1,1,425,0,0.557564," ","integrate(x^5*(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","\frac{2 \, a d^{3} x^{6} - 3 \, b d^{2} x^{4} \log\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + 1\right) - 3 \, b d^{2} x^{4} \log\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + 1\right) - 6 i \, b d x^{2} {\rm Li}_2\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) + 6 i \, b d x^{2} {\rm Li}_2\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) - 6 i \, b d x^{2} {\rm Li}_2\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) + 6 i \, b d x^{2} {\rm Li}_2\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) + 3 \, b c^{2} \log\left(-\frac{1}{2} \, \cos\left(d x^{2} + c\right) + \frac{1}{2} i \, \sin\left(d x^{2} + c\right) + \frac{1}{2}\right) + 3 \, b c^{2} \log\left(-\frac{1}{2} \, \cos\left(d x^{2} + c\right) - \frac{1}{2} i \, \sin\left(d x^{2} + c\right) + \frac{1}{2}\right) + 3 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \log\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + 1\right) + 3 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \log\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + 1\right) + 6 \, b {\rm polylog}\left(3, \cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) + 6 \, b {\rm polylog}\left(3, \cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) - 6 \, b {\rm polylog}\left(3, -\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) - 6 \, b {\rm polylog}\left(3, -\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right)}{12 \, d^{3}}"," ",0,"1/12*(2*a*d^3*x^6 - 3*b*d^2*x^4*log(cos(d*x^2 + c) + I*sin(d*x^2 + c) + 1) - 3*b*d^2*x^4*log(cos(d*x^2 + c) - I*sin(d*x^2 + c) + 1) - 6*I*b*d*x^2*dilog(cos(d*x^2 + c) + I*sin(d*x^2 + c)) + 6*I*b*d*x^2*dilog(cos(d*x^2 + c) - I*sin(d*x^2 + c)) - 6*I*b*d*x^2*dilog(-cos(d*x^2 + c) + I*sin(d*x^2 + c)) + 6*I*b*d*x^2*dilog(-cos(d*x^2 + c) - I*sin(d*x^2 + c)) + 3*b*c^2*log(-1/2*cos(d*x^2 + c) + 1/2*I*sin(d*x^2 + c) + 1/2) + 3*b*c^2*log(-1/2*cos(d*x^2 + c) - 1/2*I*sin(d*x^2 + c) + 1/2) + 3*(b*d^2*x^4 - b*c^2)*log(-cos(d*x^2 + c) + I*sin(d*x^2 + c) + 1) + 3*(b*d^2*x^4 - b*c^2)*log(-cos(d*x^2 + c) - I*sin(d*x^2 + c) + 1) + 6*b*polylog(3, cos(d*x^2 + c) + I*sin(d*x^2 + c)) + 6*b*polylog(3, cos(d*x^2 + c) - I*sin(d*x^2 + c)) - 6*b*polylog(3, -cos(d*x^2 + c) + I*sin(d*x^2 + c)) - 6*b*polylog(3, -cos(d*x^2 + c) - I*sin(d*x^2 + c)))/d^3","C",0
2,0,0,0,0.609475," ","integrate(x^4*(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{4} \csc\left(d x^{2} + c\right) + a x^{4}, x\right)"," ",0,"integral(b*x^4*csc(d*x^2 + c) + a*x^4, x)","F",0
3,1,288,0,0.591725," ","integrate(x^3*(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d^{2} x^{4} - b d x^{2} \log\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + 1\right) - b d x^{2} \log\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + 1\right) - b c \log\left(-\frac{1}{2} \, \cos\left(d x^{2} + c\right) + \frac{1}{2} i \, \sin\left(d x^{2} + c\right) + \frac{1}{2}\right) - b c \log\left(-\frac{1}{2} \, \cos\left(d x^{2} + c\right) - \frac{1}{2} i \, \sin\left(d x^{2} + c\right) + \frac{1}{2}\right) - i \, b {\rm Li}_2\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) + i \, b {\rm Li}_2\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) - i \, b {\rm Li}_2\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) + i \, b {\rm Li}_2\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) + {\left(b d x^{2} + b c\right)} \log\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + 1\right) + {\left(b d x^{2} + b c\right)} \log\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + 1\right)}{4 \, d^{2}}"," ",0,"1/4*(a*d^2*x^4 - b*d*x^2*log(cos(d*x^2 + c) + I*sin(d*x^2 + c) + 1) - b*d*x^2*log(cos(d*x^2 + c) - I*sin(d*x^2 + c) + 1) - b*c*log(-1/2*cos(d*x^2 + c) + 1/2*I*sin(d*x^2 + c) + 1/2) - b*c*log(-1/2*cos(d*x^2 + c) - 1/2*I*sin(d*x^2 + c) + 1/2) - I*b*dilog(cos(d*x^2 + c) + I*sin(d*x^2 + c)) + I*b*dilog(cos(d*x^2 + c) - I*sin(d*x^2 + c)) - I*b*dilog(-cos(d*x^2 + c) + I*sin(d*x^2 + c)) + I*b*dilog(-cos(d*x^2 + c) - I*sin(d*x^2 + c)) + (b*d*x^2 + b*c)*log(-cos(d*x^2 + c) + I*sin(d*x^2 + c) + 1) + (b*d*x^2 + b*c)*log(-cos(d*x^2 + c) - I*sin(d*x^2 + c) + 1))/d^2","B",0
4,0,0,0,0.481921," ","integrate(x^2*(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{2} \csc\left(d x^{2} + c\right) + a x^{2}, x\right)"," ",0,"integral(b*x^2*csc(d*x^2 + c) + a*x^2, x)","F",0
5,1,44,0,0.494468," ","integrate(x*(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","\frac{2 \, a d x^{2} - b \log\left(\frac{1}{2} \, \cos\left(d x^{2} + c\right) + \frac{1}{2}\right) + b \log\left(-\frac{1}{2} \, \cos\left(d x^{2} + c\right) + \frac{1}{2}\right)}{4 \, d}"," ",0,"1/4*(2*a*d*x^2 - b*log(1/2*cos(d*x^2 + c) + 1/2) + b*log(-1/2*cos(d*x^2 + c) + 1/2))/d","A",0
6,0,0,0,0.499333," ","integrate((a+b*csc(d*x^2+c))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \csc\left(d x^{2} + c\right) + a}{x}, x\right)"," ",0,"integral((b*csc(d*x^2 + c) + a)/x, x)","F",0
7,0,0,0,0.557779," ","integrate((a+b*csc(d*x^2+c))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \csc\left(d x^{2} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*csc(d*x^2 + c) + a)/x^2, x)","F",0
8,1,683,0,0.584333," ","integrate(x^5*(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{a^{2} d^{3} x^{6} \sin\left(d x^{2} + c\right) - 3 \, b^{2} d^{2} x^{4} \cos\left(d x^{2} + c\right) + 6 \, a b {\rm polylog}\left(3, \cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) + 6 \, a b {\rm polylog}\left(3, \cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) - 6 \, a b {\rm polylog}\left(3, -\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) - 6 \, a b {\rm polylog}\left(3, -\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) + {\left(-6 i \, a b d x^{2} - 3 i \, b^{2}\right)} {\rm Li}_2\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) + {\left(6 i \, a b d x^{2} + 3 i \, b^{2}\right)} {\rm Li}_2\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) + {\left(-6 i \, a b d x^{2} + 3 i \, b^{2}\right)} {\rm Li}_2\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) + {\left(6 i \, a b d x^{2} - 3 i \, b^{2}\right)} {\rm Li}_2\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) - 3 \, {\left(a b d^{2} x^{4} - b^{2} d x^{2}\right)} \log\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + 1\right) \sin\left(d x^{2} + c\right) - 3 \, {\left(a b d^{2} x^{4} - b^{2} d x^{2}\right)} \log\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + 1\right) \sin\left(d x^{2} + c\right) + 3 \, {\left(a b c^{2} - b^{2} c\right)} \log\left(-\frac{1}{2} \, \cos\left(d x^{2} + c\right) + \frac{1}{2} i \, \sin\left(d x^{2} + c\right) + \frac{1}{2}\right) \sin\left(d x^{2} + c\right) + 3 \, {\left(a b c^{2} - b^{2} c\right)} \log\left(-\frac{1}{2} \, \cos\left(d x^{2} + c\right) - \frac{1}{2} i \, \sin\left(d x^{2} + c\right) + \frac{1}{2}\right) \sin\left(d x^{2} + c\right) + 3 \, {\left(a b d^{2} x^{4} + b^{2} d x^{2} - a b c^{2} + b^{2} c\right)} \log\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + 1\right) \sin\left(d x^{2} + c\right) + 3 \, {\left(a b d^{2} x^{4} + b^{2} d x^{2} - a b c^{2} + b^{2} c\right)} \log\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + 1\right) \sin\left(d x^{2} + c\right)}{6 \, d^{3} \sin\left(d x^{2} + c\right)}"," ",0,"1/6*(a^2*d^3*x^6*sin(d*x^2 + c) - 3*b^2*d^2*x^4*cos(d*x^2 + c) + 6*a*b*polylog(3, cos(d*x^2 + c) + I*sin(d*x^2 + c))*sin(d*x^2 + c) + 6*a*b*polylog(3, cos(d*x^2 + c) - I*sin(d*x^2 + c))*sin(d*x^2 + c) - 6*a*b*polylog(3, -cos(d*x^2 + c) + I*sin(d*x^2 + c))*sin(d*x^2 + c) - 6*a*b*polylog(3, -cos(d*x^2 + c) - I*sin(d*x^2 + c))*sin(d*x^2 + c) + (-6*I*a*b*d*x^2 - 3*I*b^2)*dilog(cos(d*x^2 + c) + I*sin(d*x^2 + c))*sin(d*x^2 + c) + (6*I*a*b*d*x^2 + 3*I*b^2)*dilog(cos(d*x^2 + c) - I*sin(d*x^2 + c))*sin(d*x^2 + c) + (-6*I*a*b*d*x^2 + 3*I*b^2)*dilog(-cos(d*x^2 + c) + I*sin(d*x^2 + c))*sin(d*x^2 + c) + (6*I*a*b*d*x^2 - 3*I*b^2)*dilog(-cos(d*x^2 + c) - I*sin(d*x^2 + c))*sin(d*x^2 + c) - 3*(a*b*d^2*x^4 - b^2*d*x^2)*log(cos(d*x^2 + c) + I*sin(d*x^2 + c) + 1)*sin(d*x^2 + c) - 3*(a*b*d^2*x^4 - b^2*d*x^2)*log(cos(d*x^2 + c) - I*sin(d*x^2 + c) + 1)*sin(d*x^2 + c) + 3*(a*b*c^2 - b^2*c)*log(-1/2*cos(d*x^2 + c) + 1/2*I*sin(d*x^2 + c) + 1/2)*sin(d*x^2 + c) + 3*(a*b*c^2 - b^2*c)*log(-1/2*cos(d*x^2 + c) - 1/2*I*sin(d*x^2 + c) + 1/2)*sin(d*x^2 + c) + 3*(a*b*d^2*x^4 + b^2*d*x^2 - a*b*c^2 + b^2*c)*log(-cos(d*x^2 + c) + I*sin(d*x^2 + c) + 1)*sin(d*x^2 + c) + 3*(a*b*d^2*x^4 + b^2*d*x^2 - a*b*c^2 + b^2*c)*log(-cos(d*x^2 + c) - I*sin(d*x^2 + c) + 1)*sin(d*x^2 + c))/(d^3*sin(d*x^2 + c))","C",0
9,0,0,0,0.439568," ","integrate(x^4*(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{4} \csc\left(d x^{2} + c\right)^{2} + 2 \, a b x^{4} \csc\left(d x^{2} + c\right) + a^{2} x^{4}, x\right)"," ",0,"integral(b^2*x^4*csc(d*x^2 + c)^2 + 2*a*b*x^4*csc(d*x^2 + c) + a^2*x^4, x)","F",0
10,1,451,0,0.667075," ","integrate(x^3*(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{a^{2} d^{2} x^{4} \sin\left(d x^{2} + c\right) - 2 \, b^{2} d x^{2} \cos\left(d x^{2} + c\right) - 2 i \, a b {\rm Li}_2\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) + 2 i \, a b {\rm Li}_2\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) - 2 i \, a b {\rm Li}_2\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) + 2 i \, a b {\rm Li}_2\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right)\right) \sin\left(d x^{2} + c\right) - {\left(2 \, a b d x^{2} - b^{2}\right)} \log\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + 1\right) \sin\left(d x^{2} + c\right) - {\left(2 \, a b d x^{2} - b^{2}\right)} \log\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + 1\right) \sin\left(d x^{2} + c\right) - {\left(2 \, a b c - b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x^{2} + c\right) + \frac{1}{2} i \, \sin\left(d x^{2} + c\right) + \frac{1}{2}\right) \sin\left(d x^{2} + c\right) - {\left(2 \, a b c - b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x^{2} + c\right) - \frac{1}{2} i \, \sin\left(d x^{2} + c\right) + \frac{1}{2}\right) \sin\left(d x^{2} + c\right) + 2 \, {\left(a b d x^{2} + a b c\right)} \log\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + 1\right) \sin\left(d x^{2} + c\right) + 2 \, {\left(a b d x^{2} + a b c\right)} \log\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + 1\right) \sin\left(d x^{2} + c\right)}{4 \, d^{2} \sin\left(d x^{2} + c\right)}"," ",0,"1/4*(a^2*d^2*x^4*sin(d*x^2 + c) - 2*b^2*d*x^2*cos(d*x^2 + c) - 2*I*a*b*dilog(cos(d*x^2 + c) + I*sin(d*x^2 + c))*sin(d*x^2 + c) + 2*I*a*b*dilog(cos(d*x^2 + c) - I*sin(d*x^2 + c))*sin(d*x^2 + c) - 2*I*a*b*dilog(-cos(d*x^2 + c) + I*sin(d*x^2 + c))*sin(d*x^2 + c) + 2*I*a*b*dilog(-cos(d*x^2 + c) - I*sin(d*x^2 + c))*sin(d*x^2 + c) - (2*a*b*d*x^2 - b^2)*log(cos(d*x^2 + c) + I*sin(d*x^2 + c) + 1)*sin(d*x^2 + c) - (2*a*b*d*x^2 - b^2)*log(cos(d*x^2 + c) - I*sin(d*x^2 + c) + 1)*sin(d*x^2 + c) - (2*a*b*c - b^2)*log(-1/2*cos(d*x^2 + c) + 1/2*I*sin(d*x^2 + c) + 1/2)*sin(d*x^2 + c) - (2*a*b*c - b^2)*log(-1/2*cos(d*x^2 + c) - 1/2*I*sin(d*x^2 + c) + 1/2)*sin(d*x^2 + c) + 2*(a*b*d*x^2 + a*b*c)*log(-cos(d*x^2 + c) + I*sin(d*x^2 + c) + 1)*sin(d*x^2 + c) + 2*(a*b*d*x^2 + a*b*c)*log(-cos(d*x^2 + c) - I*sin(d*x^2 + c) + 1)*sin(d*x^2 + c))/(d^2*sin(d*x^2 + c))","B",0
11,0,0,0,0.444461," ","integrate(x^2*(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \csc\left(d x^{2} + c\right)^{2} + 2 \, a b x^{2} \csc\left(d x^{2} + c\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*csc(d*x^2 + c)^2 + 2*a*b*x^2*csc(d*x^2 + c) + a^2*x^2, x)","F",0
12,1,94,0,0.476297," ","integrate(x*(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{a^{2} d x^{2} \sin\left(d x^{2} + c\right) - a b \log\left(\frac{1}{2} \, \cos\left(d x^{2} + c\right) + \frac{1}{2}\right) \sin\left(d x^{2} + c\right) + a b \log\left(-\frac{1}{2} \, \cos\left(d x^{2} + c\right) + \frac{1}{2}\right) \sin\left(d x^{2} + c\right) - b^{2} \cos\left(d x^{2} + c\right)}{2 \, d \sin\left(d x^{2} + c\right)}"," ",0,"1/2*(a^2*d*x^2*sin(d*x^2 + c) - a*b*log(1/2*cos(d*x^2 + c) + 1/2)*sin(d*x^2 + c) + a*b*log(-1/2*cos(d*x^2 + c) + 1/2)*sin(d*x^2 + c) - b^2*cos(d*x^2 + c))/(d*sin(d*x^2 + c))","B",0
13,0,0,0,0.477800," ","integrate((a+b*csc(d*x^2+c))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \csc\left(d x^{2} + c\right)^{2} + 2 \, a b \csc\left(d x^{2} + c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*csc(d*x^2 + c)^2 + 2*a*b*csc(d*x^2 + c) + a^2)/x, x)","F",0
14,0,0,0,0.491659," ","integrate((a+b*csc(d*x^2+c))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \csc\left(d x^{2} + c\right)^{2} + 2 \, a b \csc\left(d x^{2} + c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*csc(d*x^2 + c)^2 + 2*a*b*csc(d*x^2 + c) + a^2)/x^2, x)","F",0
