1,1,286,0,0.551347," ","integrate(x^3*tan(b*x+a),x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{3} \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, b^{3} x^{3} \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + 6 \, b x {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 \, b x {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 i \, {\rm polylog}\left(4, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 3 i \, {\rm polylog}\left(4, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right)}{8 \, b^{4}}"," ",0,"-1/8*(4*b^3*x^3*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 4*b^3*x^3*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 6*I*b^2*x^2*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - 6*I*b^2*x^2*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + 6*b*x*polylog(3, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 6*b*x*polylog(3, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 3*I*polylog(4, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 3*I*polylog(4, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)))/b^4","C",0
2,1,200,0,0.568172," ","integrate(x^2*tan(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, b^{2} x^{2} \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, b^{2} x^{2} \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 i \, b x {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 2 i \, b x {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right)}{4 \, b^{3}}"," ",0,"-1/4*(2*b^2*x^2*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 2*b^2*x^2*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 2*I*b*x*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - 2*I*b*x*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + polylog(3, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + polylog(3, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)))/b^3","C",0
3,1,122,0,0.553246," ","integrate(x*tan(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, b x \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, b x \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + i \, {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - i \, {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right)}{4 \, b^{2}}"," ",0,"-1/4*(2*b*x*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 2*b*x*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + I*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - I*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1))/b^2","B",0
4,0,0,0,0.574659," ","integrate(tan(b*x+a)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(b x + a\right)}{x}, x\right)"," ",0,"integral(tan(b*x + a)/x, x)","F",0
5,0,0,0,0.467719," ","integrate(tan(b*x+a)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(b x + a\right)}{x^{2}}, x\right)"," ",0,"integral(tan(b*x + a)/x^2, x)","F",0
6,1,225,0,0.640514," ","integrate(x^3*tan(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{4} x^{4} - 4 \, b^{3} x^{3} \tan\left(b x + a\right) - 6 \, b^{2} x^{2} \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, b^{2} x^{2} \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 i \, b x {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + 6 i \, b x {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 3 \, {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 \, {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right)}{4 \, b^{4}}"," ",0,"-1/4*(b^4*x^4 - 4*b^3*x^3*tan(b*x + a) - 6*b^2*x^2*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 6*b^2*x^2*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 6*I*b*x*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + 6*I*b*x*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - 3*polylog(3, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 3*polylog(3, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)))/b^4","C",0
7,1,144,0,0.534369," ","integrate(x^2*tan(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{3} x^{3} - 6 \, b^{2} x^{2} \tan\left(b x + a\right) - 6 \, b x \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, b x \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 i \, {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + 3 i \, {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right)}{6 \, b^{3}}"," ",0,"-1/6*(2*b^3*x^3 - 6*b^2*x^2*tan(b*x + a) - 6*b*x*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 6*b*x*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 3*I*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + 3*I*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1))/b^3","B",0
8,1,38,0,0.571847," ","integrate(x*tan(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{2} x^{2} - 2 \, b x \tan\left(b x + a\right) - \log\left(\frac{1}{\tan\left(b x + a\right)^{2} + 1}\right)}{2 \, b^{2}}"," ",0,"-1/2*(b^2*x^2 - 2*b*x*tan(b*x + a) - log(1/(tan(b*x + a)^2 + 1)))/b^2","A",0
9,0,0,0,0.454197," ","integrate(tan(b*x+a)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(b x + a\right)^{2}}{x}, x\right)"," ",0,"integral(tan(b*x + a)^2/x, x)","F",0
10,0,0,0,0.581428," ","integrate(tan(b*x+a)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(b x + a\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(tan(b*x + a)^2/x^2, x)","F",0
11,1,342,0,0.569721," ","integrate(x^3*tan(b*x+a)^3,x, algorithm=""fricas"")","\frac{4 \, b^{3} x^{3} \tan\left(b x + a\right)^{2} + 4 \, b^{3} x^{3} - 12 \, b^{2} x^{2} \tan\left(b x + a\right) + 6 \, b x {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 \, b x {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + {\left(6 i \, b^{2} x^{2} - 6 i\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-6 i \, b^{2} x^{2} + 6 i\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + 4 \, {\left(b^{3} x^{3} - 3 \, b x\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(b^{3} x^{3} - 3 \, b x\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 i \, {\rm polylog}\left(4, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 3 i \, {\rm polylog}\left(4, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right)}{8 \, b^{4}}"," ",0,"1/8*(4*b^3*x^3*tan(b*x + a)^2 + 4*b^3*x^3 - 12*b^2*x^2*tan(b*x + a) + 6*b*x*polylog(3, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 6*b*x*polylog(3, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + (6*I*b^2*x^2 - 6*I)*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + (-6*I*b^2*x^2 + 6*I)*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + 4*(b^3*x^3 - 3*b*x)*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 4*(b^3*x^3 - 3*b*x)*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 3*I*polylog(4, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 3*I*polylog(4, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)))/b^4","C",0
12,1,240,0,0.535966," ","integrate(x^2*tan(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} \tan\left(b x + a\right)^{2} + 2 \, b^{2} x^{2} + 2 i \, b x {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 2 i \, b x {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 4 \, b x \tan\left(b x + a\right) + 2 \, {\left(b^{2} x^{2} - 1\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b^{2} x^{2} - 1\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right)}{4 \, b^{3}}"," ",0,"1/4*(2*b^2*x^2*tan(b*x + a)^2 + 2*b^2*x^2 + 2*I*b*x*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - 2*I*b*x*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - 4*b*x*tan(b*x + a) + 2*(b^2*x^2 - 1)*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 2*(b^2*x^2 - 1)*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + polylog(3, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + polylog(3, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)))/b^3","C",0
13,1,146,0,0.495300," ","integrate(x*tan(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, b x \tan\left(b x + a\right)^{2} + 2 \, b x \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, b x \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, b x + i \, {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - i \, {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 2 \, \tan\left(b x + a\right)}{4 \, b^{2}}"," ",0,"1/4*(2*b*x*tan(b*x + a)^2 + 2*b*x*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 2*b*x*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 2*b*x + I*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - I*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - 2*tan(b*x + a))/b^2","B",0
14,0,0,0,0.463512," ","integrate(tan(b*x+a)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(b x + a\right)^{3}}{x}, x\right)"," ",0,"integral(tan(b*x + a)^3/x, x)","F",0
15,0,0,0,0.573417," ","integrate(tan(b*x+a)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(b x + a\right)^{3}}{x^{2}}, x\right)"," ",0,"integral(tan(b*x + a)^3/x^2, x)","F",0
16,1,16,0,0.609604," ","integrate(-4*x/b/tan(b*x+a)^(1/2)+x^2*tan(b*x+a)^(1/2)+x^2/tan(b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, x^{2}}{b \sqrt{\tan\left(b x + a\right)}}"," ",0,"-2*x^2/(b*sqrt(tan(b*x + a)))","A",0
17,1,15,0,0.860656," ","integrate(x^2/tan(b*x^2+a)^(1/2)+tan(b*x^2+a)^(1/2)/b+x^2*tan(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{x \sqrt{\tan\left(b x^{2} + a\right)}}{b}"," ",0,"x*sqrt(tan(b*x^2 + a))/b","A",0
