{2} + 11 \, B a^{4} b^{3} + 4 \, {\left(5 \, A + 4 \, C\right)} a^{3} b^{4} + B a^{2} b^{5} + 2 \, {\left(5 \, A + 4 \, C\right)} a b^{6} - 3 \, B b^{7}\right)} c^{5} d^{4} - {\left(2 \, B a^{7} + 17 \, {\left(A - C\right)} a^{6} b + 16 \, B a^{5} b^{2} + {\left(25 \, A - 34 \, C\right)} a^{4} b^{3} + 26 \, B a^{3} b^{4} - {\left(A + 17 \, C\right)} a^{2} b^{5} + 12 \, B a b^{6} - 9 \, A b^{7}\right)} c^{4} d^{5} + {\left(6 \, {\left(A - C\right)} a^{7} - 9 \, B a^{6} b + 2 \, {\left(14 \, A - 5 \, C\right)} a^{5} b^{2} - 19 \, B a^{4} b^{3} + 2 \, {\left(19 \, A - C\right)} a^{3} b^{4} - 11 \, B a^{2} b^{5} + 2 \, {\left(8 \, A + C\right)} a b^{6} - B b^{7}\right)} c^{3} d^{6} + {\left(6 \, B a^{7} - 5 \, {\left(A - C\right)} a^{6} b + 8 \, B a^{5} b^{2} - {\left(7 \, A - 10 \, C\right)} a^{4} b^{3} - 2 \, B a^{3} b^{4} + {\left(A + 5 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 3 \, A b^{7}\right)} c^{2} d^{7} - 2 \, {\left({\left(A - C\right)} a^{7} + 2 \, B a^{6} b - {\left(A + 2 \, C\right)} a^{5} b^{2} + 4 \, B a^{4} b^{3} - {\left(5 \, A + C\right)} a^{3} b^{4} + 2 \, B a^{2} b^{5} - 3 \, A a b^{6}\right)} c d^{8}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(2 \, {\left(C a^{3} b^{4} - B a^{2} b^{5} + A a b^{6}\right)} c^{9} - 2 \, {\left(C a^{4} b^{3} - B a^{3} b^{4} + {\left(A + 2 \, C\right)} a^{2} b^{5} - 2 \, B a b^{6} + 2 \, A b^{7}\right)} c^{8} d + 2 \, {\left(3 \, C a^{5} b^{2} + 11 \, C a^{3} b^{4} - 5 \, B a^{2} b^{5} + {\left(5 \, A + 3 \, C\right)} a b^{6}\right)} c^{7} d^{2} - {\left(8 \, C a^{6} b + 8 \, B a^{5} b^{2} + 29 \, C a^{4} b^{3} + 10 \, B a^{3} b^{4} + 2 \, {\left(3 \, A + 17 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + {\left(12 \, A + 7 \, C\right)} b^{7}\right)} c^{6} d^{3} + {\left(2 \, C a^{7} + 12 \, B a^{6} b + 2 \, {\left(5 \, A + 4 \, C\right)} a^{5} b^{2} + 33 \, B a^{4} b^{3} + 4 \, {\left(5 \, A + 7 \, C\right)} a^{3} b^{4} + 12 \, B a^{2} b^{5} + 4 \, {\left(7 \, A + C\right)} a b^{6} + 9 \, B b^{7}\right)} c^{5} d^{4} - {\left(4 \, B a^{7} + {\left(16 \, A - 9 \, C\right)} a^{6} b + 16 \, B a^{5} b^{2} + {\left(43 \, A - 11 \, C\right)} a^{4} b^{3} + 14 \, B a^{3} b^{4} + {\left(44 \, A + 5 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + {\left(23 \, A + C\right)} b^{7}\right)} c^{4} d^{5} + {\left(6 \, {\left(A - C\right)} a^{7} - 7 \, B a^{6} b + 2 \, {\left(12 \, A - 7 \, C\right)} a^{5} b^{2} - 11 \, B a^{4} b^{3} + 2 \, {\left(15 \, A + 2 \, C\right)} a^{3} b^{4} - 15 \, B a^{2} b^{5} + 2 \, {\left(13 \, A - C\right)} a b^{6} + 3 \, B b^{7}\right)} c^{3} d^{6} + {\left(6 \, B a^{7} + {\left(5 \, A - C\right)} a^{6} b + 12 \, B a^{5} b^{2} + {\left(5 \, A - 4 \, C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - {\left(7 \, A + 5 \, C\right)} a^{2} b^{5} + 4 \, B a b^{6} - 9 \, A b^{7}\right)} c^{2} d^{7} - {\left(2 \, {\left(3 \, A - 2 \, C\right)} a^{7} + B a^{6} b + 2 \, {\left(5 \, A - 4 \, C\right)} a^{5} b^{2} + 2 \, B a^{4} b^{3} + 2 \, {\left(A - 4 \, C\right)} a^{3} b^{4} + 5 \, B a^{2} b^{5} - 6 \, A a b^{6}\right)} c d^{8} - {\left(2 \, B a^{7} - 3 \, A a^{6} b + 4 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} + 2 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} d^{9} + 2 \, {\left({\left({\left(A - C\right)} a^{2} b^{5} + 2 \, B a b^{6} - {\left(A - C\right)} b^{7}\right)} c^{9} - {\left(2 \, {\left(A - C\right)} a^{3} b^{4} + B a^{2} b^{5} + 4 \, {\left(A - C\right)} a b^{6} + 