1,1,495,0,1.189292," ","integrate(x^5*(a+b*sec(d*x^2+c)),x, algorithm=""fricas"")","\frac{2 \, a d^{3} x^{6} - 6 i \, b d x^{2} {\rm Li}_2\left(i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) - 6 i \, b d x^{2} {\rm Li}_2\left(i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) + 6 i \, b d x^{2} {\rm Li}_2\left(-i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) + 6 i \, b d x^{2} {\rm Li}_2\left(-i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) + 3 \, b c^{2} \log\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + i\right) - 3 \, b c^{2} \log\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + i\right) + 3 \, b c^{2} \log\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + i\right) - 3 \, b c^{2} \log\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + i\right) + 3 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \log\left(i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right) + 1\right) - 3 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \log\left(i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right) + 1\right) + 3 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \log\left(-i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right) + 1\right) - 3 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \log\left(-i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right) + 1\right) - 6 \, b {\rm polylog}\left(3, i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) + 6 \, b {\rm polylog}\left(3, i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) - 6 \, b {\rm polylog}\left(3, -i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) + 6 \, b {\rm polylog}\left(3, -i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right)}{12 \, d^{3}}"," ",0,"1/12*(2*a*d^3*x^6 - 6*I*b*d*x^2*dilog(I*cos(d*x^2 + c) + sin(d*x^2 + c)) - 6*I*b*d*x^2*dilog(I*cos(d*x^2 + c) - sin(d*x^2 + c)) + 6*I*b*d*x^2*dilog(-I*cos(d*x^2 + c) + sin(d*x^2 + c)) + 6*I*b*d*x^2*dilog(-I*cos(d*x^2 + c) - sin(d*x^2 + c)) + 3*b*c^2*log(cos(d*x^2 + c) + I*sin(d*x^2 + c) + I) - 3*b*c^2*log(cos(d*x^2 + c) - I*sin(d*x^2 + c) + I) + 3*b*c^2*log(-cos(d*x^2 + c) + I*sin(d*x^2 + c) + I) - 3*b*c^2*log(-cos(d*x^2 + c) - I*sin(d*x^2 + c) + I) + 3*(b*d^2*x^4 - b*c^2)*log(I*cos(d*x^2 + c) + sin(d*x^2 + c) + 1) - 3*(b*d^2*x^4 - b*c^2)*log(I*cos(d*x^2 + c) - sin(d*x^2 + c) + 1) + 3*(b*d^2*x^4 - b*c^2)*log(-I*cos(d*x^2 + c) + sin(d*x^2 + c) + 1) - 3*(b*d^2*x^4 - b*c^2)*log(-I*cos(d*x^2 + c) - sin(d*x^2 + c) + 1) - 6*b*polylog(3, I*cos(d*x^2 + c) + sin(d*x^2 + c)) + 6*b*polylog(3, I*cos(d*x^2 + c) - sin(d*x^2 + c)) - 6*b*polylog(3, -I*cos(d*x^2 + c) + sin(d*x^2 + c)) + 6*b*polylog(3, -I*cos(d*x^2 + c) - sin(d*x^2 + c)))/d^3","C",0
2,0,0,0,0.644091," ","integrate(x^4*(a+b*sec(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{4} \sec\left(d x^{2} + c\right) + a x^{4}, x\right)"," ",0,"integral(b*x^4*sec(d*x^2 + c) + a*x^4, x)","F",0
3,1,346,0,0.786567," ","integrate(x^3*(a+b*sec(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d^{2} x^{4} - b c \log\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + i\right) + b c \log\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + i\right) - b c \log\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + i\right) + b c \log\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + i\right) - i \, b {\rm Li}_2\left(i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) - i \, b {\rm Li}_2\left(i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) + i \, b {\rm Li}_2\left(-i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) + i \, b {\rm Li}_2\left(-i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) + {\left(b d x^{2} + b c\right)} \log\left(i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right) + 1\right) - {\left(b d x^{2} + b c\right)} \log\left(i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right) + 1\right) + {\left(b d x^{2} + b c\right)} \log\left(-i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right) + 1\right) - {\left(b d x^{2} + b c\right)} \log\left(-i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right) + 1\right)}{4 \, d^{2}}"," ",0,"1/4*(a*d^2*x^4 - b*c*log(cos(d*x^2 + c) + I*sin(d*x^2 + c) + I) + b*c*log(cos(d*x^2 + c) - I*sin(d*x^2 + c) + I) - b*c*log(-cos(d*x^2 + c) + I*sin(d*x^2 + c) + I) + b*c*log(-cos(d*x^2 + c) - I*sin(d*x^2 + c) + I) - I*b*dilog(I*cos(d*x^2 + c) + sin(d*x^2 + c)) - I*b*dilog(I*cos(d*x^2 + c) - sin(d*x^2 + c)) + I*b*dilog(-I*cos(d*x^2 + c) + sin(d*x^2 + c)) + I*b*dilog(-I*cos(d*x^2 + c) - sin(d*x^2 + c)) + (b*d*x^2 + b*c)*log(I*cos(d*x^2 + c) + sin(d*x^2 + c) + 1) - (b*d*x^2 + b*c)*log(I*cos(d*x^2 + c) - sin(d*x^2 + c) + 1) + (b*d*x^2 + b*c)*log(-I*cos(d*x^2 + c) + sin(d*x^2 + c) + 1) - (b*d*x^2 + b*c)*log(-I*cos(d*x^2 + c) - sin(d*x^2 + c) + 1))/d^2","B",0
4,0,0,0,0.792196," ","integrate(x^2*(a+b*sec(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{2} \sec\left(d x^{2} + c\right) + a x^{2}, x\right)"," ",0,"integral(b*x^2*sec(d*x^2 + c) + a*x^2, x)","F",0
5,1,42,0,0.745667," ","integrate(x*(a+b*sec(d*x^2+c)),x, algorithm=""fricas"")","\frac{2 \, a d x^{2} + b \log\left(\sin\left(d x^{2} + c\right) + 1\right) - b \log\left(-\sin\left(d x^{2} + c\right) + 1\right)}{4 \, d}"," ",0,"1/4*(2*a*d*x^2 + b*log(sin(d*x^2 + c) + 1) - b*log(-sin(d*x^2 + c) + 1))/d","A",0
6,0,0,0,0.696872," ","integrate((a+b*sec(d*x^2+c))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d x^{2} + c\right) + a}{x}, x\right)"," ",0,"integral((b*sec(d*x^2 + c) + a)/x, x)","F",0
7,0,0,0,0.768929," ","integrate((a+b*sec(d*x^2+c))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d x^{2} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*sec(d*x^2 + c) + a)/x^2, x)","F",0
8,1,795,0,0.750685," ","integrate(x^5*(a+b*sec(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{a^{2} d^{3} x^{6} \cos\left(d x^{2} + c\right) + 3 \, b^{2} d^{2} x^{4} \sin\left(d x^{2} + c\right) - 6 \, a b \cos\left(d x^{2} + c\right) {\rm polylog}\left(3, i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) + 6 \, a b \cos\left(d x^{2} + c\right) {\rm polylog}\left(3, i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) - 6 \, a b \cos\left(d x^{2} + c\right) {\rm polylog}\left(3, -i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) + 6 \, a b \cos\left(d x^{2} + c\right) {\rm polylog}\left(3, -i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) + {\left(-6 i \, a b d x^{2} + 3 i \, b^{2}\right)} \cos\left(d x^{2} + c\right) {\rm Li}_2\left(i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) + {\left(-6 i \, a b d x^{2} - 3 i \, b^{2}\right)} \cos\left(d x^{2} + c\right) {\rm Li}_2\left(i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) + {\left(6 i \, a b d x^{2} - 3 i \, b^{2}\right)} \cos\left(d x^{2} + c\right) {\rm Li}_2\left(-i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) + {\left(6 i \, a b d x^{2} + 3 i \, b^{2}\right)} \cos\left(d x^{2} + c\right) {\rm Li}_2\left(-i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) + 3 \, {\left(a b c^{2} - b^{2} c\right)} \cos\left(d x^{2} + c\right) \log\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + i\right) - 3 \, {\left(a b