18,1,162,0,0.505733," ","integrate((d*x+c)^3/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(4 i \, d^{3} f^{3} x^{3} + 4 i \, c^{3} f^{3} + 6 \, c^{2} d f^{2} - 6 i \, c d^{2} f - 3 \, d^{3} + {\left(12 i \, c d^{2} f^{3} + 6 \, d^{3} f^{2}\right)} x^{2} + {\left(12 i \, c^{2} d f^{3} + 12 \, c d^{2} f^{2} - 6 i \, d^{3} f\right)} x + 2 \, {\left(d^{3} f^{4} x^{4} + 4 \, c d^{2} f^{4} x^{3} + 6 \, c^{2} d f^{4} x^{2} + 4 \, c^{3} f^{4} x\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{16 \, a f^{4}}"," ",0,"1/16*(4*I*d^3*f^3*x^3 + 4*I*c^3*f^3 + 6*c^2*d*f^2 - 6*I*c*d^2*f - 3*d^3 + (12*I*c*d^2*f^3 + 6*d^3*f^2)*x^2 + (12*I*c^2*d*f^3 + 12*c*d^2*f^2 - 6*I*d^3*f)*x + 2*(d^3*f^4*x^4 + 4*c*d^2*f^4*x^3 + 6*c^2*d*f^4*x^2 + 4*c^3*f^4*x)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a*f^4)","A",0
19,1,104,0,0.562936," ","integrate((d*x+c)^2/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(6 i \, d^{2} f^{2} x^{2} + 6 i \, c^{2} f^{2} + 6 \, c d f - 3 i \, d^{2} + {\left(12 i \, c d f^{2} + 6 \, d^{2} f\right)} x + 4 \, {\left(d^{2} f^{3} x^{3} + 3 \, c d f^{3} x^{2} + 3 \, c^{2} f^{3} x\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{24 \, a f^{3}}"," ",0,"1/24*(6*I*d^2*f^2*x^2 + 6*I*c^2*f^2 + 6*c*d*f - 3*I*d^2 + (12*I*c*d*f^2 + 6*d^2*f)*x + 4*(d^2*f^3*x^3 + 3*c*d*f^3*x^2 + 3*c^2*f^3*x)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a*f^3)","A",0
20,1,55,0,0.520586," ","integrate((d*x+c)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 i \, d f x + 2 i \, c f + 2 \, {\left(d f^{2} x^{2} + 2 \, c f^{2} x\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + d\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a f^{2}}"," ",0,"1/8*(2*I*d*f*x + 2*I*c*f + 2*(d*f^2*x^2 + 2*c*f^2*x)*e^(2*I*f*x + 2*I*e) + d)*e^(-2*I*f*x - 2*I*e)/(a*f^2)","A",0
21,1,49,0,0.575418," ","integrate(1/(d*x+c)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\rm Ei}\left(\frac{-2 i \, d f x - 2 i \, c f}{d}\right) e^{\left(\frac{-2 i \, d e + 2 i \, c f}{d}\right)} + \log\left(\frac{d x + c}{d}\right)}{2 \, a d}"," ",0,"1/2*(Ei((-2*I*d*f*x - 2*I*c*f)/d)*e^((-2*I*d*e + 2*I*c*f)/d) + log((d*x + c)/d))/(a*d)","A",0
22,1,84,0,0.581260," ","integrate(1/(d*x+c)^2/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left({\left({\left(-2 i \, d f x - 2 i \, c f\right)} {\rm Ei}\left(\frac{-2 i \, d f x - 2 i \, c f}{d}\right) e^{\left(\frac{-2 i \, d e + 2 i \, c f}{d}\right)} - d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - d\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(a d^{3} x + a c d^{2}\right)}}"," ",0,"1/2*(((-2*I*d*f*x - 2*I*c*f)*Ei((-2*I*d*f*x - 2*I*c*f)/d)*e^((-2*I*d*e + 2*I*c*f)/d) - d)*e^(2*I*f*x + 2*I*e) - d)*e^(-2*I*f*x - 2*I*e)/(a*d^3*x + a*c*d^2)","A",0
23,1,128,0,0.744594," ","integrate(1/(d*x+c)^3/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 i \, d^{2} f x + 2 i \, c d f - d^{2} - {\left(4 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} {\rm Ei}\left(\frac{-2 i \, d f x - 2 i \, c f}{d}\right) e^{\left(\frac{-2 i \, d e + 2 i \, c f}{d}\right)} + d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, {\left(a d^{5} x^{2} + 2 \, a c d^{4} x + a c^{2} d^{3}\right)}}"," ",0,"1/4*(2*I*d^2*f*x + 2*I*c*d*f - d^2 - (4*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*Ei((-2*I*d*f*x - 2*I*c*f)/d)*e^((-2*I*d*e + 2*I*c*f)/d) + d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a*d^5*x^2 + 2*a*c*d^4*x + a*c^2*d^3)","A",0
24,1,262,0,0.536345," ","integrate((d*x+c)^3/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(32 i \, d^{3} f^{3} x^{3} + 32 i \, c^{3} f^{3} + 24 \, c^{2} d f^{2} - 12 i \, c d^{2} f - 3 \, d^{3} + {\left(96 i \, c d^{2} f^{3} + 24 \, d^{3} f^{2}\right)} x^{2} + {\left(96 i \, c^{2} d f^{3} + 48 \, c d^{2} f^{2} - 12 i \, d^{3} f\right)} x + 32 \, {\left(d^{3} f^{4} x^{4} + 4 \, c d^{2} f^{4} x^{3} + 6 \, c^{2} d f^{4} x^{2} + 4 \, c^{3} f^{4} x\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(128 i \, d^{3} f^{3} x^{3} + 128 i \, c^{3} f^{3} + 192 \, c^{2} d f^{2} - 192 i \, c d^{2} f - 96 \, d^{3} + {\left(384 i \, c d^{2} f^{3} + 192 \, d^{3} f^{2}\right)} x^{2} + {\left(384 i \, c^{2} d f^{3} + 384 \, c d^{2} f^{2} - 192 i \, d^{3} f\right)} x\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{512 \, a^{2} f^{4}}"," ",0,"1/512*(32*I*d^3*f^3*x^3 + 32*I*c^3*f^3 + 24*c^2*d*f^2 - 12*I*c*d^2*f - 3*d^3 + (96*I*c*d^2*f^3 + 24*d^3*f^2)*x^2 + (96*I*c^2*d*f^3 + 48*c*d^2*f^2 - 12*I*d^3*f)*x + 32*(d^3*f^4*x^4 + 4*c*d^2*f^4*x^3 + 6*c^2*d*f^4*x^2 + 4*c^3*f^4*x)*e^(4*I*f*x + 4*I*e) + (128*I*d^3*f^3*x^3 + 128*I*c^3*f^3 + 192*c^2*d*f^2 - 192*I*c*d^2*f - 96*d^3 + (384*I*c*d^2*f^3 + 192*d^3*f^2)*x^2 + (384*I*c^2*d*f^3 + 384*c*d^2*f^2 - 192*I*d^3*f)*x)*e^(2*I*f*x + 2*I*e))*e^(-4*I*f*x - 4*I*e)/(a^2*f^4)","A",0
25,1,160,0,0.637600," ","integrate((d*x+c)^2/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(24 i \, d^{2} f^{2} x^{2} + 24 i \, c^{2} f^{2} + 12 \, c d f - 3 i \, d^{2} + {\left(48 i \, c d f^{2} + 12 \, d^{2} f\right)} x + 32 \, {\left(d^{2} f^{3} x^{3} + 3 \, c d f^{3} x^{2} + 3 \, c^{2} f^{3} x\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(96 i \, d^{2} f^{2} x^{2} + 96 i \, c^{2} f^{2} + 96 \, c d f - 48 i \, d^{2} + {\left(192 i \, c d f^{2} + 96 \, d^{2} f\right)} x\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{384 \, a^{2} f^{3}}"," ",0,"1/384*(24*I*d^2*f^2*x^2 + 24*I*c^2*f^2 + 12*c*d*f - 3*I*d^2 + (48*I*c*d*f^2 + 12*d^2*f)*x + 32*(d^2*f^3*x^3 + 3*c*d*f^3*x^2 + 3*c^2*f^3*x)*e^(4*I*f*x + 4*I*e) + (96*I*d^2*f^2*x^2 + 96*I*c^2*f^2 + 96*c*d*f - 48*I*d^2 + (192*I*c*d*f^2 + 96*d^2*f)*x)*e^(2*I*f*x + 2*I*e))*e^(-4*I*f*x - 4*I*e)/(a^2*f^3)","A",0
26,1,78,0,0.609827," ","integrate((d*x+c)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(4 i \, d f x + 4 i \, c f + 8 \, {\left(d f^{2} x^{2} + 2 \, c f^{2} x\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(16 i \, d f x + 16 i \, c f + 8 \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + d\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{64 \, a^{2} f^{2}}"," ",0,"1/64*(4*I*d*f*x + 4*I*c*f + 8*(d*f^2*x^2 + 2*c*f^2*x)*e^(4*I*f*x + 4*I*e) + (16*I*d*f*x + 16*I*c*f + 8*d)*e^(2*I*f*x + 2*I*e) + d)*e^(-4*I*f*x - 4*I*e)/(a^2*f^2)","A",0
27,1,80,0,0.556554," ","integrate(1/(d*x+c)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\rm Ei}\left(\frac{-2 i \, d f x - 2 i \, c f}{d}\right) e^{\left(\frac{-2 i \, d e + 2 i \, c f}{d}\right)} + {\rm Ei}\left(\frac{-4 i \, d f x - 4 i \, c f}{d}\right) e^{\left(\frac{-4 i \, d e + 4 i \, c f}{d}\right)} + \log\left(\frac{d x + c}{d}\right)}{4 \, a^{2} d}"," ",0,"1/4*(2*Ei((-2*I*d*f*x - 2*I*c*f)/d)*e^((-2*I*d*e + 2*I*c*f)/d) + Ei((-4*I*d*f*x - 4*I*c*f)/d)*e^((-4*I*d*e + 4*I*c*f)/d) + log((d*x + c)/d))/(a^2*d)","A",0
28,1,140,0,0.438123," ","integrate(1/(d*x+c)^2/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left({\left({\left(-4 i \, d f x - 4 i \, c f\right)} {\rm Ei}\left(\frac{-2 i \, d f x - 2 i \, c f}{d}\right) e^{\left(\frac{-2 i \, d e + 2 i \, c f}{d}\right)} + {\left(-4 i \, d f x - 4 i \, c f\right)} {\rm Ei}\left(\frac{-4 i \, d f x - 4 i \, c f}{d}\right) e^{\left(\frac{-4 i \, d e + 4 i \, c f}{d}\right)} - d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d e^{\left(2 i \, f x + 2 i \, e\right)} - d\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{4 \, {\left(a^{2} d^{3} x + a^{2} c d^{2}\right)}}"," ",0,"1/4*(((-4*I*d*f*x - 4*I*c*f)*Ei((-2*I*d*f*x - 2*I*c*f)/d)*e^((-2*I*d*e + 2*I*c*f)/d) + (-4*I*d*f*x - 4*I*c*f)*Ei((-4*I*d*f*x - 4*I*c*f)/d)*e^((-4*I*d*e + 4*I*c*f)/d) - d)*e^(4*I*f*x + 4*I*e) - 2*d*e^(2*I*f*x + 2*I*e) - d)*e^(-4*I*f*x - 4*I*e)/(a^2*d^3*x + a^2*c*d^2)","A",0
29,1,362,0,0.610613," ","integrate((d*x+c)^3/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(576 i \, d^{3} f^{3} x^{3} + 576 i \, c^{3} f^{3} + 288 \, c^{2} d f^{2} - 96 i \, c d^{2} f - 16 \, d^{3} + {\left(1728 i \, c d^{2} f^{3} + 288 \, d^{3} f^{2}\right)} x^{2} + {\left(1728 i \, c^{2} d f^{3} + 576 \, c d^{2} f^{2} - 96 i \, d^{3} f\right)} x + 864 \, {\left(d^{3} f^{4} x^{4} + 4 \, c d^{2} f^{4} x^{3} + 6 \, c^{2} d f^{4} x^{2} + 4 \, c^{3} f^{4} x\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(5184 i \, d^{3} f^{3} x^{3} + 5184 i \, c^{3} f^{3} + 7776 \, c^{2} d f^{2} - 7776 i \, c d^{2} f - 3888 \, d^{3} + {\left(15552 i \, c d^{2} f^{3} + 7776 \, d^{3} f^{2}\right)} x^{2} + {\left(15552 i \, c^{2} d f^{3} + 15552 \, c d^{2} f^{2} - 7776 i \, d^{3} f\right)} x\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(2592 i \, d^{3} f^{3} x^{3} + 2592 i \, c^{3} f^{3} + 1944 \, c^{2} d f^{2} - 972 i \, c d^{2} f - 243 \, d^{3} + {\left(7776 i \, c d^{2} f^{3} + 1944 \, d^{3} f^{2}\right)} x^{2} + {\left(7776 i \, c^{2} d f^{3} + 3888 \, c d^{2} f^{2} - 972 i \, d^{3} f\right)} x\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{27648 \, a^{3} f^{4}}"," ",0,"1/27648*(576*I*d^3*f^3*x^3 + 576*I*c^3*f^3 + 288*c^2*d*f^2 - 96*I*c*d^2*f - 16*d^3 + (1728*I*c*d^2*f^3 + 288*d^3*f^2)*x^2 + (1728*I*c^2*d*f^3 + 576*c*d^2*f^2 - 96*I*d^3*f)*x + 864*(d^3*f^4*x^4 + 4*c*d^2*f^4*x^3 + 6*c^2*d*f^4*x^2 + 4*c^3*f^4*x)*e^(6*I*f*x + 6*I*e) + (5184*I*d^3*f^3*x^3 + 5184*I*c^3*f^3 + 7776*c^2*d*f^2 - 7776*I*c*d^2*f - 3888*d^3 + (15552*I*c*d^2*f^3 + 7776*d^3*f^2)*x^2 + (15552*I*c^2*d*f^3 + 15552*c*d^2*f^2 - 7776*I*d^3*f)*x)*e^(4*I*f*x + 4*I*e) + (2592*I*d^3*f^3*x^3 + 2592*I*c^3*f^3 + 1944*c^2*d*f^2 - 972*I*c*d^2*f - 243*d^3 + (7776*I*c*d^2*f^3 + 1944*d^3*f^2)*x^2 + (7776*I*c^2*d*f^3 + 3888*c*d^2*f^2 - 972*I*d^3*f)*x)*e^(2*I*f*x + 2*I*e))*e^(-6*I*f*x - 6*I*e)/(a^3*f^4)","A",0
