1,1,306,0,0.556807," ","integrate(x^3*cot(b*x+a),x, algorithm=""fricas"")","\frac{-6 i \, b^{2} x^{2} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) - 4 \, a^{3} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 4 \, a^{3} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 6 \, b x {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, b x {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 i \, {\rm polylog}\left(4, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) - 3 i \, {\rm polylog}\left(4, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right)}{8 \, b^{4}}"," ",0,"1/8*(-6*I*b^2*x^2*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + 6*I*b^2*x^2*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) - 4*a^3*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2) - 4*a^3*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2) + 6*b*x*polylog(3, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + 6*b*x*polylog(3, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 4*(b^3*x^3 + a^3)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1) + 4*(b^3*x^3 + a^3)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1) + 3*I*polylog(4, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) - 3*I*polylog(4, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)))/b^4","C",0
2,1,244,0,0.573969," ","integrate(x^2*cot(b*x+a),x, algorithm=""fricas"")","\frac{-2 i \, b x {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 2 i \, b x {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 2 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right)}{4 \, b^{3}}"," ",0,"1/4*(-2*I*b*x*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + 2*I*b*x*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 2*a^2*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*a^2*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(b^2*x^2 - a^2)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1) + 2*(b^2*x^2 - a^2)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1) + polylog(3, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + polylog(3, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)))/b^3","C",0
3,1,174,0,0.526111," ","integrate(x*cot(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, a \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 2 \, {\left(b x + a\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b x + a\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + i \, {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) - i \, {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right)}{4 \, b^{2}}"," ",0,"-1/4*(2*a*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*a*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2) - 2*(b*x + a)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1) - 2*(b*x + a)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1) + I*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) - I*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)))/b^2","B",0
4,0,0,0,0.544469," ","integrate(cot(b*x+a)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)}{x}, x\right)"," ",0,"integral(cot(b*x + a)/x, x)","F",0
5,0,0,0,0.623598," ","integrate(cot(b*x+a)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)}{x^{2}}, x\right)"," ",0,"integral(cot(b*x + a)/x^2, x)","F",0
6,1,372,0,0.687541," ","integrate(x^3*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{4} x^{4} \sin\left(2 \, b x + 2 \, a\right) + 4 \, b^{3} x^{3} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{3} x^{3} + 6 i \, b x {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - 6 i \, b x {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) \sin\left(2 \, b x + 2 \, a\right) - 3 \, {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - 3 \, {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right)}{4 \, b^{4} \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"-1/4*(b^4*x^4*sin(2*b*x + 2*a) + 4*b^3*x^3*cos(2*b*x + 2*a) + 4*b^3*x^3 + 6*I*b*x*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - 6*I*b*x*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - 6*a^2*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) - 6*a^2*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) - 6*(b^2*x^2 - a^2)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1)*sin(2*b*x + 2*a) - 6*(b^2*x^2 - a^2)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1)*sin(2*b*x + 2*a) - 3*polylog(3, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - 3*polylog(3, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a))/(b^4*sin(2*b*x + 2*a))","C",0
7,1,281,0,1.162601," ","integrate(x^2*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{3} x^{3} \sin\left(2 \, b x + 2 \, a\right) + 6 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right) + 6 \, b^{2} x^{2} + 6 \, a \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right) + 6 \, a \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b x + a\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b x + a\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) \sin\left(2 \, b x + 2 \, a\right) + 3 i \, {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - 3 i \, {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right)}{6 \, b^{3} \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"-1/6*(2*b^3*x^3*sin(2*b*x + 2*a) + 6*b^2*x^2*cos(2*b*x + 2*a) + 6*b^2*x^2 + 6*a*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) + 6*a*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) - 6*(b*x + a)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1)*sin(2*b*x + 2*a) - 6*(b*x + a)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1)*sin(2*b*x + 2*a) + 3*I*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - 3*I*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a))/(b^3*sin(2*b*x + 2*a))","B",0
8,1,75,0,0.740499," ","integrate(x*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{2} x^{2} \sin\left(2 \, b x + 2 \, a\right) + 2 \, b x \cos\left(2 \, b x + 2 \, a\right) + 2 \, b x - \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right)}{2 \, b^{2} \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"-1/2*(b^2*x^2*sin(2*b*x + 2*a) + 2*b*x*cos(2*b*x + 2*a) + 2*b*x - log(-1/2*cos(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a))/(b^2*sin(2*b*x + 2*a))","B",0
9,0,0,0,2.102093," ","integrate(cot(b*x+a)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)^{2}}{x}, x\right)"," ",0,"integral(cot(b*x + a)^2/x, x)","F",0
10,0,0,0,0.857315," ","integrate(cot(b*x+a)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(cot(b*x + a)^2/x^2, x)","F",0
11,1,565,0,2.052706," ","integrate(x^3*cot(b*x+a)^3,x, algorithm=""fricas"")","\frac{8 \, b^{3} x^{3} + 12 \, b^{2} x^{2} \sin\left(2 \, b x + 2 \, a\right) + {\left(-6 i \, b^{2} x^{2} + {\left(6 i \, b^{2} x^{2} - 6 i\right)} \cos\left(2 \, b x + 2 \, a\right) + 6 i\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(6 i \, b^{2} x^{2} + {\left(-6 i \, b^{2} x^{2} + 6 i\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 i\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) - 4 \, {\left(a^{3} - {\left(a^{3} - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, a\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 4 \, {\left(a^{3} - {\left(a^{3} - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, a\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 4 \, {\left(b^{3} x^{3} + a^{3} - 3 \, b x - {\left(b^{3} x^{3} + a^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, a\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 4 \, {\left(b^{3} x^{3} + a^{3} - 3 \, b x - {\left(b^{3} x^{3} + a^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, a\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-3 i \, \cos\left(2 \, b x + 2 \, a\right) + 3 i\right)} {\rm polylog}\left(4, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(3 i \, \cos\left(2 \, b x + 2 \, a\right) - 3 i\right)} {\rm polylog}\left(4, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) - 6 \, {\left(b x \cos\left(2 \, b x + 2 \, a\right) - b x\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) - 6 \, {\left(b x \cos\left(2 \, b x + 2 \, a\right) - b x\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right)}{8 \, {\left(b^{4} \cos\left(2 \, b x + 2 \, a\right) - b^{4}\right)}}"," ",0,"1/8*(8*b^3*x^3 + 12*b^2*x^2*sin(2*b*x + 2*a) + (-6*I*b^2*x^2 + (6*I*b^2*x^2 - 6*I)*cos(2*b*x + 2*a) + 6*I)*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + (6*I*b^2*x^2 + (-6*I*b^2*x^2 + 6*I)*cos(2*b*x + 2*a) - 6*I)*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) - 4*(a^3 - (a^3 - 3*a)*cos(2*b*x + 2*a) - 3*a)*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2) - 4*(a^3 - (a^3 - 3*a)*cos(2*b*x + 2*a) - 3*a)*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2) + 4*(b^3*x^3 + a^3 - 3*b*x - (b^3*x^3 + a^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*a)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1) + 4*(b^3*x^3 + a^3 - 3*b*x - (b^3*x^3 + a^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*a)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1) + (-3*I*cos(2*b*x + 2*a) + 3*I)*polylog(4, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + (3*I*cos(2*b*x + 2*a) - 3*I)*polylog(4, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) - 6*(b*x*cos(2*b*x + 2*a) - b*x)*polylog(3, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) - 6*(b*x*cos(2*b*x + 2*a) - b*x)*polylog(3, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)))/(b^4*cos(2*b*x + 2*a) - b^4)","C",0