15,1,183,0,0.517219," ","integrate(x*csc(b*x^2+a)^7,x, algorithm=""fricas"")","\frac{30 \, \cos\left(b x^{2} + a\right)^{5} - 80 \, \cos\left(b x^{2} + a\right)^{3} - 15 \, {\left(\cos\left(b x^{2} + a\right)^{6} - 3 \, \cos\left(b x^{2} + a\right)^{4} + 3 \, \cos\left(b x^{2} + a\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x^{2} + a\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(b x^{2} + a\right)^{6} - 3 \, \cos\left(b x^{2} + a\right)^{4} + 3 \, \cos\left(b x^{2} + a\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x^{2} + a\right) + \frac{1}{2}\right) + 66 \, \cos\left(b x^{2} + a\right)}{192 \, {\left(b \cos\left(b x^{2} + a\right)^{6} - 3 \, b \cos\left(b x^{2} + a\right)^{4} + 3 \, b \cos\left(b x^{2} + a\right)^{2} - b\right)}}"," ",0,"1/192*(30*cos(b*x^2 + a)^5 - 80*cos(b*x^2 + a)^3 - 15*(cos(b*x^2 + a)^6 - 3*cos(b*x^2 + a)^4 + 3*cos(b*x^2 + a)^2 - 1)*log(1/2*cos(b*x^2 + a) + 1/2) + 15*(cos(b*x^2 + a)^6 - 3*cos(b*x^2 + a)^4 + 3*cos(b*x^2 + a)^2 - 1)*log(-1/2*cos(b*x^2 + a) + 1/2) + 66*cos(b*x^2 + a))/(b*cos(b*x^2 + a)^6 - 3*b*cos(b*x^2 + a)^4 + 3*b*cos(b*x^2 + a)^2 - b)","B",0
16,1,1445,0,0.660228," ","integrate(x^5/(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(a^{2} - b^{2}\right)} d^{3} x^{6} + 12 i \, a b d x^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) - 12 i \, a b d x^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) - 12 i \, a b d x^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) + 12 i \, a b d x^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) + 6 \, a b c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(d x^{2} + c\right) + 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) + 6 \, a b c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(d x^{2} + c\right) - 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) - 6 \, a b c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(d x^{2} + c\right) + 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) - 6 \, a b c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(d x^{2} + c\right) - 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) + 12 \, a b \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{i \, b \cos\left(d x^{2} + c\right) + b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}}{a}\right) - 12 \, a b \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{i \, b \cos\left(d x^{2} + c\right) + b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}}{a}\right) + 12 \, a b \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{-i \, b \cos\left(d x^{2} + c\right) + b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}}{a}\right) - 12 \, a b \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{-i \, b \cos\left(d x^{2} + c\right) + b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}}{a}\right) - 6 \, {\left(a b d^{2} x^{4} - a b c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) + 6 \, {\left(a b d^{2} x^{4} - a b c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) - 6 \, {\left(a b d^{2} x^{4} - a b c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) + 6 \, {\left(a b d^{2} x^{4} - a b c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right)}{24 \, {\left(a^{3} - a b^{2}\right)} d^{3}}"," ",0,"1/24*(4*(a^2 - b^2)*d^3*x^6 + 12*I*a*b*d*x^2*sqrt((a^2 - b^2)/a^2)*dilog((I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) - 12*I*a*b*d*x^2*sqrt((a^2 - b^2)/a^2)*dilog((I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) - 12*I*a*b*d*x^2*sqrt((a^2 - b^2)/a^2)*dilog((-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) + 12*I*a*b*d*x^2*sqrt((a^2 - b^2)/a^2)*dilog((-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) + 6*a*b*c^2*sqrt((a^2 - b^2)/a^2)*log(2*a*cos(d*x^2 + c) + 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) + 6*a*b*c^2*sqrt((a^2 - b^2)/a^2)*log(2*a*cos(d*x^2 + c) - 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) - 6*a*b*c^2*sqrt((a^2 - b^2)/a^2)*log(-2*a*cos(d*x^2 + c) + 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) - 6*a*b*c^2*sqrt((a^2 - b^2)/a^2)*log(-2*a*cos(d*x^2 + c) - 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) + 12*a*b*sqrt((a^2 - b^2)/a^2)*polylog(3, -(I*b*cos(d*x^2 + c) + b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))/a) - 12*a*b*sqrt((a^2 - b^2)/a^2)*polylog(3, -(I*b*cos(d*x^2 + c) + b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))/a) + 12*a*b*sqrt((a^2 - b^2)/a^2)*polylog(3, -(-I*b*cos(d*x^2 + c) + b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))/a) - 12*a*b*sqrt((a^2 - b^2)/a^2)*polylog(3, -(-I*b*cos(d*x^2 + c) + b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))/a) - 6*(a*b*d^2*x^4 - a*b*c^2)*sqrt((a^2 - b^2)/a^2)*log(-(I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) + 6*(a*b*d^2*x^4 - a*b*c^2)*sqrt((a^2 - b^2)/a^2)*log(-(I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) - 6*(a*b*d^2*x^4 - a*b*c^2)*sqrt((a^2 - b^2)/a^2)*log(-(-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) + 6*(a*b*d^2*x^4 - a*b*c^2)*sqrt((a^2 - b^2)/a^2)*log(-(-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a))/((a^3 - a*b^2)*d^3)","C",0
17,0,0,0,0.573311," ","integrate(x^4/(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{b \csc\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral(x^4/(b*csc(d*x^2 + c) + a), x)","F",0
18,1,1055,0,0.680433," ","integrate(x^3/(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} - b^{2}\right)} d^{2} x^{4} - 2 \, a b c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(d x^{2} + c\right) + 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) - 2 \, a b c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(d x^{2} + c\right) - 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) + 2 \, a b c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(d x^{2} + c\right) + 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) + 2 \, a b c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(d x^{2} + c\right) - 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) + 2 i \, a b \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) - 2 i \, a b \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) - 2 i \, a b \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) + 2 i \, a b \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) - 2 \, {\left(a b d x^{2} + a b c\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) + 2 \, {\left(a b d x^{2} + a b c\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) - 2 \, {\left(a b d x^{2} + a b c\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) + 2 \, {\left(a b d x^{2} + a b c\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right)}{8 \, {\left(a^{3} - a b^{2}\right)} d^{2}}"," ",0,"1/8*(2*(a^2 - b^2)*d^2*x^4 - 2*a*b*c*sqrt((a^2 - b^2)/a^2)*log(2*a*cos(d*x^2 + c) + 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) - 2*a*b*c*sqrt((a^2 - b^2)/a^2)*log(2*a*cos(d*x^2 + c) - 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) + 2*a*b*c*sqrt((a^2 - b^2)/a^2)*log(-2*a*cos(d*x^2 + c) + 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) + 2*a*b*c*sqrt((a^2 - b^2)/a^2)*log(-2*a*cos(d*x^2 + c) - 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) + 2*I*a*b*sqrt((a^2 - b^2)/a^2)*dilog((I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) - 2*I*a*b*sqrt((a^2 - b^2)/a^2)*dilog((I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) - 2*I*a*b*sqrt((a^2 - b^2)/a^2)*dilog((-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) + 2*I*a*b*sqrt((a^2 - b^2)/a^2)*dilog((-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) - 2*(a*b*d*x^2 + a*b*c)*sqrt((a^2 - b^2)/a^2)*log(-(I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) + 2*(a*b*d*x^2 + a*b*c)*sqrt((a^2 - b^2)/a^2)*log(-(I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) - 2*(a*b*d*x^2 + a*b*c)*sqrt((a^2 - b^2)/a^2)*log(-(-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) + 2*(a*b*d*x^2 + a*b*c)*sqrt((a^2 - b^2)/a^2)*log(-(-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a))/((a^3 - a*b^2)*d^2)","B",0
19,0,0,0,0.442840," ","integrate(x^2/(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b \csc\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral(x^2/(b*csc(d*x^2 + c) + a), x)","F",0
20,1,261,0,0.540485," ","integrate(x/(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} - b^{2}\right)} d x^{2} + \sqrt{a^{2} - b^{2}} b \log\left(\frac{{\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x^{2} + c\right)^{2} + 2 \, a b \sin\left(d x^{2} + c\right) + a^{2} + b^{2} + 2 \, {\left(b \cos\left(d x^{2} + c\right) \sin\left(d x^{2} + c\right) + a \cos\left(d x^{2} + c\right)\right)} \sqrt{a^{2} - b^{2}}}{a^{2} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b \sin\left(d x^{2} + c\right) - a^{2} - b^{2}}\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d}, \frac{{\left(a^{2} - b^{2}\right)} d x^{2} + \sqrt{-a^{2} + b^{2}} b \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \sin\left(d x^{2} + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \cos\left(d x^{2} + c\right)}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[1/4*(2*(a^2 - b^2)*d*x^2 + sqrt(a^2 - b^2)*b*log(((a^2 - 2*b^2)*cos(d*x^2 + c)^2 + 2*a*b*sin(d*x^2 + c) + a^2 + b^2 + 2*(b*cos(d*x^2 + c)*sin(d*x^2 + c) + a*cos(d*x^2 + c))*sqrt(a^2 - b^2))/(a^2*cos(d*x^2 + c)^2 - 2*a*b*sin(d*x^2 + c) - a^2 - b^2)))/((a^3 - a*b^2)*d), 1/2*((a^2 - b^2)*d*x^2 + sqrt(-a^2 + b^2)*b*arctan(-sqrt(-a^2 + b^2)*(b*sin(d*x^2 + c) + a)/((a^2 - b^2)*cos(d*x^2 + c))))/((a^3 - a*b^2)*d)]","A",0
21,0,0,0,0.573260," ","integrate(1/x/(a+b*csc(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \csc\left(d x^{2} + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*csc(d*x^2 + c) + a*x), x)","F",0
22,0,0,0,0.495193," ","integrate((a+b*csc(d*x^2+c))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \csc\left(d x^{2} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*csc(d*x^2 + c) + a)/x^2, x)","F",0
23,1,3032,0,0.880020," ","integrate(x^5/(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} x^{6} \sin\left(d x^{2} + c\right) + 4 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} x^{6} - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{2} x^{4} \cos\left(d x^{2} + c\right) + 12 \, {\left(2 \, a^{3} b^{2} - a b^{4} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{i \, b \cos\left(d x^{2} + c\right) + b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}}{a}\right) - 12 \, {\left(2 \, a^{3} b^{2} - a b^{4} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{i \, b \cos\left(d x^{2} + c\right) + b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}}{a}\right) + 12 \, {\left(2 \, a^{3} b^{2} - a b^{4} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{-i \, b \cos\left(d x^{2} + c\right) + b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}}{a}\right) - 12 \, {\left(2 \, a^{3} b^{2} - a b^{4} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{-i \, b \cos\left(d x^{2} + c\right) + b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}}{a}\right) + {\left(-12 i \, a^{2} b^{3} + 12 i \, b^{5} + {\left(-12 i \, a^{3} b^{2} + 12 i \, a b^{4}\right)} \sin\left(d x^{2} + c\right) + 2 \, {\left(6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} \sin\left(d x^{2} + c\right) + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) + {\left(-12 i \, a^{2} b^{3} + 12 i \, b^{5} + {\left(-12 i \, a^{3} b^{2} + 12 i \, a b^{4}\right)} \sin\left(d x^{2} + c\right) + 2 \, {\left(-6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} \sin\left(d x^{2} + c\right) - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) + {\left(12 i \, a^{2} b^{3} - 12 i \, b^{5} + {\left(12 i \, a^{3} b^{2} - 12 i \, a b^{4}\right)} \sin\left(d x^{2} + c\right) + 2 \, {\left(-6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} \sin\left(d x^{2} + c\right) - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) + {\left(12 i \, a^{2} b^{3} - 12 i \, b^{5} + {\left(12 i \, a^{3} b^{2} - 12 i \, a b^{4}\right)} \sin\left(d x^{2} + c\right) + 2 \, {\left(6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} \sin\left(d x^{2} + c\right) + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) - 6 \, {\left(2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c \sin\left(d x^{2} + c\right) + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c - {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sin\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cos\left(d x^{2} + c\right) + 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) - 6 \, {\left(2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c \sin\left(d x^{2} + c\right) + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c - {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sin\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cos\left(d x^{2} + c\right) - 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) - 6 \, {\left(2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c \sin\left(d x^{2} + c\right) + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sin\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-2 \, a \cos\left(d