1,1,86,0,0.536453," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, C b \tan\left(d x + c\right)^{3} + 3 \, {\left(C a + B b\right)} \tan\left(d x + c\right)^{2} - 6 \, {\left(B a - C b\right)} {\left(d x + c\right)} - 3 \, {\left(C a + B b\right)} \log\left(\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 + 3*(C*a + B*b)*tan(d*x + c)^2 - 6*(B*a - C*b)*(d*x + c) - 3*(C*a + B*b)*log(tan(d*x + c)^2 + 1) + 6*(B*a - C*b)*tan(d*x + c))/d","A",0
2,1,66,0,0.654682," ","integrate((a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{C b \tan\left(d x + c\right)^{2} - 2 \, {\left(C a + B b\right)} {\left(d x + c\right)} + {\left(B a - C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\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 + c) + (B*a - C*b)*log(tan(d*x + c)^2 + 1) + 2*(C*a + B*b)*tan(d*x + c))/d","A",0
3,1,50,0,0.598262," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, C b \tan\left(d x + c\right) + 2 \, {\left(B a - C b\right)} {\left(d x + c\right)} + {\left(C a + B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*C*b*tan(d*x + c) + 2*(B*a - C*b)*(d*x + c) + (C*a + B*b)*log(tan(d*x + c)^2 + 1))/d","A",0
4,1,52,0,0.594264," ","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=""maxima"")","\frac{2 \, B a \log\left(\tan\left(d x + c\right)\right) + 2 \, {\left(C a + B b\right)} {\left(d x + c\right)} - {\left(B a - C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*B*a*log(tan(d*x + c)) + 2*(C*a + B*b)*(d*x + c) - (B*a - C*b)*log(tan(d*x + c)^2 + 1))/d","A",0
5,1,68,0,0.461522," ","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=""maxima"")","-\frac{2 \, {\left(B a - C b\right)} {\left(d x + c\right)} + {\left(C a + B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, {\left(C a + B b\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{2 \, B a}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(B*a - C*b)*(d*x + c) + (C*a + B*b)*log(tan(d*x + c)^2 + 1) - 2*(C*a + B*b)*log(tan(d*x + c)) + 2*B*a/tan(d*x + c))/d","A",0
6,1,86,0,0.663275," ","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=""maxima"")","-\frac{2 \, {\left(C a + B b\right)} {\left(d x + c\right)} - {\left(B a - C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(B a - C b\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{B a + 2 \, {\left(C a + B b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(C*a + B*b)*(d*x + c) - (B*a - C*b)*log(tan(d*x + c)^2 + 1) + 2*(B*a - C*b)*log(tan(d*x + c)) + (B*a + 2*(C*a + B*b)*tan(d*x + c))/tan(d*x + c)^2)/d","A",0
7,1,104,0,0.765195," ","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=""maxima"")","\frac{6 \, {\left(B a - C b\right)} {\left(d x + c\right)} + 3 \, {\left(C a + B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, {\left(C a + B b\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{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)}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(B*a - C*b)*(d*x + c) + 3*(C*a + B*b)*log(tan(d*x + c)^2 + 1) - 6*(C*a + B*b)*log(tan(d*x + c)) + (6*(B*a - C*b)*tan(d*x + c)^2 - 2*B*a - 3*(C*a + B*b)*tan(d*x + c))/tan(d*x + c)^3)/d","A",0
8,1,122,0,0.926113," ","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=""maxima"")","\frac{12 \, {\left(C a + B b\right)} {\left(d x + c\right)} - 6 \, {\left(B a - C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(B a - C b\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{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)}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(C*a + B*b)*(d*x + c) - 6*(B*a - C*b)*log(tan(d*x + c)^2 + 1) + 12*(B*a - C*b)*log(tan(d*x + c)) + (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))/tan(d*x + c)^4)/d","A",0
9,1,147,0,0.626499," ","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=""maxima"")","\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} + 6 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \tan\left(d x + c\right)^{2} - 12 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)} - 6 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\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 + 6*(C*a^2 + 2*B*a*b - C*b^2)*tan(d*x + c)^2 - 12*(B*a^2 - 2*C*a*b - B*b^2)*(d*x + c) - 6*(C*a^2 + 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1) + 12*(B*a^2 - 2*C*a*b - B*b^2)*tan(d*x + c))/d","A",0
10,1,120,0,0.797012," ","integrate((a+b*tan(d*x+c))^2*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, C b^{2} \tan\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a b + B b^{2}\right)} \tan\left(d x + c\right)^{2} - 6 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)} + 3 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\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 + 3*(2*C*a*b + B*b^2)*tan(d*x + c)^2 - 6*(C*a^2 + 2*B*a*b - C*b^2)*(d*x + c) + 3*(B*a^2 - 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1) + 6*(C*a^2 + 2*B*a*b - C*b^2)*tan(d*x + c))/d","A",0
11,1,91,0,0.800612," ","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=""maxima"")","\frac{C b^{2} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)} + {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(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) + (C*a^2 + 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1) + 2*(2*C*a*b + B*b^2)*tan(d*x + c))/d","A",0
12,1,85,0,0.983520," ","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=""maxima"")","\frac{2 \, B a^{2} \log\left(\tan\left(d x + c\right)\right) + 2 \, C b^{2} \tan\left(d x + c\right) + 2 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)} - {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*B*a^2*log(tan(d*x + c)) + 2*C*b^2*tan(d*x + c) + 2*(C*a^2 + 2*B*a*b - C*b^2)*(d*x + c) - (B*a^2 - 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1))/d","A",0
13,1,93,0,0.735713," ","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=""maxima"")","-\frac{2 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)} + {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, {\left(C a^{2} + 2 \, B a b\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{2 \, B a^{2}}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(B*a^2 - 2*C*a*b - B*b^2)*(d*x + c) + (C*a^2 + 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1) - 2*(C*a^2 + 2*B*a*b)*log(tan(d*x + c)) + 2*B*a^2/tan(d*x + c))/d","A",0
14,1,120,0,0.703375," ","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=""maxima"")","-\frac{2 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)} - {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{B a^{2} + 2 \, {\left(C a^{2} + 2 \, B a b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(C*a^2 + 2*B*a*b - C*b^2)*(d*x + c) - (B*a^2 - 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1) + 2*(B*a^2 - 2*C*a*b - B*b^2)*log(tan(d*x + c)) + (B*a^2 + 2*(C*a^2 + 2*B*a*b)*tan(d*x + c))/tan(d*x + c)^2)/d","A",0
15,1,149,0,0.747649," ","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=""maxima"")","\frac{6 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)} + 3 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{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)}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(B*a^2 - 2*C*a*b - B*b^2)*(d*x + c) + 3*(C*a^2 + 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1) - 6*(C*a^2 + 2*B*a*b - C*b^2)*log(tan(d*x + c)) - (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))/tan(d*x + c)^3)/d","A",0
16,1,175,0,0.863709," ","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=""maxima"")","\frac{12 \, {\left(C a^{2} + 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)} - 6 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(B a^{2} - 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{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)}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(C*a^2 + 2*B*a*b - C*b^2)*(d*x + c) - 6*(B*a^2 - 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1) + 12*(B*a^2 - 2*C*a*b - B*b^2)*log(tan(d*x + c)) + (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))/tan(d*x + c)^4)/d","A",0
17,1,179,0,0.520379," ","integrate((a+b*tan(d*x+c))^3*(B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""maxima"")","\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} + 6 \, {\left(3 \, C a^{2} b + 3 \, B a b^{2} - C b^{3}\right)} \tan\left(d x + c\right)^{2} - 12 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} {\left(d x + c\right)} + 6 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 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 + 6*(3*C*a^2*b + 3*B*a*b^2 - C*b^3)*tan(d*x + c)^2 - 12*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*(d*x + c) + 6*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(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
18,1,143,0,1.019372," ","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=""maxima"")","\frac{2 \, C b^{3} \tan\left(d x + c\right)^{3} + 3 \, {\left(3 \, C a b^{2} + B 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)} {\left(d x + c\right)} + 3 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\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 + 3*(3*C*a*b^2 + B*b^3)*tan(d*x + c)^2 + 6*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*(d*x + c) + 3*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(d*x + c)^2 + 1) + 6*(3*C*a^2*b + 3*B*a*b^2 - C*b^3)*tan(d*x + c))/d","A",0
19,1,124,0,0.599726," ","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=""maxima"")","\frac{C b^{3} \tan\left(d x + c\right)^{2} + 2 \, B a^{3} \log\left(\tan\left(d x + c\right)\right) + 2 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} {\left(d x + c\right)} - {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\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 + 2*B*a^3*log(tan(d*x + c)) + 2*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*(d*x + c) - (B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(tan(d*x + c)^2 + 1) + 2*(3*C*a*b^2 + B*b^3)*tan(d*x + c))/d","A",0
20,1,125,0,0.783530," ","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=""maxima"")","\frac{2 \, C b^{3} \tan\left(d x + c\right) - \frac{2 \, B a^{3}}{\tan\left(d x + c\right)} - 2 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} {\left(d x + c\right)} - {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \log\left(\tan\left(d x + c\right)\right)}{2 \, d}"," ",0,"1/2*(2*C*b^3*tan(d*x + c) - 2*B*a^3/tan(d*x + c) - 2*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*(d*x + c) - (C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(d*x + c)^2 + 1) + 2*(C*a^3 + 3*B*a^2*b)*log(tan(d*x + c)))/d","A",0
21,1,142,0,0.603439," ","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=""maxima"")","-\frac{2 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} {\left(d x + c\right)} - {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{B a^{3} + 2 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*(d*x + c) - (B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(tan(d*x + c)^2 + 1) + 2*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2)*log(tan(d*x + c)) + (B*a^3 + 2*(C*a^3 + 3*B*a^2*b)*tan(d*x + c))/tan(d*x + c)^2)/d","A",0
22,1,180,0,0.573855," ","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=""maxima"")","\frac{6 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{2 \, B a^{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)}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*(d*x + c) + 3*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(d*x + c)^2 + 1) - 6*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(d*x + c)) - (2*B*a^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))/tan(d*x + c)^3)/d","A",0
23,1,215,0,0.738140," ","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=""maxima"")","\frac{12 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{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)}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*(d*x + c) - 6*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(tan(d*x + c)^2 + 1) + 12*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*log(tan(d*x + c)) - (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))/tan(d*x + c)^4)/d","A",0
24,1,250,0,0.764438," ","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=""maxima"")","-\frac{60 \, {\left(B a^{3} - 3 \, C a^{2} b - 3 \, B a b^{2} + C b^{3}\right)} {\left(d x + c\right)} + 30 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 \, {\left(C a^{3} + 3 \, B a^{2} b - 3 \, C a b^{2} - B b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{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)}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*(B*a^3 - 3*C*a^2*b - 3*B*a*b^2 + C*b^3)*(d*x + c) + 30*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(d*x + c)^2 + 1) - 60*(C*a^3 + 3*B*a^2*b - 3*C*a*b^2 - B*b^3)*log(tan(d*x + c)) + (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))/tan(d*x + c)^5)/d","A",0
25,1,130,0,0.715126," ","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=""maxima"")","\frac{\frac{2 \, {\left(C a - B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{2 \, {\left(C a^{4} - B a^{3} b\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2} b^{3} + b^{5}} - \frac{{\left(B a + C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{C b \tan\left(d x + c\right)^{2} - 2 \, {\left(C a - B b\right)} \tan\left(d x + c\right)}{b^{2}}}{2 \, d}"," ",0,"1/2*(2*(C*a - B*b)*(d*x + c)/(a^2 + b^2) + 2*(C*a^4 - B*a^3*b)*log(b*tan(d*x + c) + a)/(a^2*b^3 + b^5) - (B*a + C*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + (C*b*tan(d*x + c)^2 - 2*(C*a - B*b)*tan(d*x + c))/b^2)/d","A",0