12,1,423,0,0.664838," ","integrate(x^2*cot(b*x+a)^3,x, algorithm=""fricas"")","\frac{4 \, b^{2} x^{2} + 4 \, b x \sin\left(2 \, b x + 2 \, a\right) + {\left(2 i \, b x \cos\left(2 \, b x + 2 \, a\right) - 2 i \, b x\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-2 i \, b x \cos\left(2 \, b x + 2 \, a\right) + 2 i \, b x\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 2 \, {\left(a^{2} - {\left(a^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(a^{2} - {\left(a^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(b^{2} x^{2} - a^{2} - {\left(b^{2} x^{2} - a^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b^{2} x^{2} - a^{2} - {\left(b^{2} x^{2} - a^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) - {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right)}{4 \, {\left(b^{3} \cos\left(2 \, b x + 2 \, a\right) - b^{3}\right)}}"," ",0,"1/4*(4*b^2*x^2 + 4*b*x*sin(2*b*x + 2*a) + (2*I*b*x*cos(2*b*x + 2*a) - 2*I*b*x)*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + (-2*I*b*x*cos(2*b*x + 2*a) + 2*I*b*x)*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 2*(a^2 - (a^2 - 1)*cos(2*b*x + 2*a) - 1)*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(a^2 - (a^2 - 1)*cos(2*b*x + 2*a) - 1)*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(b^2*x^2 - a^2 - (b^2*x^2 - a^2)*cos(2*b*x + 2*a))*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1) + 2*(b^2*x^2 - a^2 - (b^2*x^2 - a^2)*cos(2*b*x + 2*a))*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1) - (cos(2*b*x + 2*a) - 1)*polylog(3, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) - (cos(2*b*x + 2*a) - 1)*polylog(3, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)))/(b^3*cos(2*b*x + 2*a) - b^3)","C",0
13,1,291,0,0.656824," ","integrate(x*cot(b*x+a)^3,x, algorithm=""fricas"")","\frac{4 \, b x + {\left(i \, \cos\left(2 \, b x + 2 \, a\right) - i\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + i\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 2 \, {\left(a \cos\left(2 \, b x + 2 \, a\right) - a\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(a \cos\left(2 \, b x + 2 \, a\right) - a\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)}{4 \, {\left(b^{2} \cos\left(2 \, b x + 2 \, a\right) - b^{2}\right)}}"," ",0,"1/4*(4*b*x + (I*cos(2*b*x + 2*a) - I)*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + (-I*cos(2*b*x + 2*a) + I)*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 2*(a*cos(2*b*x + 2*a) - a)*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(a*cos(2*b*x + 2*a) - a)*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(b*x - (b*x + a)*cos(2*b*x + 2*a) + a)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1) + 2*(b*x - (b*x + a)*cos(2*b*x + 2*a) + a)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1) + 2*sin(2*b*x + 2*a))/(b^2*cos(2*b*x + 2*a) - b^2)","B",0
14,0,0,0,0.552306," ","integrate(cot(b*x+a)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)^{3}}{x}, x\right)"," ",0,"integral(cot(b*x + a)^3/x, x)","F",0
15,0,0,0,0.919925," ","integrate(cot(b*x+a)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)^{3}}{x^{2}}, x\right)"," ",0,"integral(cot(b*x + a)^3/x^2, x)","F",0
16,1,153,0,0.755200," ","integrate((d*x+c)^3/(a+I*a*cot(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, d^{3} f^{4} x^{4} + 8 \, c d^{2} f^{4} x^{3} + 12 \, c^{2} d f^{4} x^{2} + 8 \, c^{3} f^{4} x + {\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\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{16 \, a f^{4}}"," ",0,"1/16*(2*d^3*f^4*x^4 + 8*c*d^2*f^4*x^3 + 12*c^2*d*f^4*x^2 + 8*c^3*f^4*x + (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)*e^(2*I*f*x + 2*I*e))/(a*f^4)","A",0
17,1,95,0,0.498781," ","integrate((d*x+c)^2/(a+I*a*cot(f*x+e)),x, algorithm=""fricas"")","\frac{4 \, d^{2} f^{3} x^{3} + 12 \, c d f^{3} x^{2} + 12 \, c^{2} f^{3} x + {\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\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{24 \, a f^{3}}"," ",0,"1/24*(4*d^2*f^3*x^3 + 12*c*d*f^3*x^2 + 12*c^2*f^3*x + (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)*e^(2*I*f*x + 2*I*e))/(a*f^3)","A",0
18,1,48,0,0.482601," ","integrate((d*x+c)/(a+I*a*cot(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, d f^{2} x^{2} + 4 \, c f^{2} x + {\left(2 i \, d f x + 2 i \, c f - d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{8 \, a f^{2}}"," ",0,"1/8*(2*d*f^2*x^2 + 4*c*f^2*x + (2*I*d*f*x + 2*I*c*f - d)*e^(2*I*f*x + 2*I*e))/(a*f^2)","A",0
19,1,51,0,0.565468," ","integrate(1/(d*x+c)/(a+I*a*cot(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
20,1,72,0,0.643931," ","integrate(1/(d*x+c)^2/(a+I*a*cot(f*x+e)),x, algorithm=""fricas"")","\frac{{\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 e^{\left(2 i \, f x + 2 i \, e\right)} - d}{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)/(a*d^3*x + a*c*d^2)","A",0
21,1,118,0,0.832643," ","integrate(1/(d*x+c)^3/(a+I*a*cot(f*x+e)),x, algorithm=""fricas"")","\frac{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} + {\left(2 i \, d^{2} f x + 2 i \, c d f + d^{2}\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*(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 + (2*I*d^2*f*x + 2*I*c*d*f + d^2)*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
22,1,253,0,1.904788," ","integrate((d*x+c)^3/(a+I*a*cot(f*x+e))^2,x, algorithm=""fricas"")","\frac{32 \, d^{3} f^{4} x^{4} + 128 \, c d^{2} f^{4} x^{3} + 192 \, c^{2} d f^{4} x^{2} + 128 \, c^{3} f^{4} x + {\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\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)}}{512 \, a^{2} f^{4}}"," ",0,"1/512*(32*d^3*f^4*x^4 + 128*c*d^2*f^4*x^3 + 192*c^2*d*f^4*x^2 + 128*c^3*f^4*x + (-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)*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))/(a^2*f^4)","A",0
23,1,151,0,1.514239," ","integrate((d*x+c)^2/(a+I*a*cot(f*x+e))^2,x, algorithm=""fricas"")","\frac{32 \, d^{2} f^{3} x^{3} + 96 \, c d f^{3} x^{2} + 96 \, c^{2} f^{3} x + {\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\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)}}{384 \, a^{2} f^{3}}"," ",0,"1/384*(32*d^2*f^3*x^3 + 96*c*d*f^3*x^2 + 96*c^2*f^3*x + (-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)*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))/(a^2*f^3)","A",0
24,1,69,0,0.757664," ","integrate((d*x+c)/(a+I*a*cot(f*x+e))^2,x, algorithm=""fricas"")","\frac{8 \, d f^{2} x^{2} + 16 \, c f^{2} x + {\left(-4 i \, d f x - 4 i \, c f + d\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)}}{64 \, a^{2} f^{2}}"," ",0,"1/64*(8*d*f^2*x^2 + 16*c*f^2*x + (-4*I*d*f*x - 4*I*c*f + d)*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))/(a^2*f^2)","A",0
25,1,80,0,0.882021," ","integrate(1/(d*x+c)/(a+I*a*cot(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\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)} - 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)} + \log\left(\frac{d x + c}{d}\right)}{4 \, a^{2} d}"," ",0,"1/4*(Ei((4*I*d*f*x + 4*I*c*f)/d)*e^((4*I*d*e - 4*I*c*f)/d) - 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^2*d)","A",0
26,1,129,0,0.604924," ","integrate(1/(d*x+c)^2/(a+I*a*cot(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\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)} + {\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)} - d e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d e^{\left(2 i \, f x + 2 i \, e\right)} - d}{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((4*I*d*f*x + 4*I*c*f)/d)*e^((4*I*d*e - 4*I*c*f)/d) + (-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) - d*e^(4*I*f*x + 4*I*e) + 2*d*e^(2*I*f*x + 2*I*e) - d)/(a^2*d^3*x + a^2*c*d^2)","A",0
27,1,353,0,0.949392," ","integrate((d*x+c)^3/(a+I*a*cot(f*x+e))^3,x, algorithm=""fricas"")","\frac{864 \, d^{3} f^{4} x^{4} + 3456 \, c d^{2} f^{4} x^{3} + 5184 \, c^{2} d f^{4} x^{2} + 3456 \, c^{3} f^{4} x + {\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\right)} e^{\left(6 i \, f x + 6 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(4 i \, f x + 4 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(2 i \, f x + 2 i \, e\right)}}{27648 \, a^{3} f^{4}}"," ",0,"1/27648*(864*d^3*f^4*x^4 + 3456*c*d^2*f^4*x^3 + 5184*c^2*d*f^4*x^2 + 3456*c^3*f^4*x + (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)*e^(6*I*f*x + 6*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^(4*I*f*x + 4*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^(2*I*f*x + 2*I*e))/(a^3*f^4)","A",0
28,1,207,0,0.812745," ","integrate((d*x+c)^2/(a+I*a*cot(f*x+e))^3,x, algorithm=""fricas"")","\frac{288 \, d^{2} f^{3} x^{3} + 864 \, c d f^{3} x^{2} + 864 \, c^{2} f^{3} x + {\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\right)} e^{\left(6 i \, f x + 6 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(4 i \, f x + 4 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(2 i \, f x + 2 i \, e\right)}}{6912 \, a^{3} f^{3}}"," ",0,"1/6912*(288*d^2*f^3*x^3 + 864*c*d*f^3*x^2 + 864*c^2*f^3*x + (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)*e^(6*I*f*x + 6*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^(4*I*f*x + 4*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^(2*I*f*x + 2*I*e))/(a^3*f^3)","A",0
29,1,94,0,0.658046," ","integrate((d*x+c)/(a+I*a*cot(f*x+e))^3,x, algorithm=""fricas"")","\frac{72 \, d f^{2} x^{2} + 144 \, c f^{2} x + {\left(24 i \, d f x + 24 i \, c f - 4 \, d\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-108 i \, d f x - 108 i \, c f + 27 \, d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(216 i \, d f x + 216 i \, c f - 108 \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{1152 \, a^{3} f^{2}}"," ",0,"1/1152*(72*d*f^2*x^2 + 144*c*f^2*x + (24*I*d*f*x + 24*I*c*f - 4*d)*e^(6*I*f*x + 6*I*e) + (-108*I*d*f*x - 108*I*c*f + 27*d)*e^(4*I*f*x + 4*I*e) + (216*I*d*f*x + 216*I*c*f - 108*d)*e^(2*I*f*x + 2*I*e))/(a^3*f^2)","A",0