30,1,216,0,0.523604," ","integrate((d*x+c)^2/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(144 i \, d^{2} f^{2} x^{2} + 144 i \, c^{2} f^{2} + 48 \, c d f - 8 i \, d^{2} + {\left(288 i \, c d f^{2} + 48 \, d^{2} f\right)} x + 288 \, {\left(d^{2} f^{3} x^{3} + 3 \, c d f^{3} x^{2} + 3 \, c^{2} f^{3} x\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(1296 i \, d^{2} f^{2} x^{2} + 1296 i \, c^{2} f^{2} + 1296 \, c d f - 648 i \, d^{2} + {\left(2592 i \, c d f^{2} + 1296 \, d^{2} f\right)} x\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(648 i \, d^{2} f^{2} x^{2} + 648 i \, c^{2} f^{2} + 324 \, c d f - 81 i \, d^{2} + {\left(1296 i \, c d f^{2} + 324 \, d^{2} f\right)} x\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{6912 \, a^{3} f^{3}}"," ",0,"1/6912*(144*I*d^2*f^2*x^2 + 144*I*c^2*f^2 + 48*c*d*f - 8*I*d^2 + (288*I*c*d*f^2 + 48*d^2*f)*x + 288*(d^2*f^3*x^3 + 3*c*d*f^3*x^2 + 3*c^2*f^3*x)*e^(6*I*f*x + 6*I*e) + (1296*I*d^2*f^2*x^2 + 1296*I*c^2*f^2 + 1296*c*d*f - 648*I*d^2 + (2592*I*c*d*f^2 + 1296*d^2*f)*x)*e^(4*I*f*x + 4*I*e) + (648*I*d^2*f^2*x^2 + 648*I*c^2*f^2 + 324*c*d*f - 81*I*d^2 + (1296*I*c*d*f^2 + 324*d^2*f)*x)*e^(2*I*f*x + 2*I*e))*e^(-6*I*f*x - 6*I*e)/(a^3*f^3)","A",0
31,1,103,0,0.703597," ","integrate((d*x+c)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(24 i \, d f x + 24 i \, c f + 72 \, {\left(d f^{2} x^{2} + 2 \, c f^{2} x\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(216 i \, d f x + 216 i \, c f + 108 \, d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(108 i \, d f x + 108 i \, c f + 27 \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 \, d\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{1152 \, a^{3} f^{2}}"," ",0,"1/1152*(24*I*d*f*x + 24*I*c*f + 72*(d*f^2*x^2 + 2*c*f^2*x)*e^(6*I*f*x + 6*I*e) + (216*I*d*f*x + 216*I*c*f + 108*d)*e^(4*I*f*x + 4*I*e) + (108*I*d*f*x + 108*I*c*f + 27*d)*e^(2*I*f*x + 2*I*e) + 4*d)*e^(-6*I*f*x - 6*I*e)/(a^3*f^2)","A",0
32,1,111,0,0.438700," ","integrate(1/(d*x+c)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{3 \, {\rm Ei}\left(\frac{-2 i \, d f x - 2 i \, c f}{d}\right) e^{\left(\frac{-2 i \, d e + 2 i \, c f}{d}\right)} + 3 \, {\rm Ei}\left(\frac{-4 i \, d f x - 4 i \, c f}{d}\right) e^{\left(\frac{-4 i \, d e + 4 i \, c f}{d}\right)} + {\rm Ei}\left(\frac{-6 i \, d f x - 6 i \, c f}{d}\right) e^{\left(\frac{-6 i \, d e + 6 i \, c f}{d}\right)} + \log\left(\frac{d x + c}{d}\right)}{8 \, a^{3} d}"," ",0,"1/8*(3*Ei((-2*I*d*f*x - 2*I*c*f)/d)*e^((-2*I*d*e + 2*I*c*f)/d) + 3*Ei((-4*I*d*f*x - 4*I*c*f)/d)*e^((-4*I*d*e + 4*I*c*f)/d) + Ei((-6*I*d*f*x - 6*I*c*f)/d)*e^((-6*I*d*e + 6*I*c*f)/d) + log((d*x + c)/d))/(a^3*d)","A",0
33,1,192,0,0.446611," ","integrate(1/(d*x+c)^2/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left({\left({\left(-6 i \, d f x - 6 i \, c f\right)} {\rm Ei}\left(\frac{-2 i \, d f x - 2 i \, c f}{d}\right) e^{\left(\frac{-2 i \, d e + 2 i \, c f}{d}\right)} + {\left(-12 i \, d f x - 12 i \, c f\right)} {\rm Ei}\left(\frac{-4 i \, d f x - 4 i \, c f}{d}\right) e^{\left(\frac{-4 i \, d e + 4 i \, c f}{d}\right)} + {\left(-6 i \, d f x - 6 i \, c f\right)} {\rm Ei}\left(\frac{-6 i \, d f x - 6 i \, c f}{d}\right) e^{\left(\frac{-6 i \, d e + 6 i \, c f}{d}\right)} - d\right)} e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d e^{\left(4 i \, f x + 4 i \, e\right)} - 3 \, d e^{\left(2 i \, f x + 2 i \, e\right)} - d\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{8 \, {\left(a^{3} d^{3} x + a^{3} c d^{2}\right)}}"," ",0,"1/8*(((-6*I*d*f*x - 6*I*c*f)*Ei((-2*I*d*f*x - 2*I*c*f)/d)*e^((-2*I*d*e + 2*I*c*f)/d) + (-12*I*d*f*x - 12*I*c*f)*Ei((-4*I*d*f*x - 4*I*c*f)/d)*e^((-4*I*d*e + 4*I*c*f)/d) + (-6*I*d*f*x - 6*I*c*f)*Ei((-6*I*d*f*x - 6*I*c*f)/d)*e^((-6*I*d*e + 6*I*c*f)/d) - d)*e^(6*I*f*x + 6*I*e) - 3*d*e^(4*I*f*x + 4*I*e) - 3*d*e^(2*I*f*x + 2*I*e) - d)*e^(-6*I*f*x - 6*I*e)/(a^3*d^3*x + a^3*c*d^2)","A",0
34,0,0,0,0.523091," ","integrate((d*x+c)^m*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{-2 i \, {\left(d x + c\right)}^{m} a^{2} + {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} {\rm integral}\left(-\frac{2 \, {\left(-i \, a^{2} d m - 2 \, {\left(a^{2} d f x + a^{2} c f\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} {\left(d x + c\right)}^{m}}{d f x + c f + {\left(d f x + c f\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}, x\right)}{f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"(-2*I*(d*x + c)^m*a^2 + (f*e^(2*I*f*x + 2*I*e) + f)*integral(-2*(-I*a^2*d*m - 2*(a^2*d*f*x + a^2*c*f)*e^(2*I*f*x + 2*I*e))*(d*x + c)^m/(d*f*x + c*f + (d*f*x + c*f)*e^(2*I*f*x + 2*I*e)), x))/(f*e^(2*I*f*x + 2*I*e) + f)","F",0
35,0,0,0,0.573512," ","integrate((d*x+c)^m*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, {\left(d x + c\right)}^{m} a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(2*(d*x + c)^m*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
36,1,84,0,0.458260," ","integrate((d*x+c)^m/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(i \, d m + i \, d\right)} e^{\left(-\frac{d m \log\left(\frac{2 i \, f}{d}\right) + 2 i \, d e - 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, d f x + 2 i \, c f}{d}\right) + 2 \, {\left(d f x + c f\right)} {\left(d x + c\right)}^{m}}{4 \, {\left(a d f m + a d f\right)}}"," ",0,"1/4*((I*d*m + I*d)*e^(-(d*m*log(2*I*f/d) + 2*I*d*e - 2*I*c*f)/d)*gamma(m + 1, (2*I*d*f*x + 2*I*c*f)/d) + 2*(d*f*x + c*f)*(d*x + c)^m)/(a*d*f*m + a*d*f)","A",0
37,1,140,0,0.603436," ","integrate((d*x+c)^m/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(i \, d m + i \, d\right)} e^{\left(-\frac{d m \log\left(\frac{4 i \, f}{d}\right) + 4 i \, d e - 4 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{4 i \, d f x + 4 i \, c f}{d}\right) + {\left(4 i \, d m + 4 i \, d\right)} e^{\left(-\frac{d m \log\left(\frac{2 i \, f}{d}\right) + 2 i \, d e - 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, d f x + 2 i \, c f}{d}\right) + 4 \, {\left(d f x + c f\right)} {\left(d x + c\right)}^{m}}{16 \, {\left(a^{2} d f m + a^{2} d f\right)}}"," ",0,"1/16*((I*d*m + I*d)*e^(-(d*m*log(4*I*f/d) + 4*I*d*e - 4*I*c*f)/d)*gamma(m + 1, (4*I*d*f*x + 4*I*c*f)/d) + (4*I*d*m + 4*I*d)*e^(-(d*m*log(2*I*f/d) + 2*I*d*e - 2*I*c*f)/d)*gamma(m + 1, (2*I*d*f*x + 2*I*c*f)/d) + 4*(d*f*x + c*f)*(d*x + c)^m)/(a^2*d*f*m + a^2*d*f)","A",0
38,1,192,0,0.618606," ","integrate((d*x+c)^m/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(2 i \, d m + 2 i \, d\right)} e^{\left(-\frac{d m \log\left(\frac{6 i \, f}{d}\right) + 6 i \, d e - 6 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{6 i \, d f x + 6 i \, c f}{d}\right) + {\left(9 i \, d m + 9 i \, d\right)} e^{\left(-\frac{d m \log\left(\frac{4 i \, f}{d}\right) + 4 i \, d e - 4 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{4 i \, d f x + 4 i \, c f}{d}\right) + {\left(18 i \, d m + 18 i \, d\right)} e^{\left(-\frac{d m \log\left(\frac{2 i \, f}{d}\right) + 2 i \, d e - 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, d f x + 2 i \, c f}{d}\right) + 12 \, {\left(d f x + c f\right)} {\left(d x + c\right)}^{m}}{96 \, {\left(a^{3} d f m + a^{3} d f\right)}}"," ",0,"1/96*((2*I*d*m + 2*I*d)*e^(-(d*m*log(6*I*f/d) + 6*I*d*e - 6*I*c*f)/d)*gamma(m + 1, (6*I*d*f*x + 6*I*c*f)/d) + (9*I*d*m + 9*I*d)*e^(-(d*m*log(4*I*f/d) + 4*I*d*e - 4*I*c*f)/d)*gamma(m + 1, (4*I*d*f*x + 4*I*c*f)/d) + (18*I*d*m + 18*I*d)*e^(-(d*m*log(2*I*f/d) + 2*I*d*e - 2*I*c*f)/d)*gamma(m + 1, (2*I*d*f*x + 2*I*c*f)/d) + 12*(d*f*x + c*f)*(d*x + c)^m)/(a^3*d*f*m + a^3*d*f)","A",0
39,1,498,0,0.698599," ","integrate((d*x+c)^3*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, a d^{3} f^{4} x^{4} + 8 \, a c d^{2} f^{4} x^{3} + 12 \, a c^{2} d f^{4} x^{2} + 8 \, a c^{3} f^{4} x + 3 i \, b d^{3} {\rm polylog}\left(4, \frac{\tan\left(f x + e\right)^{2} + 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) - 3 i \, b d^{3} {\rm polylog}\left(4, \frac{\tan\left(f x + e\right)^{2} - 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(-6 i \, b d^{3} f^{2} x^{2} - 12 i \, b c d^{2} f^{2} x - 6 i \, b c^{2} d f^{2}\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) + {\left(6 i \, b d^{3} f^{2} x^{2} + 12 i \, b c d^{2} f^{2} x + 6 i \, b c^{2} d f^{2}\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) - 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b c^{3} f^{3}\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) - 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b c^{3} f^{3}\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) - 6 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} + 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) - 6 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} - 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right)}{8 \, f^{4}}"," ",0,"1/8*(2*a*d^3*f^4*x^4 + 8*a*c*d^2*f^4*x^3 + 12*a*c^2*d*f^4*x^2 + 8*a*c^3*f^4*x + 3*I*b*d^3*polylog(4, (tan(f*x + e)^2 + 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 3*I*b*d^3*polylog(4, (tan(f*x + e)^2 - 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + (-6*I*b*d^3*f^2*x^2 - 12*I*b*c*d^2*f^2*x - 6*I*b*c^2*d*f^2)*dilog(2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) + (6*I*b*d^3*f^2*x^2 + 12*I*b*c*d^2*f^2*x + 6*I*b*c^2*d*f^2)*dilog(2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) - 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*c^3*f^3)*log(-2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*c^3*f^3)*log(-2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 6*(b*d^3*f*x + b*c*d^2*f)*polylog(3, (tan(f*x + e)^2 + 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 6*(b*d^3*f*x + b*c*d^2*f)*polylog(3, (tan(f*x + e)^2 - 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)))/f^4","C",0