26,1,109,0,0.548986," ","integrate(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(B a + C b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{2 \, {\left(C a^{3} - B a^{2} b\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2} b^{2} + b^{4}} + \frac{{\left(C a - B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, C \tan\left(d x + c\right)}{b}}{2 \, d}"," ",0,"-1/2*(2*(B*a + C*b)*(d*x + c)/(a^2 + b^2) + 2*(C*a^3 - B*a^2*b)*log(b*tan(d*x + c) + a)/(a^2*b^2 + b^4) + (C*a - B*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*C*tan(d*x + c)/b)/d","A",0
27,1,94,0,0.774363," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(C a - B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{2 \, {\left(C a^{2} - B a b\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2} b + b^{3}} - \frac{{\left(B a + C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, d}"," ",0,"-1/2*(2*(C*a - B*b)*(d*x + c)/(a^2 + b^2) - 2*(C*a^2 - B*a*b)*log(b*tan(d*x + c) + a)/(a^2*b + b^3) - (B*a + C*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
28,1,88,0,0.634624," ","integrate(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(B a + C b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{2 \, {\left(C a - B b\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2} + b^{2}} + \frac{{\left(C a - B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, d}"," ",0,"1/2*(2*(B*a + C*b)*(d*x + c)/(a^2 + b^2) - 2*(C*a - B*b)*log(b*tan(d*x + c) + a)/(a^2 + b^2) + (C*a - B*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
29,1,107,0,0.464650," ","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=""maxima"")","\frac{\frac{2 \, {\left(C a - B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{2 \, {\left(C a b - B b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{3} + a b^{2}} - \frac{{\left(B a + C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, B \log\left(\tan\left(d x + c\right)\right)}{a}}{2 \, d}"," ",0,"1/2*(2*(C*a - B*b)*(d*x + c)/(a^2 + b^2) + 2*(C*a*b - B*b^2)*log(b*tan(d*x + c) + a)/(a^3 + a*b^2) - (B*a + C*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 2*B*log(tan(d*x + c))/a)/d","A",0
30,1,131,0,0.967131," ","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=""maxima"")","-\frac{\frac{2 \, {\left(B a + C b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{2 \, {\left(C a b^{2} - B b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} + a^{2} b^{2}} + \frac{{\left(C a - B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, {\left(C a - B b\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{2}} + \frac{2 \, B}{a \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(B*a + C*b)*(d*x + c)/(a^2 + b^2) + 2*(C*a*b^2 - B*b^3)*log(b*tan(d*x + c) + a)/(a^4 + a^2*b^2) + (C*a - B*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*(C*a - B*b)*log(tan(d*x + c))/a^2 + 2*B/(a*tan(d*x + c)))/d","A",0
31,1,158,0,0.616778," ","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=""maxima"")","-\frac{\frac{2 \, {\left(C a - B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{2 \, {\left(C a b^{3} - B b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{5} + a^{3} b^{2}} - \frac{{\left(B a + C b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(B a^{2} + C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{3}} + \frac{B a + 2 \, {\left(C a - B b\right)} \tan\left(d x + c\right)}{a^{2} \tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(C*a - B*b)*(d*x + c)/(a^2 + b^2) - 2*(C*a*b^3 - B*b^4)*log(b*tan(d*x + c) + a)/(a^5 + a^3*b^2) - (B*a + C*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 2*(B*a^2 + C*a*b - B*b^2)*log(tan(d*x + c))/a^3 + (B*a + 2*(C*a - B*b)*tan(d*x + c))/(a^2*tan(d*x + c)^2))/d","A",0
32,1,220,0,0.573021," ","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=""maxima"")","\frac{\frac{2 \, {\left(C a^{2} - 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(2 \, C a^{5} - B a^{4} b + 4 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}} - \frac{{\left(B a^{2} + 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(C a^{4} - B a^{3} b\right)}}{a^{3} b^{3} + a b^{5} + {\left(a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)} + \frac{2 \, C \tan\left(d x + c\right)}{b^{2}}}{2 \, d}"," ",0,"1/2*(2*(C*a^2 - 2*B*a*b - C*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - 2*(2*C*a^5 - B*a^4*b + 4*C*a^3*b^2 - 3*B*a^2*b^3)*log(b*tan(d*x + c) + a)/(a^4*b^3 + 2*a^2*b^5 + b^7) - (B*a^2 + 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(C*a^4 - B*a^3*b)/(a^3*b^3 + a*b^5 + (a^2*b^4 + b^6)*tan(d*x + c)) + 2*C*tan(d*x + c)/b^2)/d","A",0
33,1,197,0,0.613249," ","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=""maxima"")","-\frac{\frac{2 \, {\left(B a^{2} + 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(C a^{4} + 3 \, C a^{2} b^{2} - 2 \, B a b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}} + \frac{{\left(C a^{2} - 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(C a^{3} - B a^{2} b\right)}}{a^{3} b^{2} + a b^{4} + {\left(a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(B*a^2 + 2*C*a*b - B*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - 2*(C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3)*log(b*tan(d*x + c) + a)/(a^4*b^2 + 2*a^2*b^4 + b^6) + (C*a^2 - 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(C*a^3 - B*a^2*b)/(a^3*b^2 + a*b^4 + (a^2*b^3 + b^5)*tan(d*x + c)))/d","A",0
34,1,185,0,0.636315," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(C a^{2} - 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(B a^{2} + 2 \, C a b - B b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(B a^{2} + 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(C a^{2} - B a b\right)}}{a^{3} b + a b^{3} + {\left(a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(C*a^2 - 2*B*a*b - C*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + 2*(B*a^2 + 2*C*a*b - B*b^2)*log(b*tan(d*x + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - (B*a^2 + 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(C*a^2 - B*a*b)/(a^3*b + a*b^3 + (a^2*b^2 + b^4)*tan(d*x + c)))/d","A",0
35,1,177,0,0.572736," ","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=""maxima"")","\frac{\frac{2 \, {\left(B a^{2} + 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(C a^{2} - 2 \, B a b - C b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(C a^{2} - 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(C a - B b\right)}}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*(B*a^2 + 2*C*a*b - B*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - 2*(C*a^2 - 2*B*a*b - C*b^2)*log(b*tan(d*x + c) + a)/(a^4 + 2*a^2*b^2 + b^4) + (C*a^2 - 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(C*a - B*b)/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x + c)))/d","A",0
36,1,208,0,1.328595," ","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=""maxima"")","\frac{\frac{2 \, {\left(C a^{2} - 2 \, B a b - C b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(2 \, C a^{3} b - 3 \, B a^{2} b^{2} - B b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}} - \frac{{\left(B a^{2} + 2 \, C a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(C a b - B b^{2}\right)}}{a^{4} + a^{2} b^{2} + {\left(a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)} + \frac{2 \, B \log\left(\tan\left(d x + c\right)\right)}{a^{2}}}{2 \, d}"," ",0,"1/2*(2*(C*a^2 - 2*B*a*b - C*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + 2*(2*C*a^3*b - 3*B*a^2*b^2 - B*b^4)*log(b*tan(d*x + c) + a)/(a^6 + 2*a^4*b^2 + a^2*b^4) - (B*a^2 + 2*C*a*b - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(C*a*b - B*b^2)/(a^4 + a^2*b^2 + (a^3*b + a*b^3)*tan(d*x + c)) + 2*B*log(tan(d*x + c))/a^2)/d","A",0
37,1,262,0,0.822721," ","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=""maxima"")","-\frac{\frac{2 \, {\left(B a^{2} + 2 \, C a b - B b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(3 \, C a^{3} b^{2} - 4 \, B a^{2} b^{3} + C a b^{4} - 2 \, B b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}} + \frac{{\left(C a^{2} - 2 \, B a b - C b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(B a^{3} + B a b^{2} + {\left(B a^{2} b - C a b^{2} + 2 \, B b^{3}\right)} \tan\left(d x + c\right)\right)}}{{\left(a^{4} b + a^{2} b^{3}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} \tan\left(d x + c\right)} - \frac{2 \, {\left(C a - 2 \, B b\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{3}}}{2 \, d}"," ",0,"-1/2*(2*(B*a^2 + 2*C*a*b - B*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + 2*(3*C*a^3*b^2 - 4*B*a^2*b^3 + C*a*b^4 - 2*B*b^5)*log(b*tan(d*x + c) + a)/(a^7 + 2*a^5*b^2 + a^3*b^4) + (C*a^2 - 2*B*a*b - C*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(B*a^3 + B*a*b^2 + (B*a^2*b - C*a*b^2 + 2*B*b^3)*tan(d*x + c))/((a^4*b + a^2*b^3)*tan(d*x + c)^2 + (a^5 + a^3*b^2)*tan(d*x + c)) - 2*(C*a - 2*B*b)*log(tan(d*x + c))/a^3)/d","A",0
38,1,389,0,1.040478," ","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=""maxima"")","\frac{\frac{2 \, {\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(3 \, C a^{7} - B a^{6} b + 9 \, C a^{5} b^{2} - 3 \, B a^{4} b^{3} + 10 \, C a^{3} b^{4} - 6 \, B a^{2} b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}} + \frac{{\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{5 \, C a^{7} - 3 \, B a^{6} b + 9 \, C a^{5} b^{2} - 7 \, B a^{4} b^{3} + 2 \, {\left(3 \, C a^{6} b - 2 \, B a^{5} b^{2} + 5 \, C a^{4} b^{3} - 4 \, B a^{3} b^{4}\right)} \tan\left(d x + c\right)}{a^{6} b^{4} + 2 \, a^{4} b^{6} + a^{2} b^{8} + {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{5} + 2 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)} + \frac{2 \, C \tan\left(d x + c\right)}{b^{3}}}{2 \, d}"," ",0,"1/2*(2*(B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(3*C*a^7 - B*a^6*b + 9*C*a^5*b^2 - 3*B*a^4*b^3 + 10*C*a^3*b^4 - 6*B*a^2*b^5)*log(b*tan(d*x + c) + a)/(a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10) + (C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (5*C*a^7 - 3*B*a^6*b + 9*C*a^5*b^2 - 7*B*a^4*b^3 + 2*(3*C*a^6*b - 2*B*a^5*b^2 + 5*C*a^4*b^3 - 4*B*a^3*b^4)*tan(d*x + c))/(a^6*b^4 + 2*a^4*b^6 + a^2*b^8 + (a^4*b^6 + 2*a^2*b^8 + b^10)*tan(d*x + c)^2 + 2*(a^5*b^5 + 2*a^3*b^7 + a*b^9)*tan(d*x + c)) + 2*C*tan(d*x + c)/b^3)/d","A",0
39,1,366,0,0.648978," ","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=""maxima"")","\frac{\frac{2 \, {\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(C a^{6} + 3 \, C a^{4} b^{2} + B a^{3} b^{3} + 6 \, C a^{2} b^{4} - 3 \, B a b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}} - \frac{{\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{3 \, C a^{6} - B a^{5} b + 7 \, C a^{4} b^{2} - 5 \, B a^{3} b^{3} + 2 \, {\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)}{a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7} + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*(C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(C*a^6 + 3*C*a^4*b^2 + B*a^3*b^3 + 6*C*a^2*b^4 - 3*B*a*b^5)*log(b*tan(d*x + c) + a)/(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9) - (B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*C*a^6 - B*a^5*b + 7*C*a^4*b^2 - 5*B*a^3*b^3 + 2*(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))/(a^6*b^3 + 2*a^4*b^5 + a^2*b^7 + (a^4*b^5 + 2*a^2*b^7 + b^9)*tan(d*x + c)^2 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*tan(d*x + c)))/d","A",0
40,1,333,0,0.871049," ","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=""maxima"")","-\frac{\frac{2 \, {\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{C a^{5} + B a^{4} b + 5 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} + 2 \, {\left(C a^{4} b + 3 \, C a^{2} b^{3} - 2 \, B a b^{4}\right)} \tan\left(d x + c\right)}{a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*log(b*tan(d*x + c) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (C*a^5 + B*a^4*b + 5*C*a^3*b^2 - 3*B*a^2*b^3 + 2*(C*a^4*b + 3*C*a^2*b^3 - 2*B*a*b^4)*tan(d*x + c))/(a^6*b^2 + 2*a^4*b^4 + a^2*b^6 + (a^4*b^4 + 2*a^2*b^6 + b^8)*tan(d*x + c)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*tan(d*x + c)))/d","A",0
41,1,330,0,0.637659," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{C a^{4} - 3 \, B a^{3} b - 3 \, C a^{2} b^{2} + B a b^{3} - 2 \, {\left(B a^{2} b^{2} + 2 \, C a b^{3} - B b^{4}\right)} \tan\left(d x + c\right)}{a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*log(b*tan(d*x + c) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (C*a^4 - 3*B*a^3*b - 3*C*a^2*b^2 + B*a*b^3 - 2*(B*a^2*b^2 + 2*C*a*b^3 - B*b^4)*tan(d*x + c))/(a^6*b + 2*a^4*b^3 + a^2*b^5 + (a^4*b^3 + 2*a^2*b^5 + b^7)*tan(d*x + c)^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*tan(d*x + c)))/d","A",0
42,1,321,0,0.476432," ","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=""maxima"")","\frac{\frac{2 \, {\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{3 \, C a^{3} - 5 \, B a^{2} b - C a b^{2} - B b^{3} + 2 \, {\left(C a^{2} b - 2 \, B a b^{2} - C b^{3}\right)} \tan\left(d x + c\right)}{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*(B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*log(b*tan(d*x + c) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*C*a^3 - 5*B*a^2*b - C*a*b^2 - B*b^3 + 2*(C*a^2*b - 2*B*a*b^2 - C*b^3)*tan(d*x + c))/(a^6 + 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 + 2*a^2*b^4 + b^6)*tan(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*tan(d*x + c)))/d","A",0