30,1,113,0,0.833364," ","integrate(1/(d*x+c)/(a+I*a*cot(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\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)} - 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)} + 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)} - \log\left(\frac{d x + c}{d}\right)}{8 \, a^{3} d}"," ",0,"-1/8*(Ei((6*I*d*f*x + 6*I*c*f)/d)*e^((6*I*d*e - 6*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) + 3*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^3*d)","A",0
31,1,180,0,0.764203," ","integrate(1/(d*x+c)^2/(a+I*a*cot(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\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)} + {\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{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 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}{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((6*I*d*f*x + 6*I*c*f)/d)*e^((6*I*d*e - 6*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((2*I*d*f*x + 2*I*c*f)/d)*e^((2*I*d*e - 2*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)/(a^3*d^3*x + a^3*c*d^2)","A",0
32,0,0,0,0.714010," ","integrate((d*x+c)^m*(a+I*a*cot(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{{\left(4 \, a^{2} d f x + 4 \, a^{2} c f + 2 i \, a^{2} d m\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((4*a^2*d*f*x + 4*a^2*c*f + 2*I*a^2*d*m)*(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
33,0,0,0,0.632636," ","integrate((d*x+c)^m*(a+I*a*cot(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)} - 1}, x\right)"," ",0,"integral(-2*(d*x + c)^m*a/(e^(2*I*f*x + 2*I*e) - 1), x)","F",0
34,1,84,0,0.542393," ","integrate((d*x+c)^m/(a+I*a*cot(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
35,1,140,0,0.680649," ","integrate((d*x+c)^m/(a+I*a*cot(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\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) + {\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) + 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*((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) + (-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*(d*f*x + c*f)*(d*x + c)^m)/(a^2*d*f*m + a^2*d*f)","A",0
36,1,192,0,0.551475," ","integrate((d*x+c)^m/(a+I*a*cot(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\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) + {\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(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) + 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*((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) + (-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) + (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) + 12*(d*f*x + c*f)*(d*x + c)^m)/(a^3*d*f*m + a^3*d*f)","A",0
37,1,626,0,0.738923," ","integrate((d*x+c)^3*(a+b*cot(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, \cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) - 3 i \, b d^{3} {\rm polylog}\left(4, \cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\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(\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\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(\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\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{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{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{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) - \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{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(-\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right) + 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(-\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) + 6 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, \cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) + 6 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, \cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\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, cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) - 3*I*b*d^3*polylog(4, cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) + (-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(cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) + (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(cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) - 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(-1/2*cos(2*f*x + 2*e) + 1/2*I*sin(2*f*x + 2*e) + 1/2) - 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(-1/2*cos(2*f*x + 2*e) - 1/2*I*sin(2*f*x + 2*e) + 1/2) + 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(-cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e) + 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(-cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e) + 1) + 6*(b*d^3*f*x + b*c*d^2*f)*polylog(3, cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) + 6*(b*d^3*f*x + b*c*d^2*f)*polylog(3, cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)))/f^4","C",0
38,1,403,0,0.606765," ","integrate((d*x+c)^2*(a+b*cot(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, \cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) + 3 \, b d^{2} {\rm polylog}\left(3, \cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) + {\left(-6 i \, b d^{2} f x - 6 i \, b c d f\right)} {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) + {\left(6 i \, b d^{2} f x + 6 i \, b c d f\right)} {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) + 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) + 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) - \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{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(-\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right) + 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(-\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right) + 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, cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) + 3*b*d^2*polylog(3, cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) + (-6*I*b*d^2*f*x - 6*I*b*c*d*f)*dilog(cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) + (6*I*b*d^2*f*x + 6*I*b*c*d*f)*dilog(cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) + 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(-1/2*cos(2*f*x + 2*e) + 1/2*I*sin(2*f*x + 2*e) + 1/2) + 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(-1/2*cos(2*f*x + 2*e) - 1/2*I*sin(2*f*x + 2*e) + 1/2) + 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(-cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e) + 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(-cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e) + 1))/f^3","C",0
39,1,224,0,0.520248," ","integrate((d*x+c)*(a+b*cot(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(\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) + i \, b d {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) - 2 \, {\left(b d e - b c f\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) - 2 \, {\left(b d e - b c f\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) - \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) + 2 \, {\left(b d f x + b d e\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) + 2 \, {\left(b d f x + b d e\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right) + 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(cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) + I*b*d*dilog(cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) - 2*(b*d*e - b*c*f)*log(-1/2*cos(2*f*x + 2*e) + 1/2*I*sin(2*f*x + 2*e) + 1/2) - 2*(b*d*e - b*c*f)*log(-1/2*cos(2*f*x + 2*e) - 1/2*I*sin(2*f*x + 2*e) + 1/2) + 2*(b*d*f*x + b*d*e)*log(-cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e) + 1) + 2*(b*d*f*x + b*d*e)*log(-cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e) + 1))/f^2","B",0
40,0,0,0,0.648160," ","integrate((a+b*cot(f*x+e))/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \cot\left(f x + e\right) + a}{d x + c}, x\right)"," ",0,"integral((b*cot(f*x + e) + a)/(d*x + c), x)","F",0
41,0,0,0,0.502598," ","integrate((a+b*cot(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \cot\left(f x + e\right) + a}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b*cot(f*x + e) + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