3 \, B b^{7}\right)} c^{8} d - {\left(2 \, {\left(A - C\right)} a^{4} b^{3} + 10 \, B a^{3} b^{4} - 11 \, {\left(A - C\right)} a^{2} b^{5} - 3 \, {\left(A - C\right)} b^{7}\right)} c^{7} d^{2} + {\left(8 \, {\left(A - C\right)} a^{5} b^{2} + 10 \, B a^{4} b^{3} + 10 \, {\left(A - C\right)} a^{3} b^{4} + 17 \, B a^{2} b^{5} - 4 \, {\left(A - C\right)} a b^{6} + B b^{7}\right)} c^{6} d^{3} - {\left(7 \, {\left(A - C\right)} a^{6} b - 10 \, B a^{5} b^{2} + 35 \, {\left(A - C\right)} a^{4} b^{3} + 10 \, B a^{3} b^{4} + 10 \, {\left(A - C\right)} a^{2} b^{5} + 2 \, B a b^{6}\right)} c^{5} d^{4} + {\left(2 \, {\left(A - C\right)} a^{7} - 17 \, B a^{6} b + 16 \, {\left(A - C\right)} a^{5} b^{2} - 25 \, B a^{4} b^{3} + 20 \, {\left(A - C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5}\right)} c^{4} d^{5} + {\left(6 \, B a^{7} + 9 \, {\left(A - C\right)} a^{6} b + 28 \, B a^{5} b^{2} - 5 \, {\left(A - C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4}\right)} c^{3} d^{6} - {\left(6 \, {\left(A - C\right)} a^{7} + 5 \, B a^{6} b + 8 \, {\left(A - C\right)} a^{5} b^{2} + 7 \, B a^{4} b^{3}\right)} c^{2} d^{7} - 2 \, {\left(B a^{7} - 2 \, {\left(A - C\right)} a^{6} b - B a^{5} b^{2}\right)} c d^{8}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} c^{10} d^{2} - 4 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{9} d^{3} + 3 \, {\left(2 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} c^{8} d^{4} - 4 \, {\left(a^{7} b^{2} + 5 \, a^{5} b^{4} + 7 \, a^{3} b^{6} + 3 \, a b^{8}\right)} c^{7} d^{5} + {\left(a^{8} b + 20 \, a^{6} b^{3} + 40 \, a^{4} b^{5} + 24 \, a^{2} b^{7} + 3 \, b^{9}\right)} c^{6} d^{6} - 12 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} c^{5} d^{7} + {\left(3 \, a^{8} b + 24 \, a^{6} b^{3} + 40 \, a^{4} b^{5} + 20 \, a^{2} b^{7} + b^{9}\right)} c^{4} d^{8} - 4 \, {\left(3 \, a^{7} b^{2} + 7 \, a^{5} b^{4} + 5 \, a^{3} b^{6} + a b^{8}\right)} c^{3} d^{9} + 3 \, {\left(a^{8} b + 4 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + 2 \, a^{2} b^{7}\right)} c^{2} d^{10} - 4 \, {\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} c d^{11} + {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d^{12}\right)} f \tan\left(f x + e\right)^{3} + {\left(2 \, {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} c^{11} d - 7 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{10} d^{2} + 2 \, {\left(4 \, a^{6} b^{3} + 11 \, a^{4} b^{5} + 10 \, a^{2} b^{7} + 3 \, b^{9}\right)} c^{9} d^{3} - {\left(2 \, a^{7} b^{2} + 25 \, a^{5} b^{4} + 44 \, a^{3} b^{6} + 21 \, a b^{8}\right)} c^{8} d^{4} - 2 \, {\left(a^{8} b - 10 \, a^{6} b^{3} - 26 \, a^{4} b^{5} - 18 \, a^{2} b^{7} - 3 \, b^{9}\right)} c^{7} d^{5} + {\left(a^{9} - 4 \, a^{7} b^{2} - 32 \, a^{5} b^{4} - 48 \, a^{3} b^{6} - 21 \, a b^{8}\right)} c^{6} d^{6} - 2 \, {\left(3 \, a^{8} b - 6 \, a^{6} b^{3} - 22 \, a^{4} b^{5} - 14 \, a^{2} b^{7} - b^{9}\right)} c^{5} d^{7} + {\left(3 \, a^{9} - 16 \, a^{5} b^{4} - 20 \, a^{3} b^{6} - 7 \, a b^{8}\right)} c^{4} d^{8} - 2 \, {\left(3 \, a^{8} b + 2 \, a^{6} b^{3} - 5 \, a^{4} b^{5} - 4 \, a^{2} b^{7}\right)} c^{3} d^{9} + {\left(3 \, a^{9} + 4 \, a^{7} b^{2} - a^{5} b^{4} - 2 \, a^{3} b^{6}\right)} c^{2} d^{10} - 2 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} c d^{11} + {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d^{12}\right)} f \tan\left(f x + e\right)^{2} + {\left({\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} c^{12} - 