43,1,372,0,0.934643," ","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=""maxima"")","\frac{\frac{2 \, {\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(3 \, C a^{5} b - 6 \, B a^{4} b^{2} - C a^{3} b^{3} - 3 \, B a^{2} b^{4} - B b^{6}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}} - \frac{{\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{5 \, C a^{4} b - 7 \, B a^{3} b^{2} + C a^{2} b^{3} - 3 \, B a b^{4} + 2 \, {\left(2 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - B b^{5}\right)} \tan\left(d x + c\right)}{a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4} + {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \tan\left(d x + c\right)} + \frac{2 \, B \log\left(\tan\left(d x + c\right)\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*(2*(C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(3*C*a^5*b - 6*B*a^4*b^2 - C*a^3*b^3 - 3*B*a^2*b^4 - B*b^6)*log(b*tan(d*x + c) + a)/(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6) - (B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (5*C*a^4*b - 7*B*a^3*b^2 + C*a^2*b^3 - 3*B*a*b^4 + 2*(2*C*a^3*b^2 - 3*B*a^2*b^3 - B*b^5)*tan(d*x + c))/(a^8 + 2*a^6*b^2 + a^4*b^4 + (a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*tan(d*x + c)^2 + 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)*tan(d*x + c)) + 2*B*log(tan(d*x + c))/a^3)/d","A",0
44,1,454,0,0.722152," ","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=""maxima"")","-\frac{\frac{2 \, {\left(B a^{3} + 3 \, C a^{2} b - 3 \, B a b^{2} - C b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(6 \, C a^{5} b^{2} - 10 \, B a^{4} b^{3} + 3 \, C a^{3} b^{4} - 9 \, B a^{2} b^{5} + C a b^{6} - 3 \, B b^{7}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6}} + \frac{{\left(C a^{3} - 3 \, B a^{2} b - 3 \, C a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, B a^{6} + 4 \, B a^{4} b^{2} + 2 \, B a^{2} b^{4} + 2 \, {\left(B a^{4} b^{2} - 3 \, C a^{3} b^{3} + 6 \, B a^{2} b^{4} - C a b^{5} + 3 \, B b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(4 \, B a^{5} b - 7 \, C a^{4} b^{2} + 17 \, B a^{3} b^{3} - 3 \, C a^{2} b^{4} + 9 \, B a b^{5}\right)} \tan\left(d x + c\right)}{{\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} \tan\left(d x + c\right)} - \frac{2 \, {\left(C a - 3 \, B b\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{4}}}{2 \, d}"," ",0,"-1/2*(2*(B*a^3 + 3*C*a^2*b - 3*B*a*b^2 - C*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(6*C*a^5*b^2 - 10*B*a^4*b^3 + 3*C*a^3*b^4 - 9*B*a^2*b^5 + C*a*b^6 - 3*B*b^7)*log(b*tan(d*x + c) + a)/(a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6) + (C*a^3 - 3*B*a^2*b - 3*C*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (2*B*a^6 + 4*B*a^4*b^2 + 2*B*a^2*b^4 + 2*(B*a^4*b^2 - 3*C*a^3*b^3 + 6*B*a^2*b^4 - C*a*b^5 + 3*B*b^6)*tan(d*x + c)^2 + (4*B*a^5*b - 7*C*a^4*b^2 + 17*B*a^3*b^3 - 3*C*a^2*b^4 + 9*B*a*b^5)*tan(d*x + c))/((a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*tan(d*x + c)^3 + 2*(a^8*b + 2*a^6*b^3 + a^4*b^5)*tan(d*x + c)^2 + (a^9 + 2*a^7*b^2 + a^5*b^4)*tan(d*x + c)) - 2*(C*a - 3*B*b)*log(tan(d*x + c))/a^4)/d","A",0
45,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(b*tan(d*x+c))^n*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \tan\left(d x + c\right)^{2} + B \tan\left(d x + c\right) + A\right)} \left(b \tan\left(d x + c\right)\right)^{n} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*tan(d*x + c)^2 + B*tan(d*x + c) + A)*(b*tan(d*x + c))^n*tan(d*x + c)^2, x)","F",0
46,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(b*tan(d*x+c))^n*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \tan\left(d x + c\right)^{2} + B \tan\left(d x + c\right) + A\right)} \left(b \tan\left(d x + c\right)\right)^{n} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*tan(d*x + c)^2 + B*tan(d*x + c) + A)*(b*tan(d*x + c))^n*tan(d*x + c)^m, x)","F",0
47,-1,0,0,0.000000," ","integrate(tan(d*x+c)^m*(b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)+C*tan(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c)+C*tan(d*x+c)^2)/(b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c)+C*tan(d*x+c)^2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \tan\left(d x + c\right)^{2} + B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*tan(d*x + c)^2 + B*tan(d*x + c) + A)*tan(d*x + c)^m/sqrt(b*tan(d*x + c) + a), x)","F",0
50,1,416,0,0.544000," ","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=""maxima"")","\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} + 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} + 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)} {\left(f x + e\right)} + 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(\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 + 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 + 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 + e) + 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(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
51,1,274,0,0.565803," ","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=""maxima"")","\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} + 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} + 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)} {\left(f x + e\right)} + 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(\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 + 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 + 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 + e) + 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(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
52,1,151,0,0.444784," ","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=""maxima"")","\frac{2 \, C b d \tan\left(f x + e\right)^{3} + 3 \, {\left(C b c + {\left(C a + B b\right)} d\right)} \tan\left(f x + e\right)^{2} + 6 \, {\left({\left({\left(A - C\right)} a - B b\right)} c - {\left(B a + {\left(A - C\right)} b\right)} d\right)} {\left(f x + e\right)} + 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(\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 + 3*(C*b*c + (C*a + B*b)*d)*tan(f*x + e)^2 + 6*(((A - C)*a - B*b)*c - (B*a + (A - C)*b)*d)*(f*x + e) + 3*((B*a + (A - C)*b)*c + ((A - C)*a - B*b)*d)*log(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
53,1,74,0,0.508082," ","integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{C d \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(A - C\right)} c - B d\right)} {\left(f x + e\right)} + {\left(B c + {\left(A - C\right)} d\right)} \log\left(\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 + e) + (B*c + (A - C)*d)*log(tan(f*x + e)^2 + 1) + 2*(C*c + B*d)*tan(f*x + e))/f","A",0
54,1,183,0,0.439864," ","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=""maxima"")","\frac{\frac{2 \, C d \tan\left(f x + e\right)}{b} + \frac{2 \, {\left({\left({\left(A - C\right)} a + B b\right)} c - {\left(B a - {\left(A - C\right)} b\right)} d\right)} {\left(f x + e\right)}}{a^{2} + b^{2}} + \frac{2 \, {\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(b \tan\left(f x + e\right) + a\right)}{a^{2} b^{2} + b^{4}} + \frac{{\left({\left(B a - {\left(A - C\right)} b\right)} c + {\left({\left(A - C\right)} a + B b\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, f}"," ",0,"1/2*(2*C*d*tan(f*x + e)/b + 2*(((A - C)*a + B*b)*c - (B*a - (A - C)*b)*d)*(f*x + e)/(a^2 + b^2) + 2*((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*tan(f*x + e) + a)/(a^2*b^2 + b^4) + ((B*a - (A - C)*b)*c + ((A - C)*a + B*b)*d)*log(tan(f*x + e)^2 + 1)/(a^2 + b^2))/f","A",0
55,1,338,0,0.459802," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left({\left(B a^{2} b^{2} - 2 \, {\left(A - C\right)} a b^{3} - B b^{4}\right)} c - {\left(C a^{4} - {\left(A - 3 \, C\right)} a^{2} b^{2} - 2 \, B a b^{3} + A b^{4}\right)} d\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\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)}}{a^{3} b^{2} + a b^{4} + {\left(a^{2} b^{3} + b^{5}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/(a^4 + 2*a^2*b^2 + b^4) - 2*((B*a^2*b^2 - 2*(A - C)*a*b^3 - B*b^4)*c - (C*a^4 - (A - 3*C)*a^2*b^2 - 2*B*a*b^3 + A*b^4)*d)*log(b*tan(f*x + e) + a)/(a^4*b^2 + 2*a^2*b^4 + b^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(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*((C*a^2*b - B*a*b^2 + A*b^3)*c - (C*a^3 - B*a^2*b + A*a*b^2)*d)/(a^3*b^2 + a*b^4 + (a^2*b^3 + b^5)*tan(f*x + e)))/f","A",0
56,1,574,0,0.643318," ","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=""maxima"")","\frac{\frac{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 - {\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)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\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(b \tan\left(f x + e\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(C a^{4} b - 3 \, B a^{3} b^{2} + {\left(5 \, A - 3 \, C\right)} a^{2} b^{3} + B a b^{4} + A b^{5}\right)} c + {\left(C a^{5} + B a^{4} b - {\left(3 \, A - 5 \, C\right)} a^{3} b^{2} - 3 \, B a^{2} b^{3} + A a b^{4}\right)} d - 2 \, {\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)}{a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*((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(b*tan(f*x + e) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + ((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(tan(f*x + e)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((C*a^4*b - 3*B*a^3*b^2 + (5*A - 3*C)*a^2*b^3 + B*a*b^4 + A*b^5)*c + (C*a^5 + B*a^4*b - (3*A - 5*C)*a^3*b^2 - 3*B*a^2*b^3 + A*a*b^4)*d - 2*((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))/(a^6*b^2 + 2*a^4*b^4 + a^2*b^6 + (a^4*b^4 + 2*a^2*b^6 + b^8)*tan(f*x + e)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*tan(f*x + e)))/f","A",0
57,1,691,0,0.632144," ","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=""maxima"")","\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} + 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} + 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)} {\left(f x + e\right)} + 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(\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 + 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 + 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 + e) + 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(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
58,1,463,0,0.459711," ","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=""maxima"")","\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} + 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} + 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)} {\left(f x + e\right)} + 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(\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 + 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 + 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 + e) + 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(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
59,1,260,0,0.554277," ","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=""maxima"")","\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} + 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} + 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)} {\left(f x + e\right)} + 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(\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 + 6*(C*b*c^2 + 2*(C*a + B*b)*c*d + (B*a + (A - C)*b)*d^2)*tan(f*x + e)^2 + 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 + e) + 6*((B*a + (A - C)*b)*c^2 + 2*((A - C)*a - B*b)*c*d - (B*a + (A - C)*b)*d^2)*log(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
60,1,135,0,0.501429," ","integrate((c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{2 \, C d^{2} \tan\left(f x + e\right)^{3} + 3 \, {\left(2 \, C c d + B d^{2}\right)} \tan\left(f x + e\right)^{2} + 6 \, {\left({\left(A - C\right)} c^{2} - 2 \, B c d - {\left(A - C\right)} d^{2}\right)} {\left(f x + e\right)} + 3 \, {\left(B c^{2} + 2 \, {\left(A - C\right)} c d - B d^{2}\right)} \log\left(\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 + 3*(2*C*c*d + B*d^2)*tan(f*x + e)^2 + 6*((A - C)*c^2 - 2*B*c*d - (A - C)*d^2)*(f*x + e) + 3*(B*c^2 + 2*(A - C)*c*d - B*d^2)*log(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
61,1,290,0,0.536021," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{a^{2} + b^{2}} + \frac{2 \, {\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(b \tan\left(f x + e\right) + a\right)}{a^{2} b^{3} + b^{5}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{C b d^{2} \tan\left(f x + e\right)^{2} + 2 \, {\left(2 \, C b c d - {\left(C a - B b\right)} d^{2}\right)} \tan\left(f x + e\right)}{b^{2}}}{2 \, f}"," ",0,"1/2*(2*(((A - C)*a + B*b)*c^2 - 2*(B*a - (A - C)*b)*c*d - ((A - C)*a + B*b)*d^2)*(f*x + e)/(a^2 + b^2) + 2*((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*tan(f*x + e) + a)/(a^2*b^3 + b^5) + ((B*a - (A - C)*b)*c^2 + 2*((A - C)*a + B*b)*c*d - (B*a - (A - C)*b)*d^2)*log(tan(f*x + e)^2 + 1)/(a^2 + b^2) + (C*b*d^2*tan(f*x + e)^2 + 2*(2*C*b*c*d - (C*a - B*b)*d^2)*tan(f*x + e))/b^2)/f","A",0
62,1,496,0,0.488593," ","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=""maxima"")","\frac{\frac{2 \, C d^{2} \tan\left(f x + e\right)}{b^{2}} + \frac{2 \, {\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)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left({\left(B a^{2} b^{3} - 2 \, {\left(A - C\right)} a b^{4} - B b^{5}\right)} c^{2} - 2 \, {\left(C a^{4} b - {\left(A - 3 \, C\right)} a^{2} b^{3} - 2 \, B a b^{4} + A b^{5}\right)} c d + {\left(2 \, C a^{5} - B a^{4} b + 4 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} d^{2}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\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)}}{a^{3} b^{3} + a b^{5} + {\left(a^{2} b^{4} + b^{6}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*C*d^2*tan(f*x + e)/b^2 + 2*(((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 + e)/(a^4 + 2*a^2*b^2 + b^4) - 2*((B*a^2*b^3 - 2*(A - C)*a*b^4 - B*b^5)*c^2 - 2*(C*a^4*b - (A - 3*C)*a^2*b^3 - 2*B*a*b^4 + A*b^5)*c*d + (2*C*a^5 - B*a^4*b + 4*C*a^3*b^2 - 3*B*a^2*b^3 + 2*A*a*b^4)*d^2)*log(b*tan(f*x + e) + a)/(a^4*b^3 + 2*a^2*b^5 + b^7) + ((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(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*((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)/(a^3*b^3 + a*b^5 + (a^2*b^4 + b^6)*tan(f*x + e)))/f","A",0