40,1,315,0,0.559230," ","integrate((d*x+c)^2*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\frac{4 \, a d^{2} f^{3} x^{3} + 12 \, a c d f^{3} x^{2} + 12 \, a c^{2} f^{3} x - 3 \, b d^{2} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} + 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) - 3 \, b d^{2} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} - 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(-6 i \, b d^{2} f x - 6 i \, b c d f\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) + {\left(6 i \, b d^{2} f x + 6 i \, b c d f\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) - 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) - 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right)}{12 \, f^{3}}"," ",0,"1/12*(4*a*d^2*f^3*x^3 + 12*a*c*d*f^3*x^2 + 12*a*c^2*f^3*x - 3*b*d^2*polylog(3, (tan(f*x + e)^2 + 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 3*b*d^2*polylog(3, (tan(f*x + e)^2 - 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + (-6*I*b*d^2*f*x - 6*I*b*c*d*f)*dilog(2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) + (6*I*b*d^2*f*x + 6*I*b*c*d*f)*dilog(2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) - 6*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*log(-2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 6*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*log(-2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)))/f^3","C",0
41,1,160,0,0.551422," ","integrate((d*x+c)*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, a d f^{2} x^{2} + 4 \, a c f^{2} x - i \, b d {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) + i \, b d {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) - 2 \, {\left(b d f x + b c f\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(b d f x + b c f\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right)}{4 \, f^{2}}"," ",0,"1/4*(2*a*d*f^2*x^2 + 4*a*c*f^2*x - I*b*d*dilog(2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) + I*b*d*dilog(2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) - 2*(b*d*f*x + b*c*f)*log(-2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 2*(b*d*f*x + b*c*f)*log(-2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)))/f^2","B",0
42,0,0,0,0.463901," ","integrate((a+b*tan(f*x+e))/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \tan\left(f x + e\right) + a}{d x + c}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)/(d*x + c), x)","F",0
43,0,0,0,0.526791," ","integrate((a+b*tan(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \tan\left(f x + e\right) + a}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
44,1,757,0,0.655352," ","integrate((d*x+c)^3*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} - b^{2}\right)} d^{3} f^{4} x^{4} + 4 \, {\left(a^{2} - b^{2}\right)} c d^{2} f^{4} x^{3} + 6 \, {\left(a^{2} - b^{2}\right)} c^{2} d f^{4} x^{2} + 4 \, {\left(a^{2} - b^{2}\right)} c^{3} f^{4} x + 3 i \, a b d^{3} {\rm polylog}\left(4, \frac{\tan\left(f x + e\right)^{2} + 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) - 3 i \, a b d^{3} {\rm polylog}\left(4, \frac{\tan\left(f x + e\right)^{2} - 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(-6 i \, a b d^{3} f^{2} x^{2} - 6 i \, a b c^{2} d f^{2} + 6 i \, b^{2} c d^{2} f - 6 i \, {\left(2 \, a b c d^{2} f^{2} - b^{2} d^{3} f\right)} x\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) + {\left(6 i \, a b d^{3} f^{2} x^{2} + 6 i \, a b c^{2} d f^{2} - 6 i \, b^{2} c d^{2} f + 6 i \, {\left(2 \, a b c d^{2} f^{2} - b^{2} d^{3} f\right)} x\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) - 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b c^{3} f^{3} - 3 \, b^{2} c^{2} d f^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} - b^{2} d^{3} f^{2}\right)} x^{2} + 6 \, {\left(a b c^{2} d f^{3} - b^{2} c d^{2} f^{2}\right)} x\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b c^{3} f^{3} - 3 \, b^{2} c^{2} d f^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} - b^{2} d^{3} f^{2}\right)} x^{2} + 6 \, {\left(a b c^{2} d f^{3} - b^{2} c d^{2} f^{2}\right)} x\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) - 3 \, {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} + 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) - 3 \, {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} - 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} f^{3} x^{2} + 3 \, b^{2} c^{2} d f^{3} x + b^{2} c^{3} f^{3}\right)} \tan\left(f x + e\right)}{4 \, f^{4}}"," ",0,"1/4*((a^2 - b^2)*d^3*f^4*x^4 + 4*(a^2 - b^2)*c*d^2*f^4*x^3 + 6*(a^2 - b^2)*c^2*d*f^4*x^2 + 4*(a^2 - b^2)*c^3*f^4*x + 3*I*a*b*d^3*polylog(4, (tan(f*x + e)^2 + 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 3*I*a*b*d^3*polylog(4, (tan(f*x + e)^2 - 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + (-6*I*a*b*d^3*f^2*x^2 - 6*I*a*b*c^2*d*f^2 + 6*I*b^2*c*d^2*f - 6*I*(2*a*b*c*d^2*f^2 - b^2*d^3*f)*x)*dilog(2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) + (6*I*a*b*d^3*f^2*x^2 + 6*I*a*b*c^2*d*f^2 - 6*I*b^2*c*d^2*f + 6*I*(2*a*b*c*d^2*f^2 - b^2*d^3*f)*x)*dilog(2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) - 2*(2*a*b*d^3*f^3*x^3 + 2*a*b*c^3*f^3 - 3*b^2*c^2*d*f^2 + 3*(2*a*b*c*d^2*f^3 - b^2*d^3*f^2)*x^2 + 6*(a*b*c^2*d*f^3 - b^2*c*d^2*f^2)*x)*log(-2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 2*(2*a*b*d^3*f^3*x^3 + 2*a*b*c^3*f^3 - 3*b^2*c^2*d*f^2 + 3*(2*a*b*c*d^2*f^3 - b^2*d^3*f^2)*x^2 + 6*(a*b*c^2*d*f^3 - b^2*c*d^2*f^2)*x)*log(-2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 3*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f - b^2*d^3)*polylog(3, (tan(f*x + e)^2 + 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 3*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f - b^2*d^3)*polylog(3, (tan(f*x + e)^2 - 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 4*(b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*f^3*x^2 + 3*b^2*c^2*d*f^3*x + b^2*c^3*f^3)*tan(f*x + e))/f^4","C",0
45,1,448,0,0.504941," ","integrate((d*x+c)^2*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{3} + 6 \, {\left(a^{2} - b^{2}\right)} c d f^{3} x^{2} + 6 \, {\left(a^{2} - b^{2}\right)} c^{2} f^{3} x - 3 \, a b d^{2} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} + 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) - 3 \, a b d^{2} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} - 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(-6 i \, a b d^{2} f x - 6 i \, a b c d f + 3 i \, b^{2} d^{2}\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) + {\left(6 i \, a b d^{2} f x + 6 i \, a b c d f - 3 i \, b^{2} d^{2}\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) - 6 \, {\left(a b d^{2} f^{2} x^{2} + a b c^{2} f^{2} - b^{2} c d f + {\left(2 \, a b c d f^{2} - b^{2} d^{2} f\right)} x\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) - 6 \, {\left(a b d^{2} f^{2} x^{2} + a b c^{2} f^{2} - b^{2} c d f + {\left(2 \, a b c d f^{2} - b^{2} d^{2} f\right)} x\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} \tan\left(f x + e\right)}{6 \, f^{3}}"," ",0,"1/6*(2*(a^2 - b^2)*d^2*f^3*x^3 + 6*(a^2 - b^2)*c*d*f^3*x^2 + 6*(a^2 - b^2)*c^2*f^3*x - 3*a*b*d^2*polylog(3, (tan(f*x + e)^2 + 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 3*a*b*d^2*polylog(3, (tan(f*x + e)^2 - 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + (-6*I*a*b*d^2*f*x - 6*I*a*b*c*d*f + 3*I*b^2*d^2)*dilog(2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) + (6*I*a*b*d^2*f*x + 6*I*a*b*c*d*f - 3*I*b^2*d^2)*dilog(2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) - 6*(a*b*d^2*f^2*x^2 + a*b*c^2*f^2 - b^2*c*d*f + (2*a*b*c*d*f^2 - b^2*d^2*f)*x)*log(-2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 6*(a*b*d^2*f^2*x^2 + a*b*c^2*f^2 - b^2*c*d*f + (2*a*b*c*d*f^2 - b^2*d^2*f)*x)*log(-2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 6*(b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*tan(f*x + e))/f^3","C",0