c^{2} + b^{2} c\right)} \cos\left(d x^{2} + c\right) \log\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + i\right) + 3 \, {\left(a b d^{2} x^{4} + b^{2} d x^{2} - a b c^{2} + b^{2} c\right)} \cos\left(d x^{2} + c\right) \log\left(i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right) + 1\right) - 3 \, {\left(a b d^{2} x^{4} - b^{2} d x^{2} - a b c^{2} - b^{2} c\right)} \cos\left(d x^{2} + c\right) \log\left(i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right) + 1\right) + 3 \, {\left(a b d^{2} x^{4} + b^{2} d x^{2} - a b c^{2} + b^{2} c\right)} \cos\left(d x^{2} + c\right) \log\left(-i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right) + 1\right) - 3 \, {\left(a b d^{2} x^{4} - b^{2} d x^{2} - a b c^{2} - b^{2} c\right)} \cos\left(d x^{2} + c\right) \log\left(-i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right) + 1\right) + 3 \, {\left(a b c^{2} - b^{2} c\right)} \cos\left(d x^{2} + c\right) \log\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + i\right) - 3 \, {\left(a b c^{2} + b^{2} c\right)} \cos\left(d x^{2} + c\right) \log\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + i\right)}{6 \, d^{3} \cos\left(d x^{2} + c\right)}"," ",0,"1/6*(a^2*d^3*x^6*cos(d*x^2 + c) + 3*b^2*d^2*x^4*sin(d*x^2 + c) - 6*a*b*cos(d*x^2 + c)*polylog(3, I*cos(d*x^2 + c) + sin(d*x^2 + c)) + 6*a*b*cos(d*x^2 + c)*polylog(3, I*cos(d*x^2 + c) - sin(d*x^2 + c)) - 6*a*b*cos(d*x^2 + c)*polylog(3, -I*cos(d*x^2 + c) + sin(d*x^2 + c)) + 6*a*b*cos(d*x^2 + c)*polylog(3, -I*cos(d*x^2 + c) - sin(d*x^2 + c)) + (-6*I*a*b*d*x^2 + 3*I*b^2)*cos(d*x^2 + c)*dilog(I*cos(d*x^2 + c) + sin(d*x^2 + c)) + (-6*I*a*b*d*x^2 - 3*I*b^2)*cos(d*x^2 + c)*dilog(I*cos(d*x^2 + c) - sin(d*x^2 + c)) + (6*I*a*b*d*x^2 - 3*I*b^2)*cos(d*x^2 + c)*dilog(-I*cos(d*x^2 + c) + sin(d*x^2 + c)) + (6*I*a*b*d*x^2 + 3*I*b^2)*cos(d*x^2 + c)*dilog(-I*cos(d*x^2 + c) - sin(d*x^2 + c)) + 3*(a*b*c^2 - b^2*c)*cos(d*x^2 + c)*log(cos(d*x^2 + c) + I*sin(d*x^2 + c) + I) - 3*(a*b*c^2 + b^2*c)*cos(d*x^2 + c)*log(cos(d*x^2 + c) - I*sin(d*x^2 + c) + I) + 3*(a*b*d^2*x^4 + b^2*d*x^2 - a*b*c^2 + b^2*c)*cos(d*x^2 + c)*log(I*cos(d*x^2 + c) + sin(d*x^2 + c) + 1) - 3*(a*b*d^2*x^4 - b^2*d*x^2 - a*b*c^2 - b^2*c)*cos(d*x^2 + c)*log(I*cos(d*x^2 + c) - sin(d*x^2 + c) + 1) + 3*(a*b*d^2*x^4 + b^2*d*x^2 - a*b*c^2 + b^2*c)*cos(d*x^2 + c)*log(-I*cos(d*x^2 + c) + sin(d*x^2 + c) + 1) - 3*(a*b*d^2*x^4 - b^2*d*x^2 - a*b*c^2 - b^2*c)*cos(d*x^2 + c)*log(-I*cos(d*x^2 + c) - sin(d*x^2 + c) + 1) + 3*(a*b*c^2 - b^2*c)*cos(d*x^2 + c)*log(-cos(d*x^2 + c) + I*sin(d*x^2 + c) + I) - 3*(a*b*c^2 + b^2*c)*cos(d*x^2 + c)*log(-cos(d*x^2 + c) - I*sin(d*x^2 + c) + I))/(d^3*cos(d*x^2 + c))","C",0
9,0,0,0,0.572428," ","integrate(x^4*(a+b*sec(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{4} \sec\left(d x^{2} + c\right)^{2} + 2 \, a b x^{4} \sec\left(d x^{2} + c\right) + a^{2} x^{4}, x\right)"," ",0,"integral(b^2*x^4*sec(d*x^2 + c)^2 + 2*a*b*x^4*sec(d*x^2 + c) + a^2*x^4, x)","F",0
10,1,525,0,0.870351," ","integrate(x^3*(a+b*sec(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{a^{2} d^{2} x^{4} \cos\left(d x^{2} + c\right) + 2 \, b^{2} d x^{2} \sin\left(d x^{2} + c\right) - 2 i \, a b \cos\left(d x^{2} + c\right) {\rm Li}_2\left(i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) - 2 i \, a b \cos\left(d x^{2} + c\right) {\rm Li}_2\left(i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) + 2 i \, a b \cos\left(d x^{2} + c\right) {\rm Li}_2\left(-i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right)\right) + 2 i \, a b \cos\left(d x^{2} + c\right) {\rm Li}_2\left(-i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right) - {\left(2 \, a b c - b^{2}\right)} \cos\left(d x^{2} + c\right) \log\left(\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + i\right) + {\left(2 \, a b c + b^{2}\right)} \cos\left(d x^{2} + c\right) \log\left(\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + i\right) + 2 \, {\left(a b d x^{2} + a b c\right)} \cos\left(d x^{2} + c\right) \log\left(i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right) + 1\right) - 2 \, {\left(a b d x^{2} + a b c\right)} \cos\left(d x^{2} + c\right) \log\left(i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right) + 1\right) + 2 \, {\left(a b d x^{2} + a b c\right)} \cos\left(d x^{2} + c\right) \log\left(-i \, \cos\left(d x^{2} + c\right) + \sin\left(d x^{2} + c\right) + 1\right) - 2 \, {\left(a b d x^{2} + a b c\right)} \cos\left(d x^{2} + c\right) \log\left(-i \, \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right) + 1\right) - {\left(2 \, a b c - b^{2}\right)} \cos\left(d x^{2} + c\right) \log\left(-\cos\left(d x^{2} + c\right) + i \, \sin\left(d x^{2} + c\right) + i\right) + {\left(2 \, a b c + b^{2}\right)} \cos\left(d x^{2} + c\right) \log\left(-\cos\left(d x^{2} + c\right) - i \, \sin\left(d x^{2} + c\right) + i\right)}{4 \, d^{2} \cos\left(d x^{2} + c\right)}"," ",0,"1/4*(a^2*d^2*x^4*cos(d*x^2 + c) + 2*b^2*d*x^2*sin(d*x^2 + c) - 2*I*a*b*cos(d*x^2 + c)*dilog(I*cos(d*x^2 + c) + sin(d*x^2 + c)) - 2*I*a*b*cos(d*x^2 + c)*dilog(I*cos(d*x^2 + c) - sin(d*x^2 + c)) + 2*I*a*b*cos(d*x^2 + c)*dilog(-I*cos(d*x^2 + c) + sin(d*x^2 + c)) + 2*I*a*b*cos(d*x^2 + c)*dilog(-I*cos(d*x^2 + c) - sin(d*x^2 + c)) - (2*a*b*c - b^2)*cos(d*x^2 + c)*log(cos(d*x^2 + c) + I*sin(d*x^2 + c) + I) + (2*a*b*c + b^2)*cos(d*x^2 + c)*log(cos(d*x^2 + c) - I*sin(d*x^2 + c) + I) + 2*(a*b*d*x^2 + a*b*c)*cos(d*x^2 + c)*log(I*cos(d*x^2 + c) + sin(d*x^2 + c) + 1) - 2*(a*b*d*x^2 + a*b*c)*cos(d*x^2 + c)*log(I*cos(d*x^2 + c) - sin(d*x^2 + c) + 1) + 2*(a*b*d*x^2 + a*b*c)*cos(d*x^2 + c)*log(-I*cos(d*x^2 + c) + sin(d*x^2 + c) + 1) - 2*(a*b*d*x^2 + a*b*c)*cos(d*x^2 + c)*log(-I*cos(d*x^2 + c) - sin(d*x^2 + c) + 1) - (2*a*b*c - b^2)*cos(d*x^2 + c)*log(-cos(d*x^2 + c) + I*sin(d*x^2 + c) + I) + (2*a*b*c + b^2)*cos(d*x^2 + c)*log(-cos(d*x^2 + c) - I*sin(d*x^2 + c) + I))/(d^2*cos(d*x^2 + c))","B",0
11,0,0,0,0.616907," ","integrate(x^2*(a+b*sec(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \sec\left(d x^{2} + c\right)^{2} + 2 \, a b x^{2} \sec\left(d x^{2} + c\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*sec(d*x^2 + c)^2 + 2*a*b*x^2*sec(d*x^2 + c) + a^2*x^2, x)","F",0
12,1,91,0,0.663641," ","integrate(x*(a+b*sec(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{a^{2} d x^{2} \cos\left(d x^{2} + c\right) + a b \cos\left(d x^{2} + c\right) \log\left(\sin\left(d x^{2} + c\right) + 1\right) - a b \cos\left(d x^{2} + c\right) \log\left(-\sin\left(d x^{2} + c\right) + 1\right) + b^{2} \sin\left(d x^{2} + c\right)}{2 \, d \cos\left(d x^{2} + c\right)}"," ",0,"1/2*(a^2*d*x^2*cos(d*x^2 + c) + a*b*cos(d*x^2 + c)*log(sin(d*x^2 + c) + 1) - a*b*cos(d*x^2 + c)*log(-sin(d*x^2 + c) + 1) + b^2*sin(d*x^2 + c))/(d*cos(d*x^2 + c))","B",0
13,0,0,0,0.531929," ","integrate((a+b*sec(d*x^2+c))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d x^{2} + c\right)^{2} + 2 \, a b \sec\left(d x^{2} + c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*sec(d*x^2 + c)^2 + 2*a*b*sec(d*x^2 + c) + a^2)/x, x)","F",0
14,0,0,0,1.367173," ","integrate((a+b*sec(d*x^2+c))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d x^{2} + c\right)^{2} + 2 \, a b \sec\left(d x^{2} + c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*sec(d*x^2 + c)^2 + 2*a*b*sec(d*x^2 + c) + a^2)/x^2, x)","F",0