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{11} d - {\left(2 \, a^{6} b^{3} + a^{4} b^{5} - 4 \, a^{2} b^{7} - 3 \, b^{9}\right)} c^{10} d^{2} + 2 \, {\left(4 \, a^{7} b^{2} + 5 \, a^{5} b^{4} - 2 \, a^{3} b^{6} - 3 \, a b^{8}\right)} c^{9} d^{3} - {\left(7 \, a^{8} b + 20 \, a^{6} b^{3} + 16 \, a^{4} b^{5} - 3 \, b^{9}\right)} c^{8} d^{4} + 2 \, {\left(a^{9} + 14 \, a^{7} b^{2} + 22 \, a^{5} b^{4} + 6 \, a^{3} b^{6} - 3 \, a b^{8}\right)} c^{7} d^{5} - {\left(21 \, a^{8} b + 48 \, a^{6} b^{3} + 32 \, a^{4} b^{5} + 4 \, a^{2} b^{7} - b^{9}\right)} c^{6} d^{6} + 2 \, {\left(3 \, a^{9} + 18 \, a^{7} b^{2} + 26 \, a^{5} b^{4} + 10 \, a^{3} b^{6} - a b^{8}\right)} c^{5} d^{7} - {\left(21 \, a^{8} b + 44 \, a^{6} b^{3} + 25 \, a^{4} b^{5} + 2 \, a^{2} b^{7}\right)} c^{4} d^{8} + 2 \, {\left(3 \, a^{9} + 10 \, a^{7} b^{2} + 11 \, a^{5} b^{4} + 4 \, a^{3} b^{6}\right)} c^{3} d^{9} - 7 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} c^{2} d^{10} + 2 \, {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} c d^{11}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{12} - 4 \, {\left(a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{11} d + 3 \, {\left(2 \, a^{7} b^{2} + 5 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} c^{10} d^{2} - 4 \, {\left(a^{8} b + 5 \, a^{6} b^{3} + 7 \, a^{4} b^{5} + 3 \, a^{2} b^{7}\right)} c^{9} d^{3} + {\left(a^{9} + 20 \, a^{7} b^{2} + 40 \, a^{5} b^{4} + 24 \, a^{3} b^{6} + 3 \, a b^{8}\right)} c^{8} d^{4} - 12 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{7} d^{5} + {\left(3 \, a^{9} + 24 \, a^{7} b^{2} + 40 \, a^{5} b^{4} + 20 \, a^{3} b^{6} + a b^{8}\right)} c^{6} d^{6} - 4 \, {\left(3 \, a^{8} b + 7 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{5} d^{7} + 3 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 5 \, a^{5} b^{4} + 2 \, a^{3} b^{6}\right)} c^{4} d^{8} - 4 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} c^{3} d^{9} + {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} c^{2} d^{10}\right)} f\right)}}"," ",0,"-1/2*(2*(C*a^2*b^5 - B*a*b^6 + A*b^7)*c^9 - 2*(C*a^3*b^4 - B*a^2*b^5 + A*a*b^6)*c^8*d + 6*(C*a^2*b^5 - B*a*b^6 + A*b^7)*c^7*d^2 + (7*C*a^5*b^2 + 8*C*a^3*b^4 + 6*B*a^2*b^5 - (6*A - 7*C)*a*b^6)*c^6*d^3 - (10*C*a^6*b + 9*B*a^5*b^2 + 20*C*a^4*b^3 + 18*B*a^3*b^4 + 4*C*a^2*b^5 + 15*B*a*b^6 - 6*A*b^7)*c^5*d^4 + (3*C*a^7 + 14*B*a^6*b + (11*A + 7*C)*a^5*b^2 + 28*B*a^4*b^3 + (22*A - C)*a^3*b^4 + 20*B*a^2*b^5 + (5*A + C)*a*b^6)*c^4*d^5 - (5*B*a^7 + 2*(9*A - C)*a^6*b + 13*B*a^5*b^2 + 4*(9*A - C)*a^4*b^3 + 11*B*a^3*b^4 + 2*(9*A - 2*C)*a^2*b^5 + 5*B*a*b^6 - 2*A*b^7)*c^3*d^6 + ((7*A - 3*C)*a^7 + 2*B*a^6*b + (19*A - 6*C)*a^5*b^2 + 4*B*a^4*b^3 + (17*A - 5*C)*a^3*b^4 + 4*B*a^2*b^5 + 3*A*a*b^6)*c^2*d^7 + (B*a^7 - 6*A*a^6*b + 2*B*a^5*b^2 - 12*A*a^4*b^3 + B*a^3*b^4 - 6*A*a^2*b^5)*c*d^8 + (A*a^7 + 2*A*a^5*b^2 + A*a^3*b^4)*d^9 - (2*(C*a^3*b^4 - B*a^2*b^5 + A*a*b^6)*c^7*d^2 + (3*C*a^4*b^3 + 2*B*a^3*b^4 - 2*(A - 5*C)*a^2*b^5 + 5*C*b^7)*c^6*d^3 - (6*C*a^5*b^2 + 7*B*a^4*b^3 + 6*C*a^3*b^4 + 20*B*a^2*b^5 - 6*(A - C)*a*b^6 + 7*B*b^7)*c^5*d^4 + (C*a^6*b + 10*B*a^5*b^2 + (9*A - 5*C)*a^4*b^3 + 26*B*a^3*b^4 + (12*A - C)*a^2*b^5 + 10*B*a*b^6 + (9*A - C)*b^7)*c^4*d^5 - (3*B*a^6*b + 2*(7*A - 3*C)*a^5*b^2 + 7*B*a^4*b^3 + 2*(14*A - 9*C)*a^3*b^4 + 11*B*a^2*b^5 + 2*(4*A - 3*C)*a*b^6 + B*b^7)*c^3*d^6 + (5*(A - C)*a^6*b - 2*B*a^5*b^2 + (13*A - 16*C)*a^4*b^3 + 2*B*a^3*b^4 + 5*(A - C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7)*c^2*d^7 + (3*B*a^6*b - 2*A*a^5*b^2 + 6*B*a^4*b^3 - 2*(2*A - C)*a^3*b^4 + B*a^2*b^5)*c*d^8 - (A*a^6*b + 2*(A + C)*a^4*b^3 - 2*B*a^3*b^4 + 3*A*a^2*b^5)*d^9 + 2*(((A - C)*a^2*b^5 + 2*B*a*b^6 - (A - C)*b^7)*c^7*d^2 - (4*(A - C)*a^3*b^4 + 5*B*a^2*b^5 + 2*(A - C)*a*b^6 + 3*B*b^7)*c^6*d^3 + 3*(2*(A - C)*a^4*b^3 + 5*(A - C)*a^2*b^5 + 2*B*a*b^6 + (A - C)*b^7)*c^5*d^4 - (4*(A - C)*a^5*b^2 - 10*B*a^4*b^3 + 20*(A - C)*a^3*b^4 - 5*B*a^2*b^5 + 10*(A - C)*a*b^6 - B*b^7)*c^4*d^5 + ((A - C)*a^6*b - 10*B*a^5*b^2 + 5*(A - C)*a^4*b^3 - 20*B*a^3*b^4 + 10*(A - C)*a^2*b^5 - 4*B*a*b^6)*c^3*d^6 + 3*(B*a^6*b + 2*(A - C)*a^5*b^2 + 5*B*a^4*b^3 + 2*B*a^2*b^5)*c^2*d^7 - (3*(A - C)*a^6*b + 2*B*a^5*b^2 + 5*(A - C)*a^4*b^3 + 4*B*a^3*b^4)*c*d^8 - (B*a^6*b - 2*(A - C)*a^5*b^2 - B*a^4*b^3)*d^9)*f*x)*tan(f*x + e)^3 - 2*(((A - C)*a^3*b^4 + 2*B*a^2*b^5 - (A - C)*a*b^6)*c^9 - (4*(A - C)*a^4*b^3 + 5*B*a^3*b^4 + 2*(A - C)*a^2*b^5 + 3*B*a*b^6)*c^8*d + 3*(2*(A - C)*a^5*b^2 + 5*(A - C)*a^3*b^4 + 2*B*a^2*b^5 + (A - C)*a*b^6)*c^7*d^2 - (4*(A - C)*a^6*b - 10*B*a^5*b^2 + 20*(A - C)*a^4*b^3 - 5*B*a^3*b^4 + 10*(A - C)*a^2*b^5 - B*a*b^6)*c^6*d^3 + ((A - C)*a^7 - 10*B*a^6*b + 5*(A - C)*a^5*b^2 - 20*B*a^4*b^3 + 10*(A - C)*a^3*b^4 - 4*B*a^2*b^5)*c^5*d^4 + 3*(B*a^7 + 2*(A - C)*a^6*b + 5*B*a^5*b^2 + 2*B*a^3*b^4)*c^4*d^5 - (3*(A - C)*a^7 + 2*B*a^6*b + 5*(A - C)*a^5*b^2 + 4*B*a^4*b^3)*c^3*d^6 - (B*a^7 - 2*(A - C)*a^6*b - B*a^5*b^2)*c^2*d^7)*f*x - (4*(C*a^3*b^4 - B*a^2*b^5 + A*a*b^6)*c^8*d + 2*(C*a^4*b^3 + 2*B*a^3*b^4 - (2*A - 5*C)*a^2*b^5 + B*a*b^6 - (A - 3*C)*b^7)*c^7*d^2 - (3*C*a^5*b^2 + 8*B*a^4*b^3 - 8*C*a^3*b^4 + 30*B*a^2*b^5 - (14*A - 3*C)*a*b^6 + 8*B*b^7)*c^6*d^3 - (4*C*a^6*b - 5*B*a^5*b^2 - 2*(5*A - 13*C)*a^4*b^3 - 22*B*a^3*b^4 - 2*(4*A - 11*C)*a^2*b^5 - 11*B*a*b^6 - 2*(2*A - 3*C)*b^7)*c^5*d^4 + (C*a^7 + 6*B*a^6*b - (7*A - 13*C)*a^5*b^2 + 18*B*a^4*b^3 - (14*A - 41*C)*a^3*b^4 + 11*(A + C)*a*b^6 + 6*B*b^7)*c^4*d^5 - (3*B*a^7 + 8*A*a^6*b + 19*B*a^5*b^2 + 2*(11*A + 6*C)*a^4*b^3 + 17*B*a^3*b^4 + 2*(16*A + 3*C)*a^2*b^5 + 7*B*a*b^6 + 12*A*b^7)*c^3*d^6 + (5*(A - C)*a^7 + 4*B*a^6*b + (25*A - 14*C)*a^5*b^2 + 10*B*a^4*b^3 + (35*A - 3*C)*a^3*b^4 - 2*B*a^2*b^5 + (25*A - 4*C)*a*b^6 + 2*B*b^7)*c^2*d^7 + (3*B*a^7 - 4*(2*A - C)*a^6*b + 6*B*a^5*b^2 - 4*(5*A - C)*a^4*b^3 + 7*B*a^3*b^4 - 2*(10*A - C)*a^2*b^5 + 2*B*a*b^6 - 6*A*b^7)*c*d^8 - (A*a^7 + 2*B*a^6*b - 2*A*a^5*b^2 + 4*B*a^4*b^3 - (7*A + 2*C)*a^3*b^4 + 4*B*a^2*b^5 - 6*A*a*b^6)*d^9 + 2*(2*((A - C)*a^2*b^5 + 2*B*a*b^6 - (A - C)*b^7)*c^8*d - (7*(A - C)*a^3*b^4 + 8*B*a^2*b^5 + 5*(A - C)*a*b^6 + 6*B*b^7)*c^7*d^2 + (8*(A - C)*a^4*b^3 - 5*B*a^3*b^4 + 28*(A - C)*a^2*b^5 + 9*B*a*b^6 + 6*(A - C)*b^7)*c^6*d^3 - (2*(A - C)*a^5*b^2 - 20*B*a^4*b^3 + 25*(A - C)*a^3*b^4 - 16*B*a^2*b^5 + 17*(A - C)*a*b^6 - 2*B*b^7)*c^5*d^4 - (2*(A - C)*a^6*b + 10*B*a^5*b^2 + 10*(A - C)*a^4*b^3 + 35*B*a^3*b^4 - 10*(A - C)*a^2*b^5 + 7*B*a*b^6)*c^4*d^5 + ((A - C)*a^7 - 4*B*a^6*b + 17*(A - C)*a^5*b^2 + 10*B*a^4*b^3 + 10*(A - C)*a^3*b^4 + 8*B*a^2*b^5)*c^3*d^6 + (3*B*a^7 + 11*B*a^5*b^2 - 10*(A - C)*a^4*b^3 - 2*B*a^3*b^4)*c^2*d^7 - (3*(A - C)*a^7 + 4*B*a^6*b + (A - C)*a^5*b^2 + 2*B*a^4*b^3)*c*d^8 - (B*a^7 - 2*(A - C)*a^6*b - B*a^5*b^2)*d^9)*f*x)*tan(f*x + e)^2 + ((B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^9 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*c^8*d + 3*(B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^7*d^2 + 3*(3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*c^6*d^3 + 3*(B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^5*d^4 + 3*(3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*c^4*d^5 + (B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^3*d^6 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*c^2*d^7 + ((B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^7*d^2 + (3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A + C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7)*c^6*d^3 + 3*(B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^5*d^4 + 3*(3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A + C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7)*c^4*d^5 + 3*(B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^3*d^6 + 3*(3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A + C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7)*c^2*d^7 + (B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c*d^8 + (3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A + C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7)*d^9)*tan(f*x + e)^3 + (2*(B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^8*d + (6*C*a^4*b^3 - 7*B*a^3*b^4 + 4*(2*A + C)*a^2*b^5 - 5*B*a*b^6 + 6*A*b^7)*c^7*d^2 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 + 4*B*a^2*b^5 - 3*(3*A - 4*C)*a*b^6 - 6*B*b^7)*c^6*d^3 + 3*(6*C*a^4*b^3 - 7*B*a^3*b^4 + 4*(2*A + C)*a^2*b^5 - 5*B*a*b^6 + 6*A*b^7)*c^5*d^4 + 3*(3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - (A - 4*C)*a*b^6 - 2*B*b^7)*c^4*d^5 + 3*(6*C*a^4*b^3 - 7*B*a^3*b^4 + 4*(2*A + C)*a^2*b^5 - 5*B*a*b^6 + 6*A*b^7)*c^3*d^6 + (9*C*a^5*b^2 - 12*B*a^4*b^3 + 3*(5*A + C)*a^3*b^4 - 4*B*a^2*b^5 + (5*A + 4*C)*a*b^6 - 2*B*b^7)*c^2*d^7 + (6*C*a^4*b^3 - 7*B*a^3*b^4 + 4*(2*A + C)*a^2*b^5 - 5*B*a*b^6 + 6*A*b^7)*c*d^8 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*d^9)*tan(f*x + e)^2 + ((B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^9 + (3*C*a^4*b^3 - 2*B*a^3*b^4 + (A + 5*C)*a^2*b^5 - 4*B*a*b^6 + 3*A*b^7)*c^8*d + (6*C*a^5*b^2 - 8*B*a^4*b^3 + 2*(5*A + C)*a^3*b^4 - B*a^2*b^5 + 6*C*a*b^6 - 3*B*b^7)*c^7*d^2 + 3*(3*C*a^4*b^3 - 2*B*a^3*b^4 + (A + 5*C)*a^2*b^5 - 4*B*a*b^6 + 3*A*b^7)*c^6*d^3 + 3*(6*C*a^5*b^2 - 8*B*a^4*b^3 + 2*(5*A + C)*a^3*b^4 - 3*B*a^2*b^5 + 2*(2*A + C)*a*b^6 - B*b^7)*c^5*d^4 + 3*(3*C*a^4*b^3 - 2*B*a^3*b^4 + (A + 5*C)*a^2*b^5 - 4*B*a*b^6 + 3*A*b^7)*c^4*d^5 + (18*C*a^5*b^2 - 24*B*a^4*b^3 + 6*(5*A + C)*a^3*b^4 - 11*B*a^2*b^5 + 2*(8*A + C)*a*b^6 - B*b^7)*c^3*d^6 + (3*C*a^4*b^3 - 2*B*a^3*b^4 + (A + 5*C)*a^2*b^5 - 4*B*a*b^6 + 3*A*b^7)*c^2*d^7 + 2*(3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*c*d^8)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (3*(C*a^5*b^2 + 2*C*a^3*b^4 + C*a*b^6)*c^8*d - 6*(B*a^5*b^2 + 2*B*a^3*b^4 + B*a*b^6)*c^7*d^2 + (4*B*a^6*b + (10*A - C)*a^5*b^2 + 8*B*a^4*b^3 + 2*(10*A - C)*a^3*b^4 + 4*B*a^2*b^5 + (10*A - C)*a*b^6)*c^6*d^3 - (B*a^7 + 10*(A - C)*a^6*b + 5*B*a^5*b^2 + 20*(A - C)*a^4*b^3 + 7*B*a^3*b^4 + 10*(A - C)*a^2*b^5 + 3*B*a*b^6)*c^5*d^4 + 3*((A - C)*a^7 - 2*B*a^6*b + (5*A - 2*C)*a^5*b^2 - 4*B*a^4*b^3 + (7*A - C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*c^4*d^5 + (3*B*a^7 - 2*(A - C)*a^6*b + 5*B*a^5*b^2 - 4*(A - C)*a^4*b^3 + B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^3*d^6 - ((A - C)*a^7 + 2*B*a^6*b - (A + 2*C)*a^5*b^2 + 4*B*a^4*b^3 - (5*A + C)*a^3*b^4 + 2*B*a^2*b^5 - 3*A*a*b^6)*c^2*d^7 + (3*(C*a^4*b^3 + 2*C*a^2*b^5 + C*b^7)*c^6*d^3 - 6*(B*a^4*b^3 + 2*B*a^2*b^5 + B*b^7)*c^5*d^4 + (4*B*a^5*b^2 + (10*A - C)*a^4*b^3 + 8*B*a^3*b^4 + 2*(10*A - C)*a^2*b^5 + 4*B*a*b^6 + (10*A - C)*b^7)*c^4*d^5 - (B*a^6*b + 10*(A - C)*a^5*b^2 + 5*B*a^4*b^3 + 20*(A - C)*a^3*b^4 + 7*B*a^2*b^5 + 10*(A - C)*a*b^6 + 3*B*b^7)*c^3*d^6 + 3*((A - C)*a^6*b - 2*B*a^5*b^2 + (5*A - 2*C)*a^4*b^3 - 4*B*a^3*b^4 + (7*A - C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7)*c^2*d^7 + (3*B*a^6*b - 2*(A - C)*a^5*b^2 + 5*B*a^4*b^3 - 4*(A - C)*a^3*b^4 + B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c*d^8 - ((A - C)*a^6*b + 2*B*a^5*b^2 - (A + 2*C)*a^4*b^3 + 4*B*a^3*b^4 - (5*A + C)*a^2*b^5 + 2*B*a*b^6 - 3*A*b^7)*d^9)*tan(f*x + e)^3 + (6*(C*a^4*b^3 + 2*C*a^2*b^5 + C*b^7)*c^7*d^2 + 3*(C*a^5*b^2 - 4*B*a^4*b^3 + 2*C*a^3*b^4 - 8*B*a^2*b^5 + C*a*b^6 - 4*B*b^7)*c^6*d^3 + 2*(B*a^5*b^2 + (10*A - C)*a^4*b^3 + 2*B*a^3*b^4 + 2*(10*A - C)*a^2*b^5 + B*a*b^6 + (10*A - C)*b^7)*c^5*d^4 + (2*B*a^6*b - (10*A - 19*C)*a^5*b^2 - 2*B*a^4*b^3 - 2*(10*A - 19*C)*a^3*b^4 - 10*B*a^2*b^5 - (10*A - 19*C)*a*b^6 - 6*B*b^7)*c^4*d^5 - (B*a^7 + 4*(A - C)*a^6*b + 17*B*a^5*b^2 - 2*(5*A + 4*C)*a^4*b^3 + 31*B*a^3*b^4 - 4*(8*A + C)*a^2*b^5 + 15*B*a*b^6 - 18*A*b^7)*c^3*d^6 + (3*(A - C)*a^7 + (11*A - 2*C)*a^5*b^2 - 2*B*a^4*b^3 + (13*A + 5*C)*a^3*b^4 - 4*B*a^2*b^5 + (5*A + 4*C)*a*b^6 - 2*B*b^7)*c^2*d^7 + (3*B*a^7 - 4*(A - C)*a^6*b + B*a^5*b^2 - 2*(A - 4*C)*a^4*b^3 - 7*B*a^3*b^4 + 4*(2*A + C)*a^2*b^5 - 5*B*a*b^6 + 6*A*b^7)*c*d^8 - ((A - C)*a^7 + 2*B*a^6*b - (A + 2*C)*a^5*b^2 + 4*B*a^4*b^3 - (5*A + C)*a^3*b^4 + 2*B*a^2*b^5 - 3*A*a*b^6)*d^9)*tan(f*x + e)^2 + (3*(C*a^4*b^3 + 2*C*a^2*b^5 + C*b^7)*c^8*d + 6*(C*a^5*b^2 - B*a^4*b^3 + 2*C*a^3*b^4 - 2*B*a^2*b^5 + C*a*b^6 - B*b^7)*c^7*d^2 - (8*B*a^5*b^2 - (10*A - C)*a^4*b^3 + 16*B*a^3*b^4 - 2*(10*A - C)*a^2*b^5 + 8*B*a*b^6 - (10*A - C)*b^7)*c^6*d^3 + (7*B*a^6*b + 2*(5*A + 4*C)*a^5*b^2 + 11*B*a^4*b^3 + 4*(5*A + 4*C)*a^3*b^4 + B*a^2*b^5 + 2*(5*A + 4*C)*a*b^6 - 3*B*b^7)*c^5*d^4 - (2*B*a^7 + 17*(A - C)*a^6*b + 16*B*a^5*b^2 + (25*A - 34*C)*a^4*b^3 + 26*B*a^3*b^4 - (A + 17*C)*a^2*b^5 + 12*B*a*b^6 - 9*A*b^7)*c^4*d^5 + (6*(A - C)*a^7 - 9*B*a^6*b + 2*(14*A - 5*C)*a^5*b^2 - 19*B*a^4*b^3 + 2*(19*A - C)*a^3*b^4 - 11*B*a^2*b^5 + 2*(8*A + C)*a*b^6 - B*b^7)*c^3*d^6 + (6*B*a^7 - 5*(A - C)*a^6*b + 8*B*a^5*b^2 - (7*A - 10*C)*a^4*b^3 - 2*B*a^3*b^4 + (A + 5*C)*a^2*b^5 - 4*B*a*b^6 + 3*A*b^7)*c^2*d^7 - 2*((A - C)*a^7 + 2*B*a^6*b - (A + 2*C)*a^5*b^2 + 4*B*a^4*b^3 - (5*A + C)*a^3*b^4 + 2*B*a^2*b^5 - 3*A*a*b^6)*c*d^8)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (2*(C*a^3*b^4 - B*a^2*b^5 + A*a*b^6)*c^9 - 2*(C*a^4*b^3 - B*a^3*b^4 + (A + 2*C)*a^2*b^5 - 2*B*a*b^6 + 2*A*b^7)*c^8*d + 2*(3*C*a^5*b^2 + 11*C*a^3*b^4 - 5*B*a^2*b^5 + (5*A + 3*C)*a*b^6)*c^7*d^2 - (8*C*a^6*b + 8*B*a^5*b^2 + 29*C*a^4*b^3 + 10*B*a^3*b^4 + 2*(3*A + 17*C)*a^2*b^5 - 4*B*a*b^6 + (12*A + 7*C)*b^7)*c^6*d^3 + (2*C*a^7 + 12*B*a^6*b + 2*(5*A + 4*C)*a^5*b^2 + 33*B*a^4*b^3 + 4*(5*A + 7*C)*a^3*b^4 + 12*B*a^2*b^5 + 4*(7*A + C)*a*b^6 + 9*B*b^7)*c^5*d^4 - (4*B*a^7 + (16*A - 9*C)*a^6*b + 16*B*a^5*b^2 + (43*A - 11*C)*a^4*b^3 + 14*B*a^3*b^4 + (44*A + 5*C)*a^2*b^5 - 4*B*a*b^6 + (23*A + C)*b^7)*c^4*d^5 + (6*(A - C)*a^7 - 7*B*a^6*b + 2*(12*A - 7*C)*a^5*b^2 - 11*B*a^4*b^3 + 2*(15*A + 2*C)*a^3*b^4 - 15*B*a^2*b^5 + 2*(13*A - C)*a*b^6 + 3*B*b^7)*c^3*d^6 + (6*B*a^7 + (5*A - C)*a^6*b + 12*B*a^5*b^2 + (5*A - 4*C)*a^4*b^3 + 8*B*a^3*b^4 - (7*A + 5*C)*a^2*b^5 + 4*B*a*b^6 - 9*A*b^7)*c^2*d^7 - (2*(3*A - 2*C)*a^7 + B*a^6*b + 2*(5*A - 4*C)*a^5*b^2 + 2*B*a^4*b^3 + 2*(A - 4*C)*a^3*b^4 + 5*B*a^2*b^5 - 6*A*a*b^6)*c*d^8 - (2*B*a^7 - 3*A*a^6*b + 4*B*a^5*b^2 - 