46,1,219,0,0.535084," ","integrate((d*x+c)*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} - b^{2}\right)} d f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} c f^{2} x - i \, a b d {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) + i \, a b d {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) - {\left(2 \, a b d f x + 2 \, a b c f - b^{2} d\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(2 \, a b d f x + 2 \, a b c f - b^{2} d\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \tan\left(f x + e\right)}{2 \, f^{2}}"," ",0,"1/2*((a^2 - b^2)*d*f^2*x^2 + 2*(a^2 - b^2)*c*f^2*x - I*a*b*d*dilog(2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) + I*a*b*d*dilog(2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) - (2*a*b*d*f*x + 2*a*b*c*f - b^2*d)*log(-2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - (2*a*b*d*f*x + 2*a*b*c*f - b^2*d)*log(-2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 2*(b^2*d*f*x + b^2*c*f)*tan(f*x + e))/f^2","A",0
47,0,0,0,0.623938," ","integrate((a+b*tan(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{d x + c}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(d*x + c), x)","F",0
48,0,0,0,0.479291," ","integrate((a+b*tan(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
49,1,1175,0,0.540696," ","integrate((d*x+c)^3*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d^{3} f^{4} x^{4} + 3 i \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} {\rm polylog}\left(4, \frac{\tan\left(f x + e\right)^{2} + 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) - 3 i \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} {\rm polylog}\left(4, \frac{\tan\left(f x + e\right)^{2} - 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) + 4 \, {\left(b^{3} d^{3} f^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{2} f^{4}\right)} x^{3} + 12 \, {\left(b^{3} c d^{2} f^{3} + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d f^{4}\right)} x^{2} + 4 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} c d^{2} f^{3} x^{2} + 3 \, b^{3} c^{2} d f^{3} x + b^{3} c^{3} f^{3}\right)} \tan\left(f x + e\right)^{2} + 4 \, {\left(3 \, b^{3} c^{2} d f^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{3} f^{4}\right)} x + {\left(-6 i \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 36 i \, a b^{2} c d^{2} f - 6 i \, b^{3} d^{3} - 6 i \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} + 12 i \, {\left(3 \, a b^{2} d^{3} f - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f^{2}\right)} x\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) + {\left(6 i \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} - 36 i \, a b^{2} c d^{2} f + 6 i \, b^{3} d^{3} + 6 i \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 12 i \, {\left(3 \, a b^{2} d^{3} f - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f^{2}\right)} x\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) - 4 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b - b^{3}\right)} c^{3} f^{3} - 3 \, {\left(3 \, a b^{2} d^{3} f^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f^{3}\right)} x^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} - b^{3} d^{3} f - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) - 4 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b - b^{3}\right)} c^{3} f^{3} - 3 \, {\left(3 \, a b^{2} d^{3} f^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f^{3}\right)} x^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} - b^{3} d^{3} f - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} f x - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} + 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} f x - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} - 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) + 12 \, {\left(2 \, a b^{2} d^{3} f^{3} x^{3} + 2 \, a b^{2} c^{3} f^{3} - b^{3} c^{2} d f^{2} + {\left(6 \, a b^{2} c d^{2} f^{3} - b^{3} d^{3} f^{2}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c^{2} d f^{3} - b^{3} c d^{2} f^{2}\right)} x\right)} \tan\left(f x + e\right)}{8 \, f^{4}}"," ",0,"1/8*(2*(a^3 - 3*a*b^2)*d^3*f^4*x^4 + 3*I*(3*a^2*b - b^3)*d^3*polylog(4, (tan(f*x + e)^2 + 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 3*I*(3*a^2*b - b^3)*d^3*polylog(4, (tan(f*x + e)^2 - 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 4*(b^3*d^3*f^3 + 2*(a^3 - 3*a*b^2)*c*d^2*f^4)*x^3 + 12*(b^3*c*d^2*f^3 + (a^3 - 3*a*b^2)*c^2*d*f^4)*x^2 + 4*(b^3*d^3*f^3*x^3 + 3*b^3*c*d^2*f^3*x^2 + 3*b^3*c^2*d*f^3*x + b^3*c^3*f^3)*tan(f*x + e)^2 + 4*(3*b^3*c^2*d*f^3 + 2*(a^3 - 3*a*b^2)*c^3*f^4)*x + (-6*I*(3*a^2*b - b^3)*d^3*f^2*x^2 + 36*I*a*b^2*c*d^2*f - 6*I*b^3*d^3 - 6*I*(3*a^2*b - b^3)*c^2*d*f^2 + 12*I*(3*a*b^2*d^3*f - (3*a^2*b - b^3)*c*d^2*f^2)*x)*dilog(2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) + (6*I*(3*a^2*b - b^3)*d^3*f^2*x^2 - 36*I*a*b^2*c*d^2*f + 6*I*b^3*d^3 + 6*I*(3*a^2*b - b^3)*c^2*d*f^2 - 12*I*(3*a*b^2*d^3*f - (3*a^2*b - b^3)*c*d^2*f^2)*x)*dilog(2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) - 4*((3*a^2*b - b^3)*d^3*f^3*x^3 - 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b - b^3)*c^3*f^3 - 3*(3*a*b^2*d^3*f^2 - (3*a^2*b - b^3)*c*d^2*f^3)*x^2 - 3*(6*a*b^2*c*d^2*f^2 - b^3*d^3*f - (3*a^2*b - b^3)*c^2*d*f^3)*x)*log(-2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 4*((3*a^2*b - b^3)*d^3*f^3*x^3 - 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b - b^3)*c^3*f^3 - 3*(3*a*b^2*d^3*f^2 - (3*a^2*b - b^3)*c*d^2*f^3)*x^2 - 3*(6*a*b^2*c*d^2*f^2 - b^3*d^3*f - (3*a^2*b - b^3)*c^2*d*f^3)*x)*log(-2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 6*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*f*x - (3*a^2*b - b^3)*c*d^2*f)*polylog(3, (tan(f*x + e)^2 + 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 6*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*f*x - (3*a^2*b - b^3)*c*d^2*f)*polylog(3, (tan(f*x + e)^2 - 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 12*(2*a*b^2*d^3*f^3*x^3 + 2*a*b^2*c^3*f^3 - b^3*c^2*d*f^2 + (6*a*b^2*c*d^2*f^3 - b^3*d^3*f^2)*x^2 + 2*(3*a*b^2*c^2*d*f^3 - b^3*c*d^2*f^2)*x)*tan(f*x + e))/f^4","C",0
50,1,686,0,0.535426," ","integrate((d*x+c)^2*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{3} x^{3} - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{2} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} + 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{2} {\rm polylog}\left(3, \frac{\tan\left(f x + e\right)^{2} - 2 i \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(b^{3} d^{2} f^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} c d f^{2} x + b^{3} c^{2} f^{2}\right)} \tan\left(f x + e\right)^{2} + 12 \, {\left(b^{3} c d f^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{3}\right)} x + {\left(18 i \, a b^{2} d^{2} - 6 i \, {\left(3 \, a^{2} b - b^{3}\right)} d^{2} f x - 6 i \, {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) + {\left(-18 i \, a b^{2} d^{2} + 6 i \, {\left(3 \, a^{2} b - b^{3}\right)} d^{2} f x + 6 i \, {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) - 6 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} d^{2} f - {\left(3 \, a^{2} b - b^{3}\right)} c d f^{2}\right)} x\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) - 6 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} d^{2} f - {\left(3 \, a^{2} b - b^{3}\right)} c d f^{2}\right)} x\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) + 12 \, {\left(3 \, a b^{2} d^{2} f^{2} x^{2} + 3 \, a b^{2} c^{2} f^{2} - b^{3} c d f + {\left(6 \, a b^{2} c d f^{2} - b^{3} d^{2} f\right)} x\right)} \tan\left(f x + e\right)}{12 \, f^{3}}"," ",0,"1/12*(4*(a^3 - 3*a*b^2)*d^2*f^3*x^3 - 3*(3*a^2*b - b^3)*d^2*polylog(3, (tan(f*x + e)^2 + 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 3*(3*a^2*b - b^3)*d^2*polylog(3, (tan(f*x + e)^2 - 2*I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 6*(b^3*d^2*f^2 + 2*(a^3 - 3*a*b^2)*c*d*f^3)*x^2 + 6*(b^3*d^2*f^2*x^2 + 2*b^3*c*d*f^2*x + b^3*c^2*f^2)*tan(f*x + e)^2 + 12*(b^3*c*d*f^2 + (a^3 - 3*a*b^2)*c^2*f^3)*x + (18*I*a*b^2*d^2 - 6*I*(3*a^2*b - b^3)*d^2*f*x - 6*I*(3*a^2*b - b^3)*c*d*f)*dilog(2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) + (-18*I*a*b^2*d^2 + 6*I*(3*a^2*b - b^3)*d^2*f*x + 6*I*(3*a^2*b - b^3)*c*d*f)*dilog(2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) - 6*((3*a^2*b - b^3)*d^2*f^2*x^2 - 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b - b^3)*c^2*f^2 - 2*(3*a*b^2*d^2*f - (3*a^2*b - b^3)*c*d*f^2)*x)*log(-2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) - 6*((3*a^2*b - b^3)*d^2*f^2*x^2 - 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b - b^3)*c^2*f^2 - 2*(3*a*b^2*d^2*f - (3*a^2*b - b^3)*c*d*f^2)*x)*log(-2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 12*(3*a*b^2*d^2*f^2*x^2 + 3*a*b^2*c^2*f^2 - b^3*c*d*f + (6*a*b^2*c*d*f^2 - b^3*d^2*f)*x)*tan(f*x + e))/f^3","C",0