15,1,100,0,0.655679," ","integrate(x*sec(b*x^2+a)^7,x, algorithm=""fricas"")","\frac{15 \, \cos\left(b x^{2} + a\right)^{6} \log\left(\sin\left(b x^{2} + a\right) + 1\right) - 15 \, \cos\left(b x^{2} + a\right)^{6} \log\left(-\sin\left(b x^{2} + a\right) + 1\right) + 2 \, {\left(15 \, \cos\left(b x^{2} + a\right)^{4} + 10 \, \cos\left(b x^{2} + a\right)^{2} + 8\right)} \sin\left(b x^{2} + a\right)}{192 \, b \cos\left(b x^{2} + a\right)^{6}}"," ",0,"1/192*(15*cos(b*x^2 + a)^6*log(sin(b*x^2 + a) + 1) - 15*cos(b*x^2 + a)^6*log(-sin(b*x^2 + a) + 1) + 2*(15*cos(b*x^2 + a)^4 + 10*cos(b*x^2 + a)^2 + 8)*sin(b*x^2 + a))/(b*cos(b*x^2 + a)^6)","A",0
16,1,1457,0,0.947809," ","integrate(x^5/(a+b*sec(d*x^2+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(a^{2} - b^{2}\right)} d^{3} x^{6} - 12 \, a b d x^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) + i \, 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 \, a b d x^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) + i \, 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 \, a b d x^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) - i \, 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 \, a b d x^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) - i \, 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 i \, 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 \, b\right) - 6 i \, 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 \, b\right) + 6 i \, 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 \, b\right) - 6 i \, 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 \, b\right) - 12 i \, a b \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{b \cos\left(d x^{2} + c\right) + i \, 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 i \, a b \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{b \cos\left(d x^{2} + c\right) + i \, 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 i \, a b \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{b \cos\left(d x^{2} + c\right) - i \, 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 i \, a b \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{b \cos\left(d x^{2} + c\right) - i \, 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) - 2 \, {\left(3 i \, a b d^{2} x^{4} - 3 i \, a b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) + i \, 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(-3 i \, a b d^{2} x^{4} + 3 i \, a b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) + i \, 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(-3 i \, a b d^{2} x^{4} + 3 i \, a b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) - i \, 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(3 i \, a b d^{2} x^{4} - 3 i \, a b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) - i \, 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*a*b*d*x^2*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) + I*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*a*b*d*x^2*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) + I*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*a*b*d*x^2*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) - I*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*a*b*d*x^2*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) - I*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*I*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*b) - 6*I*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*b) + 6*I*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*b) - 6*I*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*b) - 12*I*a*b*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -(b*cos(d*x^2 + c) + I*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*b*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -(b*cos(d*x^2 + c) + I*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*b*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -(b*cos(d*x^2 + c) - I*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*b*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -(b*cos(d*x^2 + c) - I*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) - 2*(3*I*a*b*d^2*x^4 - 3*I*a*b*c^2)*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) + I*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*(-3*I*a*b*d^2*x^4 + 3*I*a*b*c^2)*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) + I*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*(-3*I*a*b*d^2*x^4 + 3*I*a*b*c^2)*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) - I*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*(3*I*a*b*d^2*x^4 - 3*I*a*b*c^2)*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) - I*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
17,0,0,0,0.575867," ","integrate(x^4/(a+b*sec(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{b \sec\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral(x^4/(b*sec(d*x^2 + c) + a), x)","F",0
18,1,1063,0,1.097180," ","integrate(x^3/(a+b*sec(d*x^2+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} - b^{2}\right)} d^{2} x^{4} - 2 i \, 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 \, b\right) + 2 i \, 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 \, b\right) - 2 i \, 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 \, b\right) + 2 i \, 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 \, b\right) - 2 \, a b \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) + i \, 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 \, a b \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) + i \, 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 \, a b \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) - i \, 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 \, a b \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) - i \, 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(i \, a b d x^{2} + i \, a b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) + i \, 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(-i \, a b d x^{2} - i \, a b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) + i \, 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(-i \, a b d x^{2} - i \, a b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) - i \, 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(i \, a b d x^{2} + i \, a b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) - i \, 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*I*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*b) + 2*I*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*b) - 2*I*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*b) + 2*I*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*b) - 2*a*b*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) + I*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*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) + I*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*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) - I*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*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) - I*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*d*x^2 + I*a*b*c)*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) + I*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*(-I*a*b*d*x^2 - I*a*b*c)*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) + I*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*(-I*a*b*d*x^2 - I*a*b*c)*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) - I*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*(I*a*b*d*x^2 + I*a*b*c)*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) - I*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