63,1,839,0,0.566353," ","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=""maxima"")","\frac{\frac{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} - 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)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left({\left(B a^{3} b^{3} - 3 \, {\left(A - C\right)} a^{2} b^{4} - 3 \, B a b^{5} + {\left(A - C\right)} b^{6}\right)} c^{2} + 2 \, {\left({\left(A - C\right)} a^{3} b^{3} + 3 \, B a^{2} b^{4} - 3 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c d - {\left(C a^{6} + 3 \, C a^{4} b^{2} + B a^{3} b^{3} - 3 \, {\left(A - 2 \, C\right)} a^{2} b^{4} - 3 \, B a b^{5} + A b^{6}\right)} d^{2}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(C a^{4} b^{2} - 3 \, B a^{3} b^{3} + {\left(5 \, A - 3 \, C\right)} a^{2} b^{4} + B a b^{5} + A b^{6}\right)} c^{2} + 2 \, {\left(C a^{5} b + B a^{4} b^{2} - {\left(3 \, A - 5 \, C\right)} a^{3} b^{3} - 3 \, B a^{2} b^{4} + A a b^{5}\right)} c d - {\left(3 \, C a^{6} - B a^{5} b - {\left(A - 7 \, C\right)} a^{4} b^{2} - 5 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} - 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)}{a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7} + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*((B*a^3*b^3 - 3*(A - C)*a^2*b^4 - 3*B*a*b^5 + (A - C)*b^6)*c^2 + 2*((A - C)*a^3*b^3 + 3*B*a^2*b^4 - 3*(A - C)*a*b^5 - B*b^6)*c*d - (C*a^6 + 3*C*a^4*b^2 + B*a^3*b^3 - 3*(A - 2*C)*a^2*b^4 - 3*B*a*b^5 + A*b^6)*d^2)*log(b*tan(f*x + e) + a)/(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9) + ((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(tan(f*x + e)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((C*a^4*b^2 - 3*B*a^3*b^3 + (5*A - 3*C)*a^2*b^4 + B*a*b^5 + A*b^6)*c^2 + 2*(C*a^5*b + B*a^4*b^2 - (3*A - 5*C)*a^3*b^3 - 3*B*a^2*b^4 + A*a*b^5)*c*d - (3*C*a^6 - B*a^5*b - (A - 7*C)*a^4*b^2 - 5*B*a^3*b^3 + 3*A*a^2*b^4)*d^2 - 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))/(a^6*b^3 + 2*a^4*b^5 + a^2*b^7 + (a^4*b^5 + 2*a^2*b^7 + b^9)*tan(f*x + e)^2 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*tan(f*x + e)))/f","A",0
64,1,680,0,0.479702," ","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=""maxima"")","\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} + 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} + 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)} {\left(f x + e\right)} + 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(\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 + 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 + 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 + e) + 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(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
65,1,387,0,0.449064," ","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=""maxima"")","\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} + 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} + 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)} {\left(f x + e\right)} + 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(\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 + 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 + 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 + e) + 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(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
66,1,202,0,0.580270," ","integrate((c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""maxima"")","\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} + 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} + 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)} {\left(f x + e\right)} + 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(\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 + 6*(3*C*c^2*d + 3*B*c*d^2 + (A - C)*d^3)*tan(f*x + e)^2 + 12*((A - C)*c^3 - 3*B*c^2*d - 3*(A - C)*c*d^2 + B*d^3)*(f*x + e) + 6*(B*c^3 + 3*(A - C)*c^2*d - 3*B*c*d^2 - (A - C)*d^3)*log(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
67,1,436,0,0.541381," ","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=""maxima"")","\frac{\frac{6 \, {\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)} {\left(f x + e\right)}}{a^{2} + b^{2}} + \frac{6 \, {\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(b \tan\left(f x + e\right) + a\right)}{a^{2} b^{4} + b^{6}} + \frac{3 \, {\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(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, C b^{2} d^{3} \tan\left(f x + e\right)^{3} + 3 \, {\left(3 \, C b^{2} c d^{2} - {\left(C a b - B b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} + 6 \, {\left(3 \, C b^{2} c^{2} d - 3 \, {\left(C a b - B b^{2}\right)} c d^{2} + {\left(C a^{2} - B a b + {\left(A - C\right)} b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)}{b^{3}}}{6 \, f}"," ",0,"1/6*(6*(((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 + e)/(a^2 + b^2) + 6*((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*tan(f*x + e) + a)/(a^2*b^4 + b^6) + 3*((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(tan(f*x + e)^2 + 1)/(a^2 + b^2) + (2*C*b^2*d^3*tan(f*x + e)^3 + 3*(3*C*b^2*c*d^2 - (C*a*b - B*b^2)*d^3)*tan(f*x + e)^2 + 6*(3*C*b^2*c^2*d - 3*(C*a*b - B*b^2)*c*d^2 + (C*a^2 - B*a*b + (A - C)*b^2)*d^3)*tan(f*x + e))/b^3)/f","A",0
68,1,685,0,0.587943," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left({\left(B a^{2} b^{4} - 2 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c^{3} - 3 \, {\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^{2} d + 3 \, {\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)} c d^{2} - {\left(3 \, C a^{6} - 2 \, B a^{5} b + {\left(A + 5 \, C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\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)}}{a^{3} b^{4} + a b^{6} + {\left(a^{2} b^{5} + b^{7}\right)} \tan\left(f x + e\right)} + \frac{C b d^{3} \tan\left(f x + e\right)^{2} + 2 \, {\left(3 \, C b c d^{2} - {\left(2 \, C a - B b\right)} d^{3}\right)} \tan\left(f x + e\right)}{b^{3}}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/(a^4 + 2*a^2*b^2 + b^4) - 2*((B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c^3 - 3*(C*a^4*b^2 - (A - 3*C)*a^2*b^4 - 2*B*a*b^5 + A*b^6)*c^2*d + 3*(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)*c*d^2 - (3*C*a^6 - 2*B*a^5*b + (A + 5*C)*a^4*b^2 - 4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3)*log(b*tan(f*x + e) + a)/(a^4*b^4 + 2*a^2*b^6 + b^8) + ((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(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*((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)/(a^3*b^4 + a*b^6 + (a^2*b^5 + b^7)*tan(f*x + e)) + (C*b*d^3*tan(f*x + e)^2 + 2*(3*C*b*c*d^2 - (2*C*a - B*b)*d^3)*tan(f*x + e))/b^3)/f","A",0
69,1,1119,0,0.550159," ","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=""maxima"")","\frac{\frac{2 \, C d^{3} \tan\left(f x + e\right)}{b^{3}} + \frac{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} - 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 - 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^{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)} d^{3}\right)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left({\left(B a^{3} b^{4} - 3 \, {\left(A - C\right)} a^{2} b^{5} - 3 \, B a b^{6} + {\left(A - C\right)} b^{7}\right)} c^{3} + 3 \, {\left({\left(A - C\right)} a^{3} b^{4} + 3 \, B a^{2} b^{5} - 3 \, {\left(A - C\right)} a b^{6} - B b^{7}\right)} c^{2} d - 3 \, {\left(C a^{6} b + 3 \, C a^{4} b^{3} + B a^{3} b^{4} - 3 \, {\left(A - 2 \, C\right)} a^{2} b^{5} - 3 \, B a b^{6} + A b^{7}\right)} c d^{2} + {\left(3 \, C a^{7} - B a^{6} b + 9 \, C a^{5} b^{2} - 3 \, B a^{4} b^{3} - {\left(A - 10 \, C\right)} a^{3} b^{4} - 6 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} d^{3}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}} + \frac{{\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^{3} + 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 - 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 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)} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(C a^{4} b^{3} - 3 \, B a^{3} b^{4} + {\left(5 \, A - 3 \, C\right)} a^{2} b^{5} + B a b^{6} + A b^{7}\right)} c^{3} + 3 \, {\left(C a^{5} b^{2} + B a^{4} b^{3} - {\left(3 \, A - 5 \, C\right)} a^{3} b^{4} - 3 \, B a^{2} b^{5} + A a b^{6}\right)} c^{2} d - 3 \, {\left(3 \, C a^{6} b - B a^{5} b^{2} - {\left(A - 7 \, C\right)} a^{4} b^{3} - 5 \, B a^{3} b^{4} + 3 \, A a^{2} b^{5}\right)} c d^{2} + {\left(5 \, C a^{7} - 3 \, B a^{6} b + {\left(A + 9 \, C\right)} a^{5} b^{2} - 7 \, B a^{4} b^{3} + 5 \, A a^{3} b^{4}\right)} d^{3} - 2 \, {\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)}{a^{6} b^{4} + 2 \, a^{4} b^{6} + a^{2} b^{8} + {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{5} b^{5} + 2 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*C*d^3*tan(f*x + e)/b^3 + 2*(((A - C)*a^3 + 3*B*a^2*b - 3*(A - C)*a*b^2 - B*b^3)*c^3 - 3*(B*a^3 - 3*(A - C)*a^2*b - 3*B*a*b^2 + (A - C)*b^3)*c^2*d - 3*((A - C)*a^3 + 3*B*a^2*b - 3*(A - C)*a*b^2 - B*b^3)*c*d^2 + (B*a^3 - 3*(A - C)*a^2*b - 3*B*a*b^2 + (A - C)*b^3)*d^3)*(f*x + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*((B*a^3*b^4 - 3*(A - C)*a^2*b^5 - 3*B*a*b^6 + (A - C)*b^7)*c^3 + 3*((A - C)*a^3*b^4 + 3*B*a^2*b^5 - 3*(A - C)*a*b^6 - B*b^7)*c^2*d - 3*(C*a^6*b + 3*C*a^4*b^3 + B*a^3*b^4 - 3*(A - 2*C)*a^2*b^5 - 3*B*a*b^6 + A*b^7)*c*d^2 + (3*C*a^7 - B*a^6*b + 9*C*a^5*b^2 - 3*B*a^4*b^3 - (A - 10*C)*a^3*b^4 - 6*B*a^2*b^5 + 3*A*a*b^6)*d^3)*log(b*tan(f*x + e) + a)/(a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10) + ((B*a^3 - 3*(A - C)*a^2*b - 3*B*a*b^2 + (A - C)*b^3)*c^3 + 3*((A - C)*a^3 + 3*B*a^2*b - 3*(A - C)*a*b^2 - B*b^3)*c^2*d - 3*(B*a^3 - 3*(A - C)*a^2*b - 3*B*a*b^2 + (A - C)*b^3)*c*d^2 - ((A - C)*a^3 + 3*B*a^2*b - 3*(A - C)*a*b^2 - B*b^3)*d^3)*log(tan(f*x + e)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((C*a^4*b^3 - 3*B*a^3*b^4 + (5*A - 3*C)*a^2*b^5 + B*a*b^6 + A*b^7)*c^3 + 3*(C*a^5*b^2 + B*a^4*b^3 - (3*A - 5*C)*a^3*b^4 - 3*B*a^2*b^5 + A*a*b^6)*c^2*d - 3*(3*C*a^6*b - B*a^5*b^2 - (A - 7*C)*a^4*b^3 - 5*B*a^3*b^4 + 3*A*a^2*b^5)*c*d^2 + (5*C*a^7 - 3*B*a^6*b + (A + 9*C)*a^5*b^2 - 7*B*a^4*b^3 + 5*A*a^3*b^4)*d^3 - 2*((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))/(a^6*b^4 + 2*a^4*b^6 + a^2*b^8 + (a^4*b^6 + 2*a^2*b^8 + b^10)*tan(f*x + e)^2 + 2*(a^5*b^5 + 2*a^3*b^7 + a*b^9)*tan(f*x + e)))/f","A",0
70,1,445,0,0.585282," ","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=""maxima"")","\frac{\frac{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 + {\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)} {\left(f x + e\right)}}{c^{2} + d^{2}} - \frac{6 \, {\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(d \tan\left(f x + e\right) + c\right)}{c^{2} d^{4} + d^{6}} + \frac{3 \, {\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(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} + \frac{2 \, C b^{3} d^{2} \tan\left(f x + e\right)^{3} - 3 \, {\left(C b^{3} c d - {\left(3 \, C a b^{2} + B b^{3}\right)} d^{2}\right)} \tan\left(f x + e\right)^{2} + 6 \, {\left(C b^{3} c^{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)}{d^{3}}}{6 \, f}"," ",0,"1/6*(6*(((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 + e)/(c^2 + d^2) - 6*(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*tan(f*x + e) + c)/(c^2*d^4 + d^6) + 3*((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(tan(f*x + e)^2 + 1)/(c^2 + d^2) + (2*C*b^3*d^2*tan(f*x + e)^3 - 3*(C*b^3*c*d - (3*C*a*b^2 + B*b^3)*d^2)*tan(f*x + e)^2 + 6*(C*b^3*c^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))/d^3)/f","A",0
71,1,294,0,0.550122," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{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(d \tan\left(f x + e\right) + c\right)}{c^{2} d^{3} + d^{5}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} + \frac{C b^{2} d \tan\left(f x + e\right)^{2} - 2 \, {\left(C b^{2} c - {\left(2 \, C a b + B b^{2}\right)} d\right)} \tan\left(f x + e\right)}{d^{2}}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/(c^2 + d^2) + 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*tan(f*x + e) + c)/(c^2*d^3 + d^5) + ((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(tan(f*x + e)^2 + 1)/(c^2 + d^2) + (C*b^2*d*tan(f*x + e)^2 - 2*(C*b^2*c - (2*C*a*b + B*b^2)*d)*tan(f*x + e))/d^2)/f","A",0
72,1,178,0,1.490404," ","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=""maxima"")","\frac{\frac{2 \, C b \tan\left(f x + e\right)}{d} + \frac{2 \, {\left({\left({\left(A - C\right)} a - B b\right)} c + {\left(B a + {\left(A - C\right)} b\right)} d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} - \frac{2 \, {\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(d \tan\left(f x + e\right) + c\right)}{c^{2} d^{2} + d^{4}} + \frac{{\left({\left(B a + {\left(A - C\right)} b\right)} c - {\left({\left(A - C\right)} a - B b\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}}}{2 \, f}"," ",0,"1/2*(2*C*b*tan(f*x + e)/d + 2*(((A - C)*a - B*b)*c + (B*a + (A - C)*b)*d)*(f*x + e)/(c^2 + d^2) - 2*(C*b*c^3 - A*a*d^3 - (C*a + B*b)*c^2*d + (B*a + A*b)*c*d^2)*log(d*tan(f*x + e) + c)/(c^2*d^2 + d^4) + ((B*a + (A - C)*b)*c - ((A - C)*a - B*b)*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2))/f","A",0
73,1,106,0,0.554909," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(A - C\right)} c + B d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{2 \, {\left(C c^{2} - B c d + A d^{2}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{2} d + d^{3}} + \frac{{\left(B c - {\left(A - C\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}}}{2 \, f}"," ",0,"1/2*(2*((A - C)*c + B*d)*(f*x + e)/(c^2 + d^2) + 2*(C*c^2 - B*c*d + A*d^2)*log(d*tan(f*x + e) + c)/(c^2*d + d^3) + (B*c - (A - C)*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2))/f","A",0