51,1,327,0,0.631094," ","integrate((d*x+c)*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d f^{2} x^{2} - i \, {\left(3 \, a^{2} b - b^{3}\right)} d {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) + i \, {\left(3 \, a^{2} b - b^{3}\right)} d {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1} + 1\right) + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(b^{3} d f + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c f^{2}\right)} x + 2 \, {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b - b^{3}\right)} d f x - {\left(3 \, a^{2} b - b^{3}\right)} c f\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b - b^{3}\right)} d f x - {\left(3 \, a^{2} b - b^{3}\right)} c f\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(f x + e\right) - 1\right)}}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(6 \, a b^{2} d f x + 6 \, a b^{2} c f - b^{3} d\right)} \tan\left(f x + e\right)}{4 \, f^{2}}"," ",0,"1/4*(2*(a^3 - 3*a*b^2)*d*f^2*x^2 - I*(3*a^2*b - b^3)*d*dilog(2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) + I*(3*a^2*b - b^3)*d*dilog(2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1) + 1) + 2*(b^3*d*f*x + b^3*c*f)*tan(f*x + e)^2 + 2*(b^3*d*f + 2*(a^3 - 3*a*b^2)*c*f^2)*x + 2*(3*a*b^2*d - (3*a^2*b - b^3)*d*f*x - (3*a^2*b - b^3)*c*f)*log(-2*(I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 2*(3*a*b^2*d - (3*a^2*b - b^3)*d*f*x - (3*a^2*b - b^3)*c*f)*log(-2*(-I*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1)) + 2*(6*a*b^2*d*f*x + 6*a*b^2*c*f - b^3*d)*tan(f*x + e))/f^2","A",0
52,0,0,0,0.948344," ","integrate((a+b*tan(f*x+e))^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}}{d x + c}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)/(d*x + c), x)","F",0
53,0,0,0,0.516179," ","integrate((a+b*tan(f*x+e))^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
54,1,1183,0,0.540239," ","integrate((d*x+c)^3/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, a d^{3} f^{4} x^{4} + 8 \, a c d^{2} f^{4} x^{3} + 12 \, a c^{2} d f^{4} x^{2} + 8 \, a c^{3} f^{4} x - 3 i \, b d^{3} {\rm polylog}\left(4, \frac{{\left(a^{2} + 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} - 2 i \, a b + b^{2} + {\left(2 i \, a^{2} - 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 3 i \, b d^{3} {\rm polylog}\left(4, \frac{{\left(a^{2} - 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + 2 i \, a b + b^{2} + {\left(-2 i \, a^{2} - 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + {\left(6 i \, b d^{3} f^{2} x^{2} + 12 i \, b c d^{2} f^{2} x + 6 i \, b c^{2} d f^{2}\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + {\left(-6 i \, b d^{3} f^{2} x^{2} - 12 i \, b c d^{2} f^{2} x - 6 i \, b c^{2} d f^{2}\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \log\left(-\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \log\left(-\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) - 4 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(\frac{{\left(i \, a b + b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right) - 4 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(\frac{{\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, \frac{{\left(a^{2} + 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} - 2 i \, a b + b^{2} + {\left(2 i \, a^{2} - 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 6 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, \frac{{\left(a^{2} - 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + 2 i \, a b + b^{2} + {\left(-2 i \, a^{2} - 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right)}{8 \, {\left(a^{2} + b^{2}\right)} f^{4}}"," ",0,"1/8*(2*a*d^3*f^4*x^4 + 8*a*c*d^2*f^4*x^3 + 12*a*c^2*d*f^4*x^2 + 8*a*c^3*f^4*x - 3*I*b*d^3*polylog(4, ((a^2 + 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 - 2*I*a*b + b^2 + (2*I*a^2 - 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 3*I*b*d^3*polylog(4, ((a^2 - 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 + 2*I*a*b + b^2 + (-2*I*a^2 - 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + (6*I*b*d^3*f^2*x^2 + 12*I*b*c*d^2*f^2*x + 6*I*b*c^2*d*f^2)*dilog((2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + (-6*I*b*d^3*f^2*x^2 - 12*I*b*c*d^2*f^2*x - 6*I*b*c^2*d*f^2)*dilog((2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*log(-(2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*log(-(2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) - 4*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(((I*a*b + b^2)*tan(f*x + e)^2 - a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)) - 4*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(((I*a*b - b^2)*tan(f*x + e)^2 + a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)) + 6*(b*d^3*f*x + b*c*d^2*f)*polylog(3, ((a^2 + 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 - 2*I*a*b + b^2 + (2*I*a^2 - 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 6*(b*d^3*f*x + b*c*d^2*f)*polylog(3, ((a^2 - 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 + 2*I*a*b + b^2 + (-2*I*a^2 - 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)))/((a^2 + b^2)*f^4)","C",0
55,1,836,0,1.222119," ","integrate((d*x+c)^2/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\frac{4 \, a d^{2} f^{3} x^{3} + 12 \, a c d f^{3} x^{2} + 12 \, a c^{2} f^{3} x + 3 \, b d^{2} {\rm polylog}\left(3, \frac{{\left(a^{2} + 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} - 2 i \, a b + b^{2} + {\left(2 i \, a^{2} - 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 3 \, b d^{2} {\rm polylog}\left(3, \frac{{\left(a^{2} - 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + 2 i \, a b + b^{2} + {\left(-2 i \, a^{2} - 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + {\left(6 i \, b d^{2} f x + 6 i \, b c d f\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + {\left(-6 i \, b d^{2} f x - 6 i \, b c d f\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \log\left(-\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \log\left(-\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(\frac{{\left(i \, a b + b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(\frac{{\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right)}{12 \, {\left(a^{2} + b^{2}\right)} f^{3}}"," ",0,"1/12*(4*a*d^2*f^3*x^3 + 12*a*c*d*f^3*x^2 + 12*a*c^2*f^3*x + 3*b*d^2*polylog(3, ((a^2 + 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 - 2*I*a*b + b^2 + (2*I*a^2 - 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 3*b*d^2*polylog(3, ((a^2 - 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 + 2*I*a*b + b^2 + (-2*I*a^2 - 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + (6*I*b*d^2*f*x + 6*I*b*c*d*f)*dilog((2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + (-6*I*b*d^2*f*x - 6*I*b*c*d*f)*dilog((2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + 6*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*log(-(2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 6*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*log(-(2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(((I*a*b + b^2)*tan(f*x + e)^2 - a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)) + 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(((I*a*b - b^2)*tan(f*x + e)^2 + a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)))/((a^2 + b^2)*f^3)","C",0
56,1,533,0,0.462621," ","integrate((d*x+c)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, a d f^{2} x^{2} + 4 \, a c f^{2} x + i \, b d {\rm Li}_2\left(\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) - i \, b d {\rm Li}_2\left(\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + 2 \, {\left(b d f x + b d e\right)} \log\left(-\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 2 \, {\left(b d f x + b d e\right)} \log\left(-\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) - 2 \, {\left(b d e - b c f\right)} \log\left(\frac{{\left(i \, a b + b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(b d e - b c f\right)} \log\left(\frac{{\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right)}{4 \, {\left(a^{2} + b^{2}\right)} f^{2}}"," ",0,"1/4*(2*a*d*f^2*x^2 + 4*a*c*f^2*x + I*b*d*dilog((2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) - I*b*d*dilog((2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + 2*(b*d*f*x + b*d*e)*log(-(2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 2*(b*d*f*x + b*d*e)*log(-(2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) - 2*(b*d*e - b*c*f)*log(((I*a*b + b^2)*tan(f*x + e)^2 - a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)) - 2*(b*d*e - b*c*f)*log(((I*a*b - b^2)*tan(f*x + e)^2 + a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)))/((a^2 + b^2)*f^2)","B",0
57,0,0,0,0.642823," ","integrate(1/(d*x+c)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(b d x + b c\right)} \tan\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (b*d*x + b*c)*tan(f*x + e)), x)","F",0
58,0,0,0,0.490873," ","integrate(1/(d*x+c)^2/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \tan\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*tan(f*x + e)), x)","F",0