19,0,0,0,0.668004," ","integrate(x^2/(a+b*sec(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b \sec\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral(x^2/(b*sec(d*x^2 + c) + a), x)","F",0
20,1,251,0,0.754277," ","integrate(x/(a+b*sec(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{2 \, a b \cos\left(d x^{2} + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x^{2} + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x^{2} + c\right) + a\right)} \sin\left(d x^{2} + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x^{2} + c\right)^{2} + 2 \, a b \cos\left(d x^{2} + c\right) + 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 \cos\left(d x^{2} + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\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((2*a*b*cos(d*x^2 + c) - (a^2 - 2*b^2)*cos(d*x^2 + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x^2 + c) + a)*sin(d*x^2 + c) + 2*a^2 - b^2)/(a^2*cos(d*x^2 + c)^2 + 2*a*b*cos(d*x^2 + c) + 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*cos(d*x^2 + c) + a)/((a^2 - b^2)*sin(d*x^2 + c))))/((a^3 - a*b^2)*d)]","A",0
21,0,0,0,0.606458," ","integrate(1/x/(a+b*sec(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \sec\left(d x^{2} + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*sec(d*x^2 + c) + a*x), x)","F",0
22,0,0,0,0.585691," ","integrate((a+b*sec(d*x^2+c))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d x^{2} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*sec(d*x^2 + c) + a)/x^2, x)","F",0
23,1,3048,0,1.068558," ","integrate(x^5/(a+b*sec(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} \cos\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} \sin\left(d x^{2} + c\right) + 2 \, {\left(-12 i \, a^{3} b^{2} + 6 i \, a b^{4} + {\left(-12 i \, a^{4} b + 6 i \, a^{2} b^{3}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{b \cos\left(d x^{2} + c\right) + i \, 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) + 2 \, {\left(12 i \, a^{3} b^{2} - 6 i \, a b^{4} + {\left(12 i \, a^{4} b - 6 i \, a^{2} b^{3}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{b \cos\left(d x^{2} + c\right) + i \, 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) + 2 \, {\left(12 i \, a^{3} b^{2} - 6 i \, a b^{4} + {\left(12 i \, a^{4} b - 6 i \, a^{2} b^{3}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{b \cos\left(d x^{2} + c\right) - i \, 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) + 2 \, {\left(-12 i \, a^{3} b^{2} + 6 i \, a b^{4} + {\left(-12 i \, a^{4} b + 6 i \, a^{2} b^{3}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{b \cos\left(d x^{2} + c\right) - i \, 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)} \cos\left(d x^{2} + c\right) - 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} \cos\left(d x^{2} + c\right) + {\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{b \cos\left(d x^{2} + c\right) + i \, 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)} \cos\left(d x^{2} + c\right) + 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} \cos\left(d x^{2} + c\right) + {\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{b \cos\left(d x^{2} + c\right) + i \, 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)} \cos\left(d x^{2} + c\right) - 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} \cos\left(d x^{2} + c\right) + {\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{b \cos\left(d x^{2} + c\right) - i \, 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)} \cos\left(d x^{2} + c\right) + 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} \cos\left(d x^{2} + c\right) + {\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{b \cos\left(d x^{2} + c\right) - i \, 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(6 \, {\left(a^{3} b^{2} - a b^{4}\right)} c \cos\left(d x^{2} + c\right) + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c - {\left(3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \cos\left(d x^{2} + c\right) + 3 i \, {\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 \, b\right) - 2 \, {\left(6 \, {\left(a^{3} b^{2} - a b^{4}\right)} c \cos\left(d x^{2} + c\right) + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c - {\left(-3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \cos\left(d x^{2} + c\right) - 3 i \, {\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 \, b\right) - 2 \, {\left(6 \, {\left(a^{3} b^{2} - a b^{4}\right)} c \cos\left(d x^{2} + c\right) + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c - {\left(3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \cos\left(d x^{2} + c\right) + 3 i \, {\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 \, b\right) - 2 \, {\left(6 \, {\left(a^{3} b^{2} - a b^{4}\right)} c \cos\left(d x^{2} + c\right) + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c - {\left(-3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \cos\left(d x^{2} + c\right) - 3 i \, {\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 \, b\right) + 2 \, {\left(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d x^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} \cos\left(d x^{2} + c\right) + {\left(-3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} x^{4} + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} + {\left(-3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} x^{4} + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{b \cos\left(d x^{2} + c\right) + i \, 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(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d x^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} \cos\left(d x^{2} + c\right) + {\left(3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} x^{4} - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} + {\left(3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} x^{4} - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{b \cos\left(d x^{2} + c\right) + i \, 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(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d x^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} \cos\left(d x^{2} + c\right) + {\left(3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} x^{4} - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} + {\left(3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} x^{4} - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{b \cos\left(d x^{2} + c\right) - i \, 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(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d