6*A*a^4*b^3 + 2*B*a^3*b^4 - 3*A*a^2*b^5)*d^9 + 2*(((A - C)*a^2*b^5 + 2*B*a*b^6 - (A - C)*b^7)*c^9 - (2*(A - C)*a^3*b^4 + B*a^2*b^5 + 4*(A - C)*a*b^6 + 3*B*b^7)*c^8*d - (2*(A - C)*a^4*b^3 + 10*B*a^3*b^4 - 11*(A - C)*a^2*b^5 - 3*(A - C)*b^7)*c^7*d^2 + (8*(A - C)*a^5*b^2 + 10*B*a^4*b^3 + 10*(A - C)*a^3*b^4 + 17*B*a^2*b^5 - 4*(A - C)*a*b^6 + B*b^7)*c^6*d^3 - (7*(A - C)*a^6*b - 10*B*a^5*b^2 + 35*(A - C)*a^4*b^3 + 10*B*a^3*b^4 + 10*(A - C)*a^2*b^5 + 2*B*a*b^6)*c^5*d^4 + (2*(A - C)*a^7 - 17*B*a^6*b + 16*(A - C)*a^5*b^2 - 25*B*a^4*b^3 + 20*(A - C)*a^3*b^4 - 2*B*a^2*b^5)*c^4*d^5 + (6*B*a^7 + 9*(A - C)*a^6*b + 28*B*a^5*b^2 - 5*(A - C)*a^4*b^3 + 8*B*a^3*b^4)*c^3*d^6 - (6*(A - C)*a^7 + 5*B*a^6*b + 8*(A - C)*a^5*b^2 + 7*B*a^4*b^3)*c^2*d^7 - 2*(B*a^7 - 2*(A - C)*a^6*b - B*a^5*b^2)*c*d^8)*f*x)*tan(f*x + e))/(((a^4*b^5 + 2*a^2*b^7 + b^9)*c^10*d^2 - 4*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^9*d^3 + 3*(2*a^6*b^3 + 5*a^4*b^5 + 4*a^2*b^7 + b^9)*c^8*d^4 - 4*(a^7*b^2 + 5*a^5*b^4 + 7*a^3*b^6 + 3*a*b^8)*c^7*d^5 + (a^8*b + 20*a^6*b^3 + 40*a^4*b^5 + 24*a^2*b^7 + 3*b^9)*c^6*d^6 - 12*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*c^5*d^7 + (3*a^8*b + 24*a^6*b^3 + 40*a^4*b^5 + 20*a^2*b^7 + b^9)*c^4*d^8 - 4*(3*a^7*b^2 + 7*a^5*b^4 + 5*a^3*b^6 + a*b^8)*c^3*d^9 + 3*(a^8*b + 4*a^6*b^3 + 5*a^4*b^5 + 2*a^2*b^7)*c^2*d^10 - 4*(a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*c*d^11 + (a^8*b + 2*a^6*b^3 + a^4*b^5)*d^12)*f*tan(f*x + e)^3 + (2*(a^4*b^5 + 2*a^2*b^7 + b^9)*c^11*d - 7*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^10*d^2 + 2*(4*a^6*b^3 + 11*a^4*b^5 + 10*a^2*b^7 + 3*b^9)*c^9*d^3 - (2*a^7*b^2 + 25*a^5*b^4 + 44*a^3*b^6 + 21*a*b^8)*c^8*d^4 - 2*(a^8*b - 10*a^6*b^3 - 26*a^4*b^5 - 18*a^2*b^7 - 3*b^9)*c^7*d^5 + (a^9 - 4*a^7*b^2 - 32*a^5*b^4 - 48*a^3*b^6 - 21*a*b^8)*c^6*d^6 - 2*(3*a^8*b - 6*a^6*b^3 - 22*a^4*b^5 - 14*a^2*b^7 - b^9)*c^5*d^7 + (3*a^9 - 16*a^5*b^4 - 20*a^3*b^6 - 7*a*b^8)*c^4*d^8 - 2*(3*a^8*b + 2*a^6*b^3 - 5*a^4*b^5 - 4*a^2*b^7)*c^3*d^9 + (3*a^9 + 4*a^7*b^2 - a^5*b^4 - 2*a^3*b^6)*c^2*d^10 - 2*(a^8*b + 2*a^6*b^3 + a^4*b^5)*c*d^11 + (a^9 + 2*a^7*b^2 + a^5*b^4)*d^12)*f*tan(f*x + e)^2 + ((a^4*b^5 + 2*a^2*b^7 + b^9)*c^12 - 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^11*d - (2*a^6*b^3 + a^4*b^5 - 4*a^2*b^7 - 3*b^9)*c^10*d^2 + 2*(4*a^7*b^2 + 5*a^5*b^4 - 2*a^3*b^6 - 3*a*b^8)*c^9*d^3 - (7*a^8*b + 20*a^6*b^3 + 16*a^4*b^5 - 3*b^9)*c^8*d^4 + 2*(a^9 + 14*a^7*b^2 + 22*a^5*b^4 + 6*a^3*b^6 - 3*a*b^8)*c^7*d^5 - (21*a^8*b + 48*a^6*b^3 + 32*a^4*b^5 + 4*a^2*b^7 - b^9)*c^6*d^6 + 2*(3*a^9 + 18*a^7*b^2 + 26*a^5*b^4 + 10*a^3*b^6 - a*b^8)*c^5*d^7 - (21*a^8*b + 44*a^6*b^3 + 25*a^4*b^5 + 2*a^2*b^7)*c^4*d^8 + 2*(3*a^9 + 10*a^7*b^2 + 11*a^5*b^4 + 4*a^3*b^6)*c^3*d^9 - 7*(a^8*b + 2*a^6*b^3 + a^4*b^5)*c^2*d^10 + 2*(a^9 + 2*a^7*b^2 + a^5*b^4)*c*d^11)*f*tan(f*x + e) + ((a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^12 - 4*(a^6*b^3 + 2*a^4*b^5 + a^2*b^7)*c^11*d + 3*(2*a^7*b^2 + 5*a^5*b^4 + 4*a^3*b^6 + a*b^8)*c^10*d^2 - 4*(a^8*b + 5*a^6*b^3 + 7*a^4*b^5 + 3*a^2*b^7)*c^9*d^3 + (a^9 + 20*a^7*b^2 + 40*a^5*b^4 + 24*a^3*b^6 + 3*a*b^8)*c^8*d^4 - 12*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*c^7*d^5 + (3*a^9 + 24*a^7*b^2 + 40*a^5*b^4 + 20*a^3*b^6 + a*b^8)*c^6*d^6 - 4*(3*a^8*b + 7*a^6*b^3 + 5*a^4*b^5 + a^2*b^7)*c^5*d^7 + 3*(a^9 + 4*a^7*b^2 + 5*a^5*b^4 + 2*a^3*b^6)*c^4*d^8 - 4*(a^8*b + 2*a^6*b^3 + a^4*b^5)*c^3*d^9 + (a^9 + 2*a^7*b^2 + a^5*b^4)*c^2*d^10)*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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,0,0,0,1.699822," ","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=""fricas"")","{\rm integral}\left({\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}, x\right)"," ",0,"integral((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