74,1,243,0,0.466528," ","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=""maxima"")","\frac{\frac{2 \, {\left({\left({\left(A - C\right)} a + B b\right)} c + {\left(B a - {\left(A - C\right)} b\right)} d\right)} {\left(f x + e\right)}}{{\left(a^{2} + b^{2}\right)} c^{2} + {\left(a^{2} + b^{2}\right)} d^{2}} + \frac{2 \, {\left(C a^{2} - B a b + A b^{2}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{2} b + b^{3}\right)} c - {\left(a^{3} + a b^{2}\right)} d} - \frac{2 \, {\left(C c^{2} - B c d + A d^{2}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b c^{3} - a c^{2} d + b c d^{2} - a d^{3}} + \frac{{\left({\left(B a - {\left(A - C\right)} b\right)} c - {\left({\left(A - C\right)} a + B b\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{2} + b^{2}\right)} c^{2} + {\left(a^{2} + b^{2}\right)} d^{2}}}{2 \, f}"," ",0,"1/2*(2*(((A - C)*a + B*b)*c + (B*a - (A - C)*b)*d)*(f*x + e)/((a^2 + b^2)*c^2 + (a^2 + b^2)*d^2) + 2*(C*a^2 - B*a*b + A*b^2)*log(b*tan(f*x + e) + a)/((a^2*b + b^3)*c - (a^3 + a*b^2)*d) - 2*(C*c^2 - B*c*d + A*d^2)*log(d*tan(f*x + e) + c)/(b*c^3 - a*c^2*d + b*c*d^2 - a*d^3) + ((B*a - (A - C)*b)*c - ((A - C)*a + B*b)*d)*log(tan(f*x + e)^2 + 1)/((a^2 + b^2)*c^2 + (a^2 + b^2)*d^2))/f","A",0
75,1,520,0,0.509990," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}} - \frac{2 \, {\left({\left(B a^{2} b^{2} - 2 \, {\left(A - C\right)} a b^{3} - B b^{4}\right)} c + {\left(C a^{4} - 2 \, B a^{3} b + {\left(3 \, A - C\right)} a^{2} b^{2} + A b^{4}\right)} d\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} c^{2} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c d + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2}} + \frac{2 \, {\left(C c^{2} d - B c d^{2} + A d^{3}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{2} c^{4} - 2 \, a b c^{3} d - 2 \, a b c d^{3} + a^{2} d^{4} + {\left(a^{2} + b^{2}\right)} c^{2} d^{2}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}} - \frac{2 \, {\left(C a^{2} - B a b + A b^{2}\right)}}{{\left(a^{3} b + a b^{3}\right)} c - {\left(a^{4} + a^{2} b^{2}\right)} d + {\left({\left(a^{2} b^{2} + b^{4}\right)} c - {\left(a^{3} b + a b^{3}\right)} d\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2) - 2*((B*a^2*b^2 - 2*(A - C)*a*b^3 - B*b^4)*c + (C*a^4 - 2*B*a^3*b + (3*A - C)*a^2*b^2 + A*b^4)*d)*log(b*tan(f*x + e) + a)/((a^4*b^2 + 2*a^2*b^4 + b^6)*c^2 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*c*d + (a^6 + 2*a^4*b^2 + a^2*b^4)*d^2) + 2*(C*c^2*d - B*c*d^2 + A*d^3)*log(d*tan(f*x + e) + c)/(b^2*c^4 - 2*a*b*c^3*d - 2*a*b*c*d^3 + a^2*d^4 + (a^2 + b^2)*c^2*d^2) + ((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(tan(f*x + e)^2 + 1)/((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2) - 2*(C*a^2 - B*a*b + A*b^2)/((a^3*b + a*b^3)*c - (a^4 + a^2*b^2)*d + ((a^2*b^2 + b^4)*c - (a^3*b + a*b^3)*d)*tan(f*x + e)))/f","A",0
76,1,1096,0,0.677030," ","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=""maxima"")","\frac{\frac{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 + {\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)} {\left(f x + e\right)}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{2}} - \frac{2 \, {\left({\left(B a^{3} b^{3} - 3 \, {\left(A - C\right)} a^{2} b^{4} - 3 \, B a b^{5} + {\left(A - C\right)} b^{6}\right)} c^{2} - {\left(3 \, B a^{4} b^{2} - 8 \, {\left(A - C\right)} a^{3} b^{3} - 6 \, B a^{2} b^{4} - B b^{6}\right)} c d - {\left(C a^{6} - 3 \, B a^{5} b + 3 \, {\left(2 \, A - C\right)} a^{4} b^{2} + B a^{3} b^{3} + 3 \, A a^{2} b^{4} + A b^{6}\right)} d^{2}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} c^{3} - 3 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} c^{2} d + 3 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} c d^{2} - {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{3}} - \frac{2 \, {\left(C c^{2} d^{2} - B c d^{3} + A d^{4}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c d^{4} - a^{3} d^{5} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} d^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} d^{3}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{2}} - \frac{{\left(C a^{4} b - 3 \, B a^{3} b^{2} + {\left(5 \, A - 3 \, C\right)} a^{2} b^{3} + B a b^{4} + A b^{5}\right)} c - {\left(3 \, C a^{5} - 5 \, B a^{4} b + {\left(7 \, A - C\right)} a^{3} b^{2} - B a^{2} b^{3} + 3 \, A a b^{4}\right)} d - 2 \, {\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 - 2 \, B a^{3} b^{2} + {\left(3 \, A - C\right)} a^{2} b^{3} + A b^{5}\right)} d\right)} \tan\left(f x + e\right)}{{\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 2 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} c d + {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d^{2} + {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} c^{2} - 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c d + {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{2}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c^{2} - 2 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c d + {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d^{2}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^2) - 2*((B*a^3*b^3 - 3*(A - C)*a^2*b^4 - 3*B*a*b^5 + (A - C)*b^6)*c^2 - (3*B*a^4*b^2 - 8*(A - C)*a^3*b^3 - 6*B*a^2*b^4 - B*b^6)*c*d - (C*a^6 - 3*B*a^5*b + 3*(2*A - C)*a^4*b^2 + B*a^3*b^3 + 3*A*a^2*b^4 + A*b^6)*d^2)*log(b*tan(f*x + e) + a)/((a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*c^3 - 3*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*c^2*d + 3*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*c*d^2 - (a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^3) - 2*(C*c^2*d^2 - B*c*d^3 + A*d^4)*log(d*tan(f*x + e) + c)/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c*d^4 - a^3*d^5 + (3*a^2*b + b^3)*c^3*d^2 - (a^3 + 3*a*b^2)*c^2*d^3) + ((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(tan(f*x + e)^2 + 1)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^2) - ((C*a^4*b - 3*B*a^3*b^2 + (5*A - 3*C)*a^2*b^3 + B*a*b^4 + A*b^5)*c - (3*C*a^5 - 5*B*a^4*b + (7*A - C)*a^3*b^2 - B*a^2*b^3 + 3*A*a*b^4)*d - 2*((B*a^2*b^3 - 2*(A - C)*a*b^4 - B*b^5)*c + (C*a^4*b - 2*B*a^3*b^2 + (3*A - C)*a^2*b^3 + A*b^5)*d)*tan(f*x + e))/((a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^2 - 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c*d + (a^8 + 2*a^6*b^2 + a^4*b^4)*d^2 + ((a^4*b^4 + 2*a^2*b^6 + b^8)*c^2 - 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*c*d + (a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*d^2)*tan(f*x + e)^2 + 2*((a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^2 - 2*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c*d + (a^7*b + 2*a^5*b^3 + a^3*b^5)*d^2)*tan(f*x + e)))/f","B",0
77,1,684,0,0.731408," ","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=""maxima"")","\frac{\frac{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} + 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)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{2 \, {\left(3 \, C b^{3} c^{6} - 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{5} d + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + {\left(A + 5 \, C\right)} b^{3}\right)} c^{4} d^{2} - 4 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3} 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^{2} d^{4} + 2 \, {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} c d^{5} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{6}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{4} d^{4} + 2 \, c^{2} d^{6} + d^{8}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{2 \, {\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)}}{c^{3} d^{4} + c d^{6} + {\left(c^{2} d^{5} + d^{7}\right)} \tan\left(f x + e\right)} + \frac{C b^{3} d \tan\left(f x + e\right)^{2} - 2 \, {\left(2 \, C b^{3} c - {\left(3 \, C a b^{2} + B b^{3}\right)} d\right)} \tan\left(f x + e\right)}{d^{3}}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/(c^4 + 2*c^2*d^2 + d^4) + 2*(3*C*b^3*c^6 - 2*(3*C*a*b^2 + B*b^3)*c^5*d + (3*C*a^2*b + 3*B*a*b^2 + (A + 5*C)*b^3)*c^4*d^2 - 4*(3*C*a*b^2 + B*b^3)*c^3*d^3 - (B*a^3 + 3*(A - 3*C)*a^2*b - 9*B*a*b^2 - 3*A*b^3)*c^2*d^4 + 2*((A - C)*a^3 - 3*B*a^2*b - 3*A*a*b^2)*c*d^5 + (B*a^3 + 3*A*a^2*b)*d^6)*log(d*tan(f*x + e) + c)/(c^4*d^4 + 2*c^2*d^6 + d^8) + ((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(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) + 2*(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)/(c^3*d^4 + c*d^6 + (c^2*d^5 + d^7)*tan(f*x + e)) + (C*b^3*d*tan(f*x + e)^2 - 2*(2*C*b^3*c - (3*C*a*b^2 + B*b^3)*d)*tan(f*x + e))/d^3)/f","A",0
78,1,493,0,0.537704," ","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=""maxima"")","\frac{\frac{2 \, C b^{2} \tan\left(f x + e\right)}{d^{2}} + \frac{2 \, {\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)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{2 \, {\left(2 \, C b^{2} c^{5} + 4 \, C b^{2} c^{3} d^{2} - {\left(2 \, C a b + B b^{2}\right)} c^{4} d + {\left(B a^{2} + 2 \, {\left(A - 3 \, C\right)} a b - 3 \, B b^{2}\right)} c^{2} d^{3} - 2 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - A b^{2}\right)} c d^{4} - {\left(B a^{2} + 2 \, A a b\right)} d^{5}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{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)}}{c^{3} d^{3} + c d^{5} + {\left(c^{2} d^{4} + d^{6}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*C*b^2*tan(f*x + e)/d^2 + 2*(((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 + e)/(c^4 + 2*c^2*d^2 + d^4) - 2*(2*C*b^2*c^5 + 4*C*b^2*c^3*d^2 - (2*C*a*b + B*b^2)*c^4*d + (B*a^2 + 2*(A - 3*C)*a*b - 3*B*b^2)*c^2*d^3 - 2*((A - C)*a^2 - 2*B*a*b - A*b^2)*c*d^4 - (B*a^2 + 2*A*a*b)*d^5)*log(d*tan(f*x + e) + c)/(c^4*d^3 + 2*c^2*d^5 + d^7) + ((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(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) - 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)/(c^3*d^3 + c*d^5 + (c^2*d^4 + d^6)*tan(f*x + e)))/f","A",0
79,1,319,0,0.496145," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{2 \, {\left(C b c^{4} - {\left(B a + {\left(A - 3 \, C\right)} b\right)} c^{2} d^{2} + 2 \, {\left({\left(A - C\right)} a - B b\right)} c d^{3} + {\left(B a + A b\right)} d^{4}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{4} d^{2} + 2 \, c^{2} d^{4} + d^{6}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{2 \, {\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)}}{c^{3} d^{2} + c d^{4} + {\left(c^{2} d^{3} + d^{5}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((A - C)*a - B*b)*c^2 + 2*(B*a + (A - C)*b)*c*d - ((A - C)*a - B*b)*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + 2*(C*b*c^4 - (B*a + (A - 3*C)*b)*c^2*d^2 + 2*((A - C)*a - B*b)*c*d^3 + (B*a + A*b)*d^4)*log(d*tan(f*x + e) + c)/(c^4*d^2 + 2*c^2*d^4 + d^6) + ((B*a + (A - C)*b)*c^2 - 2*((A - C)*a - B*b)*c*d - (B*a + (A - C)*b)*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) + 2*(C*b*c^3 - A*a*d^3 - (C*a + B*b)*c^2*d + (B*a + A*b)*c*d^2)/(c^3*d^2 + c*d^4 + (c^2*d^3 + d^5)*tan(f*x + e)))/f","A",0
80,1,205,0,0.665644," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(A - C\right)} c^{2} + 2 \, B c d - {\left(A - C\right)} d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{2 \, {\left(B c^{2} - 2 \, {\left(A - C\right)} c d - B d^{2}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(B c^{2} - 2 \, {\left(A - C\right)} c d - B d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{2 \, {\left(C c^{2} - B c d + A d^{2}\right)}}{c^{3} d + c d^{3} + {\left(c^{2} d^{2} + d^{4}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*((A - C)*c^2 + 2*B*c*d - (A - C)*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) - 2*(B*c^2 - 2*(A - C)*c*d - B*d^2)*log(d*tan(f*x + e) + c)/(c^4 + 2*c^2*d^2 + d^4) + (B*c^2 - 2*(A - C)*c*d - B*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) - 2*(C*c^2 - B*c*d + A*d^2)/(c^3*d + c*d^3 + (c^2*d^2 + d^4)*tan(f*x + e)))/f","A",0
81,1,513,0,0.504820," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{{\left(a^{2} + b^{2}\right)} c^{4} + 2 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{2} + {\left(a^{2} + b^{2}\right)} d^{4}} + \frac{2 \, {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{2} b^{2} + b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c d + {\left(a^{4} + a^{2} b^{2}\right)} d^{2}} - \frac{2 \, {\left(C b c^{4} - 2 \, B b c^{3} d - 2 \, {\left(A - C\right)} a c d^{3} + {\left(B a + {\left(3 \, A - C\right)} b\right)} c^{2} d^{2} - {\left(B a - A b\right)} d^{4}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{2} c^{6} - 2 \, a b c^{5} d - 4 \, a b c^{3} d^{3} - 2 \, a b c d^{5} + a^{2} d^{6} + {\left(a^{2} + 2 \, b^{2}\right)} c^{4} d^{2} + {\left(2 \, a^{2} + b^{2}\right)} c^{2} d^{4}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{2} + b^{2}\right)} c^{4} + 2 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{2} + {\left(a^{2} + b^{2}\right)} d^{4}} + \frac{2 \, {\left(C c^{2} - B c d + A d^{2}\right)}}{b c^{4} - a c^{3} d + b c^{2} d^{2} - a c d^{3} + {\left(b c^{3} d - a c^{2} d^{2} + b c d^{3} - a d^{4}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((A - C)*a + B*b)*c^2 + 2*(B*a - (A - C)*b)*c*d - ((A - C)*a + B*b)*d^2)*(f*x + e)/((a^2 + b^2)*c^4 + 2*(a^2 + b^2)*c^2*d^2 + (a^2 + b^2)*d^4) + 2*(C*a^2*b - B*a*b^2 + A*b^3)*log(b*tan(f*x + e) + a)/((a^2*b^2 + b^4)*c^2 - 2*(a^3*b + a*b^3)*c*d + (a^4 + a^2*b^2)*d^2) - 2*(C*b*c^4 - 2*B*b*c^3*d - 2*(A - C)*a*c*d^3 + (B*a + (3*A - C)*b)*c^2*d^2 - (B*a - A*b)*d^4)*log(d*tan(f*x + e) + c)/(b^2*c^6 - 2*a*b*c^5*d - 4*a*b*c^3*d^3 - 2*a*b*c*d^5 + a^2*d^6 + (a^2 + 2*b^2)*c^4*d^2 + (2*a^2 + b^2)*c^2*d^4) + ((B*a - (A - C)*b)*c^2 - 2*((A - C)*a + B*b)*c*d - (B*a - (A - C)*b)*d^2)*log(tan(f*x + e)^2 + 1)/((a^2 + b^2)*c^4 + 2*(a^2 + b^2)*c^2*d^2 + (a^2 + b^2)*d^4) + 2*(C*c^2 - B*c*d + A*d^2)/(b*c^4 - a*c^3*d + b*c^2*d^2 - a*c*d^3 + (b*c^3*d - a*c^2*d^2 + b*c*d^3 - a*d^4)*tan(f*x + e)))/f","A",0