x^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} \cos\left(d x^{2} + c\right) + {\left(-3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} x^{4} + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} + {\left(-3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} x^{4} + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{b \cos\left(d x^{2} + c\right) - i \, 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} \cos\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*cos(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*sin(d*x^2 + c) + 2*(-12*I*a^3*b^2 + 6*I*a*b^4 + (-12*I*a^4*b + 6*I*a^2*b^3)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -(b*cos(d*x^2 + c) + I*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) + 2*(12*I*a^3*b^2 - 6*I*a*b^4 + (12*I*a^4*b - 6*I*a^2*b^3)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -(b*cos(d*x^2 + c) + I*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) + 2*(12*I*a^3*b^2 - 6*I*a*b^4 + (12*I*a^4*b - 6*I*a^2*b^3)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -(b*cos(d*x^2 + c) - I*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) + 2*(-12*I*a^3*b^2 + 6*I*a*b^4 + (-12*I*a^4*b + 6*I*a^2*b^3)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -(b*cos(d*x^2 + c) - I*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)*cos(d*x^2 + c) - 12*((2*a^4*b - a^2*b^3)*d*x^2*cos(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*d*x^2)*sqrt(-(a^2 - b^2)/a^2))*dilog(-(b*cos(d*x^2 + c) + I*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)*cos(d*x^2 + c) + 12*((2*a^4*b - a^2*b^3)*d*x^2*cos(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*d*x^2)*sqrt(-(a^2 - b^2)/a^2))*dilog(-(b*cos(d*x^2 + c) + I*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)*cos(d*x^2 + c) - 12*((2*a^4*b - a^2*b^3)*d*x^2*cos(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*d*x^2)*sqrt(-(a^2 - b^2)/a^2))*dilog(-(b*cos(d*x^2 + c) - I*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)*cos(d*x^2 + c) + 12*((2*a^4*b - a^2*b^3)*d*x^2*cos(d*x^2 + c) + (2*a^3*b^2 - a*b^4)*d*x^2)*sqrt(-(a^2 - b^2)/a^2))*dilog(-(b*cos(d*x^2 + c) - I*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*(6*(a^3*b^2 - a*b^4)*c*cos(d*x^2 + c) + 6*(a^2*b^3 - b^5)*c - (3*I*(2*a^4*b - a^2*b^3)*c^2*cos(d*x^2 + c) + 3*I*(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*b) - 2*(6*(a^3*b^2 - a*b^4)*c*cos(d*x^2 + c) + 6*(a^2*b^3 - b^5)*c - (-3*I*(2*a^4*b - a^2*b^3)*c^2*cos(d*x^2 + c) - 3*I*(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*b) - 2*(6*(a^3*b^2 - a*b^4)*c*cos(d*x^2 + c) + 6*(a^2*b^3 - b^5)*c - (3*I*(2*a^4*b - a^2*b^3)*c^2*cos(d*x^2 + c) + 3*I*(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*b) - 2*(6*(a^3*b^2 - a*b^4)*c*cos(d*x^2 + c) + 6*(a^2*b^3 - b^5)*c - (-3*I*(2*a^4*b - a^2*b^3)*c^2*cos(d*x^2 + c) - 3*I*(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*b) + 2*(6*(a^2*b^3 - b^5)*d*x^2 + 6*(a^2*b^3 - b^5)*c + 6*((a^3*b^2 - a*b^4)*d*x^2 + (a^3*b^2 - a*b^4)*c)*cos(d*x^2 + c) + (-3*I*(2*a^3*b^2 - a*b^4)*d^2*x^4 + 3*I*(2*a^3*b^2 - a*b^4)*c^2 + (-3*I*(2*a^4*b - a^2*b^3)*d^2*x^4 + 3*I*(2*a^4*b - a^2*b^3)*c^2)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2))*log((b*cos(d*x^2 + c) + I*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*(6*(a^2*b^3 - b^5)*d*x^2 + 6*(a^2*b^3 - b^5)*c + 6*((a^3*b^2 - a*b^4)*d*x^2 + (a^3*b^2 - a*b^4)*c)*cos(d*x^2 + c) + (3*I*(2*a^3*b^2 - a*b^4)*d^2*x^4 - 3*I*(2*a^3*b^2 - a*b^4)*c^2 + (3*I*(2*a^4*b - a^2*b^3)*d^2*x^4 - 3*I*(2*a^4*b - a^2*b^3)*c^2)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2))*log((b*cos(d*x^2 + c) + I*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*(6*(a^2*b^3 - b^5)*d*x^2 + 6*(a^2*b^3 - b^5)*c + 6*((a^3*b^2 - a*b^4)*d*x^2 + (a^3*b^2 - a*b^4)*c)*cos(d*x^2 + c) + (3*I*(2*a^3*b^2 - a*b^4)*d^2*x^4 - 3*I*(2*a^3*b^2 - a*b^4)*c^2 + (3*I*(2*a^4*b - a^2*b^3)*d^2*x^4 - 3*I*(2*a^4*b - a^2*b^3)*c^2)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2))*log((b*cos(d*x^2 + c) - I*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*(6*(a^2*b^3 - b^5)*d*x^2 + 6*(a^2*b^3 - b^5)*c + 6*((a^3*b^2 - a*b^4)*d*x^2 + (a^3*b^2 - a*b^4)*c)*cos(d*x^2 + c) + (-3*I*(2*a^3*b^2 - a*b^4)*d^2*x^4 + 3*I*(2*a^3*b^2 - a*b^4)*c^2 + (-3*I*(2*a^4*b - a^2*b^3)*d^2*x^4 + 3*I*(2*a^4*b - a^2*b^3)*c^2)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2))*log((b*cos(d*x^2 + c) - I*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*cos(d*x^2 + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^3)","C",0
24,0,0,0,0.623061," ","integrate(x^4/(a+b*sec(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{b^{2} \sec\left(d x^{2} + c\right)^{2} + 2 \, a b \sec\left(d x^{2} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^4/(b^2*sec(d*x^2 + c)^2 + 2*a*b*sec(d*x^2 + c) + a^2), x)","F",0
25,1,1928,0,1.010898," ","integrate(x^3/(a+b*sec(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} \cos\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} \sin\left(d x^{2} + c\right) - {\left(2 \, a^{3} b^{2} - a b^{4} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) + i \, 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 \, a^{3} b^{2} - a b^{4} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) + i \, 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 \, a^{3} b^{2} - a b^{4} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) - i \, 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 \, a^{3} b^{2} - a b^{4} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{b \cos\left(d x^{2} + c\right) - i \, 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(-i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2} - i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) + i \, 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(i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2} + i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) + i \, 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(i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2} + i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) - i \, 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(-i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d x^{2} - i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d x^{2} - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{b \cos\left(d x^{2} + c\right) - i \, 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)} \cos\left(d x^{2} + c\right) + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \cos\left(d x^{2} + c\right) - i \, {\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 \, b\right) + {\left(a^{2} b^{3} - b^{5} + {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x^{2} + c\right) + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \cos\left(d x^{2} + c\right) + i \, {\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 \, b\right) + {\left(a^{2} b^{3} - b^{5} + {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x^{2} + c\right) + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \cos\left(d x^{2} + c\right) - i \, {\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 \, b\right) + {\left(a^{2} b^{3} - b^{5} + {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x^{2} + c\right) + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \cos\left(d x^{2} + c\right) + i \, {\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 \, b\right)}{4 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cos\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*cos(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*sin(d*x^2 + c) - (2*a^3*b^2 - a*b^4 + (2*a^4*b - a^2*b^3)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) + I*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 + (2*a^4*b - a^2*b^3)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) + I*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 + (2*a^4*b - a^2*b^3)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) - I*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 + (2*a^4*b - a^2*b^3)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*dilog(-(b*cos(d*x^2 + c) - I*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) + (-I*(2*a^3*b^2 - a*b^4)*d*x^2 - I*(2*a^3*b^2 - a*b^4)*c + (-I*(2*a^4*b - a^2*b^3)*d*x^2 - I*(2*a^4*b - a^2*b^3)*c)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) + I*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) + (I*(2*a^3*b^2 - a*b^4)*d*x^2 + I*(2*a^3*b^2 - a*b^4)*c + (I*(2*a^4*b - a^2*b^3)*d*x^2 + I*(2*a^4*b - a^2*b^3)*c)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) + I*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) + (I*(2*a^3*b^2 - a*b^4)*d*x^2 + I*(2*a^3*b^2 - a*b^4)*c + (I*(2*a^4*b - a^2*b^3)*d*x^2 + I*(2*a^4*b - a^2*b^3)*c)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) - I*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) + (-I*(2*a^3*b^2 - a*b^4)*d*x^2 - I*(2*a^3*b^2 - a*b^4)*c + (-I*(2*a^4*b - a^2*b^3)*d*x^2 - I*(2*a^4*b - a^2*b^3)*c)*cos(d*x^2 + c))*sqrt(-(a^2 - b^2)/a^2)*log((b*cos(d*x^2 + c) - I*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)*cos(d*x^2 + c) + (-I*(2*a^4*b - a^2*b^3)*c*cos(d*x^2 + c) - I*(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*b) + (a^2*b^3 - b^5 + (a^3*b^2 - a*b^4)*cos(d*x^2 + c) + (I*(2*a^4*b - a^2*b^3)*c*cos(d*x^2 + c) + I*(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*b) + (a^2*b^3 - b^5 + (a^3*b^2 - a*b^4)*cos(d*x^2 + c) + (-I*(2*a^4*b - a^2*b^3)*c*cos(d*x^2 + c) - I*(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*b) + (a^2*b^3 - b^5 + (a^3*b^2 - a*b^4)*cos(d*x^2 + c) + (I*(2*a^4*b - a^2*b^3)*c*cos(d*x^2 + c) + I*(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*b))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d^2*cos(d*x^2 + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^2)","B",0
26,0,0,0,0.609483," ","integrate(x^2/(a+b*sec(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b^{2} \sec\left(d x^{2} + c\right)^{2} + 2 \, a b \sec\left(d x^{2} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^2/(b^2*sec(d*x^2 + c)^2 + 2*a*b*sec(d*x^2 + c) + a^2), x)","F",0
27,1,525,0,2.059737," ","integrate(x/(a+b*sec(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} \cos\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)} \cos\left(d x^{2} + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x^{2} + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x^{2} + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x^{2} + c\right) + a\right)} \sin\left(d x^{2} + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x^{2} + c\right)^{2} + 2 \, a b \cos\left(d x^{2} + c\right) + b^{2}}\right) + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x^{2} + c\right)}{4 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\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} \cos\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)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x^{2} + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x^{2} + c\right)}\right) + {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x^{2} + c\right)}{2 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\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*cos(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)*cos(d*x^2 + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x^2 + c) - (a^2 - 2*b^2)*cos(d*x^2 + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x^2 + c) + a)*sin(d*x^2 + c) + 2*a^2 - b^2)/(a^2*cos(d*x^2 + c)^2 + 2*a*b*cos(d*x^2 + c) + b^2)) + 2*(a^3*b^2 - a*b^4)*sin(d*x^2 + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(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*cos(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)*cos(d*x^2 + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x^2 + c) + a)/((a^2 - b^2)*sin(d*x^2 + c))) + (a^3*b^2 - a*b^4)*sin(d*x^2 + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x^2 + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d)]","B",0
28,0,0,0,0.671849," ","integrate(1/x/(a+b*sec(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x \sec\left(d x^{2} + c\right)^{2} + 2 \, a b x \sec\left(d x^{2} + c\right) + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*sec(d*x^2 + c)^2 + 2*a*b*x*sec(d*x^2 + c) + a^2*x), x)","F",0
29,0,0,0,0.993605," ","integrate(1/x^2/(a+b*sec(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} \sec\left(d x^{2} + c\right)^{2} + 2 \, a b x^{2} \sec\left(d x^{2} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*sec(d*x^2 + c)^2 + 2*a*b*x^2*sec(d*x^2 + c) + a^2*x^2), x)","F",0
30,0,0,0,0.841229," ","integrate(1/x^3/(a+b*sec(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{3} \sec\left(d x^{2} + c\right)^{2} + 2 \, a b x^{3} \sec\left(d x^{2} + c\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(1/(b^2*x^3*sec(d*x^2 + c)^2 + 2*a*b*x^3*sec(d*x^2 + c) + a^2*x^3), x)","F",0
31,0,0,0,2.105538," ","integrate(x^3*(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{3} \sec\left(d \sqrt{x} + c\right) + a x^{3}, x\right)"," ",0,"integral(b*x^3*sec(d*sqrt(x) + c) + a*x^3, x)","F",0
32,0,0,0,0.590843," ","integrate(x^2*(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{2} \sec\left(d \sqrt{x} + c\right) + a x^{2}, x\right)"," ",0,"integral(b*x^2*sec(d*sqrt(x) + c) + a*x^2, x)","F",0
33,0,0,0,0.819532," ","integrate(x*(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x \sec\left(d \sqrt{x} + c\right) + a x, x\right)"," ",0,"integral(b*x*sec(d*sqrt(x) + c) + a*x, x)","F",0
34,0,0,0,0.750138," ","integrate((a+b*sec(c+d*x^(1/2)))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d \sqrt{x} + c\right) + a}{x}, x\right)"," ",0,"integral((b*sec(d*sqrt(x) + c) + a)/x, x)","F",0
35,0,0,0,0.476768," ","integrate((a+b*sec(c+d*x^(1/2)))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d \sqrt{x} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*sec(d*sqrt(x) + c) + a)/x^2, x)","F",0
36,0,0,0,0.582546," ","integrate(x^3*(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{3} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{3} \sec\left(d \sqrt{x} + c\right) + a^{2} x^{3}, x\right)"," ",0,"integral(b^2*x^3*sec(d*sqrt(x) + c)^2 + 2*a*b*x^3*sec(d*sqrt(x) + c) + a^2*x^3, x)","F",0
37,0,0,0,0.617502," ","integrate(x^2*(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \sec\left(d \sqrt{x} + c\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*sec(d*sqrt(x) + c)^2 + 2*a*b*x^2*sec(d*sqrt(x) + c) + a^2*x^2, x)","F",0