42,1,1154,0,0.904118," ","integrate((d*x+c)^3*(a+b*cot(f*x+e))^2,x, algorithm=""fricas"")","-\frac{4 \, b^{2} d^{3} f^{3} x^{3} + 12 \, b^{2} c d^{2} f^{3} x^{2} + 12 \, b^{2} c^{2} d f^{3} x + 4 \, b^{2} c^{3} f^{3} - 3 i \, a b d^{3} {\rm polylog}\left(4, \cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\right) + 3 i \, a b d^{3} {\rm polylog}\left(4, \cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\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(\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\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(\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(2 \, a b d^{3} e^{3} - 2 \, a b c^{3} f^{3} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c^{2} d e - b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(2 \, a b d^{3} e^{3} - 2 \, a b c^{3} f^{3} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c^{2} d e - b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) - \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b c^{2} d e f^{2} - 3 \, b^{2} d^{3} e^{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 d^{2} e^{2} - b^{2} c d^{2} e\right)} f + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b c^{2} d e f^{2} - 3 \, b^{2} d^{3} e^{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 d^{2} e^{2} - b^{2} c d^{2} e\right)} f + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(2 \, f x + 2 \, e\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, \cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\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, \cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\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)} \cos\left(2 \, f x + 2 \, e\right) - {\left({\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\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f^{4} \sin\left(2 \, f x + 2 \, e\right)}"," ",0,"-1/4*(4*b^2*d^3*f^3*x^3 + 12*b^2*c*d^2*f^3*x^2 + 12*b^2*c^2*d*f^3*x + 4*b^2*c^3*f^3 - 3*I*a*b*d^3*polylog(4, cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) + 3*I*a*b*d^3*polylog(4, cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) - (-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(cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) - (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(cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) + 2*(2*a*b*d^3*e^3 - 2*a*b*c^3*f^3 - 3*b^2*d^3*e^2 + 3*(2*a*b*c^2*d*e - b^2*c^2*d)*f^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f)*log(-1/2*cos(2*f*x + 2*e) + 1/2*I*sin(2*f*x + 2*e) + 1/2)*sin(2*f*x + 2*e) + 2*(2*a*b*d^3*e^3 - 2*a*b*c^3*f^3 - 3*b^2*d^3*e^2 + 3*(2*a*b*c^2*d*e - b^2*c^2*d)*f^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f)*log(-1/2*cos(2*f*x + 2*e) - 1/2*I*sin(2*f*x + 2*e) + 1/2)*sin(2*f*x + 2*e) - 2*(2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*c^2*d*e*f^2 - 3*b^2*d^3*e^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*log(-cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e) + 1)*sin(2*f*x + 2*e) - 2*(2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*c^2*d*e*f^2 - 3*b^2*d^3*e^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*log(-cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e) + 1)*sin(2*f*x + 2*e) - 3*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3)*polylog(3, cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) - 3*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3)*polylog(3, cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) + 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)*cos(2*f*x + 2*e) - ((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)*sin(2*f*x + 2*e))/(f^4*sin(2*f*x + 2*e))","C",0
43,1,715,0,0.826654," ","integrate((d*x+c)^2*(a+b*cot(f*x+e))^2,x, algorithm=""fricas"")","-\frac{6 \, b^{2} d^{2} f^{2} x^{2} + 12 \, b^{2} c d f^{2} x + 6 \, b^{2} c^{2} f^{2} - 3 \, a b d^{2} {\rm polylog}\left(3, \cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\right) - 3 \, a b d^{2} {\rm polylog}\left(3, \cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\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(\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\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(\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\right) - 6 \, {\left(a b d^{2} e^{2} + a b c^{2} f^{2} - b^{2} d^{2} e - {\left(2 \, a b c d e - b^{2} c d\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) \sin\left(2 \, f x + 2 \, e\right) - 6 \, {\left(a b d^{2} e^{2} + a b c^{2} f^{2} - b^{2} d^{2} e - {\left(2 \, a b c d e - b^{2} c d\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) - \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) \sin\left(2 \, f x + 2 \, e\right) - 6 \, {\left(a b d^{2} f^{2} x^{2} - a b d^{2} e^{2} + 2 \, a b c d e f + b^{2} d^{2} e + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(2 \, f x + 2 \, e\right) - 6 \, {\left(a b d^{2} f^{2} x^{2} - a b d^{2} e^{2} + 2 \, a b c d e f + b^{2} d^{2} e + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(2 \, f x + 2 \, e\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)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} c d f^{3} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} f^{3} x\right)} \sin\left(2 \, f x + 2 \, e\right)}{6 \, f^{3} \sin\left(2 \, f x + 2 \, e\right)}"," ",0,"-1/6*(6*b^2*d^2*f^2*x^2 + 12*b^2*c*d*f^2*x + 6*b^2*c^2*f^2 - 3*a*b*d^2*polylog(3, cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) - 3*a*b*d^2*polylog(3, cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) - (-6*I*a*b*d^2*f*x - 6*I*a*b*c*d*f - 3*I*b^2*d^2)*dilog(cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) - (6*I*a*b*d^2*f*x + 6*I*a*b*c*d*f + 3*I*b^2*d^2)*dilog(cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) - 6*(a*b*d^2*e^2 + a*b*c^2*f^2 - b^2*d^2*e - (2*a*b*c*d*e - b^2*c*d)*f)*log(-1/2*cos(2*f*x + 2*e) + 1/2*I*sin(2*f*x + 2*e) + 1/2)*sin(2*f*x + 2*e) - 6*(a*b*d^2*e^2 + a*b*c^2*f^2 - b^2*d^2*e - (2*a*b*c*d*e - b^2*c*d)*f)*log(-1/2*cos(2*f*x + 2*e) - 1/2*I*sin(2*f*x + 2*e) + 1/2)*sin(2*f*x + 2*e) - 6*(a*b*d^2*f^2*x^2 - a*b*d^2*e^2 + 2*a*b*c*d*e*f + b^2*d^2*e + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*log(-cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e) + 1)*sin(2*f*x + 2*e) - 6*(a*b*d^2*f^2*x^2 - a*b*d^2*e^2 + 2*a*b*c*d*e*f + b^2*d^2*e + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*log(-cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e) + 1)*sin(2*f*x + 2*e) + 6*(b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*cos(2*f*x + 2*e) - 2*((a^2 - b^2)*d^2*f^3*x^3 + 3*(a^2 - b^2)*c*d*f^3*x^2 + 3*(a^2 - b^2)*c^2*f^3*x)*sin(2*f*x + 2*e))/(f^3*sin(2*f*x + 2*e))","C",0
44,1,378,0,0.875040," ","integrate((d*x+c)*(a+b*cot(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, b^{2} d f x + i \, a b d {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\right) - i \, a b d {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) \sin\left(2 \, f x + 2 \, e\right) + 2 \, b^{2} c f + {\left(2 \, a b d e - 2 \, a b c f - b^{2} d\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) \sin\left(2 \, f x + 2 \, e\right) + {\left(2 \, a b d e - 2 \, a b c f - b^{2} d\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) - \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a b d f x + a b d e\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a b d f x + a b d e\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left({\left(a^{2} - b^{2}\right)} d f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} c f^{2} x\right)} \sin\left(2 \, f x + 2 \, e\right)}{2 \, f^{2} \sin\left(2 \, f x + 2 \, e\right)}"," ",0,"-1/2*(2*b^2*d*f*x + I*a*b*d*dilog(cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) - I*a*b*d*dilog(cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e))*sin(2*f*x + 2*e) + 2*b^2*c*f + (2*a*b*d*e - 2*a*b*c*f - b^2*d)*log(-1/2*cos(2*f*x + 2*e) + 1/2*I*sin(2*f*x + 2*e) + 1/2)*sin(2*f*x + 2*e) + (2*a*b*d*e - 2*a*b*c*f - b^2*d)*log(-1/2*cos(2*f*x + 2*e) - 1/2*I*sin(2*f*x + 2*e) + 1/2)*sin(2*f*x + 2*e) - 2*(a*b*d*f*x + a*b*d*e)*log(-cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e) + 1)*sin(2*f*x + 2*e) - 2*(a*b*d*f*x + a*b*d*e)*log(-cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e) + 1)*sin(2*f*x + 2*e) + 2*(b^2*d*f*x + b^2*c*f)*cos(2*f*x + 2*e) - ((a^2 - b^2)*d*f^2*x^2 + 2*(a^2 - b^2)*c*f^2*x)*sin(2*f*x + 2*e))/(f^2*sin(2*f*x + 2*e))","B",0
45,0,0,0,0.502389," ","integrate((a+b*cot(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \cot\left(f x + e\right)^{2} + 2 \, a b \cot\left(f x + e\right) + a^{2}}{d x + c}, x\right)"," ",0,"integral((b^2*cot(f*x + e)^2 + 2*a*b*cot(f*x + e) + a^2)/(d*x + c), x)","F",0
46,0,0,0,0.455844," ","integrate((a+b*cot(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \cot\left(f x + e\right)^{2} + 2 \, a b \cot\left(f x + e\right) + a^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b^2*cot(f*x + e)^2 + 2*a*b*cot(f*x + e) + a^2)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
47,1,2749,0,0.706161," ","integrate((d*x+c)^3*(a+b*cot(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d^{3} f^{4} x^{4} - 8 \, b^{3} c^{3} f^{3} - 8 \, {\left(b^{3} d^{3} f^{3} - {\left(a^{3} - 3 \, a b^{2}\right)} c d^{2} f^{4}\right)} x^{3} - 12 \, {\left(2 \, b^{3} c d^{2} f^{3} - {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d f^{4}\right)} x^{2} - 8 \, {\left(3 \, b^{3} c^{2} d f^{3} - {\left(a^{3} - 3 \, a b^{2}\right)} c^{3} f^{4}\right)} x - 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} f^{4} x^{4} + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{2} f^{4} x^{3} + 6 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d f^{4} x^{2} + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{3} f^{4} x\right)} \cos\left(2 \, f x + 2 \, e\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) + 4 \, {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b - b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e^{2}\right)} f - {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b - b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) + 4 \, {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b - b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e^{2}\right)} f - {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b - b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) - \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) + 4 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d e f^{2} + 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} e - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e^{2}\right)} f + 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 - {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d e f^{2} + 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} e - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e^{2}\right)} f + 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)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) + 4 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d e f^{2} + 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} e - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e^{2}\right)} f + 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 - {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d e f^{2} + 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} e - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e^{2}\right)} f + 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)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) - {\left(3 i \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} \cos\left(2 \, f x + 2 \, e\right) - 3 i \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} {\rm polylog}\left(4, \cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) - {\left(-3 i \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} \cos\left(2 \, f x + 2 \, e\right) + 3 i \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} {\rm polylog}\left(4, \cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\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 - {\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)} \cos\left(2 \, f x + 2 \, e\right)\right)} {\rm polylog}\left(3, \cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\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 - {\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)} \cos\left(2 \, f x + 2 \, e\right)\right)} {\rm polylog}\left(3, \cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\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)} \sin\left(2 \, f x + 2 \, e\right)}{8 \, {\left(f^{4} \cos\left(2 \, f x + 2 \, e\right) - f^{4}\right)}}"," ",0,"-1/8*(2*(a^3 - 3*a*b^2)*d^3*f^4*x^4 - 8*b^3*c^3*f^3 - 8*(b^3*d^3*f^3 - (a^3 - 3*a*b^2)*c*d^2*f^4)*x^3 - 12*(2*b^3*c*d^2*f^3 - (a^3 - 3*a*b^2)*c^2*d*f^4)*x^2 - 8*(3*b^3*c^2*d*f^3 - (a^3 - 3*a*b^2)*c^3*f^4)*x - 2*((a^3 - 3*a*b^2)*d^3*f^4*x^4 + 4*(a^3 - 3*a*b^2)*c*d^2*f^4*x^3 + 6*(a^3 - 3*a*b^2)*c^2*d*f^4*x^2 + 4*(a^3 - 3*a*b^2)*c^3*f^4*x)*cos(2*f*x + 2*e) - (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 + (-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)*cos(2*f*x + 2*e))*dilog(cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) - (-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 + (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)*cos(2*f*x + 2*e))*dilog(cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) + 4*(9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b - b^3)*d^3*e^3 + (3*a^2*b - b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b - b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b - b^3)*c*d^2*e^2)*f - (9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b - b^3)*d^3*e^3 + (3*a^2*b - b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b - b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b - b^3)*c*d^2*e^2)*f)*cos(2*f*x + 2*e))*log(-1/2*cos(2*f*x + 2*e) + 1/2*I*sin(2*f*x + 2*e) + 1/2) + 4*(9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b - b^3)*d^3*e^3 + (3*a^2*b - b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b - b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b - b^3)*c*d^2*e^2)*f - (9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b - b^3)*d^3*e^3 + (3*a^2*b - b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b - b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b - b^3)*c*d^2*e^2)*f)*cos(2*f*x + 2*e))*log(-1/2*cos(2*f*x + 2*e) - 1/2*I*sin(2*f*x + 2*e) + 1/2) + 4*((3*a^2*b - b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b - b^3)*d^3*e^3 + 3*(3*a^2*b - b^3)*c^2*d*e*f^2 + 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*e - (3*a^2*b - b^3)*c*d^2*e^2)*f + 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 - ((3*a^2*b - b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b - b^3)*d^3*e^3 + 3*(3*a^2*b - b^3)*c^2*d*e*f^2 + 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*e - (3*a^2*b - b^3)*c*d^2*e^2)*f + 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)*cos(2*f*x + 2*e))*log(-cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e) + 1) + 4*((3*a^2*b - b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b - b^3)*d^3*e^3 + 3*(3*a^2*b - b^3)*c^2*d*e*f^2 + 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*e - (3*a^2*b - b^3)*c*d^2*e^2)*f + 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 - ((3*a^2*b - b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b - b^3)*d^3*e^3 + 3*(3*a^2*b - b^3)*c^2*d*e*f^2 + 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*e - (3*a^2*b - b^3)*c*d^2*e^2)*f + 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)*cos(2*f*x + 2*e))*log(-cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e) + 1) - (3*I*(3*a^2*b - b^3)*d^3*cos(2*f*x + 2*e) - 3*I*(3*a^2*b - b^3)*d^3)*polylog(4, cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) - (-3*I*(3*a^2*b - b^3)*d^3*cos(2*f*x + 2*e) + 3*I*(3*a^2*b - b^3)*d^3)*polylog(4, cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) + 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 - (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)*cos(2*f*x + 2*e))*polylog(3, cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) + 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 - (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)*cos(2*f*x + 2*e))*polylog(3, cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) - 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)*sin(2*f*x + 2*e))/(f^4*cos(2*f*x + 2*e) - f^4)","C",0
48,1,1564,0,1.176489," ","integrate((d*x+c)^2*(a+b*cot(f*x+e))^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{3} x^{3} - 12 \, b^{3} c^{2} f^{2} - 12 \, {\left(b^{3} d^{2} f^{2} - {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{3}\right)} x^{2} - 12 \, {\left(2 \, b^{3} c d f^{2} - {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{3}\right)} x - 4 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{3} x^{3} + 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{3} x^{2} + 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{3} x\right)} \cos\left(2 \, f x + 2 \, e\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) - 6 \, {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b - b^{3}\right)} c d e\right)} f - {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b - b^{3}\right)} c d e\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) - 6 \, {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b - b^{3}\right)} c d e\right)} f - {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b - b^{3}\right)} c d e\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) - \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) + 6 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b - b^{3}\right)} c d f^{2}\right)} x - {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b - b^{3}\right)} c d f^{2}\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) + 6 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b - b^{3}\right)} c d f^{2}\right)} x - {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b - b^{3}\right)} c d f^{2}\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) - 3 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(3 \, a^{2} b - b^{3}\right)} d^{2}\right)} {\rm polylog}\left(3, \cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) - 3 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(3 \, a^{2} b - b^{3}\right)} d^{2}\right)} {\rm polylog}\left(3, \cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\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)} \sin\left(2 \, f x + 2 \, e\right)}{12 \, {\left(f^{3} \cos\left(2 \, f x + 2 \, e\right) - f^{3}\right)}}"," ",0,"-1/12*(4*(a^3 - 3*a*b^2)*d^2*f^3*x^3 - 12*b^3*c^2*f^2 - 12*(b^3*d^2*f^2 - (a^3 - 3*a*b^2)*c*d*f^3)*x^2 - 12*(2*b^3*c*d*f^2 - (a^3 - 3*a*b^2)*c^2*f^3)*x - 4*((a^3 - 3*a*b^2)*d^2*f^3*x^3 + 3*(a^3 - 3*a*b^2)*c*d*f^3*x^2 + 3*(a^3 - 3*a*b^2)*c^2*f^3*x)*cos(2*f*x + 2*e) - (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 + (-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)*cos(2*f*x + 2*e))*dilog(cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) - (-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 + (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)*cos(2*f*x + 2*e))*dilog(cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) - 6*(6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b - b^3)*d^2*e^2 - (3*a^2*b - b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b - b^3)*c*d*e)*f - (6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b - b^3)*d^2*e^2 - (3*a^2*b - b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b - b^3)*c*d*e)*f)*cos(2*f*x + 2*e))*log(-1/2*cos(2*f*x + 2*e) + 1/2*I*sin(2*f*x + 2*e) + 1/2) - 6*(6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b - b^3)*d^2*e^2 - (3*a^2*b - b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b - b^3)*c*d*e)*f - (6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b - b^3)*d^2*e^2 - (3*a^2*b - b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b - b^3)*c*d*e)*f)*cos(2*f*x + 2*e))*log(-1/2*cos(2*f*x + 2*e) - 1/2*I*sin(2*f*x + 2*e) + 1/2) + 6*((3*a^2*b - b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b - b^3)*d^2*e^2 + 2*(3*a^2*b - b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b - b^3)*c*d*f^2)*x - ((3*a^2*b - b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b - b^3)*d^2*e^2 + 2*(3*a^2*b - b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b - b^3)*c*d*f^2)*x)*cos(2*f*x + 2*e))*log(-cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e) + 1) + 6*((3*a^2*b - b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b - b^3)*d^2*e^2 + 2*(3*a^2*b - b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b - b^3)*c*d*f^2)*x - ((3*a^2*b - b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b - b^3)*d^2*e^2 + 2*(3*a^2*b - b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b - b^3)*c*d*f^2)*x)*cos(2*f*x + 2*e))*log(-cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e) + 1) - 3*((3*a^2*b - b^3)*d^2*cos(2*f*x + 2*e) - (3*a^2*b - b^3)*d^2)*polylog(3, cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) - 3*((3*a^2*b - b^3)*d^2*cos(2*f*x + 2*e) - (3*a^2*b - b^3)*d^2)*polylog(3, cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) - 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)*sin(2*f*x + 2*e))/(f^3*cos(2*f*x + 2*e) - f^3)","C",0