59,1,2535,0,0.687773," ","integrate((d*x+c)^3/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(a^{3} - a b^{2}\right)} d^{3} f^{4} x^{4} - 4 \, b^{3} c^{3} f^{3} - 4 \, {\left(b^{3} d^{3} f^{3} - {\left(a^{3} - a b^{2}\right)} c d^{2} f^{4}\right)} x^{3} - 6 \, {\left(2 \, b^{3} c d^{2} f^{3} - {\left(a^{3} - a b^{2}\right)} c^{2} d f^{4}\right)} x^{2} - 4 \, {\left(3 \, b^{3} c^{2} d f^{3} - {\left(a^{3} - a b^{2}\right)} c^{3} f^{4}\right)} x + {\left(6 i \, a^{2} b d^{3} f^{2} x^{2} + 6 i \, a^{2} b c^{2} d f^{2} + 6 i \, a b^{2} c d^{2} f + 6 i \, {\left(2 \, a^{2} b c d^{2} f^{2} + a b^{2} d^{3} f\right)} x + {\left(6 i \, a b^{2} d^{3} f^{2} x^{2} + 6 i \, a b^{2} c^{2} d f^{2} + 6 i \, b^{3} c d^{2} f + 6 i \, {\left(2 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f\right)} x\right)} \tan\left(f x + e\right)\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + {\left(-6 i \, a^{2} b d^{3} f^{2} x^{2} - 6 i \, a^{2} b c^{2} d f^{2} - 6 i \, a b^{2} c d^{2} f - 6 i \, {\left(2 \, a^{2} b c d^{2} f^{2} + a b^{2} d^{3} f\right)} x + {\left(-6 i \, a b^{2} d^{3} f^{2} x^{2} - 6 i \, a b^{2} c^{2} d f^{2} - 6 i \, b^{3} c d^{2} f - 6 i \, {\left(2 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f\right)} x\right)} \tan\left(f x + e\right)\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + 2 \, {\left(2 \, a^{2} b d^{3} f^{3} x^{3} + 2 \, a^{2} b d^{3} e^{3} + 6 \, a^{2} b c^{2} d e f^{2} - 3 \, a b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} b c d^{2} f^{3} + a b^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a^{2} b c d^{2} e^{2} - a b^{2} c d^{2} e\right)} f + 6 \, {\left(a^{2} b c^{2} d f^{3} + a b^{2} c d^{2} f^{2}\right)} x + {\left(2 \, a b^{2} d^{3} f^{3} x^{3} + 2 \, a b^{2} d^{3} e^{3} + 6 \, a b^{2} c^{2} d e f^{2} - 3 \, b^{3} d^{3} e^{2} + 3 \, {\left(2 \, a b^{2} c d^{2} f^{3} + b^{3} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a b^{2} c d^{2} e^{2} - b^{3} c d^{2} e\right)} f + 6 \, {\left(a b^{2} c^{2} d f^{3} + b^{3} c d^{2} f^{2}\right)} x\right)} \tan\left(f x + e\right)\right)} \log\left(-\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 2 \, {\left(2 \, a^{2} b d^{3} f^{3} x^{3} + 2 \, a^{2} b d^{3} e^{3} + 6 \, a^{2} b c^{2} d e f^{2} - 3 \, a b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} b c d^{2} f^{3} + a b^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a^{2} b c d^{2} e^{2} - a b^{2} c d^{2} e\right)} f + 6 \, {\left(a^{2} b c^{2} d f^{3} + a b^{2} c d^{2} f^{2}\right)} x + {\left(2 \, a b^{2} d^{3} f^{3} x^{3} + 2 \, a b^{2} d^{3} e^{3} + 6 \, a b^{2} c^{2} d e f^{2} - 3 \, b^{3} d^{3} e^{2} + 3 \, {\left(2 \, a b^{2} c d^{2} f^{3} + b^{3} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a b^{2} c d^{2} e^{2} - b^{3} c d^{2} e\right)} f + 6 \, {\left(a b^{2} c^{2} d f^{3} + b^{3} c d^{2} f^{2}\right)} x\right)} \tan\left(f x + e\right)\right)} \log\left(-\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) - 2 \, {\left(2 \, a^{2} b d^{3} e^{3} - 2 \, a^{2} b c^{3} f^{3} - 3 \, a b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} b c^{2} d e - a b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a^{2} b c d^{2} e^{2} - a b^{2} c d^{2} e\right)} f + {\left(2 \, a b^{2} d^{3} e^{3} - 2 \, a b^{2} c^{3} f^{3} - 3 \, b^{3} d^{3} e^{2} + 3 \, {\left(2 \, a b^{2} c^{2} d e - b^{3} c^{2} d\right)} f^{2} - 6 \, {\left(a b^{2} c d^{2} e^{2} - b^{3} c d^{2} e\right)} f\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{{\left(i \, a b + b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(2 \, a^{2} b d^{3} e^{3} - 2 \, a^{2} b c^{3} f^{3} - 3 \, a b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} b c^{2} d e - a b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a^{2} b c d^{2} e^{2} - a b^{2} c d^{2} e\right)} f + {\left(2 \, a b^{2} d^{3} e^{3} - 2 \, a b^{2} c^{3} f^{3} - 3 \, b^{3} d^{3} e^{2} + 3 \, {\left(2 \, a b^{2} c^{2} d e - b^{3} c^{2} d\right)} f^{2} - 6 \, {\left(a b^{2} c d^{2} e^{2} - b^{3} c d^{2} e\right)} f\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{{\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(-3 i \, a b^{2} d^{3} \tan\left(f x + e\right) - 3 i \, a^{2} b d^{3}\right)} {\rm polylog}\left(4, \frac{{\left(a^{2} + 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} - 2 i \, a b + b^{2} + {\left(2 i \, a^{2} - 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + {\left(3 i \, a b^{2} d^{3} \tan\left(f x + e\right) + 3 i \, a^{2} b d^{3}\right)} {\rm polylog}\left(4, \frac{{\left(a^{2} - 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + 2 i \, a b + b^{2} + {\left(-2 i \, a^{2} - 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 3 \, {\left(2 \, a^{2} b d^{3} f x + 2 \, a^{2} b c d^{2} f + a b^{2} d^{3} + {\left(2 \, a b^{2} d^{3} f x + 2 \, a b^{2} c d^{2} f + b^{3} d^{3}\right)} \tan\left(f x + e\right)\right)} {\rm polylog}\left(3, \frac{{\left(a^{2} + 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} - 2 i \, a b + b^{2} + {\left(2 i \, a^{2} - 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 3 \, {\left(2 \, a^{2} b d^{3} f x + 2 \, a^{2} b c d^{2} f + a b^{2} d^{3} + {\left(2 \, a b^{2} d^{3} f x + 2 \, a b^{2} c d^{2} f + b^{3} d^{3}\right)} \tan\left(f x + e\right)\right)} {\rm polylog}\left(3, \frac{{\left(a^{2} - 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + 2 i \, a b + b^{2} + {\left(-2 i \, a^{2} - 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{4} x^{4} + 4 \, a b^{2} c^{3} f^{3} + 4 \, {\left(a b^{2} d^{3} f^{3} + {\left(a^{2} b - b^{3}\right)} c d^{2} f^{4}\right)} x^{3} + 6 \, {\left(2 \, a b^{2} c d^{2} f^{3} + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{4}\right)} x^{2} + 4 \, {\left(3 \, a b^{2} c^{2} d f^{3} + {\left(a^{2} b - b^{3}\right)} c^{3} f^{4}\right)} x\right)} \tan\left(f x + e\right)}{4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{4} \tan\left(f x + e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{4}\right)}}"," ",0,"1/4*((a^3 - a*b^2)*d^3*f^4*x^4 - 4*b^3*c^3*f^3 - 4*(b^3*d^3*f^3 - (a^3 - a*b^2)*c*d^2*f^4)*x^3 - 6*(2*b^3*c*d^2*f^3 - (a^3 - a*b^2)*c^2*d*f^4)*x^2 - 4*(3*b^3*c^2*d*f^3 - (a^3 - a*b^2)*c^3*f^4)*x + (6*I*a^2*b*d^3*f^2*x^2 + 6*I*a^2*b*c^2*d*f^2 + 6*I*a*b^2*c*d^2*f + 6*I*(2*a^2*b*c*d^2*f^2 + a*b^2*d^3*f)*x + (6*I*a*b^2*d^3*f^2*x^2 + 6*I*a*b^2*c^2*d*f^2 + 6*I*b^3*c*d^2*f + 6*I*(2*a*b^2*c*d^2*f^2 + b^3*d^3*f)*x)*tan(f*x + e))*dilog((2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + (-6*I*a^2*b*d^3*f^2*x^2 - 6*I*a^2*b*c^2*d*f^2 - 6*I*a*b^2*c*d^2*f - 6*I*(2*a^2*b*c*d^2*f^2 + a*b^2*d^3*f)*x + (-6*I*a*b^2*d^3*f^2*x^2 - 6*I*a*b^2*c^2*d*f^2 - 6*I*b^3*c*d^2*f - 6*I*(2*a*b^2*c*d^2*f^2 + b^3*d^3*f)*x)*tan(f*x + e))*dilog((2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + 2*(2*a^2*b*d^3*f^3*x^3 + 2*a^2*b*d^3*e^3 + 6*a^2*b*c^2*d*e*f^2 - 3*a*b^2*d^3*e^2 + 3*(2*a^2*b*c*d^2*f^3 + a*b^2*d^3*f^2)*x^2 - 6*(a^2*b*c*d^2*e^2 - a*b^2*c*d^2*e)*f + 6*(a^2*b*c^2*d*f^3 + a*b^2*c*d^2*f^2)*x + (2*a*b^2*d^3*f^3*x^3 + 2*a*b^2*d^3*e^3 + 6*a*b^2*c^2*d*e*f^2 - 3*b^3*d^3*e^2 + 3*(2*a*b^2*c*d^2*f^3 + b^3*d^3*f^2)*x^2 - 6*(a*b^2*c*d^2*e^2 - b^3*c*d^2*e)*f + 6*(a*b^2*c^2*d*f^3 + b^3*c*d^2*f^2)*x)*tan(f*x + e))*log(-(2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 2*(2*a^2*b*d^3*f^3*x^3 + 2*a^2*b*d^3*e^3 + 6*a^2*b*c^2*d*e*f^2 - 3*a*b^2*d^3*e^2 + 3*(2*a^2*b*c*d^2*f^3 + a*b^2*d^3*f^2)*x^2 - 6*(a^2*b*c*d^2*e^2 - a*b^2*c*d^2*e)*f + 6*(a^2*b*c^2*d*f^3 + a*b^2*c*d^2*f^2)*x + (2*a*b^2*d^3*f^3*x^3 + 2*a*b^2*d^3*e^3 + 6*a*b^2*c^2*d*e*f^2 - 3*b^3*d^3*e^2 + 3*(2*a*b^2*c*d^2*f^3 + b^3*d^3*f^2)*x^2 - 6*(a*b^2*c*d^2*e^2 - b^3*c*d^2*e)*f + 6*(a*b^2*c^2*d*f^3 + b^3*c*d^2*f^2)*x)*tan(f*x + e))*log(-(2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) - 2*(2*a^2*b*d^3*e^3 - 2*a^2*b*c^3*f^3 - 3*a*b^2*d^3*e^2 + 3*(2*a^2*b*c^2*d*e - a*b^2*c^2*d)*f^2 - 6*(a^2*b*c*d^2*e^2 - a*b^2*c*d^2*e)*f + (2*a*b^2*d^3*e^3 - 2*a*b^2*c^3*f^3 - 3*b^3*d^3*e^2 + 3*(2*a*b^2*c^2*d*e - b^3*c^2*d)*f^2 - 6*(a*b^2*c*d^2*e^2 - b^3*c*d^2*e)*f)*tan(f*x + e))*log(((I*a*b + b^2)*tan(f*x + e)^2 - a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)) - 2*(2*a^2*b*d^3*e^3 - 2*a^2*b*c^3*f^3 - 3*a*b^2*d^3*e^2 + 3*(2*a^2*b*c^2*d*e - a*b^2*c^2*d)*f^2 - 6*(a^2*b*c*d^2*e^2 - a*b^2*c*d^2*e)*f + (2*a*b^2*d^3*e^3 - 2*a*b^2*c^3*f^3 - 3*b^3*d^3*e^2 + 3*(2*a*b^2*c^2*d*e - b^3*c^2*d)*f^2 - 6*(a*b^2*c*d^2*e^2 - b^3*c*d^2*e)*f)*tan(f*x + e))*log(((I*a*b - b^2)*tan(f*x + e)^2 + a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)) + (-3*I*a*b^2*d^3*tan(f*x + e) - 3*I*a^2*b*d^3)*polylog(4, ((a^2 + 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 - 2*I*a*b + b^2 + (2*I*a^2 - 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + (3*I*a*b^2*d^3*tan(f*x + e) + 3*I*a^2*b*d^3)*polylog(4, ((a^2 - 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 + 2*I*a*b + b^2 + (-2*I*a^2 - 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 3*(2*a^2*b*d^3*f*x + 2*a^2*b*c*d^2*f + a*b^2*d^3 + (2*a*b^2*d^3*f*x + 2*a*b^2*c*d^2*f + b^3*d^3)*tan(f*x + e))*polylog(3, ((a^2 + 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 - 2*I*a*b + b^2 + (2*I*a^2 - 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 3*(2*a^2*b*d^3*f*x + 2*a^2*b*c*d^2*f + a*b^2*d^3 + (2*a*b^2*d^3*f*x + 2*a*b^2*c*d^2*f + b^3*d^3)*tan(f*x + e))*polylog(3, ((a^2 - 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 + 2*I*a*b + b^2 + (-2*I*a^2 - 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + ((a^2*b - b^3)*d^3*f^4*x^4 + 4*a*b^2*c^3*f^3 + 4*(a*b^2*d^3*f^3 + (a^2*b - b^3)*c*d^2*f^4)*x^3 + 6*(2*a*b^2*c*d^2*f^3 + (a^2*b - b^3)*c^2*d*f^4)*x^2 + 4*(3*a*b^2*c^2*d*f^3 + (a^2*b - b^3)*c^3*f^4)*x)*tan(f*x + e))/((a^4*b + 2*a^2*b^3 + b^5)*f^4*tan(f*x + e) + (a^5 + 2*a^3*b^2 + a*b^4)*f^4)","C",0