38,0,0,0,0.902642," ","integrate(x*(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x \sec\left(d \sqrt{x} + c\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*sec(d*sqrt(x) + c)^2 + 2*a*b*x*sec(d*sqrt(x) + c) + a^2*x, x)","F",0
39,0,0,0,0.753621," ","integrate((a+b*sec(c+d*x^(1/2)))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sec\left(d \sqrt{x} + c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*sec(d*sqrt(x) + c)^2 + 2*a*b*sec(d*sqrt(x) + c) + a^2)/x, x)","F",0
40,0,0,0,0.738539," ","integrate((a+b*sec(c+d*x^(1/2)))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sec\left(d \sqrt{x} + c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*sec(d*sqrt(x) + c)^2 + 2*a*b*sec(d*sqrt(x) + c) + a^2)/x^2, x)","F",0
41,0,0,0,1.038307," ","integrate(x^3/(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{b \sec\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^3/(b*sec(d*sqrt(x) + c) + a), x)","F",0
42,0,0,0,0.847128," ","integrate(x^2/(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b \sec\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^2/(b*sec(d*sqrt(x) + c) + a), x)","F",0
43,0,0,0,0.586828," ","integrate(x/(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b \sec\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x/(b*sec(d*sqrt(x) + c) + a), x)","F",0
44,0,0,0,0.723109," ","integrate(1/x/(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \sec\left(d \sqrt{x} + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*sec(d*sqrt(x) + c) + a*x), x)","F",0
45,0,0,0,0.538804," ","integrate((a+b*sec(c+d*x^(1/2)))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d \sqrt{x} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*sec(d*sqrt(x) + c) + a)/x^2, x)","F",0
46,0,0,0,0.838145," ","integrate(x^3/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{b^{2} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sec\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^3/(b^2*sec(d*sqrt(x) + c)^2 + 2*a*b*sec(d*sqrt(x) + c) + a^2), x)","F",0
47,0,0,0,0.755352," ","integrate(x^2/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b^{2} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sec\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^2/(b^2*sec(d*sqrt(x) + c)^2 + 2*a*b*sec(d*sqrt(x) + c) + a^2), x)","F",0
48,0,0,0,0.626306," ","integrate(x/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{2} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sec\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x/(b^2*sec(d*sqrt(x) + c)^2 + 2*a*b*sec(d*sqrt(x) + c) + a^2), x)","F",0
49,0,0,0,1.387147," ","integrate(1/x/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x \sec\left(d \sqrt{x} + c\right) + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*sec(d*sqrt(x) + c)^2 + 2*a*b*x*sec(d*sqrt(x) + c) + a^2*x), x)","F",0
50,0,0,0,0.820504," ","integrate(1/x^2/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \sec\left(d \sqrt{x} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*sec(d*sqrt(x) + c)^2 + 2*a*b*x^2*sec(d*sqrt(x) + c) + a^2*x^2), x)","F",0
51,0,0,0,0.595004," ","integrate(x^(3/2)*(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{\frac{3}{2}} \sec\left(d \sqrt{x} + c\right) + a x^{\frac{3}{2}}, x\right)"," ",0,"integral(b*x^(3/2)*sec(d*sqrt(x) + c) + a*x^(3/2), x)","F",0
52,0,0,0,0.712157," ","integrate((a+b*sec(c+d*x^(1/2)))*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(b \sqrt{x} \sec\left(d \sqrt{x} + c\right) + a \sqrt{x}, x\right)"," ",0,"integral(b*sqrt(x)*sec(d*sqrt(x) + c) + a*sqrt(x), x)","F",0
53,1,41,0,0.662791," ","integrate((a+b*sec(c+d*x^(1/2)))/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, a d \sqrt{x} + b \log\left(\sin\left(d \sqrt{x} + c\right) + 1\right) - b \log\left(-\sin\left(d \sqrt{x} + c\right) + 1\right)}{d}"," ",0,"(2*a*d*sqrt(x) + b*log(sin(d*sqrt(x) + c) + 1) - b*log(-sin(d*sqrt(x) + c) + 1))/d","A",0
54,0,0,0,0.590393," ","integrate((a+b*sec(c+d*x^(1/2)))/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sqrt{x} \sec\left(d \sqrt{x} + c\right) + a \sqrt{x}}{x^{2}}, x\right)"," ",0,"integral((b*sqrt(x)*sec(d*sqrt(x) + c) + a*sqrt(x))/x^2, x)","F",0
55,0,0,0,0.553027," ","integrate((a+b*sec(c+d*x^(1/2)))/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sqrt{x} \sec\left(d \sqrt{x} + c\right) + a \sqrt{x}}{x^{3}}, x\right)"," ",0,"integral((b*sqrt(x)*sec(d*sqrt(x) + c) + a*sqrt(x))/x^3, x)","F",0
56,0,0,0,0.529591," ","integrate(x^(3/2)*(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{\frac{3}{2}} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{\frac{3}{2}} \sec\left(d \sqrt{x} + c\right) + a^{2} x^{\frac{3}{2}}, x\right)"," ",0,"integral(b^2*x^(3/2)*sec(d*sqrt(x) + c)^2 + 2*a*b*x^(3/2)*sec(d*sqrt(x) + c) + a^2*x^(3/2), x)","F",0
57,0,0,0,0.735813," ","integrate((a+b*sec(c+d*x^(1/2)))^2*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \sqrt{x} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \sec\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}, x\right)"," ",0,"integral(b^2*sqrt(x)*sec(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*sec(d*sqrt(x) + c) + a^2*sqrt(x), x)","F",0
58,1,91,0,0.785700," ","integrate((a+b*sec(c+d*x^(1/2)))^2/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} d \sqrt{x} \cos\left(d \sqrt{x} + c\right) + a b \cos\left(d \sqrt{x} + c\right) \log\left(\sin\left(d \sqrt{x} + c\right) + 1\right) - a b \cos\left(d \sqrt{x} + c\right) \log\left(-\sin\left(d \sqrt{x} + c\right) + 1\right) + b^{2} \sin\left(d \sqrt{x} + c\right)\right)}}{d \cos\left(d \sqrt{x} + c\right)}"," ",0,"2*(a^2*d*sqrt(x)*cos(d*sqrt(x) + c) + a*b*cos(d*sqrt(x) + c)*log(sin(d*sqrt(x) + c) + 1) - a*b*cos(d*sqrt(x) + c)*log(-sin(d*sqrt(x) + c) + 1) + b^2*sin(d*sqrt(x) + c))/(d*cos(d*sqrt(x) + c))","B",0
59,0,0,0,0.518107," ","integrate((a+b*sec(c+d*x^(1/2)))^2/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sqrt{x} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \sec\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}}{x^{2}}, x\right)"," ",0,"integral((b^2*sqrt(x)*sec(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*sec(d*sqrt(x) + c) + a^2*sqrt(x))/x^2, x)","F",0
60,0,0,0,0.701764," ","integrate((a+b*sec(c+d*x^(1/2)))^2/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sqrt{x} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \sec\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}}{x^{3}}, x\right)"," ",0,"integral((b^2*sqrt(x)*sec(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*sec(d*sqrt(x) + c) + a^2*sqrt(x))/x^3, x)","F",0
61,0,0,0,0.534797," ","integrate(x^(3/2)/(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{\frac{3}{2}}}{b \sec\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^(3/2)/(b*sec(d*sqrt(x) + c) + a), x)","F",0
62,0,0,0,0.617234," ","integrate(x^(1/2)/(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b \sec\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(sqrt(x)/(b*sec(d*sqrt(x) + c) + a), x)","F",0