49,1,721,0,0.607995," ","integrate((d*x+c)*(a+b*cot(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d f^{2} x^{2} - 4 \, b^{3} c f - 4 \, {\left(b^{3} d f - {\left(a^{3} - 3 \, a b^{2}\right)} c f^{2}\right)} x - 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} d f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c f^{2} x\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-i \, {\left(3 \, a^{2} b - b^{3}\right)} d \cos\left(2 \, f x + 2 \, e\right) + i \, {\left(3 \, a^{2} b - b^{3}\right)} d\right)} {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right)\right) - {\left(i \, {\left(3 \, a^{2} b - b^{3}\right)} d \cos\left(2 \, f x + 2 \, e\right) - i \, {\left(3 \, a^{2} b - b^{3}\right)} d\right)} {\rm Li}_2\left(\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right)\right) + 2 \, {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b - b^{3}\right)} d e + {\left(3 \, a^{2} b - b^{3}\right)} c f - {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b - b^{3}\right)} d e + {\left(3 \, a^{2} b - b^{3}\right)} c f\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) + 2 \, {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b - b^{3}\right)} d e + {\left(3 \, a^{2} b - b^{3}\right)} c f - {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b - b^{3}\right)} d e + {\left(3 \, a^{2} b - b^{3}\right)} c f\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, f x + 2 \, e\right) - \frac{1}{2} i \, \sin\left(2 \, f x + 2 \, e\right) + \frac{1}{2}\right) + 2 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d f x + {\left(3 \, a^{2} b - b^{3}\right)} d e - {\left({\left(3 \, a^{2} b - b^{3}\right)} d f x + {\left(3 \, a^{2} b - b^{3}\right)} d e\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) + i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) + 2 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} d f x + {\left(3 \, a^{2} b - b^{3}\right)} d e - {\left({\left(3 \, a^{2} b - b^{3}\right)} d f x + {\left(3 \, a^{2} b - b^{3}\right)} d e\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\cos\left(2 \, f x + 2 \, e\right) - i \, \sin\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, {\left(6 \, a b^{2} d f x + 6 \, a b^{2} c f + b^{3} d\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, {\left(f^{2} \cos\left(2 \, f x + 2 \, e\right) - f^{2}\right)}}"," ",0,"-1/4*(2*(a^3 - 3*a*b^2)*d*f^2*x^2 - 4*b^3*c*f - 4*(b^3*d*f - (a^3 - 3*a*b^2)*c*f^2)*x - 2*((a^3 - 3*a*b^2)*d*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*f^2*x)*cos(2*f*x + 2*e) - (-I*(3*a^2*b - b^3)*d*cos(2*f*x + 2*e) + I*(3*a^2*b - b^3)*d)*dilog(cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e)) - (I*(3*a^2*b - b^3)*d*cos(2*f*x + 2*e) - I*(3*a^2*b - b^3)*d)*dilog(cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e)) + 2*(3*a*b^2*d - (3*a^2*b - b^3)*d*e + (3*a^2*b - b^3)*c*f - (3*a*b^2*d - (3*a^2*b - b^3)*d*e + (3*a^2*b - b^3)*c*f)*cos(2*f*x + 2*e))*log(-1/2*cos(2*f*x + 2*e) + 1/2*I*sin(2*f*x + 2*e) + 1/2) + 2*(3*a*b^2*d - (3*a^2*b - b^3)*d*e + (3*a^2*b - b^3)*c*f - (3*a*b^2*d - (3*a^2*b - b^3)*d*e + (3*a^2*b - b^3)*c*f)*cos(2*f*x + 2*e))*log(-1/2*cos(2*f*x + 2*e) - 1/2*I*sin(2*f*x + 2*e) + 1/2) + 2*((3*a^2*b - b^3)*d*f*x + (3*a^2*b - b^3)*d*e - ((3*a^2*b - b^3)*d*f*x + (3*a^2*b - b^3)*d*e)*cos(2*f*x + 2*e))*log(-cos(2*f*x + 2*e) + I*sin(2*f*x + 2*e) + 1) + 2*((3*a^2*b - b^3)*d*f*x + (3*a^2*b - b^3)*d*e - ((3*a^2*b - b^3)*d*f*x + (3*a^2*b - b^3)*d*e)*cos(2*f*x + 2*e))*log(-cos(2*f*x + 2*e) - I*sin(2*f*x + 2*e) + 1) - 2*(6*a*b^2*d*f*x + 6*a*b^2*c*f + b^3*d)*sin(2*f*x + 2*e))/(f^2*cos(2*f*x + 2*e) - f^2)","B",0
50,0,0,0,0.631466," ","integrate((a+b*cot(f*x+e))^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \cot\left(f x + e\right)^{3} + 3 \, a b^{2} \cot\left(f x + e\right)^{2} + 3 \, a^{2} b \cot\left(f x + e\right) + a^{3}}{d x + c}, x\right)"," ",0,"integral((b^3*cot(f*x + e)^3 + 3*a*b^2*cot(f*x + e)^2 + 3*a^2*b*cot(f*x + e) + a^3)/(d*x + c), x)","F",0
51,0,0,0,0.507596," ","integrate((a+b*cot(f*x+e))^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \cot\left(f x + e\right)^{3} + 3 \, a b^{2} \cot\left(f x + e\right)^{2} + 3 \, a^{2} b \cot\left(f x + e\right) + a^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b^3*cot(f*x + e)^3 + 3*a*b^2*cot(f*x + e)^2 + 3*a^2*b*cot(f*x + e) + a^3)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
52,1,1029,0,0.594066," ","integrate((d*x+c)^3/(a+b*cot(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)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} - 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{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)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} - 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{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{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{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{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{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{1}{2} \, a^{2} + i \, a b - \frac{1}{2} \, b^{2} - \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\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{1}{2} \, a^{2} + i \, a b + \frac{1}{2} \, b^{2} + \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\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{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{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{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{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)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} - 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{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)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} - 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{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)*cos(2*f*x + 2*e) + (I*a^2 - 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) + 3*I*b*d^3*polylog(4, ((a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 - 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(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(-(a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(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(-(a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^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(1/2*a^2 + I*a*b - 1/2*b^2 - 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) + 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(-1/2*a^2 + I*a*b + 1/2*b^2 + 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) - 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((a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(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((a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(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)*cos(2*f*x + 2*e) + (I*a^2 - 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(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)*cos(2*f*x + 2*e) + (-I*a^2 - 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)))/((a^2 + b^2)*f^4)","C",0
53,1,730,0,0.747478," ","integrate((d*x+c)^2/(a+b*cot(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)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} - 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 3 \, b d^{2} {\rm polylog}\left(3, \frac{{\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} - 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{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{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{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{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{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{1}{2} \, a^{2} + i \, a b - \frac{1}{2} \, b^{2} - \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right) - 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, a^{2} + i \, a b + \frac{1}{2} \, b^{2} + \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\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{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{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{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\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)*cos(2*f*x + 2*e) + (I*a^2 - 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) - 3*b*d^2*polylog(3, ((a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 - 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) + (6*I*b*d^2*f*x + 6*I*b*c*d*f)*dilog(-(a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2) + 1) + (-6*I*b*d^2*f*x - 6*I*b*c*d*f)*dilog(-(a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2) + 1) - 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(1/2*a^2 + I*a*b - 1/2*b^2 - 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) - 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(-1/2*a^2 + I*a*b + 1/2*b^2 + 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) - 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((a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(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((a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)))/((a^2 + b^2)*f^3)","C",0