x^{2} + c\right) + 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) - 6 \, {\left(2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c \sin\left(d x^{2} + c\right) + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sin\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-2 \, a \cos\left(d x^{2} + c\right) - 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) + 6 \, {\left(2 \, {\left(a^{2} b^{3} - b^{5}\right)} d x^{2} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c + 2 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} \sin\left(d x^{2} + c\right) - {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} x^{4} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) + 6 \, {\left(2 \, {\left(a^{2} b^{3} - b^{5}\right)} d x^{2} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c + 2 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} \sin\left(d x^{2} + c\right) + {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} x^{4} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) + 6 \, {\left(2 \, {\left(a^{2} b^{3} - b^{5}\right)} d x^{2} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c + 2 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} \sin\left(d x^{2} + c\right) - {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} x^{4} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) + 6 \, {\left(2 \, {\left(a^{2} b^{3} - b^{5}\right)} d x^{2} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c + 2 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} \sin\left(d x^{2} + c\right) + {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} x^{4} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right)}{24 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{3} \sin\left(d x^{2} + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{3}\right)}}"," ",0,"1/24*(4*(a^5 - 2*a^3*b^2 + a*b^4)*d^3*x^6*sin(d*x^2 + c) + 4*(a^4*b - 2*a^2*b^3 + b^5)*d^3*x^6 - 12*(a^3*b^2 - a*b^4)*d^2*x^4*cos(d*x^2 + c) + 12*(2*a^3*b^2 - a*b^4 + (2*a^4*b - a^2*b^3)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*polylog(3, -(I*b*cos(d*x^2 + c) + b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))/a) - 12*(2*a^3*b^2 - a*b^4 + (2*a^4*b - a^2*b^3)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*polylog(3, -(I*b*cos(d*x^2 + c) + b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))/a) + 12*(2*a^3*b^2 - a*b^4 + (2*a^4*b - a^2*b^3)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*polylog(3, -(-I*b*cos(d*x^2 + c) + b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))/a) - 12*(2*a^3*b^2 - a*b^4 + (2*a^4*b - a^2*b^3)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*polylog(3, -(-I*b*cos(d*x^2 + c) + b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))/a) + (-12*I*a^2*b^3 + 12*I*b^5 + (-12*I*a^3*b^2 + 12*I*a*b^4)*sin(d*x^2 + c) + 2*(6*I*(2*a^4*b - a^2*b^3)*d*x^2*sin(d*x^2 + c) + 6*I*(2*a^3*b^2 - a*b^4)*d*x^2)*sqrt((a^2 - b^2)/a^2))*dilog((I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) + (-12*I*a^2*b^3 + 12*I*b^5 + (-12*I*a^3*b^2 + 12*I*a*b^4)*sin(d*x^2 + c) + 2*(-6*I*(2*a^4*b - a^2*b^3)*d*x^2*sin(d*x^2 + c) - 6*I*(2*a^3*b^2 - a*b^4)*d*x^2)*sqrt((a^2 - b^2)/a^2))*dilog((I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) + (12*I*a^2*b^3 - 12*I*b^5 + (12*I*a^3*b^2 - 12*I*a*b^4)*sin(d*x^2 + c) + 2*(-6*I*(2*a^4*b - a^2*b^3)*d*x^2*sin(d*x^2 + c) - 6*I*(2*a^3*b^2 - a*b^4)*d*x^2)*sqrt((a^2 - b^2)/a^2))*dilog((-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) + (12*I*a^2*b^3 - 12*I*b^5 + (12*I*a^3*b^2 - 12*I*a*b^4)*sin(d*x^2 + c) + 2*(6*I*(2*a^4*b - a^2*b^3)*d*x^2*sin(d*x^2 + c) + 6*I*(2*a^3*b^2 - a*b^4)*d*x^2)*sqrt((a^2 - b^2)/a^2))*dilog((-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) - 6*(2*(a^3*b^2 - a*b^4)*c*sin(d*x^2 + c) + 2*(a^2*b^3 - b^5)*c - ((2*a^4*b - a^2*b^3)*c^2*sin(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*c^2)*sqrt((a^2 - b^2)/a^2))*log(2*a*cos(d*x^2 + c) + 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) - 6*(2*(a^3*b^2 - a*b^4)*c*sin(d*x^2 + c) + 2*(a^2*b^3 - b^5)*c - ((2*a^4*b - a^2*b^3)*c^2*sin(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*c^2)*sqrt((a^2 - b^2)/a^2))*log(2*a*cos(d*x^2 + c) - 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) - 6*(2*(a^3*b^2 - a*b^4)*c*sin(d*x^2 + c) + 2*(a^2*b^3 - b^5)*c + ((2*a^4*b - a^2*b^3)*c^2*sin(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*c^2)*sqrt((a^2 - b^2)/a^2))*log(-2*a*cos(d*x^2 + c) + 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) - 6*(2*(a^3*b^2 - a*b^4)*c*sin(d*x^2 + c) + 2*(a^2*b^3 - b^5)*c + ((2*a^4*b - a^2*b^3)*c^2*sin(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*c^2)*sqrt((a^2 - b^2)/a^2))*log(-2*a*cos(d*x^2 + c) - 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) + 6*(2*(a^2*b^3 - b^5)*d*x^2 + 2*(a^2*b^3 - b^5)*c + 2*((a^3*b^2 - a*b^4)*d*x^2 + (a^3*b^2 - a*b^4)*c)*sin(d*x^2 + c) - ((2*a^3*b^2 - a*b^4)*d^2*x^4 - (2*a^3*b^2 - a*b^4)*c^2 + ((2*a^4*b - a^2*b^3)*d^2*x^4 - (2*a^4*b - a^2*b^3)*c^2)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))*log(-(I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) + 6*(2*(a^2*b^3 - b^5)*d*x^2 + 2*(a^2*b^3 - b^5)*c + 2*((a^3*b^2 - a*b^4)*d*x^2 + (a^3*b^2 - a*b^4)*c)*sin(d*x^2 + c) + ((2*a^3*b^2 - a*b^4)*d^2*x^4 - (2*a^3*b^2 - a*b^4)*c^2 + ((2*a^4*b - a^2*b^3)*d^2*x^4 - (2*a^4*b - a^2*b^3)*c^2)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))*log(-(I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) + 6*(2*(a^2*b^3 - b^5)*d*x^2 + 2*(a^2*b^3 - b^5)*c + 2*((a^3*b^2 - a*b^4)*d*x^2 + (a^3*b^2 - a*b^4)*c)*sin(d*x^2 + c) - ((2*a^3*b^2 - a*b^4)*d^2*x^4 - (2*a^3*b^2 - a*b^4)*c^2 + ((2*a^4*b - a^2*b^3)*d^2*x^4 - (2*a^4*b - a^2*b^3)*c^2)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))*log(-(-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) + 6*(2*(a^2*b^3 - b^5)*d*x^2 + 2*(a^2*b^3 - b^5)*c + 2*((a^3*b^2 - a*b^4)*d*x^2 + (a^3*b^2 - a*b^4)*c)*sin(d*x^2 + c) + ((2*a^3*b^2 - a*b^4)*d^2*x^4 - (2*a^3*b^2 - a*b^4)*c^2 + ((2*a^4*b - a^2*b^3)*d^2*x^4 - (2*a^4*b - a^2*b^3)*c^2)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2))*log(-(-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d^3*sin(d*x^2 + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^3)","C",0
24,0,0,0,0.481296," ","integrate(x^4/(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{b^{2} \csc\left(d x^{2} + c\right)^{2} + 2 \, a b \csc\left(d x^{2} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^4/(b^2*csc(d*x^2 + c)^2 + 2*a*b*csc(d*x^2 + c) + a^2), x)","F",0
25,1,1906,0,0.873791," ","integrate(x^3/(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} \sin\left(d x^{2} + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} x^{4} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x^{2} \cos\left(d x^{2} + c\right) + {\left(2 i \, a^{3} b^{2} - i \, a b^{4} + {\left(2 i \, a^{4} b - i \, a^{2} b^{3}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) + {\left(-2 i \, a^{3} b^{2} + i \, a b^{4} + {\left(-2 i \, a^{4} b + i \, a^{2} b^{3}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) + {\left(-2 i \, a^{3} b^{2} + i \, a b^{4} + {\left(-2 i \, a^{4} b + i \, a^{2} b^{3}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) + {\left(2 i \, a^{3} b^{2} - i \, a b^{4} + {\left(2 i \, a^{4} b - i \, a^{2} b^{3}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a} + 1\right) - {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) + {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) + i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) - {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) + {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) + {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-\frac{-i \, b \cos\left(d x^{2} + c\right) - b \sin\left(d x^{2} + c\right) - {\left(a \cos\left(d x^{2} + c\right) - i \, a \sin\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a}{a}\right) + {\left(a^{2} b^{3} - b^{5} + {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x^{2} + c\right) - {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sin\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cos\left(d x^{2} + c\right) + 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) + {\left(a^{2} b^{3} - b^{5} + {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x^{2} + c\right) - {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sin\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cos\left(d x^{2} + c\right) - 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) + {\left(a^{2} b^{3} - b^{5} + {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x^{2} + c\right) + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sin\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-2 \, a \cos\left(d x^{2} + c\right) + 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) + {\left(a^{2} b^{3} - b^{5} + {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x^{2} + c\right) + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sin\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c\right)} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-2 \, a \cos\left(d x^{2} + c\right) - 2 i \, a \sin\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)}{4 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \sin\left(d x^{2} + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{2}\right)}}"," ",0,"1/4*((a^5 - 2*a^3*b^2 + a*b^4)*d^2*x^4*sin(d*x^2 + c) + (a^4*b - 2*a^2*b^3 + b^5)*d^2*x^4 - 2*(a^3*b^2 - a*b^4)*d*x^2*cos(d*x^2 + c) + (2*I*a^3*b^2 - I*a*b^4 + (2*I*a^4*b - I*a^2*b^3)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*dilog((I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) + (-2*I*a^3*b^2 + I*a*b^4 + (-2*I*a^4*b + I*a^2*b^3)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*dilog((I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) + (-2*I*a^3*b^2 + I*a*b^4 + (-2*I*a^4*b + I*a^2*b^3)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*dilog((-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) + (2*I*a^3*b^2 - I*a*b^4 + (2*I*a^4*b - I*a^2*b^3)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*dilog((-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a + 1) - ((2*a^3*b^2 - a*b^4)*d*x^2 + (2*a^3*b^2 - a*b^4)*c + ((2*a^4*b - a^2*b^3)*d*x^2 + (2*a^4*b - a^2*b^3)*c)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*log(-(I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) + ((2*a^3*b^2 - a*b^4)*d*x^2 + (2*a^3*b^2 - a*b^4)*c + ((2*a^4*b - a^2*b^3)*d*x^2 + (2*a^4*b - a^2*b^3)*c)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*log(-(I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) + I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) - ((2*a^3*b^2 - a*b^4)*d*x^2 + (2*a^3*b^2 - a*b^4)*c + ((2*a^4*b - a^2*b^3)*d*x^2 + (2*a^4*b - a^2*b^3)*c)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*log(-(-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) + (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) + ((2*a^3*b^2 - a*b^4)*d*x^2 + (2*a^3*b^2 - a*b^4)*c + ((2*a^4*b - a^2*b^3)*d*x^2 + (2*a^4*b - a^2*b^3)*c)*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2)*log(-(-I*b*cos(d*x^2 + c) - b*sin(d*x^2 + c) - (a*cos(d*x^2 + c) - I*a*sin(d*x^2 + c))*sqrt((a^2 - b^2)/a^2) - a)/a) + (a^2*b^3 - b^5 + (a^3*b^2 - a*b^4)*sin(d*x^2 + c) - ((2*a^4*b - a^2*b^3)*c*sin(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*c)*sqrt((a^2 - b^2)/a^2))*log(2*a*cos(d*x^2 + c) + 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) + (a^2*b^3 - b^5 + (a^3*b^2 - a*b^4)*sin(d*x^2 + c) - ((2*a^4*b - a^2*b^3)*c*sin(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*c)*sqrt((a^2 - b^2)/a^2))*log(2*a*cos(d*x^2 + c) - 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) + (a^2*b^3 - b^5 + (a^3*b^2 - a*b^4)*sin(d*x^2 + c) + ((2*a^4*b - a^2*b^3)*c*sin(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*c)*sqrt((a^2 - b^2)/a^2))*log(-2*a*cos(d*x^2 + c) + 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) + (a^2*b^3 - b^5 + (a^3*b^2 - a*b^4)*sin(d*x^2 + c) + ((2*a^4*b - a^2*b^3)*c*sin(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*c)*sqrt((a^2 - b^2)/a^2))*log(-2*a*cos(d*x^2 + c) - 2*I*a*sin(d*x^2 + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d^2*sin(d*x^2 + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^2)","B",0
26,0,0,0,0.485389," ","integrate(x^2/(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b^{2} \csc\left(d x^{2} + c\right)^{2} + 2 \, a b \csc\left(d x^{2} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^2/(b^2*csc(d*x^2 + c)^2 + 2*a*b*csc(d*x^2 + c) + a^2), x)","F",0