82,1,1185,0,0.761184," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}} - \frac{2 \, {\left({\left(B a^{2} b^{3} - 2 \, {\left(A - C\right)} a b^{4} - B b^{5}\right)} c + {\left(2 \, C a^{4} b - 3 \, B a^{3} b^{2} + 4 \, A a^{2} b^{3} - B a b^{4} + 2 \, A b^{5}\right)} d\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} c^{3} - 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{2} d + 3 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c d^{2} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{3}} + \frac{2 \, {\left(2 \, C b c^{4} d - 3 \, B b c^{3} d^{2} + {\left(B a + 4 \, A b\right)} c^{2} d^{3} - {\left(2 \, {\left(A - C\right)} a + B b\right)} c d^{4} - {\left(B a - 2 \, A b\right)} d^{5}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c d^{6} - a^{3} d^{7} + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{5} d^{2} - {\left(a^{3} + 6 \, a b^{2}\right)} c^{4} d^{3} + {\left(6 \, a^{2} b + b^{3}\right)} c^{3} d^{4} - {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{2} d^{5}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}} - \frac{2 \, {\left({\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c^{3} + {\left(C a^{3} + C a b^{2}\right)} c^{2} d - {\left(B a^{3} - C a^{2} b + 2 \, B a b^{2} - A b^{3}\right)} c d^{2} + {\left(A a^{3} + A a b^{2}\right)} d^{3} + {\left({\left(2 \, C a^{2} b - B a b^{2} + {\left(A + C\right)} b^{3}\right)} c^{2} d - {\left(B a^{2} b + B b^{3}\right)} c d^{2} + {\left({\left(A + C\right)} a^{2} b - B a b^{2} + 2 \, A b^{3}\right)} d^{3}\right)} \tan\left(f x + e\right)\right)}}{{\left(a^{3} b^{2} + a b^{4}\right)} c^{5} - 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} c^{4} d + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c^{3} d^{2} - 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} c^{2} d^{3} + {\left(a^{5} + a^{3} b^{2}\right)} c d^{4} + {\left({\left(a^{2} b^{3} + b^{5}\right)} c^{4} d - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{3} d^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} d^{3} - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c d^{4} + {\left(a^{4} b + a^{2} b^{3}\right)} d^{5}\right)} \tan\left(f x + e\right)^{2} + {\left({\left(a^{2} b^{3} + b^{5}\right)} c^{5} - {\left(a^{3} b^{2} + a b^{4}\right)} c^{4} d - {\left(a^{4} b - b^{5}\right)} c^{3} d^{2} + {\left(a^{5} - a b^{4}\right)} c^{2} d^{3} - {\left(a^{4} b + a^{2} b^{3}\right)} c d^{4} + {\left(a^{5} + a^{3} b^{2}\right)} d^{5}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/((a^4 + 2*a^2*b^2 + b^4)*c^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^2 + (a^4 + 2*a^2*b^2 + b^4)*d^4) - 2*((B*a^2*b^3 - 2*(A - C)*a*b^4 - B*b^5)*c + (2*C*a^4*b - 3*B*a^3*b^2 + 4*A*a^2*b^3 - B*a*b^4 + 2*A*b^5)*d)*log(b*tan(f*x + e) + a)/((a^4*b^3 + 2*a^2*b^5 + b^7)*c^3 - 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^2*d + 3*(a^6*b + 2*a^4*b^3 + a^2*b^5)*c*d^2 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^3) + 2*(2*C*b*c^4*d - 3*B*b*c^3*d^2 + (B*a + 4*A*b)*c^2*d^3 - (2*(A - C)*a + B*b)*c*d^4 - (B*a - 2*A*b)*d^5)*log(d*tan(f*x + e) + c)/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c*d^6 - a^3*d^7 + (3*a^2*b + 2*b^3)*c^5*d^2 - (a^3 + 6*a*b^2)*c^4*d^3 + (6*a^2*b + b^3)*c^3*d^4 - (2*a^3 + 3*a*b^2)*c^2*d^5) + ((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(tan(f*x + e)^2 + 1)/((a^4 + 2*a^2*b^2 + b^4)*c^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^2 + (a^4 + 2*a^2*b^2 + b^4)*d^4) - 2*((C*a^2*b - B*a*b^2 + A*b^3)*c^3 + (C*a^3 + C*a*b^2)*c^2*d - (B*a^3 - C*a^2*b + 2*B*a*b^2 - A*b^3)*c*d^2 + (A*a^3 + A*a*b^2)*d^3 + ((2*C*a^2*b - B*a*b^2 + (A + C)*b^3)*c^2*d - (B*a^2*b + B*b^3)*c*d^2 + ((A + C)*a^2*b - B*a*b^2 + 2*A*b^3)*d^3)*tan(f*x + e))/((a^3*b^2 + a*b^4)*c^5 - 2*(a^4*b + a^2*b^3)*c^4*d + (a^5 + 2*a^3*b^2 + a*b^4)*c^3*d^2 - 2*(a^4*b + a^2*b^3)*c^2*d^3 + (a^5 + a^3*b^2)*c*d^4 + ((a^2*b^3 + b^5)*c^4*d - 2*(a^3*b^2 + a*b^4)*c^3*d^2 + (a^4*b + 2*a^2*b^3 + b^5)*c^2*d^3 - 2*(a^3*b^2 + a*b^4)*c*d^4 + (a^4*b + a^2*b^3)*d^5)*tan(f*x + e)^2 + ((a^2*b^3 + b^5)*c^5 - (a^3*b^2 + a*b^4)*c^4*d - (a^4*b - b^5)*c^3*d^2 + (a^5 - a*b^4)*c^2*d^3 - (a^4*b + a^2*b^3)*c*d^4 + (a^5 + a^3*b^2)*d^5)*tan(f*x + e)))/f","B",0
83,1,2519,0,0.703911," ","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=""maxima"")","\frac{\frac{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} + 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)} {\left(f x + e\right)}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{4} + 2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}} - \frac{2 \, {\left({\left(B a^{3} b^{4} - 3 \, {\left(A - C\right)} a^{2} b^{5} - 3 \, B a b^{6} + {\left(A - C\right)} b^{7}\right)} c^{2} - 2 \, {\left(2 \, B a^{4} b^{3} - 5 \, {\left(A - C\right)} a^{3} b^{4} - 3 \, B a^{2} b^{5} - {\left(A - C\right)} a b^{6} - B b^{7}\right)} c d - {\left(3 \, C a^{6} b - 6 \, B a^{5} b^{2} + {\left(10 \, A - C\right)} a^{4} b^{3} - 3 \, B a^{3} b^{4} + 9 \, A a^{2} b^{5} - B a b^{6} + 3 \, A b^{7}\right)} d^{2}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}\right)} c^{4} - 4 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} c^{3} d + 6 \, {\left(a^{8} b^{2} + 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} + a^{2} b^{8}\right)} c^{2} d^{2} - 4 \, {\left(a^{9} b + 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} + a^{3} b^{7}\right)} c d^{3} + {\left(a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6}\right)} d^{4}} - \frac{2 \, {\left(3 \, C b c^{4} d^{2} - 4 \, B b c^{3} d^{3} + {\left(B a + {\left(5 \, A + C\right)} b\right)} c^{2} d^{4} - 2 \, {\left({\left(A - C\right)} a + B b\right)} c d^{5} - {\left(B a - 3 \, A b\right)} d^{6}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{4} c^{8} - 4 \, a b^{3} c^{7} d - 4 \, a^{3} b c d^{7} + a^{4} d^{8} + 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} c^{6} d^{2} - 4 \, {\left(a^{3} b + 2 \, a b^{3}\right)} c^{5} d^{3} + {\left(a^{4} + 12 \, a^{2} b^{2} + b^{4}\right)} c^{4} d^{4} - 4 \, {\left(2 \, a^{3} b + a b^{3}\right)} c^{3} d^{5} + 2 \, {\left(a^{4} + 3 \, a^{2} b^{2}\right)} c^{2} d^{6}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{4} + 2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}} - \frac{{\left(C a^{4} b^{2} - 3 \, B a^{3} b^{3} + {\left(5 \, A - 3 \, C\right)} a^{2} b^{4} + B a b^{5} + A b^{6}\right)} c^{4} - {\left(5 \, C a^{5} b - 7 \, B a^{4} b^{2} + {\left(9 \, A + C\right)} a^{3} b^{3} - 3 \, B a^{2} b^{4} + 5 \, A a b^{5}\right)} c^{3} d - {\left(2 \, C a^{6} + 3 \, C a^{4} b^{2} + 3 \, B a^{3} b^{3} - 5 \, {\left(A - C\right)} a^{2} b^{4} - B a b^{5} - A b^{6}\right)} c^{2} d^{2} + {\left(2 \, B a^{6} - 5 \, C a^{5} b + 11 \, B a^{4} b^{2} - {\left(9 \, A + C\right)} a^{3} b^{3} + 5 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c d^{3} - 2 \, {\left(A a^{6} + 2 \, A a^{4} b^{2} + A a^{2} b^{4}\right)} d^{4} - 2 \, {\left({\left(B a^{2} b^{4} - 2 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c^{3} d + {\left(3 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} + 2 \, {\left(2 \, A + C\right)} a^{2} b^{4} - B a b^{5} + {\left(2 \, A + C\right)} b^{6}\right)} c^{2} d^{2} - {\left(B a^{4} b^{2} + B a^{2} b^{4} + 2 \, {\left(A - C\right)} a b^{5} + 2 \, B b^{6}\right)} c d^{3} + {\left({\left(A + 2 \, C\right)} a^{4} b^{2} - 3 \, B a^{3} b^{3} + 6 \, A a^{2} b^{4} - B a b^{5} + 3 \, A b^{6}\right)} d^{4}\right)} \tan\left(f x + e\right)^{2} - {\left(2 \, {\left(B a^{2} b^{4} - 2 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c^{4} + 3 \, {\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 + {\left(9 \, C a^{5} b - 7 \, B a^{4} b^{2} + 9 \, {\left(A + C\right)} a^{3} b^{3} - B a^{2} b^{4} + {\left(A + 8 \, C\right)} a b^{5} - 2 \, B b^{6}\right)} c^{2} d^{2} - {\left(4 \, B a^{5} b - 3 \, C a^{4} b^{2} + 11 \, B a^{3} b^{3} - 3 \, {\left(A + C\right)} a^{2} b^{4} + 7 \, B a b^{5} - 3 \, A b^{6}\right)} c d^{3} + {\left({\left(4 \, A + 5 \, C\right)} a^{5} b - 7 \, B a^{4} b^{2} + {\left(17 \, A + C\right)} a^{3} b^{3} - 3 \, B a^{2} b^{4} + 9 \, A a b^{5}\right)} d^{4}\right)} \tan\left(f x + e\right)}{{\left(a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{6} - 3 \, {\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} c^{5} d + {\left(3 \, a^{8} b + 7 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{4} d^{2} - {\left(a^{9} + 5 \, a^{7} b^{2} + 7 \, a^{5} b^{4} + 3 \, a^{3} b^{6}\right)} c^{3} d^{3} + 3 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} c^{2} d^{4} - {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} c d^{5} + {\left({\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} c^{5} d - 3 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{4} d^{2} + {\left(3 \, a^{6} b^{3} + 7 \, a^{4} b^{5} + 5 \, a^{2} b^{7} + b^{9}\right)} c^{3} d^{3} - {\left(a^{7} b^{2} + 5 \, a^{5} b^{4} + 7 \, a^{3} b^{6} + 3 \, a b^{8}\right)} c^{2} d^{4} + 3 \, {\left(a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} c d^{5} - {\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{6}\right)} \tan\left(f x + e\right)^{3} + {\left({\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} c^{6} - {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{5} d - {\left(3 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + a^{2} b^{7} - b^{9}\right)} c^{4} d^{2} + {\left(5 \, a^{7} b^{2} + 9 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} c^{3} d^{3} - {\left(2 \, a^{8} b + 7 \, a^{6} b^{3} + 8 \, a^{4} b^{5} + 3 \, a^{2} b^{7}\right)} c^{2} d^{4} + 5 \, {\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} c d^{5} - 2 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d^{6}\right)} \tan\left(f x + e\right)^{2} + {\left(2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{6} - 5 \, {\left(a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{5} d + {\left(3 \, a^{7} b^{2} + 8 \, a^{5} b^{4} + 7 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c^{4} d^{2} + {\left(a^{8} b - 3 \, a^{6} b^{3} - 9 \, a^{4} b^{5} - 5 \, a^{2} b^{7}\right)} c^{3} d^{3} - {\left(a^{9} - a^{7} b^{2} - 5 \, a^{5} b^{4} - 3 \, a^{3} b^{6}\right)} c^{2} d^{4} + {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} c d^{5} - {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d^{6}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^4 + 2*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4) - 2*((B*a^3*b^4 - 3*(A - C)*a^2*b^5 - 3*B*a*b^6 + (A - C)*b^7)*c^2 - 2*(2*B*a^4*b^3 - 5*(A - C)*a^3*b^4 - 3*B*a^2*b^5 - (A - C)*a*b^6 - B*b^7)*c*d - (3*C*a^6*b - 6*B*a^5*b^2 + (10*A - C)*a^4*b^3 - 3*B*a^3*b^4 + 9*A*a^2*b^5 - B*a*b^6 + 3*A*b^7)*d^2)*log(b*tan(f*x + e) + a)/((a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10)*c^4 - 4*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*c^3*d + 6*(a^8*b^2 + 3*a^6*b^4 + 3*a^4*b^6 + a^2*b^8)*c^2*d^2 - 4*(a^9*b + 3*a^7*b^3 + 3*a^5*b^5 + a^3*b^7)*c*d^3 + (a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6)*d^4) - 2*(3*C*b*c^4*d^2 - 4*B*b*c^3*d^3 + (B*a + (5*A + C)*b)*c^2*d^4 - 2*((A - C)*a + B*b)*c*d^5 - (B*a - 3*A*b)*d^6)*log(d*tan(f*x + e) + c)/(b^4*c^8 - 4*a*b^3*c^7*d - 4*a^3*b*c*d^7 + a^4*d^8 + 2*(3*a^2*b^2 + b^4)*c^6*d^2 - 4*(a^3*b + 2*a*b^3)*c^5*d^3 + (a^4 + 12*a^2*b^2 + b^4)*c^4*d^4 - 4*(2*a^3*b + a*b^3)*c^3*d^5 + 2*(a^4 + 3*a^2*b^2)*c^2*d^6) + ((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(tan(f*x + e)^2 + 1)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^4 + 2*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4) - ((C*a^4*b^2 - 3*B*a^3*b^3 + (5*A - 3*C)*a^2*b^4 + B*a*b^5 + A*b^6)*c^4 - (5*C*a^5*b - 7*B*a^4*b^2 + (9*A + C)*a^3*b^3 - 3*B*a^2*b^4 + 5*A*a*b^5)*c^3*d - (2*C*a^6 + 3*C*a^4*b^2 + 3*B*a^3*b^3 - 5*(A - C)*a^2*b^4 - B*a*b^5 - A*b^6)*c^2*d^2 + (2*B*a^6 - 5*C*a^5*b + 11*B*a^4*b^2 - (9*A + C)*a^3*b^3 + 5*B*a^2*b^4 - 5*A*a*b^5)*c*d^3 - 2*(A*a^6 + 2*A*a^4*b^2 + A*a^2*b^4)*d^4 - 2*((B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c^3*d + (3*C*a^4*b^2 - 3*B*a^3*b^3 + 2*(2*A + C)*a^2*b^4 - B*a*b^5 + (2*A + C)*b^6)*c^2*d^2 - (B*a^4*b^2 + B*a^2*b^4 + 2*(A - C)*a*b^5 + 2*B*b^6)*c*d^3 + ((A + 2*C)*a^4*b^2 - 3*B*a^3*b^3 + 6*A*a^2*b^4 - B*a*b^5 + 3*A*b^6)*d^4)*tan(f*x + e)^2 - (2*(B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c^4 + 3*(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 + (9*C*a^5*b - 7*B*a^4*b^2 + 9*(A + C)*a^3*b^3 - B*a^2*b^4 + (A + 8*C)*a*b^5 - 2*B*b^6)*c^2*d^2 - (4*B*a^5*b - 3*C*a^4*b^2 + 11*B*a^3*b^3 - 3*(A + C)*a^2*b^4 + 7*B*a*b^5 - 3*A*b^6)*c*d^3 + ((4*A + 5*C)*a^5*b - 7*B*a^4*b^2 + (17*A + C)*a^3*b^3 - 3*B*a^2*b^4 + 9*A*a*b^5)*d^4)*tan(f*x + e))/((a^6*b^3 + 2*a^4*b^5 + a^2*b^7)*c^6 - 3*(a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*c^5*d + (3*a^8*b + 7*a^6*b^3 + 5*a^4*b^5 + a^2*b^7)*c^4*d^2 - (a^9 + 5*a^7*b^2 + 7*a^5*b^4 + 3*a^3*b^6)*c^3*d^3 + 3*(a^8*b + 2*a^6*b^3 + a^4*b^5)*c^2*d^4 - (a^9 + 2*a^7*b^2 + a^5*b^4)*c*d^5 + ((a^4*b^5 + 2*a^2*b^7 + b^9)*c^5*d - 3*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^4*d^2 + (3*a^6*b^3 + 7*a^4*b^5 + 5*a^2*b^7 + b^9)*c^3*d^3 - (a^7*b^2 + 5*a^5*b^4 + 7*a^3*b^6 + 3*a*b^8)*c^2*d^4 + 3*(a^6*b^3 + 2*a^4*b^5 + a^2*b^7)*c*d^5 - (a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*d^6)*tan(f*x + e)^3 + ((a^4*b^5 + 2*a^2*b^7 + b^9)*c^6 - (a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^5*d - (3*a^6*b^3 + 5*a^4*b^5 + a^2*b^7 - b^9)*c^4*d^2 + (5*a^7*b^2 + 9*a^5*b^4 + 3*a^3*b^6 - a*b^8)*c^3*d^3 - (2*a^8*b + 7*a^6*b^3 + 8*a^4*b^5 + 3*a^2*b^7)*c^2*d^4 + 5*(a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*c*d^5 - 2*(a^8*b + 2*a^6*b^3 + a^4*b^5)*d^6)*tan(f*x + e)^2 + (2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^6 - 5*(a^6*b^3 + 2*a^4*b^5 + a^2*b^7)*c^5*d + (3*a^7*b^2 + 8*a^5*b^4 + 7*a^3*b^6 + 2*a*b^8)*c^4*d^2 + (a^8*b - 3*a^6*b^3 - 9*a^4*b^5 - 5*a^2*b^7)*c^3*d^3 - (a^9 - a^7*b^2 - 5*a^5*b^4 - 3*a^3*b^6)*c^2*d^4 + (a^8*b + 2*a^6*b^3 + a^4*b^5)*c*d^5 - (a^9 + 2*a^7*b^2 + a^5*b^4)*d^6)*tan(f*x + e)))/f","B",0