54,1,475,0,0.656460," ","integrate((d*x+c)/(a+b*cot(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{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}} + 1\right) - i \, b d {\rm Li}_2\left(-\frac{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}} + 1\right) + 2 \, {\left(b d e - b c f\right)} \log\left(\frac{1}{2} \, a^{2} + i \, a b - \frac{1}{2} \, b^{2} - \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right) + 2 \, {\left(b d e - b c f\right)} \log\left(-\frac{1}{2} \, a^{2} + i \, a b + \frac{1}{2} \, b^{2} + \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right) - 2 \, {\left(b d f x + b d e\right)} \log\left(\frac{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 2 \, {\left(b d f x + b d e\right)} \log\left(\frac{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\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(-(a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2) + 1) - I*b*d*dilog(-(a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2) + 1) + 2*(b*d*e - b*c*f)*log(1/2*a^2 + I*a*b - 1/2*b^2 - 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) + 2*(b*d*e - b*c*f)*log(-1/2*a^2 + I*a*b + 1/2*b^2 + 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) - 2*(b*d*f*x + b*d*e)*log((a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) - 2*(b*d*f*x + b*d*e)*log((a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)))/((a^2 + b^2)*f^2)","B",0
55,0,0,0,0.533645," ","integrate(1/(d*x+c)/(a+b*cot(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(b d x + b c\right)} \cot\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (b*d*x + b*c)*cot(f*x + e)), x)","F",0
56,0,0,0,0.639898," ","integrate(1/(d*x+c)^2/(a+b*cot(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)} \cot\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)*cot(f*x + e)), x)","F",0
57,1,3359,0,0.874315," ","integrate((d*x+c)^3/(a+b*cot(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right) + {\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 + {\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)} \cos\left(2 \, f x + 2 \, e\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\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-\frac{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}} + 1\right) + {\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 + {\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)} \cos\left(2 \, f x + 2 \, e\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\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-\frac{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}} + 1\right) + 2 \, {\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right) + {\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\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{1}{2} \, a^{2} + i \, a b - \frac{1}{2} \, b^{2} - \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right) + 2 \, {\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right) + {\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\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\frac{1}{2} \, a^{2} + i \, a b + \frac{1}{2} \, b^{2} + \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right) - 2 \, {\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right) + {\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\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 2 \, {\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right) + {\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\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) + {\left(-3 i \, a b^{2} d^{3} \cos\left(2 \, f x + 2 \, e\right) - 3 i \, a^{2} b d^{3} \sin\left(2 \, f x + 2 \, e\right) - 3 i \, a b^{2} d^{3}\right)} {\rm polylog}\left(4, \frac{{\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} - 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) + {\left(3 i \, a b^{2} d^{3} \cos\left(2 \, f x + 2 \, e\right) + 3 i \, a^{2} b d^{3} \sin\left(2 \, f x + 2 \, e\right) + 3 i \, a b^{2} d^{3}\right)} {\rm polylog}\left(4, \frac{{\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} - 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 3 \, {\left(2 \, a b^{2} d^{3} f x + 2 \, a b^{2} c d^{2} f - b^{3} d^{3} + {\left(2 \, a b^{2} d^{3} f x + 2 \, a b^{2} c d^{2} f - b^{3} d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 \, a^{2} b d^{3} f x + 2 \, a^{2} b c d^{2} f - a b^{2} d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm polylog}\left(3, \frac{{\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} - 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 3 \, {\left(2 \, a b^{2} d^{3} f x + 2 \, a b^{2} c d^{2} f - b^{3} d^{3} + {\left(2 \, a b^{2} d^{3} f x + 2 \, a b^{2} c d^{2} f - b^{3} d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 \, a^{2} b d^{3} f x + 2 \, a^{2} b c d^{2} f - a b^{2} d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm polylog}\left(3, \frac{{\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} - 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) + {\left({\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\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{4} \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{4} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{4}\right)}}"," ",0,"1/4*((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 + ((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)*cos(2*f*x + 2*e) + (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 + (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)*cos(2*f*x + 2*e) + (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)*sin(2*f*x + 2*e))*dilog(-(a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2) + 1) + (-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 + (-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)*cos(2*f*x + 2*e) + (-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)*sin(2*f*x + 2*e))*dilog(-(a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2) + 1) + 2*(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 + (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)*cos(2*f*x + 2*e) + (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)*sin(2*f*x + 2*e))*log(1/2*a^2 + I*a*b - 1/2*b^2 - 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) + 2*(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 + (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)*cos(2*f*x + 2*e) + (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)*sin(2*f*x + 2*e))*log(-1/2*a^2 + I*a*b + 1/2*b^2 + 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) - 2*(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 + (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)*cos(2*f*x + 2*e) + (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)*sin(2*f*x + 2*e))*log((a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) - 2*(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 + (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)*cos(2*f*x + 2*e) + (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)*sin(2*f*x + 2*e))*log((a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) + (-3*I*a*b^2*d^3*cos(2*f*x + 2*e) - 3*I*a^2*b*d^3*sin(2*f*x + 2*e) - 3*I*a*b^2*d^3)*polylog(4, ((a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 - 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) + (3*I*a*b^2*d^3*cos(2*f*x + 2*e) + 3*I*a^2*b*d^3*sin(2*f*x + 2*e) + 3*I*a*b^2*d^3)*polylog(4, ((a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 - 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) - 3*(2*a*b^2*d^3*f*x + 2*a*b^2*c*d^2*f - b^3*d^3 + (2*a*b^2*d^3*f*x + 2*a*b^2*c*d^2*f - b^3*d^3)*cos(2*f*x + 2*e) + (2*a^2*b*d^3*f*x + 2*a^2*b*c*d^2*f - a*b^2*d^3)*sin(2*f*x + 2*e))*polylog(3, ((a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 - 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) - 3*(2*a*b^2*d^3*f*x + 2*a*b^2*c*d^2*f - b^3*d^3 + (2*a*b^2*d^3*f*x + 2*a*b^2*c*d^2*f - b^3*d^3)*cos(2*f*x + 2*e) + (2*a^2*b*d^3*f*x + 2*a^2*b*c*d^2*f - a*b^2*d^3)*sin(2*f*x + 2*e))*polylog(3, ((a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 - 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) + ((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)*sin(2*f*x + 2*e))/((a^4*b + 2*a^2*b^3 + b^5)*f^4*cos(2*f*x + 2*e) + (a^5 + 2*a^3*b^2 + a*b^4)*f^4*sin(2*f*x + 2*e) + (a^4*b + 2*a^2*b^3 + b^5)*f^4)","C",0