27,1,536,0,0.493883," ","integrate(x/(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} \sin\left(d x^{2} + c\right) + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x^{2} + {\left(2 \, a^{2} b^{2} - b^{4} + {\left(2 \, a^{3} b - a b^{3}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{{\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x^{2} + c\right)^{2} + 2 \, a b \sin\left(d x^{2} + c\right) + a^{2} + b^{2} + 2 \, {\left(b \cos\left(d x^{2} + c\right) \sin\left(d x^{2} + c\right) + a \cos\left(d x^{2} + c\right)\right)} \sqrt{a^{2} - b^{2}}}{a^{2} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b \sin\left(d x^{2} + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x^{2} + c\right)}{4 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \sin\left(d x^{2} + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)}}, \frac{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} \sin\left(d x^{2} + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x^{2} + {\left(2 \, a^{2} b^{2} - b^{4} + {\left(2 \, a^{3} b - a b^{3}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \sin\left(d x^{2} + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \cos\left(d x^{2} + c\right)}\right) - {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x^{2} + c\right)}{2 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \sin\left(d x^{2} + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)}}\right]"," ",0,"[1/4*(2*(a^5 - 2*a^3*b^2 + a*b^4)*d*x^2*sin(d*x^2 + c) + 2*(a^4*b - 2*a^2*b^3 + b^5)*d*x^2 + (2*a^2*b^2 - b^4 + (2*a^3*b - a*b^3)*sin(d*x^2 + c))*sqrt(a^2 - b^2)*log(((a^2 - 2*b^2)*cos(d*x^2 + c)^2 + 2*a*b*sin(d*x^2 + c) + a^2 + b^2 + 2*(b*cos(d*x^2 + c)*sin(d*x^2 + c) + a*cos(d*x^2 + c))*sqrt(a^2 - b^2))/(a^2*cos(d*x^2 + c)^2 - 2*a*b*sin(d*x^2 + c) - a^2 - b^2)) - 2*(a^3*b^2 - a*b^4)*cos(d*x^2 + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*sin(d*x^2 + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d), 1/2*((a^5 - 2*a^3*b^2 + a*b^4)*d*x^2*sin(d*x^2 + c) + (a^4*b - 2*a^2*b^3 + b^5)*d*x^2 + (2*a^2*b^2 - b^4 + (2*a^3*b - a*b^3)*sin(d*x^2 + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*sin(d*x^2 + c) + a)/((a^2 - b^2)*cos(d*x^2 + c))) - (a^3*b^2 - a*b^4)*cos(d*x^2 + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*sin(d*x^2 + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d)]","B",0
28,0,0,0,0.475343," ","integrate(1/x/(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x \csc\left(d x^{2} + c\right)^{2} + 2 \, a b x \csc\left(d x^{2} + c\right) + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*csc(d*x^2 + c)^2 + 2*a*b*x*csc(d*x^2 + c) + a^2*x), x)","F",0
29,0,0,0,0.657017," ","integrate(1/x^2/(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} \csc\left(d x^{2} + c\right)^{2} + 2 \, a b x^{2} \csc\left(d x^{2} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*csc(d*x^2 + c)^2 + 2*a*b*x^2*csc(d*x^2 + c) + a^2*x^2), x)","F",0
30,0,0,0,0.453681," ","integrate(1/x^3/(a+b*csc(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{3} \csc\left(d x^{2} + c\right)^{2} + 2 \, a b x^{3} \csc\left(d x^{2} + c\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(1/(b^2*x^3*csc(d*x^2 + c)^2 + 2*a*b*x^3*csc(d*x^2 + c) + a^2*x^3), x)","F",0
31,0,0,0,0.623817," ","integrate(x^3*(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{3} \csc\left(d \sqrt{x} + c\right) + a x^{3}, x\right)"," ",0,"integral(b*x^3*csc(d*sqrt(x) + c) + a*x^3, x)","F",0
32,0,0,0,0.589779," ","integrate(x^2*(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{2} \csc\left(d \sqrt{x} + c\right) + a x^{2}, x\right)"," ",0,"integral(b*x^2*csc(d*sqrt(x) + c) + a*x^2, x)","F",0
33,0,0,0,0.479739," ","integrate(x*(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x \csc\left(d \sqrt{x} + c\right) + a x, x\right)"," ",0,"integral(b*x*csc(d*sqrt(x) + c) + a*x, x)","F",0
34,0,0,0,0.768474," ","integrate((a+b*csc(c+d*x^(1/2)))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \csc\left(d \sqrt{x} + c\right) + a}{x}, x\right)"," ",0,"integral((b*csc(d*sqrt(x) + c) + a)/x, x)","F",0
35,0,0,0,0.470233," ","integrate((a+b*csc(c+d*x^(1/2)))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \csc\left(d \sqrt{x} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*csc(d*sqrt(x) + c) + a)/x^2, x)","F",0
36,0,0,0,0.586578," ","integrate(x^3*(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{3} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{3} \csc\left(d \sqrt{x} + c\right) + a^{2} x^{3}, x\right)"," ",0,"integral(b^2*x^3*csc(d*sqrt(x) + c)^2 + 2*a*b*x^3*csc(d*sqrt(x) + c) + a^2*x^3, x)","F",0
37,0,0,0,0.511277," ","integrate(x^2*(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \csc\left(d \sqrt{x} + c\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*csc(d*sqrt(x) + c)^2 + 2*a*b*x^2*csc(d*sqrt(x) + c) + a^2*x^2, x)","F",0
38,0,0,0,0.510994," ","integrate(x*(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x \csc\left(d \sqrt{x} + c\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*csc(d*sqrt(x) + c)^2 + 2*a*b*x*csc(d*sqrt(x) + c) + a^2*x, x)","F",0
39,0,0,0,0.526503," ","integrate((a+b*csc(c+d*x^(1/2)))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \csc\left(d \sqrt{x} + c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*csc(d*sqrt(x) + c)^2 + 2*a*b*csc(d*sqrt(x) + c) + a^2)/x, x)","F",0
40,0,0,0,0.459367," ","integrate((a+b*csc(c+d*x^(1/2)))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \csc\left(d \sqrt{x} + c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*csc(d*sqrt(x) + c)^2 + 2*a*b*csc(d*sqrt(x) + c) + a^2)/x^2, x)","F",0
41,0,0,0,0.517797," ","integrate(x^3/(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{b \csc\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^3/(b*csc(d*sqrt(x) + c) + a), x)","F",0
42,0,0,0,0.531960," ","integrate(x^2/(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b \csc\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^2/(b*csc(d*sqrt(x) + c) + a), x)","F",0
43,0,0,0,0.487753," ","integrate(x/(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b \csc\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x/(b*csc(d*sqrt(x) + c) + a), x)","F",0
44,0,0,0,0.504711," ","integrate(1/x/(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \csc\left(d \sqrt{x} + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*csc(d*sqrt(x) + c) + a*x), x)","F",0
45,0,0,0,0.618044," ","integrate((a+b*csc(c+d*x^(1/2)))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \csc\left(d \sqrt{x} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*csc(d*sqrt(x) + c) + a)/x^2, x)","F",0
46,0,0,0,0.500411," ","integrate(x^3/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{b^{2} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \csc\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^3/(b^2*csc(d*sqrt(x) + c)^2 + 2*a*b*csc(d*sqrt(x) + c) + a^2), x)","F",0
47,0,0,0,0.578684," ","integrate(x^2/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b^{2} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \csc\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^2/(b^2*csc(d*sqrt(x) + c)^2 + 2*a*b*csc(d*sqrt(x) + c) + a^2), x)","F",0
48,0,0,0,0.543148," ","integrate(x/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{2} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \csc\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x/(b^2*csc(d*sqrt(x) + c)^2 + 2*a*b*csc(d*sqrt(x) + c) + a^2), x)","F",0
49,0,0,0,0.566649," ","integrate(1/x/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x \csc\left(d \sqrt{x} + c\right) + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*csc(d*sqrt(x) + c)^2 + 2*a*b*x*csc(d*sqrt(x) + c) + a^2*x), x)","F",0
50,0,0,0,0.514211," ","integrate(1/x^2/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \csc\left(d \sqrt{x} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*csc(d*sqrt(x) + c)^2 + 2*a*b*x^2*csc(d*sqrt(x) + c) + a^2*x^2), x)","F",0
51,0,0,0,0.446086," ","integrate(x^(3/2)*(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{\frac{3}{2}} \csc\left(d \sqrt{x} + c\right) + a x^{\frac{3}{2}}, x\right)"," ",0,"integral(b*x^(3/2)*csc(d*sqrt(x) + c) + a*x^(3/2), x)","F",0
52,0,0,0,0.457872," ","integrate((a+b*csc(c+d*x^(1/2)))*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(b \sqrt{x} \csc\left(d \sqrt{x} + c\right) + a \sqrt{x}, x\right)"," ",0,"integral(b*sqrt(x)*csc(d*sqrt(x) + c) + a*sqrt(x), x)","F",0
53,1,43,0,0.537011," ","integrate((a+b*csc(c+d*x^(1/2)))/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, a d \sqrt{x} - b \log\left(\frac{1}{2} \, \cos\left(d \sqrt{x} + c\right) + \frac{1}{2}\right) + b \log\left(-\frac{1}{2} \, \cos\left(d \sqrt{x} + c\right) + \frac{1}{2}\right)}{d}"," ",0,"(2*a*d*sqrt(x) - b*log(1/2*cos(d*sqrt(x) + c) + 1/2) + b*log(-1/2*cos(d*sqrt(x) + c) + 1/2))/d","A",0
54,0,0,0,0.475247," ","integrate((a+b*csc(c+d*x^(1/2)))/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sqrt{x} \csc\left(d \sqrt{x} + c\right) + a \sqrt{x}}{x^{2}}, x\right)"," ",0,"integral((b*sqrt(x)*csc(d*sqrt(x) + c) + a*sqrt(x))/x^2, x)","F",0
55,0,0,0,0.475957," ","integrate((a+b*csc(c+d*x^(1/2)))/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sqrt{x} \csc\left(d \sqrt{x} + c\right) + a \sqrt{x}}{x^{3}}, x\right)"," ",0,"integral((b*sqrt(x)*csc(d*sqrt(x) + c) + a*sqrt(x))/x^3, x)","F",0
56,0,0,0,0.483465," ","integrate(x^(3/2)*(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{\frac{3}{2}} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{\frac{3}{2}} \csc\left(d \sqrt{x} + c\right) + a^{2} x^{\frac{3}{2}}, x\right)"," ",0,"integral(b^2*x^(3/2)*csc(d*sqrt(x) + c)^2 + 2*a*b*x^(3/2)*csc(d*sqrt(x) + c) + a^2*x^(3/2), x)","F",0
57,0,0,0,0.474973," ","integrate((a+b*csc(c+d*x^(1/2)))^2*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \sqrt{x} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \csc\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}, x\right)"," ",0,"integral(b^2*sqrt(x)*csc(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*csc(d*sqrt(x) + c) + a^2*sqrt(x), x)","F",0
58,1,94,0,0.575592," ","integrate((a+b*csc(c+d*x^(1/2)))^2/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} d \sqrt{x} \sin\left(d \sqrt{x} + c\right) - a b \log\left(\frac{1}{2} \, \cos\left(d \sqrt{x} + c\right) + \frac{1}{2}\right) \sin\left(d \sqrt{x} + c\right) + a b \log\left(-\frac{1}{2} \, \cos\left(d \sqrt{x} + c\right) + \frac{1}{2}\right) \sin\left(d \sqrt{x} + c\right) - b^{2} \cos\left(d \sqrt{x} + c\right)\right)}}{d \sin\left(d \sqrt{x} + c\right)}"," ",0,"2*(a^2*d*sqrt(x)*sin(d*sqrt(x) + c) - a*b*log(1/2*cos(d*sqrt(x) + c) + 1/2)*sin(d*sqrt(x) + c) + a*b*log(-1/2*cos(d*sqrt(x) + c) + 1/2)*sin(d*sqrt(x) + c) - b^2*cos(d*sqrt(x) + c))/(d*sin(d*sqrt(x) + c))","B",0
59,0,0,0,0.528408," ","integrate((a+b*csc(c+d*x^(1/2)))^2/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sqrt{x} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \csc\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}}{x^{2}}, x\right)"," ",0,"integral((b^2*sqrt(x)*csc(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*csc(d*sqrt(x) + c) + a^2*sqrt(x))/x^2, x)","F",0
60,0,0,0,0.481428," ","integrate((a+b*csc(c+d*x^(1/2)))^2/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sqrt{x} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \csc\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}}{x^{3}}, x\right)"," ",0,"integral((b^2*sqrt(x)*csc(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*csc(d*sqrt(x) + c) + a^2*sqrt(x))/x^3, x)","F",0
61,1,56,0,0.481177," ","integrate(csc(x^(1/2))^3/x^(1/2),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(\sqrt{x}\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(\sqrt{x}\right) + \frac{1}{2}\right) - {\left(\cos\left(\sqrt{x}\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(\sqrt{x}\right) + \frac{1}{2}\right) - 2 \, \cos\left(\sqrt{x}\right)}{2 \, {\left(\cos\left(\sqrt{x}\right)^{2} - 1\right)}}"," ",0,"-1/2*((cos(sqrt(x))^2 - 1)*log(1/2*cos(sqrt(x)) + 1/2) - (cos(sqrt(x))^2 - 1)*log(-1/2*cos(sqrt(x)) + 1/2) - 2*cos(sqrt(x)))/(cos(sqrt(x))^2 - 1)","B",0
62,0,0,0,0.548176," ","integrate(x^(3/2)/(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{\frac{3}{2}}}{b \csc\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^(3/2)/(b*csc(d*sqrt(x) + c) + a), x)","F",0
63,0,0,0,0.651961," ","integrate(x^(1/2)/(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b \csc\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(sqrt(x)/(b*csc(d*sqrt(x) + c) + a), x)","F",0
64,1,275,0,0.661989," ","integrate(1/(a+b*csc(c+d*x^(1/2)))/x^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} - b^{2}\right)} d \sqrt{x} + \sqrt{a^{2} - b^{2}} b \log\left(\frac{{\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d \sqrt{x} + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} a \cos\left(d \sqrt{x} + c\right) + a^{2} + b^{2} + 2 \, {\left(\sqrt{a^{2} - b^{2}} b \cos\left(d \sqrt{x} + c\right) + a b\right)} \sin\left(d \sqrt{x} + c\right)}{a^{2} \cos\left(d \sqrt{x} + c\right)^{2} - 2 \, a b \sin\left(d \sqrt{x} + c\right) - a^{2} - b^{2}}\right)}{{\left(a^{3} - a b^{2}\right)} d}, \frac{2 \, {\left({\left(a^{2} - b^{2}\right)} d \sqrt{x} + \sqrt{-a^{2} + b^{2}} b \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} b \sin\left(d \sqrt{x} + c\right) + \sqrt{-a^{2} + b^{2}} a}{{\left(a^{2} - b^{2}\right)} \cos\left(d \sqrt{x} + c\right)}\right)\right)}}{{\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[(2*(a^2 - b^2)*d*sqrt(x) + sqrt(a^2 - b^2)*b*log(((a^2 - 2*b^2)*cos(d*sqrt(x) + c)^2 + 2*sqrt(a^2 - b^2)*a*cos(d*sqrt(x) + c) + a^2 + b^2 + 2*(sqrt(a^2 - b^2)*b*cos(d*sqrt(x) + c) + a*b)*sin(d*sqrt(x) + c))/(a^2*cos(d*sqrt(x) + c)^2 - 2*a*b*sin(d*sqrt(x) + c) - a^2 - b^2)))/((a^3 - a*b^2)*d), 2*((a^2 - b^2)*d*sqrt(x) + sqrt(-a^2 + b^2)*b*arctan(-(sqrt(-a^2 + b^2)*b*sin(d*sqrt(x) + c) + sqrt(-a^2 + b^2)*a)/((a^2 - b^2)*cos(d*sqrt(x) + c))))/((a^3 - a*b^2)*d)]","A",0