84,1,1110,0,0.602132," ","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=""maxima"")","\frac{\frac{2 \, C b^{3} \tan\left(f x + e\right)}{d^{3}} + \frac{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} + 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 - 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^{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)} d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left(3 \, C b^{3} c^{7} + 9 \, C b^{3} c^{5} d^{2} - {\left(3 \, C a b^{2} + B b^{3}\right)} c^{6} d - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4} 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^{3} 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^{2} 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 d^{6} + {\left({\left(A - C\right)} a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} d^{7}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{6} d^{4} + 3 \, c^{4} d^{6} + 3 \, c^{2} d^{8} + d^{10}} + \frac{{\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^{3} - 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 - 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 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)} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{5 \, C b^{3} c^{7} + A a^{3} d^{7} - 3 \, {\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 + 9 \, C\right)} b^{3}\right)} c^{5} d^{2} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, {\left(A - 7 \, C\right)} a b^{2} - 7 \, B b^{3}\right)} c^{4} d^{3} - {\left(3 \, B a^{3} + 3 \, {\left(3 \, A - 5 \, C\right)} a^{2} b - 15 \, B a b^{2} - 5 \, A b^{3}\right)} c^{3} d^{4} + {\left({\left(5 \, A - 3 \, C\right)} a^{3} - 9 \, B a^{2} b - 9 \, A a b^{2}\right)} c^{2} d^{5} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{6} + 2 \, {\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)}{c^{6} d^{4} + 2 \, c^{4} d^{6} + c^{2} d^{8} + {\left(c^{4} d^{6} + 2 \, c^{2} d^{8} + d^{10}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d^{5} + 2 \, c^{3} d^{7} + c d^{9}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*C*b^3*tan(f*x + e)/d^3 + 2*(((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c^3 + 3*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c^2*d - 3*((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c*d^2 - (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*(3*C*b^3*c^7 + 9*C*b^3*c^5*d^2 - (3*C*a*b^2 + B*b^3)*c^6*d - 3*(3*C*a*b^2 + B*b^3)*c^4*d^3 + (B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - 10*C)*b^3)*c^3*d^4 - 3*((A - C)*a^3 - 3*B*a^2*b - 3*(A - 2*C)*a*b^2 + 2*B*b^3)*c^2*d^5 - 3*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - A*b^3)*c*d^6 + ((A - C)*a^3 - 3*B*a^2*b - 3*A*a*b^2)*d^7)*log(d*tan(f*x + e) + c)/(c^6*d^4 + 3*c^4*d^6 + 3*c^2*d^8 + d^10) + ((B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c^3 - 3*((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*c^2*d - 3*(B*a^3 + 3*(A - C)*a^2*b - 3*B*a*b^2 - (A - C)*b^3)*c*d^2 + ((A - C)*a^3 - 3*B*a^2*b - 3*(A - C)*a*b^2 + B*b^3)*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - (5*C*b^3*c^7 + A*a^3*d^7 - 3*(3*C*a*b^2 + B*b^3)*c^6*d + (3*C*a^2*b + 3*B*a*b^2 + (A + 9*C)*b^3)*c^5*d^2 + (C*a^3 + 3*B*a^2*b + 3*(A - 7*C)*a*b^2 - 7*B*b^3)*c^4*d^3 - (3*B*a^3 + 3*(3*A - 5*C)*a^2*b - 15*B*a*b^2 - 5*A*b^3)*c^3*d^4 + ((5*A - 3*C)*a^3 - 9*B*a^2*b - 9*A*a*b^2)*c^2*d^5 + (B*a^3 + 3*A*a^2*b)*c*d^6 + 2*(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))/(c^6*d^4 + 2*c^4*d^6 + c^2*d^8 + (c^4*d^6 + 2*c^2*d^8 + d^10)*tan(f*x + e)^2 + 2*(c^5*d^5 + 2*c^3*d^7 + c*d^9)*tan(f*x + e)))/f","A",0
85,1,827,0,0.582343," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{2 \, {\left(C b^{2} c^{6} + 3 \, C b^{2} c^{4} d^{2} - {\left(B a^{2} + 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{3} d^{3} + 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b - {\left(A - 2 \, C\right)} b^{2}\right)} c^{2} d^{4} + 3 \, {\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 - A b^{2}\right)} d^{6}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{6} d^{3} + 3 \, c^{4} d^{5} + 3 \, c^{2} d^{7} + d^{9}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{3 \, C b^{2} c^{6} - A a^{2} d^{6} - {\left(2 \, C a b + B b^{2}\right)} c^{5} d - {\left(C a^{2} + 2 \, B a b + {\left(A - 7 \, C\right)} b^{2}\right)} c^{4} d^{2} + {\left(3 \, B a^{2} + 2 \, {\left(3 \, A - 5 \, C\right)} a b - 5 \, B b^{2}\right)} c^{3} d^{3} - {\left({\left(5 \, A - 3 \, C\right)} a^{2} - 6 \, B a b - 3 \, A b^{2}\right)} c^{2} d^{4} - {\left(B a^{2} + 2 \, A a b\right)} c d^{5} + 2 \, {\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)}{c^{6} d^{3} + 2 \, c^{4} d^{5} + c^{2} d^{7} + {\left(c^{4} d^{5} + 2 \, c^{2} d^{7} + d^{9}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d^{4} + 2 \, c^{3} d^{6} + c d^{8}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + 2*(C*b^2*c^6 + 3*C*b^2*c^4*d^2 - (B*a^2 + 2*(A - C)*a*b - B*b^2)*c^3*d^3 + 3*((A - C)*a^2 - 2*B*a*b - (A - 2*C)*b^2)*c^2*d^4 + 3*(B*a^2 + 2*(A - C)*a*b - B*b^2)*c*d^5 - ((A - C)*a^2 - 2*B*a*b - A*b^2)*d^6)*log(d*tan(f*x + e) + c)/(c^6*d^3 + 3*c^4*d^5 + 3*c^2*d^7 + d^9) + ((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(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (3*C*b^2*c^6 - A*a^2*d^6 - (2*C*a*b + B*b^2)*c^5*d - (C*a^2 + 2*B*a*b + (A - 7*C)*b^2)*c^4*d^2 + (3*B*a^2 + 2*(3*A - 5*C)*a*b - 5*B*b^2)*c^3*d^3 - ((5*A - 3*C)*a^2 - 6*B*a*b - 3*A*b^2)*c^2*d^4 - (B*a^2 + 2*A*a*b)*c*d^5 + 2*(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))/(c^6*d^3 + 2*c^4*d^5 + c^2*d^7 + (c^4*d^5 + 2*c^2*d^7 + d^9)*tan(f*x + e)^2 + 2*(c^5*d^4 + 2*c^3*d^6 + c*d^8)*tan(f*x + e)))/f","A",0
86,1,543,0,0.603785," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\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(d \tan\left(f x + e\right) + c\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{C b c^{5} + A a d^{5} + {\left(C a + B b\right)} c^{4} d - {\left(3 \, B a + {\left(3 \, A - 5 \, C\right)} b\right)} c^{3} d^{2} + {\left({\left(5 \, A - 3 \, C\right)} a - 3 \, B b\right)} c^{2} d^{3} + {\left(B a + A b\right)} c d^{4} + 2 \, {\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)}{c^{6} d^{2} + 2 \, c^{4} d^{4} + c^{2} d^{6} + {\left(c^{4} d^{4} + 2 \, c^{2} d^{6} + d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d^{3} + 2 \, c^{3} d^{5} + c d^{7}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*((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(d*tan(f*x + e) + c)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + ((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(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - (C*b*c^5 + A*a*d^5 + (C*a + B*b)*c^4*d - (3*B*a + (3*A - 5*C)*b)*c^3*d^2 + ((5*A - 3*C)*a - 3*B*b)*c^2*d^3 + (B*a + A*b)*c*d^4 + 2*(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))/(c^6*d^2 + 2*c^4*d^4 + c^2*d^6 + (c^4*d^4 + 2*c^2*d^6 + d^8)*tan(f*x + e)^2 + 2*(c^5*d^3 + 2*c^3*d^5 + c*d^7)*tan(f*x + e)))/f","A",0
87,1,367,0,0.643914," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(A - C\right)} c^{3} + 3 \, B c^{2} d - 3 \, {\left(A - C\right)} c d^{2} - B d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\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(d \tan\left(f x + e\right) + c\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{C c^{4} - 3 \, B c^{3} d + {\left(5 \, A - 3 \, C\right)} c^{2} d^{2} + B c d^{3} + A d^{4} - 2 \, {\left(B c^{2} d^{2} - 2 \, {\left(A - C\right)} c d^{3} - B d^{4}\right)} \tan\left(f x + e\right)}{c^{6} d + 2 \, c^{4} d^{3} + c^{2} d^{5} + {\left(c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{4} + c d^{6}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*((A - C)*c^3 + 3*B*c^2*d - 3*(A - C)*c*d^2 - B*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*(B*c^3 - 3*(A - C)*c^2*d - 3*B*c*d^2 + (A - C)*d^3)*log(d*tan(f*x + e) + c)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (B*c^3 - 3*(A - C)*c^2*d - 3*B*c*d^2 + (A - C)*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - (C*c^4 - 3*B*c^3*d + (5*A - 3*C)*c^2*d^2 + B*c*d^3 + A*d^4 - 2*(B*c^2*d^2 - 2*(A - C)*c*d^3 - B*d^4)*tan(f*x + e))/(c^6*d + 2*c^4*d^3 + c^2*d^5 + (c^4*d^3 + 2*c^2*d^5 + d^7)*tan(f*x + e)^2 + 2*(c^5*d^2 + 2*c^3*d^4 + c*d^6)*tan(f*x + e)))/f","A",0
88,1,1078,0,0.559940," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{{\left(a^{2} + b^{2}\right)} c^{6} + 3 \, {\left(a^{2} + b^{2}\right)} c^{4} d^{2} + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{4} + {\left(a^{2} + b^{2}\right)} d^{6}} + \frac{2 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{2} b^{3} + b^{5}\right)} c^{3} - 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{2} d + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} c d^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d^{3}} - \frac{2 \, {\left(C b^{2} c^{6} - 3 \, B b^{2} c^{5} d + 3 \, B a^{2} c d^{5} + 3 \, {\left(B a b + {\left(2 \, A - C\right)} b^{2}\right)} c^{4} d^{2} - {\left(B a^{2} + 8 \, {\left(A - C\right)} a b - B b^{2}\right)} c^{3} d^{3} + 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b + A b^{2}\right)} c^{2} d^{4} - {\left({\left(A - C\right)} a^{2} + B a b - A b^{2}\right)} d^{6}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{3} c^{9} - 3 \, a b^{2} c^{8} d + 3 \, a^{2} b c d^{8} - a^{3} d^{9} + 3 \, {\left(a^{2} b + b^{3}\right)} c^{7} d^{2} - {\left(a^{3} + 9 \, a b^{2}\right)} c^{6} d^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{5} d^{4} - 3 \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{4} d^{5} + {\left(9 \, a^{2} b + b^{3}\right)} c^{3} d^{6} - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d^{7}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{2} + b^{2}\right)} c^{6} + 3 \, {\left(a^{2} + b^{2}\right)} c^{4} d^{2} + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{4} + {\left(a^{2} + b^{2}\right)} d^{6}} + \frac{3 \, C b c^{5} - A a d^{5} - {\left(C a + 5 \, B b\right)} c^{4} d + {\left(3 \, B a + {\left(7 \, A - C\right)} b\right)} c^{3} d^{2} - {\left({\left(5 \, A - 3 \, C\right)} a + B b\right)} c^{2} d^{3} - {\left(B a - 3 \, A b\right)} c d^{4} + 2 \, {\left(C b c^{4} d - 2 \, B b c^{3} d^{2} - 2 \, {\left(A - C\right)} a c d^{4} + {\left(B a + {\left(3 \, A - C\right)} b\right)} c^{2} d^{3} - {\left(B a - A b\right)} d^{5}\right)} \tan\left(f x + e\right)}{b^{2} c^{8} - 2 \, a b c^{7} d - 4 \, a b c^{5} d^{3} - 2 \, a b c^{3} d^{5} + a^{2} c^{2} d^{6} + {\left(a^{2} + 2 \, b^{2}\right)} c^{6} d^{2} + {\left(2 \, a^{2} + b^{2}\right)} c^{4} d^{4} + {\left(b^{2} c^{6} d^{2} - 2 \, a b c^{5} d^{3} - 4 \, a b c^{3} d^{5} - 2 \, a b c d^{7} + a^{2} d^{8} + {\left(a^{2} + 2 \, b^{2}\right)} c^{4} d^{4} + {\left(2 \, a^{2} + b^{2}\right)} c^{2} d^{6}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(b^{2} c^{7} d - 2 \, a b c^{6} d^{2} - 4 \, a b c^{4} d^{4} - 2 \, a b c^{2} d^{6} + a^{2} c d^{7} + {\left(a^{2} + 2 \, b^{2}\right)} c^{5} d^{3} + {\left(2 \, a^{2} + b^{2}\right)} c^{3} d^{5}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/((a^2 + b^2)*c^6 + 3*(a^2 + b^2)*c^4*d^2 + 3*(a^2 + b^2)*c^2*d^4 + (a^2 + b^2)*d^6) + 2*(C*a^2*b^2 - B*a*b^3 + A*b^4)*log(b*tan(f*x + e) + a)/((a^2*b^3 + b^5)*c^3 - 3*(a^3*b^2 + a*b^4)*c^2*d + 3*(a^4*b + a^2*b^3)*c*d^2 - (a^5 + a^3*b^2)*d^3) - 2*(C*b^2*c^6 - 3*B*b^2*c^5*d + 3*B*a^2*c*d^5 + 3*(B*a*b + (2*A - C)*b^2)*c^4*d^2 - (B*a^2 + 8*(A - C)*a*b - B*b^2)*c^3*d^3 + 3*((A - C)*a^2 - 2*B*a*b + A*b^2)*c^2*d^4 - ((A - C)*a^2 + B*a*b - A*b^2)*d^6)*log(d*tan(f*x + e) + c)/(b^3*c^9 - 3*a*b^2*c^8*d + 3*a^2*b*c*d^8 - a^3*d^9 + 3*(a^2*b + b^3)*c^7*d^2 - (a^3 + 9*a*b^2)*c^6*d^3 + 3*(3*a^2*b + b^3)*c^5*d^4 - 3*(a^3 + 3*a*b^2)*c^4*d^5 + (9*a^2*b + b^3)*c^3*d^6 - 3*(a^3 + a*b^2)*c^2*d^7) + ((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(tan(f*x + e)^2 + 1)/((a^2 + b^2)*c^6 + 3*(a^2 + b^2)*c^4*d^2 + 3*(a^2 + b^2)*c^2*d^4 + (a^2 + b^2)*d^6) + (3*C*b*c^5 - A*a*d^5 - (C*a + 5*B*b)*c^4*d + (3*B*a + (7*A - C)*b)*c^3*d^2 - ((5*A - 3*C)*a + B*b)*c^2*d^3 - (B*a - 3*A*b)*c*d^4 + 2*(C*b*c^4*d - 2*B*b*c^3*d^2 - 2*(A - C)*a*c*d^4 + (B*a + (3*A - C)*b)*c^2*d^3 - (B*a - A*b)*d^5)*tan(f*x + e))/(b^2*c^8 - 2*a*b*c^7*d - 4*a*b*c^5*d^3 - 2*a*b*c^3*d^5 + a^2*c^2*d^6 + (a^2 + 2*b^2)*c^6*d^2 + (2*a^2 + b^2)*c^4*d^4 + (b^2*c^6*d^2 - 2*a*b*c^5*d^3 - 4*a*b*c^3*d^5 - 2*a*b*c*d^7 + a^2*d^8 + (a^2 + 2*b^2)*c^4*d^4 + (2*a^2 + b^2)*c^2*d^6)*tan(f*x + e)^2 + 2*(b^2*c^7*d - 2*a*b*c^6*d^2 - 4*a*b*c^4*d^4 - 2*a*b*c^2*d^6 + a^2*c*d^7 + (a^2 + 2*b^2)*c^5*d^3 + (2*a^2 + b^2)*c^3*d^5)*tan(f*x + e)))/f","B",0