58,1,2036,0,0.602668," ","integrate((d*x+c)^2/(a+b*cot(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{3} - 6 \, a b^{2} c^{2} f^{2} - 6 \, {\left(a b^{2} d^{2} f^{2} - {\left(a^{2} b - b^{3}\right)} c d f^{3}\right)} x^{2} - 6 \, {\left(2 \, a b^{2} c d f^{2} - {\left(a^{2} b - b^{3}\right)} c^{2} f^{3}\right)} x + 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)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 i \, a b^{2} d^{2} f x + 6 i \, a b^{2} c d f - 3 i \, b^{3} 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)} \cos\left(2 \, f x + 2 \, e\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}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-\frac{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}} + 1\right) + {\left(-6 i \, a b^{2} d^{2} f x - 6 i \, a b^{2} c d f + 3 i \, b^{3} 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)} \cos\left(2 \, f x + 2 \, e\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}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-\frac{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}} + 1\right) - 6 \, {\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right) + {\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\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{1}{2} \, a^{2} + i \, a b - \frac{1}{2} \, b^{2} - \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right) - 6 \, {\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right) + {\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\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\frac{1}{2} \, a^{2} + i \, a b + \frac{1}{2} \, b^{2} + \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right) - 6 \, {\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right) + {\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\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 6 \, {\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right) + {\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\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 3 \, {\left(a b^{2} d^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} b d^{2} \sin\left(2 \, f x + 2 \, e\right) + a b^{2} d^{2}\right)} {\rm polylog}\left(3, \frac{{\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} - 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 3 \, {\left(a b^{2} d^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} b d^{2} \sin\left(2 \, f x + 2 \, e\right) + a b^{2} d^{2}\right)} {\rm polylog}\left(3, \frac{{\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} - 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) + 2 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} f^{3} x^{3} + 3 \, b^{3} c^{2} f^{2} + 3 \, {\left(b^{3} d^{2} f^{2} + {\left(a^{3} - a b^{2}\right)} c d f^{3}\right)} x^{2} + 3 \, {\left(2 \, b^{3} c d f^{2} + {\left(a^{3} - a b^{2}\right)} c^{2} f^{3}\right)} x\right)} \sin\left(2 \, f x + 2 \, e\right)}{6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{3}\right)}}"," ",0,"1/6*(2*(a^2*b - b^3)*d^2*f^3*x^3 - 6*a*b^2*c^2*f^2 - 6*(a*b^2*d^2*f^2 - (a^2*b - b^3)*c*d*f^3)*x^2 - 6*(2*a*b^2*c*d*f^2 - (a^2*b - b^3)*c^2*f^3)*x + 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)*cos(2*f*x + 2*e) + (6*I*a*b^2*d^2*f*x + 6*I*a*b^2*c*d*f - 3*I*b^3*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)*cos(2*f*x + 2*e) + (6*I*a^2*b*d^2*f*x + 6*I*a^2*b*c*d*f - 3*I*a*b^2*d^2)*sin(2*f*x + 2*e))*dilog(-(a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2) + 1) + (-6*I*a*b^2*d^2*f*x - 6*I*a*b^2*c*d*f + 3*I*b^3*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)*cos(2*f*x + 2*e) + (-6*I*a^2*b*d^2*f*x - 6*I*a^2*b*c*d*f + 3*I*a*b^2*d^2)*sin(2*f*x + 2*e))*dilog(-(a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2) + 1) - 6*(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 + (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)*cos(2*f*x + 2*e) + (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)*sin(2*f*x + 2*e))*log(1/2*a^2 + I*a*b - 1/2*b^2 - 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) - 6*(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 + (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)*cos(2*f*x + 2*e) + (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)*sin(2*f*x + 2*e))*log(-1/2*a^2 + I*a*b + 1/2*b^2 + 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) - 6*(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 + (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)*cos(2*f*x + 2*e) + (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)*sin(2*f*x + 2*e))*log((a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) - 6*(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 + (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)*cos(2*f*x + 2*e) + (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)*sin(2*f*x + 2*e))*log((a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) - 3*(a*b^2*d^2*cos(2*f*x + 2*e) + a^2*b*d^2*sin(2*f*x + 2*e) + a*b^2*d^2)*polylog(3, ((a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 - 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) - 3*(a*b^2*d^2*cos(2*f*x + 2*e) + a^2*b*d^2*sin(2*f*x + 2*e) + a*b^2*d^2)*polylog(3, ((a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 - 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) + 2*((a^3 - a*b^2)*d^2*f^3*x^3 + 3*b^3*c^2*f^2 + 3*(b^3*d^2*f^2 + (a^3 - a*b^2)*c*d*f^3)*x^2 + 3*(2*b^3*c*d*f^2 + (a^3 - a*b^2)*c^2*f^3)*x)*sin(2*f*x + 2*e))/((a^4*b + 2*a^2*b^3 + b^5)*f^3*cos(2*f*x + 2*e) + (a^5 + 2*a^3*b^2 + a*b^4)*f^3*sin(2*f*x + 2*e) + (a^4*b + 2*a^2*b^3 + b^5)*f^3)","C",0
59,1,1053,0,0.650016," ","integrate((d*x+c)/(a+b*cot(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\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 + {\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)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a b^{2} d \cos\left(2 \, f x + 2 \, e\right) + i \, a^{2} b d \sin\left(2 \, f x + 2 \, e\right) + i \, a b^{2} d\right)} {\rm Li}_2\left(-\frac{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}} + 1\right) + {\left(-i \, a b^{2} d \cos\left(2 \, f x + 2 \, e\right) - i \, a^{2} b d \sin\left(2 \, f x + 2 \, e\right) - i \, a b^{2} d\right)} {\rm Li}_2\left(-\frac{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}} + 1\right) + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f + b^{3} d + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f + b^{3} d\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 \, a^{2} b d e - 2 \, a^{2} b c f + a b^{2} d\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{1}{2} \, a^{2} + i \, a b - \frac{1}{2} \, b^{2} - \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right) + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f + b^{3} d + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f + b^{3} d\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 \, a^{2} b d e - 2 \, a^{2} b c f + a b^{2} d\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(-\frac{1}{2} \, a^{2} + i \, a b + \frac{1}{2} \, b^{2} + \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + \frac{1}{2} \, {\left(i \, a^{2} + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right) - 2 \, {\left(a b^{2} d f x + a b^{2} d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} b d f x + a^{2} b d e\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{a^{2} + b^{2} - {\left(a^{2} + 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-i \, a^{2} + 2 \, a b + i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 2 \, {\left(a b^{2} d f x + a b^{2} d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} b d f x + a^{2} b d e\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{a^{2} + b^{2} - {\left(a^{2} - 2 i \, a b - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(i \, a^{2} + 2 \, a b - i \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) + {\left({\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\right)} \sin\left(2 \, f x + 2 \, e\right)}{2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2}\right)}}"," ",0,"1/2*((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 + ((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)*cos(2*f*x + 2*e) + (I*a*b^2*d*cos(2*f*x + 2*e) + I*a^2*b*d*sin(2*f*x + 2*e) + I*a*b^2*d)*dilog(-(a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2) + 1) + (-I*a*b^2*d*cos(2*f*x + 2*e) - I*a^2*b*d*sin(2*f*x + 2*e) - I*a*b^2*d)*dilog(-(a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2) + 1) + (2*a*b^2*d*e - 2*a*b^2*c*f + b^3*d + (2*a*b^2*d*e - 2*a*b^2*c*f + b^3*d)*cos(2*f*x + 2*e) + (2*a^2*b*d*e - 2*a^2*b*c*f + a*b^2*d)*sin(2*f*x + 2*e))*log(1/2*a^2 + I*a*b - 1/2*b^2 - 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) + (2*a*b^2*d*e - 2*a*b^2*c*f + b^3*d + (2*a*b^2*d*e - 2*a*b^2*c*f + b^3*d)*cos(2*f*x + 2*e) + (2*a^2*b*d*e - 2*a^2*b*c*f + a*b^2*d)*sin(2*f*x + 2*e))*log(-1/2*a^2 + I*a*b + 1/2*b^2 + 1/2*(a^2 + b^2)*cos(2*f*x + 2*e) + 1/2*(I*a^2 + I*b^2)*sin(2*f*x + 2*e)) - 2*(a*b^2*d*f*x + a*b^2*d*e + (a*b^2*d*f*x + a*b^2*d*e)*cos(2*f*x + 2*e) + (a^2*b*d*f*x + a^2*b*d*e)*sin(2*f*x + 2*e))*log((a^2 + b^2 - (a^2 + 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (-I*a^2 + 2*a*b + I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^2)) - 2*(a*b^2*d*f*x + a*b^2*d*e + (a*b^2*d*f*x + a*b^2*d*e)*cos(2*f*x + 2*e) + (a^2*b*d*f*x + a^2*b*d*e)*sin(2*f*x + 2*e))*log((a^2 + b^2 - (a^2 - 2*I*a*b - b^2)*cos(2*f*x + 2*e) + (I*a^2 + 2*a*b - I*b^2)*sin(2*f*x + 2*e))/(a^2 + b^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)*sin(2*f*x + 2*e))/((a^4*b + 2*a^2*b^3 + b^5)*f^2*cos(2*f*x + 2*e) + (a^5 + 2*a^3*b^2 + a*b^4)*f^2*sin(2*f*x + 2*e) + (a^4*b + 2*a^2*b^3 + b^5)*f^2)","B",0
60,0,0,0,0.672827," ","integrate(1/(d*x+c)/(a+b*cot(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)} \cot\left(f x + e\right)^{2} + 2 \, {\left(a b d x + a b c\right)} \cot\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d*x + a^2*c + (b^2*d*x + b^2*c)*cot(f*x + e)^2 + 2*(a*b*d*x + a*b*c)*cot(f*x + e)), x)","F",0
61,0,0,0,0.598054," ","integrate(1/(d*x+c)^2/(a+b*cot(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)} \cot\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)} \cot\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)*cot(f*x + e)^2 + 2*(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*cot(f*x + e)), x)","F",0