65,0,0,0,0.536475," ","integrate(1/x^(3/2)/(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b x^{2} \csc\left(d \sqrt{x} + c\right) + a x^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b*x^2*csc(d*sqrt(x) + c) + a*x^2), x)","F",0
66,0,0,0,0.677114," ","integrate(1/x^(5/2)/(a+b*csc(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b x^{3} \csc\left(d \sqrt{x} + c\right) + a x^{3}}, x\right)"," ",0,"integral(sqrt(x)/(b*x^3*csc(d*sqrt(x) + c) + a*x^3), x)","F",0
67,0,0,0,0.445530," ","integrate(x^(3/2)/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{\frac{3}{2}}}{b^{2} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \csc\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^(3/2)/(b^2*csc(d*sqrt(x) + c)^2 + 2*a*b*csc(d*sqrt(x) + c) + a^2), x)","F",0
68,0,0,0,0.640405," ","integrate(x^(1/2)/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \csc\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*csc(d*sqrt(x) + c)^2 + 2*a*b*csc(d*sqrt(x) + c) + a^2), x)","F",0
69,1,576,0,0.559689," ","integrate(1/(a+b*csc(c+d*x^(1/2)))^2/x^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{x} \sin\left(d \sqrt{x} + c\right) + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \sqrt{x} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d \sqrt{x} + c\right) + {\left({\left(2 \, a^{3} b - a b^{3}\right)} \sqrt{a^{2} - b^{2}} \sin\left(d \sqrt{x} + c\right) + {\left(2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{a^{2} - b^{2}}\right)} \log\left(\frac{{\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d \sqrt{x} + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} a \cos\left(d \sqrt{x} + c\right) + a^{2} + b^{2} + 2 \, {\left(\sqrt{a^{2} - b^{2}} b \cos\left(d \sqrt{x} + c\right) + a b\right)} \sin\left(d \sqrt{x} + c\right)}{a^{2} \cos\left(d \sqrt{x} + c\right)^{2} - 2 \, a b \sin\left(d \sqrt{x} + c\right) - a^{2} - b^{2}}\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \sin\left(d \sqrt{x} + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d}, \frac{2 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{x} \sin\left(d \sqrt{x} + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \sqrt{x} + {\left({\left(2 \, a^{3} b - a b^{3}\right)} \sqrt{-a^{2} + b^{2}} \sin\left(d \sqrt{x} + c\right) + {\left(2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{-a^{2} + b^{2}}\right)} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} b \sin\left(d \sqrt{x} + c\right) + \sqrt{-a^{2} + b^{2}} a}{{\left(a^{2} - b^{2}\right)} \cos\left(d \sqrt{x} + c\right)}\right) - {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d \sqrt{x} + c\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \sin\left(d \sqrt{x} + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d}\right]"," ",0,"[(2*(a^5 - 2*a^3*b^2 + a*b^4)*d*sqrt(x)*sin(d*sqrt(x) + c) + 2*(a^4*b - 2*a^2*b^3 + b^5)*d*sqrt(x) - 2*(a^3*b^2 - a*b^4)*cos(d*sqrt(x) + c) + ((2*a^3*b - a*b^3)*sqrt(a^2 - b^2)*sin(d*sqrt(x) + c) + (2*a^2*b^2 - b^4)*sqrt(a^2 - b^2))*log(((a^2 - 2*b^2)*cos(d*sqrt(x) + c)^2 + 2*sqrt(a^2 - b^2)*a*cos(d*sqrt(x) + c) + a^2 + b^2 + 2*(sqrt(a^2 - b^2)*b*cos(d*sqrt(x) + c) + a*b)*sin(d*sqrt(x) + c))/(a^2*cos(d*sqrt(x) + c)^2 - 2*a*b*sin(d*sqrt(x) + c) - a^2 - b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*sin(d*sqrt(x) + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d), 2*((a^5 - 2*a^3*b^2 + a*b^4)*d*sqrt(x)*sin(d*sqrt(x) + c) + (a^4*b - 2*a^2*b^3 + b^5)*d*sqrt(x) + ((2*a^3*b - a*b^3)*sqrt(-a^2 + b^2)*sin(d*sqrt(x) + c) + (2*a^2*b^2 - b^4)*sqrt(-a^2 + b^2))*arctan(-(sqrt(-a^2 + b^2)*b*sin(d*sqrt(x) + c) + sqrt(-a^2 + b^2)*a)/((a^2 - b^2)*cos(d*sqrt(x) + c))) - (a^3*b^2 - a*b^4)*cos(d*sqrt(x) + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*sin(d*sqrt(x) + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d)]","B",0
70,0,0,0,0.475207," ","integrate(1/x^(3/2)/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} x^{2} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \csc\left(d \sqrt{x} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*x^2*csc(d*sqrt(x) + c)^2 + 2*a*b*x^2*csc(d*sqrt(x) + c) + a^2*x^2), x)","F",0
71,0,0,0,0.661972," ","integrate(1/x^(5/2)/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} x^{3} \csc\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{3} \csc\left(d \sqrt{x} + c\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*x^3*csc(d*sqrt(x) + c)^2 + 2*a*b*x^3*csc(d*sqrt(x) + c) + a^2*x^3), x)","F",0
72,0,0,0,0.505991," ","integrate((e*x)^m*(a+b*csc(c+d*x^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} {\left(b \csc\left(d x^{n} + c\right) + a\right)}^{p}, x\right)"," ",0,"integral((e*x)^m*(b*csc(d*x^n + c) + a)^p, x)","F",0
73,1,62,0,0.506087," ","integrate((e*x)^(-1+n)*(a+b*csc(c+d*x^n)),x, algorithm=""fricas"")","\frac{2 \, a d e^{n - 1} x^{n} - b e^{n - 1} \log\left(\frac{1}{2} \, \cos\left(d x^{n} + c\right) + \frac{1}{2}\right) + b e^{n - 1} \log\left(-\frac{1}{2} \, \cos\left(d x^{n} + c\right) + \frac{1}{2}\right)}{2 \, d n}"," ",0,"1/2*(2*a*d*e^(n - 1)*x^n - b*e^(n - 1)*log(1/2*cos(d*x^n + c) + 1/2) + b*e^(n - 1)*log(-1/2*cos(d*x^n + c) + 1/2))/(d*n)","A",0
74,1,384,0,0.531932," ","integrate((e*x)^(-1+2*n)*(a+b*csc(c+d*x^n)),x, algorithm=""fricas"")","\frac{a d^{2} e^{2 \, n - 1} x^{2 \, n} - b d e^{2 \, n - 1} x^{n} \log\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + 1\right) - b d e^{2 \, n - 1} x^{n} \log\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + 1\right) - b c e^{2 \, n - 1} \log\left(-\frac{1}{2} \, \cos\left(d x^{n} + c\right) + \frac{1}{2} i \, \sin\left(d x^{n} + c\right) + \frac{1}{2}\right) - b c e^{2 \, n - 1} \log\left(-\frac{1}{2} \, \cos\left(d x^{n} + c\right) - \frac{1}{2} i \, \sin\left(d x^{n} + c\right) + \frac{1}{2}\right) - i \, b e^{2 \, n - 1} {\rm Li}_2\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) + i \, b e^{2 \, n - 1} {\rm Li}_2\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) - i \, b e^{2 \, n - 1} {\rm Li}_2\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) + i \, b e^{2 \, n - 1} {\rm Li}_2\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) + {\left(b d e^{2 \, n - 1} x^{n} + b c e^{2 \, n - 1}\right)} \log\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + 1\right) + {\left(b d e^{2 \, n - 1} x^{n} + b c e^{2 \, n - 1}\right)} \log\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + 1\right)}{2 \, d^{2} n}"," ",0,"1/2*(a*d^2*e^(2*n - 1)*x^(2*n) - b*d*e^(2*n - 1)*x^n*log(cos(d*x^n + c) + I*sin(d*x^n + c) + 1) - b*d*e^(2*n - 1)*x^n*log(cos(d*x^n + c) - I*sin(d*x^n + c) + 1) - b*c*e^(2*n - 1)*log(-1/2*cos(d*x^n + c) + 1/2*I*sin(d*x^n + c) + 1/2) - b*c*e^(2*n - 1)*log(-1/2*cos(d*x^n + c) - 1/2*I*sin(d*x^n + c) + 1/2) - I*b*e^(2*n - 1)*dilog(cos(d*x^n + c) + I*sin(d*x^n + c)) + I*b*e^(2*n - 1)*dilog(cos(d*x^n + c) - I*sin(d*x^n + c)) - I*b*e^(2*n - 1)*dilog(-cos(d*x^n + c) + I*sin(d*x^n + c)) + I*b*e^(2*n - 1)*dilog(-cos(d*x^n + c) - I*sin(d*x^n + c)) + (b*d*e^(2*n - 1)*x^n + b*c*e^(2*n - 1))*log(-cos(d*x^n + c) + I*sin(d*x^n + c) + 1) + (b*d*e^(2*n - 1)*x^n + b*c*e^(2*n - 1))*log(-cos(d*x^n + c) - I*sin(d*x^n + c) + 1))/(d^2*n)","B",0
75,1,557,0,0.576364," ","integrate((e*x)^(-1+3*n)*(a+b*csc(c+d*x^n)),x, algorithm=""fricas"")","\frac{2 \, a d^{3} e^{3 \, n - 1} x^{3 \, n} - 3 \, b d^{2} e^{3 \, n - 1} x^{2 \, n} \log\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + 1\right) - 3 \, b d^{2} e^{3 \, n - 1} x^{2 \, n} \log\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + 1\right) - 6 i \, b d e^{3 \, n - 1} x^{n} {\rm Li}_2\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) + 6 i \, b d e^{3 \, n - 1} x^{n} {\rm Li}_2\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) - 6 i \, b d e^{3 \, n - 1} x^{n} {\rm Li}_2\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) + 6 i \, b d e^{3 \, n - 1} x^{n} {\rm Li}_2\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) + 3 \, b c^{2} e^{3 \, n - 1} \log\left(-\frac{1}{2} \, \cos\left(d x^{n} + c\right) + \frac{1}{2} i \, \sin\left(d x^{n} + c\right) + \frac{1}{2}\right) + 3 \, b c^{2} e^{3 \, n - 1} \log\left(-\frac{1}{2} \, \cos\left(d x^{n} + c\right) - \frac{1}{2} i \, \sin\left(d x^{n} + c\right) + \frac{1}{2}\right) + 6 \, b e^{3 \, n - 1} {\rm polylog}\left(3, \cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) + 6 \, b e^{3 \, n - 1} {\rm polylog}\left(3, \cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) - 6 \, b e^{3 \, n - 1} {\rm polylog}\left(3, -\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) - 6 \, b e^{3 \, n - 1} {\rm polylog}\left(3, -\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) + 3 \, {\left(b d^{2} e^{3 \, n - 1} x^{2 \, n} - b c^{2} e^{3 \, n - 1}\right)} \log\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + 1\right) + 3 \, {\left(b d^{2} e^{3 \, n - 1} x^{2 \, n} - b c^{2} e^{3 \, n - 1}\right)} \log\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + 1\right)}{6 \, d^{3} n}"," ",0,"1/6*(2*a*d^3*e^(3*n - 1)*x^(3*n) - 3*b*d^2*e^(3*n - 1)*x^(2*n)*log(cos(d*x^n + c) + I*sin(d*x^n + c) + 1) - 3*b*d^2*e^(3*n - 1)*x^(2*n)*log(cos(d*x^n + c) - I*sin(d*x^n + c) + 1) - 6*I*b*d*e^(3*n - 1)*x^n*dilog(cos(d*x^n + c) + I*sin(d*x^n + c)) + 6*I*b*d*e^(3*n - 1)*x^n*dilog(cos(d*x^n + c) - I*sin(d*x^n + c)) - 6*I*b*d*e^(3*n - 1)*x^n*dilog(-cos(d*x^n + c) + I*sin(d*x^n + c)) + 6*I*b*d*e^(3*n - 1)*x^n*dilog(-cos(d*x^n + c) - I*sin(d*x^n + c)) + 3*b*c^2*e^(3*n - 1)*log(-1/2*cos(d*x^n + c) + 1/2*I*sin(d*x^n + c) + 1/2) + 3*b*c^2*e^(3*n - 1)*log(-1/2*cos(d*x^n + c) - 1/2*I*sin(d*x^n + c) + 1/2) + 6*b*e^(3*n - 1)*polylog(3, cos(d*x^n + c) + I*sin(d*x^n + c)) + 6*b*e^(3*n - 1)*polylog(3, cos(d*x^n + c) - I*sin(d*x^n + c)) - 6*b*e^(3*n - 1)*polylog(3, -cos(d*x^n + c) + I*sin(d*x^n + c)) - 6*b*e^(3*n - 1)*polylog(3, -cos(d*x^n + c) - I*sin(d*x^n + c)) + 3*(b*d^2*e^(3*n - 1)*x^(2*n) - b*c^2*e^(3*n - 1))*log(-cos(d*x^n + c) + I*sin(d*x^n + c) + 1) + 3*(b*d^2*e^(3*n - 1)*x^(2*n) - b*c^2*e^(3*n - 1))*log(-cos(d*x^n + c) - I*sin(d*x^n + c) + 1))/(d^3*n)","C",0
76,1,116,0,0.502885," ","integrate((e*x)^(-1+n)*(a+b*csc(c+d*x^n))^2,x, algorithm=""fricas"")","\frac{a^{2} d e^{n - 1} x^{n} \sin\left(d x^{n} + c\right) - a b e^{n - 1} \log\left(\frac{1}{2} \, \cos\left(d x^{n} + c\right) + \frac{1}{2}\right) \sin\left(d x^{n} + c\right) + a b e^{n - 1} \log\left(-\frac{1}{2} \, \cos\left(d x^{n} + c\right) + \frac{1}{2}\right) \sin\left(d x^{n} + c\right) - b^{2} e^{n - 1} \cos\left(d x^{n} + c\right)}{d n \sin\left(d x^{n} + c\right)}"," ",0,"(a^2*d*e^(n - 1)*x^n*sin(d*x^n + c) - a*b*e^(n - 1)*log(1/2*cos(d*x^n + c) + 1/2)*sin(d*x^n + c) + a*b*e^(n - 1)*log(-1/2*cos(d*x^n + c) + 1/2)*sin(d*x^n + c) - b^2*e^(n - 1)*cos(d*x^n + c))/(d*n*sin(d*x^n + c))","A",0
77,1,568,0,0.599796," ","integrate((e*x)^(-1+2*n)*(a+b*csc(c+d*x^n))^2,x, algorithm=""fricas"")","\frac{a^{2} d^{2} e^{2 \, n - 1} x^{2 \, n} \sin\left(d x^{n} + c\right) - 2 \, b^{2} d e^{2 \, n - 1} x^{n} \cos\left(d x^{n} + c\right) - 2 i \, a b e^{2 \, n - 1} {\rm Li}_2\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) + 2 i \, a b e^{2 \, n - 1} {\rm Li}_2\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) - 2 i \, a b e^{2 \, n - 1} {\rm Li}_2\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) + 2 i \, a b e^{2 \, n - 1} {\rm Li}_2\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) - {\left(2 \, a b c - b^{2}\right)} e^{2 \, n - 1} \log\left(-\frac{1}{2} \, \cos\left(d x^{n} + c\right) + \frac{1}{2} i \, \sin\left(d x^{n} + c\right) + \frac{1}{2}\right) \sin\left(d x^{n} + c\right) - {\left(2 \, a b c - b^{2}\right)} e^{2 \, n - 1} \log\left(-\frac{1}{2} \, \cos\left(d x^{n} + c\right) - \frac{1}{2} i \, \sin\left(d x^{n} + c\right) + \frac{1}{2}\right) \sin\left(d x^{n} + c\right) - {\left(2 \, a b d e^{2 \, n - 1} x^{n} - b^{2} e^{2 \, n - 1}\right)} \log\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + 1\right) \sin\left(d x^{n} + c\right) - {\left(2 \, a b d e^{2 \, n - 1} x^{n} - b^{2} e^{2 \, n - 1}\right)} \log\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + 1\right) \sin\left(d x^{n} + c\right) + 2 \, {\left(a b d e^{2 \, n - 1} x^{n} + a b c e^{2 \, n - 1}\right)} \log\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + 1\right) \sin\left(d x^{n} + c\right) + 2 \, {\left(a b d e^{2 \, n - 1} x^{n} + a b c e^{2 \, n - 1}\right)} \log\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + 1\right) \sin\left(d x^{n} + c\right)}{2 \, d^{2} n \sin\left(d x^{n} + c\right)}"," ",0,"1/2*(a^2*d^2*e^(2*n - 1)*x^(2*n)*sin(d*x^n + c) - 2*b^2*d*e^(2*n - 1)*x^n*cos(d*x^n + c) - 2*I*a*b*e^(2*n - 1)*dilog(cos(d*x^n + c) + I*sin(d*x^n + c))*sin(d*x^n + c) + 2*I*a*b*e^(2*n - 1)*dilog(cos(d*x^n + c) - I*sin(d*x^n + c))*sin(d*x^n + c) - 2*I*a*b*e^(2*n - 1)*dilog(-cos(d*x^n + c) + I*sin(d*x^n + c))*sin(d*x^n + c) + 2*I*a*b*e^(2*n - 1)*dilog(-cos(d*x^n + c) - I*sin(d*x^n + c))*sin(d*x^n + c) - (2*a*b*c - b^2)*e^(2*n - 1)*log(-1/2*cos(d*x^n + c) + 1/2*I*sin(d*x^n + c) + 1/2)*sin(d*x^n + c) - (2*a*b*c - b^2)*e^(2*n - 1)*log(-1/2*cos(d*x^n + c) - 1/2*I*sin(d*x^n + c) + 1/2)*sin(d*x^n + c) - (2*a*b*d*e^(2*n - 1)*x^n - b^2*e^(2*n - 1))*log(cos(d*x^n + c) + I*sin(d*x^n + c) + 1)*sin(d*x^n + c) - (2*a*b*d*e^(2*n - 1)*x^n - b^2*e^(2*n - 1))*log(cos(d*x^n + c) - I*sin(d*x^n + c) + 1)*sin(d*x^n + c) + 2*(a*b*d*e^(2*n - 1)*x^n + a*b*c*e^(2*n - 1))*log(-cos(d*x^n + c) + I*sin(d*x^n + c) + 1)*sin(d*x^n + c) + 2*(a*b*d*e^(2*n - 1)*x^n + a*b*c*e^(2*n - 1))*log(-cos(d*x^n + c) - I*sin(d*x^n + c) + 1)*sin(d*x^n + c))/(d^2*n*sin(d*x^n + c))","B",0