165,0,0,0,0.913393," ","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=""fricas"")","{\rm integral}\left({\left(C d^{3} \tan\left(f x + e\right)^{5} + {\left(3 \, C c d^{2} + B d^{3}\right)} \tan\left(f x + e\right)^{4} + A c^{3} + {\left(3 \, C c^{2} d + 3 \, B c d^{2} + A d^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(C c^{3} + 3 \, B c^{2} d + 3 \, A c d^{2}\right)} \tan\left(f x + e\right)^{2} + {\left(B c^{3} + 3 \, A c^{2} d\right)} \tan\left(f x + e\right)\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((C*d^3*tan(f*x + e)^5 + (3*C*c*d^2 + B*d^3)*tan(f*x + e)^4 + A*c^3 + (3*C*c^2*d + 3*B*c*d^2 + A*d^3)*tan(f*x + e)^3 + (C*c^3 + 3*B*c^2*d + 3*A*c*d^2)*tan(f*x + e)^2 + (B*c^3 + 3*A*c^2*d)*tan(f*x + e))*(b*tan(f*x + e) + a)^m, x)","F",0
166,0,0,0,0.645681," ","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=""fricas"")","{\rm integral}\left({\left(C d^{2} \tan\left(f x + e\right)^{4} + {\left(2 \, C c d + B d^{2}\right)} \tan\left(f x + e\right)^{3} + A c^{2} + {\left(C c^{2} + 2 \, B c d + A d^{2}\right)} \tan\left(f x + e\right)^{2} + {\left(B c^{2} + 2 \, A c d\right)} \tan\left(f x + e\right)\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((C*d^2*tan(f*x + e)^4 + (2*C*c*d + B*d^2)*tan(f*x + e)^3 + A*c^2 + (C*c^2 + 2*B*c*d + A*d^2)*tan(f*x + e)^2 + (B*c^2 + 2*A*c*d)*tan(f*x + e))*(b*tan(f*x + e) + a)^m, x)","F",0
167,0,0,0,1.012690," ","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=""fricas"")","{\rm integral}\left({\left(C d \tan\left(f x + e\right)^{3} + {\left(C c + B d\right)} \tan\left(f x + e\right)^{2} + A c + {\left(B c + A d\right)} \tan\left(f x + e\right)\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((C*d*tan(f*x + e)^3 + (C*c + B*d)*tan(f*x + e)^2 + A*c + (B*c + A*d)*tan(f*x + e))*(b*tan(f*x + e) + a)^m, x)","F",0
168,0,0,0,1.148186," ","integrate((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left({\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}, x\right)"," ",0,"integral((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m, x)","F",0
169,0,0,0,0.743076," ","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=""fricas"")","{\rm integral}\left(\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}, x\right)"," ",0,"integral((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
170,0,0,0,1.553011," ","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=""fricas"")","{\rm integral}\left(\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^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}, x\right)"," ",0,"integral((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m/(d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2), x)","F",0
171,0,0,0,1.735438," ","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=""fricas"")","{\rm integral}\left(\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^{3} \tan\left(f x + e\right)^{3} + 3 \, c d^{2} \tan\left(f x + e\right)^{2} + 3 \, c^{2} d \tan\left(f x + e\right) + c^{3}}, x\right)"," ",0,"integral((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m/(d^3*tan(f*x + e)^3 + 3*c*d^2*tan(f*x + e)^2 + 3*c^2*d*tan(f*x + e) + c^3), x)","F",0