60,1,1578,0,0.599410," ","integrate((d*x+c)^2/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{3} x^{3} - 6 \, b^{3} c^{2} f^{2} - 6 \, {\left(b^{3} d^{2} f^{2} - {\left(a^{3} - a b^{2}\right)} c d f^{3}\right)} x^{2} - 6 \, {\left(2 \, b^{3} c d f^{2} - {\left(a^{3} - a b^{2}\right)} c^{2} f^{3}\right)} x + {\left(6 i \, a^{2} b d^{2} f x + 6 i \, a^{2} b c d f + 3 i \, a b^{2} d^{2} + {\left(6 i \, a b^{2} d^{2} f x + 6 i \, a b^{2} c d f + 3 i \, b^{3} d^{2}\right)} \tan\left(f x + e\right)\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + {\left(-6 i \, a^{2} b d^{2} f x - 6 i \, a^{2} b c d f - 3 i \, a b^{2} d^{2} + {\left(-6 i \, a b^{2} d^{2} f x - 6 i \, a b^{2} c d f - 3 i \, b^{3} d^{2}\right)} \tan\left(f x + e\right)\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + 6 \, {\left(a^{2} b d^{2} f^{2} x^{2} - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f + a b^{2} d^{2} e + {\left(2 \, a^{2} b c d f^{2} + a b^{2} d^{2} f\right)} x + {\left(a b^{2} d^{2} f^{2} x^{2} - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f + b^{3} d^{2} e + {\left(2 \, a b^{2} c d f^{2} + b^{3} d^{2} f\right)} x\right)} \tan\left(f x + e\right)\right)} \log\left(-\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 6 \, {\left(a^{2} b d^{2} f^{2} x^{2} - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f + a b^{2} d^{2} e + {\left(2 \, a^{2} b c d f^{2} + a b^{2} d^{2} f\right)} x + {\left(a b^{2} d^{2} f^{2} x^{2} - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f + b^{3} d^{2} e + {\left(2 \, a b^{2} c d f^{2} + b^{3} d^{2} f\right)} x\right)} \tan\left(f x + e\right)\right)} \log\left(-\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 6 \, {\left(a^{2} b d^{2} e^{2} + a^{2} b c^{2} f^{2} - a b^{2} d^{2} e - {\left(2 \, a^{2} b c d e - a b^{2} c d\right)} f + {\left(a b^{2} d^{2} e^{2} + a b^{2} c^{2} f^{2} - b^{3} d^{2} e - {\left(2 \, a b^{2} c d e - b^{3} c d\right)} f\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{{\left(i \, a b + b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(a^{2} b d^{2} e^{2} + a^{2} b c^{2} f^{2} - a b^{2} d^{2} e - {\left(2 \, a^{2} b c d e - a b^{2} c d\right)} f + {\left(a b^{2} d^{2} e^{2} + a b^{2} c^{2} f^{2} - b^{3} d^{2} e - {\left(2 \, a b^{2} c d e - b^{3} c d\right)} f\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{{\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right) + 3 \, {\left(a b^{2} d^{2} \tan\left(f x + e\right) + a^{2} b d^{2}\right)} {\rm polylog}\left(3, \frac{{\left(a^{2} + 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} - 2 i \, a b + b^{2} + {\left(2 i \, a^{2} - 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 3 \, {\left(a b^{2} d^{2} \tan\left(f x + e\right) + a^{2} b d^{2}\right)} {\rm polylog}\left(3, \frac{{\left(a^{2} - 2 i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + 2 i \, a b + b^{2} + {\left(-2 i \, a^{2} - 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{3} + 3 \, a b^{2} c^{2} f^{2} + 3 \, {\left(a b^{2} d^{2} f^{2} + {\left(a^{2} b - b^{3}\right)} c d f^{3}\right)} x^{2} + 3 \, {\left(2 \, a b^{2} c d f^{2} + {\left(a^{2} b - b^{3}\right)} c^{2} f^{3}\right)} x\right)} \tan\left(f x + e\right)}{6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} \tan\left(f x + e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{3}\right)}}"," ",0,"1/6*(2*(a^3 - a*b^2)*d^2*f^3*x^3 - 6*b^3*c^2*f^2 - 6*(b^3*d^2*f^2 - (a^3 - a*b^2)*c*d*f^3)*x^2 - 6*(2*b^3*c*d*f^2 - (a^3 - a*b^2)*c^2*f^3)*x + (6*I*a^2*b*d^2*f*x + 6*I*a^2*b*c*d*f + 3*I*a*b^2*d^2 + (6*I*a*b^2*d^2*f*x + 6*I*a*b^2*c*d*f + 3*I*b^3*d^2)*tan(f*x + e))*dilog((2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + (-6*I*a^2*b*d^2*f*x - 6*I*a^2*b*c*d*f - 3*I*a*b^2*d^2 + (-6*I*a*b^2*d^2*f*x - 6*I*a*b^2*c*d*f - 3*I*b^3*d^2)*tan(f*x + e))*dilog((2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + 6*(a^2*b*d^2*f^2*x^2 - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f + a*b^2*d^2*e + (2*a^2*b*c*d*f^2 + a*b^2*d^2*f)*x + (a*b^2*d^2*f^2*x^2 - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f + b^3*d^2*e + (2*a*b^2*c*d*f^2 + b^3*d^2*f)*x)*tan(f*x + e))*log(-(2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 6*(a^2*b*d^2*f^2*x^2 - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f + a*b^2*d^2*e + (2*a^2*b*c*d*f^2 + a*b^2*d^2*f)*x + (a*b^2*d^2*f^2*x^2 - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f + b^3*d^2*e + (2*a*b^2*c*d*f^2 + b^3*d^2*f)*x)*tan(f*x + e))*log(-(2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 6*(a^2*b*d^2*e^2 + a^2*b*c^2*f^2 - a*b^2*d^2*e - (2*a^2*b*c*d*e - a*b^2*c*d)*f + (a*b^2*d^2*e^2 + a*b^2*c^2*f^2 - b^3*d^2*e - (2*a*b^2*c*d*e - b^3*c*d)*f)*tan(f*x + e))*log(((I*a*b + b^2)*tan(f*x + e)^2 - a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)) + 6*(a^2*b*d^2*e^2 + a^2*b*c^2*f^2 - a*b^2*d^2*e - (2*a^2*b*c*d*e - a*b^2*c*d)*f + (a*b^2*d^2*e^2 + a*b^2*c^2*f^2 - b^3*d^2*e - (2*a*b^2*c*d*e - b^3*c*d)*f)*tan(f*x + e))*log(((I*a*b - b^2)*tan(f*x + e)^2 + a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)) + 3*(a*b^2*d^2*tan(f*x + e) + a^2*b*d^2)*polylog(3, ((a^2 + 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 - 2*I*a*b + b^2 + (2*I*a^2 - 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 3*(a*b^2*d^2*tan(f*x + e) + a^2*b*d^2)*polylog(3, ((a^2 - 2*I*a*b - b^2)*tan(f*x + e)^2 - a^2 + 2*I*a*b + b^2 + (-2*I*a^2 - 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 2*((a^2*b - b^3)*d^2*f^3*x^3 + 3*a*b^2*c^2*f^2 + 3*(a*b^2*d^2*f^2 + (a^2*b - b^3)*c*d*f^3)*x^2 + 3*(2*a*b^2*c*d*f^2 + (a^2*b - b^3)*c^2*f^3)*x)*tan(f*x + e))/((a^4*b + 2*a^2*b^3 + b^5)*f^3*tan(f*x + e) + (a^5 + 2*a^3*b^2 + a*b^4)*f^3)","C",0
61,1,849,0,0.587715," ","integrate((d*x+c)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(a^{3} - a b^{2}\right)} d f^{2} x^{2} - 2 \, b^{3} c f - 2 \, {\left(b^{3} d f - {\left(a^{3} - a b^{2}\right)} c f^{2}\right)} x + {\left(i \, a b^{2} d \tan\left(f x + e\right) + i \, a^{2} b d\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + {\left(-i \, a b^{2} d \tan\left(f x + e\right) - i \, a^{2} b d\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}} + 1\right) + 2 \, {\left(a^{2} b d f x + a^{2} b d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \tan\left(f x + e\right)\right)} \log\left(-\frac{2 \, {\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} - 2 i \, a b - {\left(-2 i \, a^{2} + 4 \, a b + 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) + 2 \, {\left(a^{2} b d f x + a^{2} b d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \tan\left(f x + e\right)\right)} \log\left(-\frac{2 \, {\left(-i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} - 2 \, a^{2} + 2 i \, a b - {\left(2 i \, a^{2} + 4 \, a b - 2 i \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{2} + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + b^{2}}\right) - {\left(2 \, a^{2} b d e - 2 \, a^{2} b c f - a b^{2} d + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f - b^{3} d\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{{\left(i \, a b + b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(2 \, a^{2} b d e - 2 \, a^{2} b c f - a b^{2} d + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f - b^{3} d\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{{\left(i \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + i \, a b + {\left(i \, a^{2} + i \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left({\left(a^{2} b - b^{3}\right)} d f^{2} x^{2} + 2 \, a b^{2} c f + 2 \, {\left(a b^{2} d f + {\left(a^{2} b - b^{3}\right)} c f^{2}\right)} x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \tan\left(f x + e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)}}"," ",0,"1/2*((a^3 - a*b^2)*d*f^2*x^2 - 2*b^3*c*f - 2*(b^3*d*f - (a^3 - a*b^2)*c*f^2)*x + (I*a*b^2*d*tan(f*x + e) + I*a^2*b*d)*dilog((2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + (-I*a*b^2*d*tan(f*x + e) - I*a^2*b*d)*dilog((2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2) + 1) + 2*(a^2*b*d*f*x + a^2*b*d*e + (a*b^2*d*f*x + a*b^2*d*e)*tan(f*x + e))*log(-(2*(I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 - 2*I*a*b - (-2*I*a^2 + 4*a*b + 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) + 2*(a^2*b*d*f*x + a^2*b*d*e + (a*b^2*d*f*x + a*b^2*d*e)*tan(f*x + e))*log(-(2*(-I*a*b - b^2)*tan(f*x + e)^2 - 2*a^2 + 2*I*a*b - (2*I*a^2 + 4*a*b - 2*I*b^2)*tan(f*x + e))/((a^2 + b^2)*tan(f*x + e)^2 + a^2 + b^2)) - (2*a^2*b*d*e - 2*a^2*b*c*f - a*b^2*d + (2*a*b^2*d*e - 2*a*b^2*c*f - b^3*d)*tan(f*x + e))*log(((I*a*b + b^2)*tan(f*x + e)^2 - a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)) - (2*a^2*b*d*e - 2*a^2*b*c*f - a*b^2*d + (2*a*b^2*d*e - 2*a*b^2*c*f - b^3*d)*tan(f*x + e))*log(((I*a*b - b^2)*tan(f*x + e)^2 + a^2 + I*a*b + (I*a^2 + I*b^2)*tan(f*x + e))/(tan(f*x + e)^2 + 1)) + ((a^2*b - b^3)*d*f^2*x^2 + 2*a*b^2*c*f + 2*(a*b^2*d*f + (a^2*b - b^3)*c*f^2)*x)*tan(f*x + e))/((a^4*b + 2*a^2*b^3 + b^5)*f^2*tan(f*x + e) + (a^5 + 2*a^3*b^2 + a*b^4)*f^2)","B",0
62,0,0,0,0.446602," ","integrate(1/(d*x+c)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d x + a^{2} c + {\left(b^{2} d x + b^{2} c\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(a b d x + a b c\right)} \tan\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d*x + a^2*c + (b^2*d*x + b^2*c)*tan(f*x + e)^2 + 2*(a*b*d*x + a*b*c)*tan(f*x + e)), x)","F",0
63,0,0,0,0.457138," ","integrate(1/(d*x+c)^2/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} \tan\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*tan(f*x + e)^2 + 2*(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*tan(f*x + e)), x)","F",0