78,1,886,0,0.574373," ","integrate((e*x)^(-1+3*n)*(a+b*csc(c+d*x^n))^2,x, algorithm=""fricas"")","\frac{a^{2} d^{3} e^{3 \, n - 1} x^{3 \, n} \sin\left(d x^{n} + c\right) - 3 \, b^{2} d^{2} e^{3 \, n - 1} x^{2 \, n} \cos\left(d x^{n} + c\right) + 6 \, a b e^{3 \, n - 1} {\rm polylog}\left(3, \cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) + 6 \, a b e^{3 \, n - 1} {\rm polylog}\left(3, \cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) - 6 \, a b e^{3 \, n - 1} {\rm polylog}\left(3, -\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) - 6 \, a b e^{3 \, n - 1} {\rm polylog}\left(3, -\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) + 3 \, {\left(a b c^{2} - b^{2} c\right)} e^{3 \, n - 1} \log\left(-\frac{1}{2} \, \cos\left(d x^{n} + c\right) + \frac{1}{2} i \, \sin\left(d x^{n} + c\right) + \frac{1}{2}\right) \sin\left(d x^{n} + c\right) + 3 \, {\left(a b c^{2} - b^{2} c\right)} e^{3 \, n - 1} \log\left(-\frac{1}{2} \, \cos\left(d x^{n} + c\right) - \frac{1}{2} i \, \sin\left(d x^{n} + c\right) + \frac{1}{2}\right) \sin\left(d x^{n} + c\right) + {\left(-6 i \, a b d e^{3 \, n - 1} x^{n} - 3 i \, b^{2} e^{3 \, n - 1}\right)} {\rm Li}_2\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) + {\left(6 i \, a b d e^{3 \, n - 1} x^{n} + 3 i \, b^{2} e^{3 \, n - 1}\right)} {\rm Li}_2\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) + {\left(-6 i \, a b d e^{3 \, n - 1} x^{n} + 3 i \, b^{2} e^{3 \, n - 1}\right)} {\rm Li}_2\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) + {\left(6 i \, a b d e^{3 \, n - 1} x^{n} - 3 i \, b^{2} e^{3 \, n - 1}\right)} {\rm Li}_2\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right)\right) \sin\left(d x^{n} + c\right) - 3 \, {\left(a b d^{2} e^{3 \, n - 1} x^{2 \, n} - b^{2} d e^{3 \, n - 1} x^{n}\right)} \log\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + 1\right) \sin\left(d x^{n} + c\right) - 3 \, {\left(a b d^{2} e^{3 \, n - 1} x^{2 \, n} - b^{2} d e^{3 \, n - 1} x^{n}\right)} \log\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + 1\right) \sin\left(d x^{n} + c\right) + 3 \, {\left(a b d^{2} e^{3 \, n - 1} x^{2 \, n} + b^{2} d e^{3 \, n - 1} x^{n} - {\left(a b c^{2} - b^{2} c\right)} e^{3 \, n - 1}\right)} \log\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + 1\right) \sin\left(d x^{n} + c\right) + 3 \, {\left(a b d^{2} e^{3 \, n - 1} x^{2 \, n} + b^{2} d e^{3 \, n - 1} x^{n} - {\left(a b c^{2} - b^{2} c\right)} e^{3 \, n - 1}\right)} \log\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + 1\right) \sin\left(d x^{n} + c\right)}{3 \, d^{3} n \sin\left(d x^{n} + c\right)}"," ",0,"1/3*(a^2*d^3*e^(3*n - 1)*x^(3*n)*sin(d*x^n + c) - 3*b^2*d^2*e^(3*n - 1)*x^(2*n)*cos(d*x^n + c) + 6*a*b*e^(3*n - 1)*polylog(3, cos(d*x^n + c) + I*sin(d*x^n + c))*sin(d*x^n + c) + 6*a*b*e^(3*n - 1)*polylog(3, cos(d*x^n + c) - I*sin(d*x^n + c))*sin(d*x^n + c) - 6*a*b*e^(3*n - 1)*polylog(3, -cos(d*x^n + c) + I*sin(d*x^n + c))*sin(d*x^n + c) - 6*a*b*e^(3*n - 1)*polylog(3, -cos(d*x^n + c) - I*sin(d*x^n + c))*sin(d*x^n + c) + 3*(a*b*c^2 - b^2*c)*e^(3*n - 1)*log(-1/2*cos(d*x^n + c) + 1/2*I*sin(d*x^n + c) + 1/2)*sin(d*x^n + c) + 3*(a*b*c^2 - b^2*c)*e^(3*n - 1)*log(-1/2*cos(d*x^n + c) - 1/2*I*sin(d*x^n + c) + 1/2)*sin(d*x^n + c) + (-6*I*a*b*d*e^(3*n - 1)*x^n - 3*I*b^2*e^(3*n - 1))*dilog(cos(d*x^n + c) + I*sin(d*x^n + c))*sin(d*x^n + c) + (6*I*a*b*d*e^(3*n - 1)*x^n + 3*I*b^2*e^(3*n - 1))*dilog(cos(d*x^n + c) - I*sin(d*x^n + c))*sin(d*x^n + c) + (-6*I*a*b*d*e^(3*n - 1)*x^n + 3*I*b^2*e^(3*n - 1))*dilog(-cos(d*x^n + c) + I*sin(d*x^n + c))*sin(d*x^n + c) + (6*I*a*b*d*e^(3*n - 1)*x^n - 3*I*b^2*e^(3*n - 1))*dilog(-cos(d*x^n + c) - I*sin(d*x^n + c))*sin(d*x^n + c) - 3*(a*b*d^2*e^(3*n - 1)*x^(2*n) - b^2*d*e^(3*n - 1)*x^n)*log(cos(d*x^n + c) + I*sin(d*x^n + c) + 1)*sin(d*x^n + c) - 3*(a*b*d^2*e^(3*n - 1)*x^(2*n) - b^2*d*e^(3*n - 1)*x^n)*log(cos(d*x^n + c) - I*sin(d*x^n + c) + 1)*sin(d*x^n + c) + 3*(a*b*d^2*e^(3*n - 1)*x^(2*n) + b^2*d*e^(3*n - 1)*x^n - (a*b*c^2 - b^2*c)*e^(3*n - 1))*log(-cos(d*x^n + c) + I*sin(d*x^n + c) + 1)*sin(d*x^n + c) + 3*(a*b*d^2*e^(3*n - 1)*x^(2*n) + b^2*d*e^(3*n - 1)*x^n - (a*b*c^2 - b^2*c)*e^(3*n - 1))*log(-cos(d*x^n + c) - I*sin(d*x^n + c) + 1)*sin(d*x^n + c))/(d^3*n*sin(d*x^n + c))","C",0
79,1,301,0,0.592975," ","integrate((e*x)^(-1+n)/(a+b*csc(c+d*x^n)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} - b^{2}\right)} d e^{n - 1} x^{n} + \sqrt{a^{2} - b^{2}} b e^{n - 1} \log\left(\frac{{\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x^{n} + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} a \cos\left(d x^{n} + c\right) + a^{2} + b^{2} + 2 \, {\left(\sqrt{a^{2} - b^{2}} b \cos\left(d x^{n} + c\right) + a b\right)} \sin\left(d x^{n} + c\right)}{a^{2} \cos\left(d x^{n} + c\right)^{2} - 2 \, a b \sin\left(d x^{n} + c\right) - a^{2} - b^{2}}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d n}, \frac{{\left(a^{2} - b^{2}\right)} d e^{n - 1} x^{n} + \sqrt{-a^{2} + b^{2}} b e^{n - 1} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} b \sin\left(d x^{n} + c\right) + \sqrt{-a^{2} + b^{2}} a}{{\left(a^{2} - b^{2}\right)} \cos\left(d x^{n} + c\right)}\right)}{{\left(a^{3} - a b^{2}\right)} d n}\right]"," ",0,"[1/2*(2*(a^2 - b^2)*d*e^(n - 1)*x^n + sqrt(a^2 - b^2)*b*e^(n - 1)*log(((a^2 - 2*b^2)*cos(d*x^n + c)^2 + 2*sqrt(a^2 - b^2)*a*cos(d*x^n + c) + a^2 + b^2 + 2*(sqrt(a^2 - b^2)*b*cos(d*x^n + c) + a*b)*sin(d*x^n + c))/(a^2*cos(d*x^n + c)^2 - 2*a*b*sin(d*x^n + c) - a^2 - b^2)))/((a^3 - a*b^2)*d*n), ((a^2 - b^2)*d*e^(n - 1)*x^n + sqrt(-a^2 + b^2)*b*e^(n - 1)*arctan(-(sqrt(-a^2 + b^2)*b*sin(d*x^n + c) + sqrt(-a^2 + b^2)*a)/((a^2 - b^2)*cos(d*x^n + c))))/((a^3 - a*b^2)*d*n)]","A",0
80,1,1259,0,0.702780," ","integrate((e*x)^(-1+2*n)/(a+b*csc(c+d*x^n)),x, algorithm=""fricas"")","-\frac{2 \, a b c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(d x^{n} + c\right) + 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) + 2 \, a b c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(d x^{n} + c\right) - 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) - 2 \, a b c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(d x^{n} + c\right) + 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) - 2 \, a b c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(d x^{n} + c\right) - 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) - 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2 \, n - 1} x^{2 \, n} - 2 i \, a b e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) - 2 i \, a b e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + 2 i \, a b e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) + 2 i \, a b e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) - 2 \, {\left(a b d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + a b c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + 2 \, {\left(a b d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + a b c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right) - 2 \, {\left(a b d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + a b c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + 2 \, {\left(a b d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + a b c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d^{2} n}"," ",0,"-1/4*(2*a*b*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*log(2*a*cos(d*x^n + c) + 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) + 2*a*b*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*log(2*a*cos(d*x^n + c) - 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) - 2*a*b*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*log(-2*a*cos(d*x^n + c) + 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) - 2*a*b*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*log(-2*a*cos(d*x^n + c) - 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) - 2*(a^2 - b^2)*d^2*e^(2*n - 1)*x^(2*n) - 2*I*a*b*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*dilog(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) + (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a + 1) - 2*I*a*b*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*dilog(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) - (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a + 1) + 2*I*a*b*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*dilog(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) + (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a + 1) + 2*I*a*b*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*dilog(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) - (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a + 1) - 2*(a*b*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + a*b*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*log(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) + (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a) + 2*(a*b*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + a*b*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*log(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) - (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a) - 2*(a*b*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + a*b*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*log(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) + (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a) + 2*(a*b*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + a*b*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*log(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) - (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a))/((a^3 - a*b^2)*d^2*n)","B",0
81,1,1697,0,0.667301," ","integrate((e*x)^(-1+3*n)/(a+b*csc(c+d*x^n)),x, algorithm=""fricas"")","-\frac{-12 i \, a b d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) - 12 i \, a b d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + 12 i \, a b d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) + 12 i \, a b d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) - 6 \, a b c^{2} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(d x^{n} + c\right) + 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) - 6 \, a b c^{2} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(d x^{n} + c\right) - 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) + 6 \, a b c^{2} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(d x^{n} + c\right) + 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) + 6 \, a b c^{2} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(d x^{n} + c\right) - 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) - 4 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{3 \, n - 1} x^{3 \, n} + 12 \, a b e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, \frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) - 12 \, a b e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) + 12 \, a b e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, \frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) - 12 \, a b e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) - 6 \, {\left(a b d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a b c^{2} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + 6 \, {\left(a b d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a b c^{2} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right) - 6 \, {\left(a b d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a b c^{2} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + 6 \, {\left(a b d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - a b c^{2} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right)}{12 \, {\left(a^{3} - a