89,1,2537,0,0.787317," ","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=""maxima"")","\frac{\frac{2 \, {\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)} {\left(f x + e\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{4} d^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{6}} - \frac{2 \, {\left({\left(B a^{2} b^{4} - 2 \, {\left(A - C\right)} a b^{5} - B b^{6}\right)} c + {\left(3 \, C a^{4} b^{2} - 4 \, B a^{3} b^{3} + {\left(5 \, A + C\right)} a^{2} b^{4} - 2 \, B a b^{5} + 3 \, A b^{6}\right)} d\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} c^{4} - 4 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c^{3} d + 6 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} d^{2} - 4 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} c d^{3} + {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d^{4}} + \frac{2 \, {\left(3 \, C b^{2} c^{6} d - 6 \, B b^{2} c^{5} d^{2} + {\left(4 \, B a b + {\left(10 \, A - C\right)} b^{2}\right)} c^{4} d^{3} - {\left(B a^{2} + 10 \, {\left(A - C\right)} a b + 3 \, B b^{2}\right)} c^{3} d^{4} + 3 \, {\left({\left(A - C\right)} a^{2} - 2 \, B a b + 3 \, A b^{2}\right)} c^{2} d^{5} + {\left(3 \, B a^{2} - 2 \, {\left(A - C\right)} a b - B b^{2}\right)} c d^{6} - {\left({\left(A - C\right)} a^{2} + 2 \, B a b - 3 \, A b^{2}\right)} d^{7}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{4} c^{10} - 4 \, a b^{3} c^{9} d - 4 \, a^{3} b c d^{9} + a^{4} d^{10} + 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} c^{8} d^{2} - 4 \, {\left(a^{3} b + 3 \, a b^{3}\right)} c^{7} d^{3} + {\left(a^{4} + 18 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{6} d^{4} - 12 \, {\left(a^{3} b + a b^{3}\right)} c^{5} d^{5} + {\left(3 \, a^{4} + 18 \, a^{2} b^{2} + b^{4}\right)} c^{4} d^{6} - 4 \, {\left(3 \, a^{3} b + a b^{3}\right)} c^{3} d^{7} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c^{2} d^{8}} + \frac{{\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(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{4} d^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{6}} - \frac{2 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c^{6} + 5 \, {\left(C a^{3} b + C a b^{3}\right)} c^{5} d - {\left(C a^{4} + 7 \, B a^{3} b - 3 \, C a^{2} b^{2} + 11 \, B a b^{3} - 4 \, A b^{4}\right)} c^{4} d^{2} + {\left(3 \, B a^{4} + {\left(9 \, A + C\right)} a^{3} b + 3 \, B a^{2} b^{2} + {\left(9 \, A + C\right)} a b^{3}\right)} c^{3} d^{3} - {\left({\left(5 \, A - 3 \, C\right)} a^{4} + 3 \, B a^{3} b + 5 \, {\left(A - C\right)} a^{2} b^{2} + 5 \, B a b^{3} - 2 \, A b^{4}\right)} c^{2} d^{4} - {\left(B a^{4} - 5 \, A a^{3} b + B a^{2} b^{2} - 5 \, A a b^{3}\right)} c d^{5} - {\left(A a^{4} + A a^{2} b^{2}\right)} d^{6} + 2 \, {\left({\left(3 \, C a^{2} b^{2} - B a b^{3} + {\left(A + 2 \, C\right)} b^{4}\right)} c^{4} d^{2} - 3 \, {\left(B a^{2} b^{2} + B b^{4}\right)} c^{3} d^{3} + {\left(B a^{3} b + 2 \, {\left(2 \, A + C\right)} a^{2} b^{2} - B a b^{3} + 6 \, A b^{4}\right)} c^{2} d^{4} - {\left(2 \, {\left(A - C\right)} a^{3} b + B a^{2} b^{2} + 2 \, {\left(A - C\right)} a b^{3} + B b^{4}\right)} c d^{5} - {\left(B a^{3} b - {\left(2 \, A + C\right)} a^{2} b^{2} + 2 \, B a b^{3} - 3 \, A b^{4}\right)} d^{6}\right)} \tan\left(f x + e\right)^{2} + {\left({\left(9 \, C a^{2} b^{2} - 4 \, B a b^{3} + {\left(4 \, A + 5 \, C\right)} b^{4}\right)} c^{5} d + {\left(3 \, C a^{3} b - 7 \, B a^{2} b^{2} + 3 \, C a b^{3} - 7 \, B b^{4}\right)} c^{4} d^{2} - {\left(3 \, B a^{3} b - 9 \, {\left(A + C\right)} a^{2} b^{2} + 11 \, B a b^{3} - {\left(17 \, A + C\right)} b^{4}\right)} c^{3} d^{3} + {\left(2 \, B a^{4} + 3 \, {\left(A + C\right)} a^{3} b - B a^{2} b^{2} + 3 \, {\left(A + C\right)} a b^{3} - 3 \, B b^{4}\right)} c^{2} d^{4} - {\left(4 \, {\left(A - C\right)} a^{4} + 3 \, B a^{3} b - {\left(A + 8 \, C\right)} a^{2} b^{2} + 7 \, B a b^{3} - 9 \, A b^{4}\right)} c d^{5} - {\left(2 \, B a^{4} - 3 \, A a^{3} b + 2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} d^{6}\right)} \tan\left(f x + e\right)}{{\left(a^{3} b^{3} + a b^{5}\right)} c^{9} - 3 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c^{8} d + {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} c^{7} d^{2} - {\left(a^{6} + 7 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} c^{6} d^{3} + {\left(6 \, a^{5} b + 7 \, a^{3} b^{3} + a b^{5}\right)} c^{5} d^{4} - {\left(2 \, a^{6} + 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} c^{4} d^{5} + 3 \, {\left(a^{5} b + a^{3} b^{3}\right)} c^{3} d^{6} - {\left(a^{6} + a^{4} b^{2}\right)} c^{2} d^{7} + {\left({\left(a^{2} b^{4} + b^{6}\right)} c^{7} d^{2} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{6} d^{3} + {\left(3 \, a^{4} b^{2} + 5 \, a^{2} b^{4} + 2 \, b^{6}\right)} c^{5} d^{4} - {\left(a^{5} b + 7 \, a^{3} b^{3} + 6 \, a b^{5}\right)} c^{4} d^{5} + {\left(6 \, a^{4} b^{2} + 7 \, a^{2} b^{4} + b^{6}\right)} c^{3} d^{6} - {\left(2 \, a^{5} b + 5 \, a^{3} b^{3} + 3 \, a b^{5}\right)} c^{2} d^{7} + 3 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c d^{8} - {\left(a^{5} b + a^{3} b^{3}\right)} d^{9}\right)} \tan\left(f x + e\right)^{3} + {\left(2 \, {\left(a^{2} b^{4} + b^{6}\right)} c^{8} d - 5 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{7} d^{2} + {\left(3 \, a^{4} b^{2} + 7 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{6} d^{3} + {\left(a^{5} b - 9 \, a^{3} b^{3} - 10 \, a b^{5}\right)} c^{5} d^{4} - {\left(a^{6} - 5 \, a^{4} b^{2} - 8 \, a^{2} b^{4} - 2 \, b^{6}\right)} c^{4} d^{5} + {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} - 5 \, a b^{5}\right)} c^{3} d^{6} - {\left(2 \, a^{6} - a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} c^{2} d^{7} + {\left(a^{5} b + a^{3} b^{3}\right)} c d^{8} - {\left(a^{6} + a^{4} b^{2}\right)} d^{9}\right)} \tan\left(f x + e\right)^{2} + {\left({\left(a^{2} b^{4} + b^{6}\right)} c^{9} - {\left(a^{3} b^{3} + a b^{5}\right)} c^{8} d - {\left(3 \, a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c^{7} d^{2} + {\left(5 \, a^{5} b + 3 \, a^{3} b^{3} - 2 \, a b^{5}\right)} c^{6} d^{3} - {\left(2 \, a^{6} + 8 \, a^{4} b^{2} + 5 \, a^{2} b^{4} - b^{6}\right)} c^{5} d^{4} + {\left(10 \, a^{5} b + 9 \, a^{3} b^{3} - a b^{5}\right)} c^{4} d^{5} - {\left(4 \, a^{6} + 7 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} c^{3} d^{6} + 5 \, {\left(a^{5} b + a^{3} b^{3}\right)} c^{2} d^{7} - 2 \, {\left(a^{6} + a^{4} b^{2}\right)} c d^{8}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(((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 + e)/((a^4 + 2*a^2*b^2 + b^4)*c^6 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^4*d^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^4 + (a^4 + 2*a^2*b^2 + b^4)*d^6) - 2*((B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c + (3*C*a^4*b^2 - 4*B*a^3*b^3 + (5*A + C)*a^2*b^4 - 2*B*a*b^5 + 3*A*b^6)*d)*log(b*tan(f*x + e) + a)/((a^4*b^4 + 2*a^2*b^6 + b^8)*c^4 - 4*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^3*d + 6*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^2*d^2 - 4*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c*d^3 + (a^8 + 2*a^6*b^2 + a^4*b^4)*d^4) + 2*(3*C*b^2*c^6*d - 6*B*b^2*c^5*d^2 + (4*B*a*b + (10*A - C)*b^2)*c^4*d^3 - (B*a^2 + 10*(A - C)*a*b + 3*B*b^2)*c^3*d^4 + 3*((A - C)*a^2 - 2*B*a*b + 3*A*b^2)*c^2*d^5 + (3*B*a^2 - 2*(A - C)*a*b - B*b^2)*c*d^6 - ((A - C)*a^2 + 2*B*a*b - 3*A*b^2)*d^7)*log(d*tan(f*x + e) + c)/(b^4*c^10 - 4*a*b^3*c^9*d - 4*a^3*b*c*d^9 + a^4*d^10 + 3*(2*a^2*b^2 + b^4)*c^8*d^2 - 4*(a^3*b + 3*a*b^3)*c^7*d^3 + (a^4 + 18*a^2*b^2 + 3*b^4)*c^6*d^4 - 12*(a^3*b + a*b^3)*c^5*d^5 + (3*a^4 + 18*a^2*b^2 + b^4)*c^4*d^6 - 4*(3*a^3*b + a*b^3)*c^3*d^7 + 3*(a^4 + 2*a^2*b^2)*c^2*d^8) + ((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(tan(f*x + e)^2 + 1)/((a^4 + 2*a^2*b^2 + b^4)*c^6 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^4*d^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^4 + (a^4 + 2*a^2*b^2 + b^4)*d^6) - (2*(C*a^2*b^2 - B*a*b^3 + A*b^4)*c^6 + 5*(C*a^3*b + C*a*b^3)*c^5*d - (C*a^4 + 7*B*a^3*b - 3*C*a^2*b^2 + 11*B*a*b^3 - 4*A*b^4)*c^4*d^2 + (3*B*a^4 + (9*A + C)*a^3*b + 3*B*a^2*b^2 + (9*A + C)*a*b^3)*c^3*d^3 - ((5*A - 3*C)*a^4 + 3*B*a^3*b + 5*(A - C)*a^2*b^2 + 5*B*a*b^3 - 2*A*b^4)*c^2*d^4 - (B*a^4 - 5*A*a^3*b + B*a^2*b^2 - 5*A*a*b^3)*c*d^5 - (A*a^4 + A*a^2*b^2)*d^6 + 2*((3*C*a^2*b^2 - B*a*b^3 + (A + 2*C)*b^4)*c^4*d^2 - 3*(B*a^2*b^2 + B*b^4)*c^3*d^3 + (B*a^3*b + 2*(2*A + C)*a^2*b^2 - B*a*b^3 + 6*A*b^4)*c^2*d^4 - (2*(A - C)*a^3*b + B*a^2*b^2 + 2*(A - C)*a*b^3 + B*b^4)*c*d^5 - (B*a^3*b - (2*A + C)*a^2*b^2 + 2*B*a*b^3 - 3*A*b^4)*d^6)*tan(f*x + e)^2 + ((9*C*a^2*b^2 - 4*B*a*b^3 + (4*A + 5*C)*b^4)*c^5*d + (3*C*a^3*b - 7*B*a^2*b^2 + 3*C*a*b^3 - 7*B*b^4)*c^4*d^2 - (3*B*a^3*b - 9*(A + C)*a^2*b^2 + 11*B*a*b^3 - (17*A + C)*b^4)*c^3*d^3 + (2*B*a^4 + 3*(A + C)*a^3*b - B*a^2*b^2 + 3*(A + C)*a*b^3 - 3*B*b^4)*c^2*d^4 - (4*(A - C)*a^4 + 3*B*a^3*b - (A + 8*C)*a^2*b^2 + 7*B*a*b^3 - 9*A*b^4)*c*d^5 - (2*B*a^4 - 3*A*a^3*b + 2*B*a^2*b^2 - 3*A*a*b^3)*d^6)*tan(f*x + e))/((a^3*b^3 + a*b^5)*c^9 - 3*(a^4*b^2 + a^2*b^4)*c^8*d + (3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*c^7*d^2 - (a^6 + 7*a^4*b^2 + 6*a^2*b^4)*c^6*d^3 + (6*a^5*b + 7*a^3*b^3 + a*b^5)*c^5*d^4 - (2*a^6 + 5*a^4*b^2 + 3*a^2*b^4)*c^4*d^5 + 3*(a^5*b + a^3*b^3)*c^3*d^6 - (a^6 + a^4*b^2)*c^2*d^7 + ((a^2*b^4 + b^6)*c^7*d^2 - 3*(a^3*b^3 + a*b^5)*c^6*d^3 + (3*a^4*b^2 + 5*a^2*b^4 + 2*b^6)*c^5*d^4 - (a^5*b + 7*a^3*b^3 + 6*a*b^5)*c^4*d^5 + (6*a^4*b^2 + 7*a^2*b^4 + b^6)*c^3*d^6 - (2*a^5*b + 5*a^3*b^3 + 3*a*b^5)*c^2*d^7 + 3*(a^4*b^2 + a^2*b^4)*c*d^8 - (a^5*b + a^3*b^3)*d^9)*tan(f*x + e)^3 + (2*(a^2*b^4 + b^6)*c^8*d - 5*(a^3*b^3 + a*b^5)*c^7*d^2 + (3*a^4*b^2 + 7*a^2*b^4 + 4*b^6)*c^6*d^3 + (a^5*b - 9*a^3*b^3 - 10*a*b^5)*c^5*d^4 - (a^6 - 5*a^4*b^2 - 8*a^2*b^4 - 2*b^6)*c^4*d^5 + (2*a^5*b - 3*a^3*b^3 - 5*a*b^5)*c^3*d^6 - (2*a^6 - a^4*b^2 - 3*a^2*b^4)*c^2*d^7 + (a^5*b + a^3*b^3)*c*d^8 - (a^6 + a^4*b^2)*d^9)*tan(f*x + e)^2 + ((a^2*b^4 + b^6)*c^9 - (a^3*b^3 + a*b^5)*c^8*d - (3*a^4*b^2 + a^2*b^4 - 2*b^6)*c^7*d^2 + (5*a^5*b + 3*a^3*b^3 - 2*a*b^5)*c^6*d^3 - (2*a^6 + 8*a^4*b^2 + 5*a^2*b^4 - b^6)*c^5*d^4 + (10*a^5*b + 9*a^3*b^3 - a*b^5)*c^4*d^5 - (4*a^6 + 7*a^4*b^2 + 3*a^2*b^4)*c^3*d^6 + 5*(a^5*b + a^3*b^3)*c^2*d^7 - 2*(a^6 + a^4*b^2)*c*d^8)*tan(f*x + e)))/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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,0,0,0,0.000000," ","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=""maxima"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)*sqrt(d*tan(f*x + e) + c), x)","F",0
93,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*sqrt(d*tan(f*x + e) + c), x)","F",0
94,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
95,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
96,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(d*tan(f*x + e) + c)^(3/2), x)","F",0
101,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
102,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
103,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
108,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
109,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A}{\sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)/sqrt(d*tan(f*x + e) + c), x)","F",0
114,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
115,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
121,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
127,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,0,0,0,0.000000," ","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=""maxima"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^(3/2)*sqrt(d*tan(f*x + e) + c), x)","F",0
130,0,0,0,0.000000," ","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=""maxima"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} \sqrt{b \tan\left(f x + e\right) + a} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*sqrt(b*tan(f*x + e) + a)*sqrt(d*tan(f*x + e) + c), x)","F",0
131,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} \sqrt{d \tan\left(f x + e\right) + c}}{\sqrt{b \tan\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*sqrt(d*tan(f*x + e) + c)/sqrt(b*tan(f*x + e) + a), x)","F",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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,0,0,0,0.000000," ","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=""maxima"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^(3/2)*(d*tan(f*x + e) + c)^(3/2), x)","F",0
136,0,0,0,0.000000," ","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=""maxima"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} \sqrt{b \tan\left(f x + e\right) + a} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*sqrt(b*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^(3/2), x)","F",0
137,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{b \tan\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(d*tan(f*x + e) + c)^(3/2)/sqrt(b*tan(f*x + e) + a), x)","F",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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{\sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^(3/2)/sqrt(d*tan(f*x + e) + c), x)","F",0
149,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} \sqrt{b \tan\left(f x + e\right) + a}}{\sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*sqrt(b*tan(f*x + e) + a)/sqrt(d*tan(f*x + e) + c), x)","F",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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,0,0,0,0.000000," ","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=""maxima"")","\int \frac{C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A}{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)/((b*tan(f*x + e) + a)^(3/2)*sqrt(d*tan(f*x + e) + c)), x)","F",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,0,0,0,0.000000," ","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=""maxima"")","\int \frac{C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A}{\sqrt{b \tan\left(f x + e\right) + a} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)/(sqrt(b*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^(3/2)), x)","F",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^n*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m} {\left(d \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m*(d*tan(f*x + e) + c)^n, x)","F",0
165,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^3*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^2*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(d \tan\left(f x + e\right) + c\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(d*tan(f*x + e) + c)*(b*tan(f*x + e) + a)^m, x)","F",0
168,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m, x)","F",0
169,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}}{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c), x)","F",0
170,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \tan\left(f x + e\right)^{2} + B \tan\left(f x + e\right) + A\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((C*tan(f*x + e)^2 + B*tan(f*x + e) + A)*(b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^2, x)","F",0
171,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