b^{2}\right)} d^{3} n}"," ",0,"-1/12*(-12*I*a*b*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2)*dilog(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) + (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a + 1) - 12*I*a*b*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2)*dilog(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) - (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a + 1) + 12*I*a*b*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2)*dilog(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) + (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a + 1) + 12*I*a*b*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2)*dilog(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) - (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a + 1) - 6*a*b*c^2*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*log(2*a*cos(d*x^n + c) + 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) - 6*a*b*c^2*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*log(2*a*cos(d*x^n + c) - 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) + 6*a*b*c^2*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*log(-2*a*cos(d*x^n + c) + 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) + 6*a*b*c^2*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*log(-2*a*cos(d*x^n + c) - 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) - 4*(a^2 - b^2)*d^3*e^(3*n - 1)*x^(3*n) + 12*a*b*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*polylog(3, 1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) + (2*I*a*sqrt((a^2 - b^2)/a^2) - 2*b)*sin(d*x^n + c))/a) - 12*a*b*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*polylog(3, -1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) - (2*I*a*sqrt((a^2 - b^2)/a^2) - 2*b)*sin(d*x^n + c))/a) + 12*a*b*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*polylog(3, 1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) + (-2*I*a*sqrt((a^2 - b^2)/a^2) - 2*b)*sin(d*x^n + c))/a) - 12*a*b*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*polylog(3, -1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) - (-2*I*a*sqrt((a^2 - b^2)/a^2) - 2*b)*sin(d*x^n + c))/a) - 6*(a*b*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) - a*b*c^2*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2))*log(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) + (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a) + 6*(a*b*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) - a*b*c^2*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2))*log(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) - (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a) - 6*(a*b*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) - a*b*c^2*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2))*log(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) + (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a) + 6*(a*b*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) - a*b*c^2*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2))*log(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) - (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a))/((a^3 - a*b^2)*d^3*n)","C",0
82,1,630,0,0.559298," ","integrate((e*x)^(-1+n)/(a+b*csc(c+d*x^n))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d e^{n - 1} x^{n} \sin\left(d x^{n} + c\right) + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d e^{n - 1} x^{n} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} e^{n - 1} \cos\left(d x^{n} + c\right) + {\left({\left(2 \, a^{3} b - a b^{3}\right)} \sqrt{a^{2} - b^{2}} e^{n - 1} \sin\left(d x^{n} + c\right) + {\left(2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{a^{2} - b^{2}} e^{n - 1}\right)} \log\left(\frac{{\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x^{n} + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} a \cos\left(d x^{n} + c\right) + a^{2} + b^{2} + 2 \, {\left(\sqrt{a^{2} - b^{2}} b \cos\left(d x^{n} + c\right) + a b\right)} \sin\left(d x^{n} + c\right)}{a^{2} \cos\left(d x^{n} + c\right)^{2} - 2 \, a b \sin\left(d x^{n} + c\right) - a^{2} - b^{2}}\right)}{2 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d n \sin\left(d x^{n} + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d n\right)}}, \frac{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d e^{n - 1} x^{n} \sin\left(d x^{n} + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d e^{n - 1} x^{n} - {\left(a^{3} b^{2} - a b^{4}\right)} e^{n - 1} \cos\left(d x^{n} + c\right) + {\left({\left(2 \, a^{3} b - a b^{3}\right)} \sqrt{-a^{2} + b^{2}} e^{n - 1} \sin\left(d x^{n} + c\right) + {\left(2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{-a^{2} + b^{2}} e^{n - 1}\right)} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} b \sin\left(d x^{n} + c\right) + \sqrt{-a^{2} + b^{2}} a}{{\left(a^{2} - b^{2}\right)} \cos\left(d x^{n} + c\right)}\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d n \sin\left(d x^{n} + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d n}\right]"," ",0,"[1/2*(2*(a^5 - 2*a^3*b^2 + a*b^4)*d*e^(n - 1)*x^n*sin(d*x^n + c) + 2*(a^4*b - 2*a^2*b^3 + b^5)*d*e^(n - 1)*x^n - 2*(a^3*b^2 - a*b^4)*e^(n - 1)*cos(d*x^n + c) + ((2*a^3*b - a*b^3)*sqrt(a^2 - b^2)*e^(n - 1)*sin(d*x^n + c) + (2*a^2*b^2 - b^4)*sqrt(a^2 - b^2)*e^(n - 1))*log(((a^2 - 2*b^2)*cos(d*x^n + c)^2 + 2*sqrt(a^2 - b^2)*a*cos(d*x^n + c) + a^2 + b^2 + 2*(sqrt(a^2 - b^2)*b*cos(d*x^n + c) + a*b)*sin(d*x^n + c))/(a^2*cos(d*x^n + c)^2 - 2*a*b*sin(d*x^n + c) - a^2 - b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*n*sin(d*x^n + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d*n), ((a^5 - 2*a^3*b^2 + a*b^4)*d*e^(n - 1)*x^n*sin(d*x^n + c) + (a^4*b - 2*a^2*b^3 + b^5)*d*e^(n - 1)*x^n - (a^3*b^2 - a*b^4)*e^(n - 1)*cos(d*x^n + c) + ((2*a^3*b - a*b^3)*sqrt(-a^2 + b^2)*e^(n - 1)*sin(d*x^n + c) + (2*a^2*b^2 - b^4)*sqrt(-a^2 + b^2)*e^(n - 1))*arctan(-(sqrt(-a^2 + b^2)*b*sin(d*x^n + c) + sqrt(-a^2 + b^2)*a)/((a^2 - b^2)*cos(d*x^n + c))))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*n*sin(d*x^n + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d*n)]","A",0
83,1,2455,0,0.858891," ","integrate((e*x)^(-1+2*n)/(a+b*csc(c+d*x^n))^2,x, algorithm=""fricas"")","\frac{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2 \, n - 1} x^{2 \, n} \sin\left(d x^{n} + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2 \, n - 1} x^{2 \, n} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} d e^{2 \, n - 1} x^{n} \cos\left(d x^{n} + c\right) + {\left({\left(2 i \, a^{4} b - i \, a^{2} b^{3}\right)} e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \sin\left(d x^{n} + c\right) + {\left(2 i \, a^{3} b^{2} - i \, a b^{4}\right)} e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) + {\left({\left(2 i \, a^{4} b - i \, a^{2} b^{3}\right)} e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \sin\left(d x^{n} + c\right) + {\left(2 i \, a^{3} b^{2} - i \, a b^{4}\right)} e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + {\left({\left(-2 i \, a^{4} b + i \, a^{2} b^{3}\right)} e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \sin\left(d x^{n} + c\right) + {\left(-2 i \, a^{3} b^{2} + i \, a b^{4}\right)} e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) + {\left({\left(-2 i \, a^{4} b + i \, a^{2} b^{3}\right)} e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \sin\left(d x^{n} + c\right) + {\left(-2 i \, a^{3} b^{2} + i \, a b^{4}\right)} e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + {\left({\left(a^{3} b^{2} - a b^{4} - {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1} \sin\left(d x^{n} + c\right) + {\left(a^{2} b^{3} - b^{5} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1}\right)} \log\left(2 \, a \cos\left(d x^{n} + c\right) + 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) + {\left({\left(a^{3} b^{2} - a b^{4} - {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1} \sin\left(d x^{n} + c\right) + {\left(a^{2} b^{3} - b^{5} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1}\right)} \log\left(2 \, a \cos\left(d x^{n} + c\right) - 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) + {\left({\left(a^{3} b^{2} - a b^{4} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1} \sin\left(d x^{n} + c\right) + {\left(a^{2} b^{3} - b^{5} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1}\right)} \log\left(-2 \, a \cos\left(d x^{n} + c\right) + 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) + {\left({\left(a^{3} b^{2} - a b^{4} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1} \sin\left(d x^{n} + c\right) + {\left(a^{2} b^{3} - b^{5} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1}\right)} \log\left(-2 \, a \cos\left(d x^{n} + c\right) - 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) + {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \sin\left(d x^{n} + c\right)\right)} \log\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) - {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \sin\left(d x^{n} + c\right)\right)} \log\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right) + {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \sin\left(d x^{n} + c\right)\right)} \log\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) - {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e^{2 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c e^{2 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} \sin\left(d x^{n} + c\right)\right)} \log\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right)}{2 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} n \sin\left(d x^{n} + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{2} n\right)}}"," ",0,"1/2*((a^5 - 2*a^3*b^2 + a*b^4)*d^2*e^(2*n - 1)*x^(2*n)*sin(d*x^n + c) + (a^4*b - 2*a^2*b^3 + b^5)*d^2*e^(2*n - 1)*x^(2*n) - 2*(a^3*b^2 - a*b^4)*d*e^(2*n - 1)*x^n*cos(d*x^n + c) + ((2*I*a^4*b - I*a^2*b^3)*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*sin(d*x^n + c) + (2*I*a^3*b^2 - I*a*b^4)*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*dilog(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) + (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a + 1) + ((2*I*a^4*b - I*a^2*b^3)*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*sin(d*x^n + c) + (2*I*a^3*b^2 - I*a*b^4)*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*dilog(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) - (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a + 1) + ((-2*I*a^4*b + I*a^2*b^3)*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*sin(d*x^n + c) + (-2*I*a^3*b^2 + I*a*b^4)*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*dilog(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) + (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a + 1) + ((-2*I*a^4*b + I*a^2*b^3)*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2)*sin(d*x^n + c) + (-2*I*a^3*b^2 + I*a*b^4)*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*dilog(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) - (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a + 1) + ((a^3*b^2 - a*b^4 - (2*a^4*b - a^2*b^3)*c*sqrt((a^2 - b^2)/a^2))*e^(2*n - 1)*sin(d*x^n + c) + (a^2*b^3 - b^5 - (2*a^3*b^2 - a*b^4)*c*sqrt((a^2 - b^2)/a^2))*e^(2*n - 1))*log(2*a*cos(d*x^n + c) + 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) + ((a^3*b^2 - a*b^4 - (2*a^4*b - a^2*b^3)*c*sqrt((a^2 - b^2)/a^2))*e^(2*n - 1)*sin(d*x^n + c) + (a^2*b^3 - b^5 - (2*a^3*b^2 - a*b^4)*c*sqrt((a^2 - b^2)/a^2))*e^(2*n - 1))*log(2*a*cos(d*x^n + c) - 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) + ((a^3*b^2 - a*b^4 + (2*a^4*b - a^2*b^3)*c*sqrt((a^2 - b^2)/a^2))*e^(2*n - 1)*sin(d*x^n + c) + (a^2*b^3 - b^5 + (2*a^3*b^2 - a*b^4)*c*sqrt((a^2 - b^2)/a^2))*e^(2*n - 1))*log(-2*a*cos(d*x^n + c) + 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) + ((a^3*b^2 - a*b^4 + (2*a^4*b - a^2*b^3)*c*sqrt((a^2 - b^2)/a^2))*e^(2*n - 1)*sin(d*x^n + c) + (a^2*b^3 - b^5 + (2*a^3*b^2 - a*b^4)*c*sqrt((a^2 - b^2)/a^2))*e^(2*n - 1))*log(-2*a*cos(d*x^n + c) - 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) + ((2*a^3*b^2 - a*b^4)*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (2*a^3*b^2 - a*b^4)*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2) + ((2*a^4*b - a^2*b^3)*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (2*a^4*b - a^2*b^3)*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*sin(d*x^n + c))*log(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) + (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a) - ((2*a^3*b^2 - a*b^4)*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (2*a^3*b^2 - a*b^4)*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2) + ((2*a^4*b - a^2*b^3)*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (2*a^4*b - a^2*b^3)*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*sin(d*x^n + c))*log(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) - (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a) + ((2*a^3*b^2 - a*b^4)*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (2*a^3*b^2 - a*b^4)*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2) + ((2*a^4*b - a^2*b^3)*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (2*a^4*b - a^2*b^3)*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*sin(d*x^n + c))*log(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) + (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a) - ((2*a^3*b^2 - a*b^4)*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (2*a^3*b^2 - a*b^4)*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2) + ((2*a^4*b - a^2*b^3)*d*e^(2*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (2*a^4*b - a^2*b^3)*c*e^(2*n - 1)*sqrt((a^2 - b^2)/a^2))*sin(d*x^n + c))*log(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) - (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d^2*n*sin(d*x^n + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^2*n)","B",0
84,1,3785,0,0.910766," ","integrate((e*x)^(-1+3*n)/(a+b*csc(c+d*x^n))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} e^{3 \, n - 1} x^{3 \, n} \sin\left(d x^{n} + c\right) + 4 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} e^{3 \, n - 1} x^{3 \, n} - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{2} e^{3 \, n - 1} x^{2 \, n} \cos\left(d x^{n} + c\right) + {\left(12 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(12 i \, a^{2} b^{3} - 12 i \, b^{5}\right)} e^{3 \, n - 1} + {\left(12 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(12 i \, a^{3} b^{2} - 12 i \, a b^{4}\right)} e^{3 \, n - 1}\right)} \sin\left(d x^{n} + c\right)\right)} {\rm Li}_2\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) + {\left(12 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(-12 i \, a^{2} b^{3} + 12 i \, b^{5}\right)} e^{3 \, n - 1} + {\left(12 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(-12 i \, a^{3} b^{2} + 12 i \, a b^{4}\right)} e^{3 \, n - 1}\right)} \sin\left(d x^{n} + c\right)\right)} {\rm Li}_2\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + {\left(-12 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(-12 i \, a^{2} b^{3} + 12 i \, b^{5}\right)} e^{3 \, n - 1} + {\left(-12 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(-12 i \, a^{3} b^{2} + 12 i \, a b^{4}\right)} e^{3 \, n - 1}\right)} \sin\left(d x^{n} + c\right)\right)} {\rm Li}_2\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) + {\left(-12 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(12 i \, a^{2} b^{3} - 12 i \, b^{5}\right)} e^{3 \, n - 1} + {\left(-12 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e^{3 \, n - 1} x^{n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + {\left(12 i \, a^{3} b^{2} - 12 i \, a b^{4}\right)} e^{3 \, n - 1}\right)} \sin\left(d x^{n} + c\right)\right)} {\rm Li}_2\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + 6 \, {\left({\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1} \sin\left(d x^{n} + c\right) + {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1}\right)} \log\left(2 \, a \cos\left(d x^{n} + c\right) + 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) + 6 \, {\left({\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1} \sin\left(d x^{n} + c\right) + {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1}\right)} \log\left(2 \, a \cos\left(d x^{n} + c\right) - 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) - 6 \, {\left({\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1} \sin\left(d x^{n} + c\right) + {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1}\right)} \log\left(-2 \, a \cos\left(d x^{n} + c\right) + 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right) - 6 \, {\left({\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1} \sin\left(d x^{n} + c\right) + {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1}\right)} \log\left(-2 \, a \cos\left(d x^{n} + c\right) - 2 i \, a \sin\left(d x^{n} + c\right) + 2 \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right) + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} d e^{3 \, n - 1} x^{n} - {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} - {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1}\right)} \sin\left(d x^{n} + c\right)\right)} \log\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) - 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{2} b^{3} - b^{5}\right)} d e^{3 \, n - 1} x^{n} - {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} - {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1}\right)} \sin\left(d x^{n} + c\right)\right)} \log\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right) + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} d e^{3 \, n - 1} x^{n} - {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} - {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1}\right)} \sin\left(d x^{n} + c\right)\right)} \log\left(\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) - 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{2} b^{3} - b^{5}\right)} d e^{3 \, n - 1} x^{n} - {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} - {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1}\right)} \sin\left(d x^{n} + c\right)\right)} \log\left(-\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right) - 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \sin\left(d x^{n} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm polylog}\left(3, \frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) + 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \sin\left(d x^{n} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm polylog}\left(3, -\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} + i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) - 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \sin\left(d x^{n} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm polylog}\left(3, \frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) + 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \sin\left(d x^{n} + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} e^{3 \, n - 1} \sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm polylog}\left(3, -\frac{2 \, {\left(a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - i \, b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right)}{12 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{3} n \sin\left(d x^{n} + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{3} n\right)}}"," ",0,"1/12*(4*(a^5 - 2*a^3*b^2 + a*b^4)*d^3*e^(3*n - 1)*x^(3*n)*sin(d*x^n + c) + 4*(a^4*b - 2*a^2*b^3 + b^5)*d^3*e^(3*n - 1)*x^(3*n) - 12*(a^3*b^2 - a*b^4)*d^2*e^(3*n - 1)*x^(2*n)*cos(d*x^n + c) + (12*I*(2*a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (12*I*a^2*b^3 - 12*I*b^5)*e^(3*n - 1) + (12*I*(2*a^4*b - a^2*b^3)*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (12*I*a^3*b^2 - 12*I*a*b^4)*e^(3*n - 1))*sin(d*x^n + c))*dilog(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) + (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a + 1) + (12*I*(2*a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (-12*I*a^2*b^3 + 12*I*b^5)*e^(3*n - 1) + (12*I*(2*a^4*b - a^2*b^3)*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (-12*I*a^3*b^2 + 12*I*a*b^4)*e^(3*n - 1))*sin(d*x^n + c))*dilog(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) - (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a + 1) + (-12*I*(2*a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (-12*I*a^2*b^3 + 12*I*b^5)*e^(3*n - 1) + (-12*I*(2*a^4*b - a^2*b^3)*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (-12*I*a^3*b^2 + 12*I*a*b^4)*e^(3*n - 1))*sin(d*x^n + c))*dilog(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) + (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a + 1) + (-12*I*(2*a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (12*I*a^2*b^3 - 12*I*b^5)*e^(3*n - 1) + (-12*I*(2*a^4*b - a^2*b^3)*d*e^(3*n - 1)*x^n*sqrt((a^2 - b^2)/a^2) + (12*I*a^3*b^2 - 12*I*a*b^4)*e^(3*n - 1))*sin(d*x^n + c))*dilog(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) - (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a + 1) + 6*(((2*a^4*b - a^2*b^3)*c^2*sqrt((a^2 - b^2)/a^2) - 2*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1)*sin(d*x^n + c) + ((2*a^3*b^2 - a*b^4)*c^2*sqrt((a^2 - b^2)/a^2) - 2*(a^2*b^3 - b^5)*c)*e^(3*n - 1))*log(2*a*cos(d*x^n + c) + 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) + 6*(((2*a^4*b - a^2*b^3)*c^2*sqrt((a^2 - b^2)/a^2) - 2*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1)*sin(d*x^n + c) + ((2*a^3*b^2 - a*b^4)*c^2*sqrt((a^2 - b^2)/a^2) - 2*(a^2*b^3 - b^5)*c)*e^(3*n - 1))*log(2*a*cos(d*x^n + c) - 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) - 6*(((2*a^4*b - a^2*b^3)*c^2*sqrt((a^2 - b^2)/a^2) + 2*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1)*sin(d*x^n + c) + ((2*a^3*b^2 - a*b^4)*c^2*sqrt((a^2 - b^2)/a^2) + 2*(a^2*b^3 - b^5)*c)*e^(3*n - 1))*log(-2*a*cos(d*x^n + c) + 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) + 2*I*b) - 6*(((2*a^4*b - a^2*b^3)*c^2*sqrt((a^2 - b^2)/a^2) + 2*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1)*sin(d*x^n + c) + ((2*a^3*b^2 - a*b^4)*c^2*sqrt((a^2 - b^2)/a^2) + 2*(a^2*b^3 - b^5)*c)*e^(3*n - 1))*log(-2*a*cos(d*x^n + c) - 2*I*a*sin(d*x^n + c) + 2*a*sqrt((a^2 - b^2)/a^2) - 2*I*b) + 6*((2*a^3*b^2 - a*b^4)*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) + 2*(a^2*b^3 - b^5)*d*e^(3*n - 1)*x^n - ((2*a^3*b^2 - a*b^4)*c^2*sqrt((a^2 - b^2)/a^2) - 2*(a^2*b^3 - b^5)*c)*e^(3*n - 1) + ((2*a^4*b - a^2*b^3)*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) + 2*(a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n - ((2*a^4*b - a^2*b^3)*c^2*sqrt((a^2 - b^2)/a^2) - 2*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1))*sin(d*x^n + c))*log(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) + (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a) - 6*((2*a^3*b^2 - a*b^4)*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) - 2*(a^2*b^3 - b^5)*d*e^(3*n - 1)*x^n - ((2*a^3*b^2 - a*b^4)*c^2*sqrt((a^2 - b^2)/a^2) + 2*(a^2*b^3 - b^5)*c)*e^(3*n - 1) + ((2*a^4*b - a^2*b^3)*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) - 2*(a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n - ((2*a^4*b - a^2*b^3)*c^2*sqrt((a^2 - b^2)/a^2) + 2*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1))*sin(d*x^n + c))*log(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) - (-2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a) + 6*((2*a^3*b^2 - a*b^4)*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) + 2*(a^2*b^3 - b^5)*d*e^(3*n - 1)*x^n - ((2*a^3*b^2 - a*b^4)*c^2*sqrt((a^2 - b^2)/a^2) - 2*(a^2*b^3 - b^5)*c)*e^(3*n - 1) + ((2*a^4*b - a^2*b^3)*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) + 2*(a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n - ((2*a^4*b - a^2*b^3)*c^2*sqrt((a^2 - b^2)/a^2) - 2*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1))*sin(d*x^n + c))*log(1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) + (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) + 2*a)/a) - 6*((2*a^3*b^2 - a*b^4)*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) - 2*(a^2*b^3 - b^5)*d*e^(3*n - 1)*x^n - ((2*a^3*b^2 - a*b^4)*c^2*sqrt((a^2 - b^2)/a^2) + 2*(a^2*b^3 - b^5)*c)*e^(3*n - 1) + ((2*a^4*b - a^2*b^3)*d^2*e^(3*n - 1)*x^(2*n)*sqrt((a^2 - b^2)/a^2) - 2*(a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n - ((2*a^4*b - a^2*b^3)*c^2*sqrt((a^2 - b^2)/a^2) + 2*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1))*sin(d*x^n + c))*log(-1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) - (2*I*a*sqrt((a^2 - b^2)/a^2) + 2*b)*sin(d*x^n + c) - 2*a)/a) - 12*((2*a^4*b - a^2*b^3)*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*sin(d*x^n + c) + (2*a^3*b^2 - a*b^4)*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2))*polylog(3, 1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) + (2*I*a*sqrt((a^2 - b^2)/a^2) - 2*b)*sin(d*x^n + c))/a) + 12*((2*a^4*b - a^2*b^3)*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*sin(d*x^n + c) + (2*a^3*b^2 - a*b^4)*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2))*polylog(3, -1/2*(2*(a*sqrt((a^2 - b^2)/a^2) + I*b)*cos(d*x^n + c) - (2*I*a*sqrt((a^2 - b^2)/a^2) - 2*b)*sin(d*x^n + c))/a) - 12*((2*a^4*b - a^2*b^3)*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*sin(d*x^n + c) + (2*a^3*b^2 - a*b^4)*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2))*polylog(3, 1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) + (-2*I*a*sqrt((a^2 - b^2)/a^2) - 2*b)*sin(d*x^n + c))/a) + 12*((2*a^4*b - a^2*b^3)*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2)*sin(d*x^n + c) + (2*a^3*b^2 - a*b^4)*e^(3*n - 1)*sqrt((a^2 - b^2)/a^2))*polylog(3, -1/2*(2*(a*sqrt((a^2 - b^2)/a^2) - I*b)*cos(d*x^n + c) - (-2*I*a*sqrt((a^2 - b^2)/a^2) - 2*b)*sin(d*x^n + c))/a))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d^3*n*sin(d*x^n + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^3*n)","C",0