63,1,274,0,0.548378," ","integrate(1/(a+b*sec(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{2 \, a b \cos\left(d \sqrt{x} + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d \sqrt{x} + c\right)^{2} + 2 \, a^{2} - b^{2} - 2 \, {\left(\sqrt{a^{2} - b^{2}} b \cos\left(d \sqrt{x} + c\right) + \sqrt{a^{2} - b^{2}} a\right)} \sin\left(d \sqrt{x} + c\right)}{a^{2} \cos\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \cos\left(d \sqrt{x} + c\right) + 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 \cos\left(d \sqrt{x} + c\right) + \sqrt{-a^{2} + b^{2}} a}{{\left(a^{2} - b^{2}\right)} \sin\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((2*a*b*cos(d*sqrt(x) + c) - (a^2 - 2*b^2)*cos(d*sqrt(x) + c)^2 + 2*a^2 - b^2 - 2*(sqrt(a^2 - b^2)*b*cos(d*sqrt(x) + c) + sqrt(a^2 - b^2)*a)*sin(d*sqrt(x) + c))/(a^2*cos(d*sqrt(x) + c)^2 + 2*a*b*cos(d*sqrt(x) + c) + 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*cos(d*sqrt(x) + c) + sqrt(-a^2 + b^2)*a)/((a^2 - b^2)*sin(d*sqrt(x) + c))))/((a^3 - a*b^2)*d)]","A",0
64,0,0,0,0.661936," ","integrate(1/x^(3/2)/(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b x^{2} \sec\left(d \sqrt{x} + c\right) + a x^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b*x^2*sec(d*sqrt(x) + c) + a*x^2), x)","F",0
65,0,0,0,0.493761," ","integrate(1/x^(5/2)/(a+b*sec(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b x^{3} \sec\left(d \sqrt{x} + c\right) + a x^{3}}, x\right)"," ",0,"integral(sqrt(x)/(b*x^3*sec(d*sqrt(x) + c) + a*x^3), x)","F",0
66,0,0,0,0.616096," ","integrate(x^(3/2)/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{\frac{3}{2}}}{b^{2} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sec\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^(3/2)/(b^2*sec(d*sqrt(x) + c)^2 + 2*a*b*sec(d*sqrt(x) + c) + a^2), x)","F",0
67,0,0,0,0.550560," ","integrate(x^(1/2)/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sec\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*sec(d*sqrt(x) + c)^2 + 2*a*b*sec(d*sqrt(x) + c) + a^2), x)","F",0
68,1,574,0,0.580778," ","integrate(1/(a+b*sec(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} \cos\left(d \sqrt{x} + c\right) + 2 \, {\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}} \cos\left(d \sqrt{x} + c\right) + {\left(2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{a^{2} - b^{2}}\right)} \log\left(\frac{2 \, a b \cos\left(d \sqrt{x} + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d \sqrt{x} + c\right)^{2} + 2 \, a^{2} - b^{2} - 2 \, {\left(\sqrt{a^{2} - b^{2}} b \cos\left(d \sqrt{x} + c\right) + \sqrt{a^{2} - b^{2}} a\right)} \sin\left(d \sqrt{x} + c\right)}{a^{2} \cos\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \cos\left(d \sqrt{x} + c\right) + b^{2}}\right) + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d \sqrt{x} + c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\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} \cos\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}} \cos\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 \cos\left(d \sqrt{x} + c\right) + \sqrt{-a^{2} + b^{2}} a}{{\left(a^{2} - b^{2}\right)} \sin\left(d \sqrt{x} + c\right)}\right) + {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d \sqrt{x} + c\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\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)*cos(d*sqrt(x) + c) + 2*(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)*cos(d*sqrt(x) + c) + (2*a^2*b^2 - b^4)*sqrt(a^2 - b^2))*log((2*a*b*cos(d*sqrt(x) + c) - (a^2 - 2*b^2)*cos(d*sqrt(x) + c)^2 + 2*a^2 - b^2 - 2*(sqrt(a^2 - b^2)*b*cos(d*sqrt(x) + c) + sqrt(a^2 - b^2)*a)*sin(d*sqrt(x) + c))/(a^2*cos(d*sqrt(x) + c)^2 + 2*a*b*cos(d*sqrt(x) + c) + b^2)) + 2*(a^3*b^2 - a*b^4)*sin(d*sqrt(x) + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(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)*cos(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)*cos(d*sqrt(x) + c) + (2*a^2*b^2 - b^4)*sqrt(-a^2 + b^2))*arctan(-(sqrt(-a^2 + b^2)*b*cos(d*sqrt(x) + c) + sqrt(-a^2 + b^2)*a)/((a^2 - b^2)*sin(d*sqrt(x) + c))) + (a^3*b^2 - a*b^4)*sin(d*sqrt(x) + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*sqrt(x) + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d)]","B",0
69,0,0,0,0.513349," ","integrate(1/x^(3/2)/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} x^{2} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \sec\left(d \sqrt{x} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*x^2*sec(d*sqrt(x) + c)^2 + 2*a*b*x^2*sec(d*sqrt(x) + c) + a^2*x^2), x)","F",0
70,0,0,0,0.574832," ","integrate(1/x^(5/2)/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} x^{3} \sec\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{3} \sec\left(d \sqrt{x} + c\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*x^3*sec(d*sqrt(x) + c)^2 + 2*a*b*x^3*sec(d*sqrt(x) + c) + a^2*x^3), x)","F",0
71,0,0,0,0.744990," ","integrate((e*x)^m*(a+b*sec(c+d*x^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} {\left(b \sec\left(d x^{n} + c\right) + a\right)}^{p}, x\right)"," ",0,"integral((e*x)^m*(b*sec(d*x^n + c) + a)^p, x)","F",0
72,1,60,0,0.753982," ","integrate((e*x)^(-1+n)*(a+b*sec(c+d*x^n)),x, algorithm=""fricas"")","\frac{2 \, a d e^{n - 1} x^{n} + b e^{n - 1} \log\left(\sin\left(d x^{n} + c\right) + 1\right) - b e^{n - 1} \log\left(-\sin\left(d x^{n} + c\right) + 1\right)}{2 \, d n}"," ",0,"1/2*(2*a*d*e^(n - 1)*x^n + b*e^(n - 1)*log(sin(d*x^n + c) + 1) - b*e^(n - 1)*log(-sin(d*x^n + c) + 1))/(d*n)","A",0
73,1,470,0,1.483648," ","integrate((e*x)^(-1+2*n)*(a+b*sec(c+d*x^n)),x, algorithm=""fricas"")","\frac{a d^{2} e^{2 \, n - 1} x^{2 \, n} - b c e^{2 \, n - 1} \log\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + i\right) + b c e^{2 \, n - 1} \log\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + i\right) - b c e^{2 \, n - 1} \log\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + i\right) + b c e^{2 \, n - 1} \log\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + i\right) - i \, b e^{2 \, n - 1} {\rm Li}_2\left(i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) - i \, b e^{2 \, n - 1} {\rm Li}_2\left(i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right)\right) + i \, b e^{2 \, n - 1} {\rm Li}_2\left(-i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) + i \, b e^{2 \, n - 1} {\rm Li}_2\left(-i \, \cos\left(d x^{n} + c\right) - \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(i \, \cos\left(d x^{n} + c\right) + \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(i \, \cos\left(d x^{n} + c\right) - \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(-i \, \cos\left(d x^{n} + c\right) + \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(-i \, \cos\left(d x^{n} + c\right) - \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*c*e^(2*n - 1)*log(cos(d*x^n + c) + I*sin(d*x^n + c) + I) + b*c*e^(2*n - 1)*log(cos(d*x^n + c) - I*sin(d*x^n + c) + I) - b*c*e^(2*n - 1)*log(-cos(d*x^n + c) + I*sin(d*x^n + c) + I) + b*c*e^(2*n - 1)*log(-cos(d*x^n + c) - I*sin(d*x^n + c) + I) - I*b*e^(2*n - 1)*dilog(I*cos(d*x^n + c) + sin(d*x^n + c)) - I*b*e^(2*n - 1)*dilog(I*cos(d*x^n + c) - sin(d*x^n + c)) + I*b*e^(2*n - 1)*dilog(-I*cos(d*x^n + c) + sin(d*x^n + c)) + I*b*e^(2*n - 1)*dilog(-I*cos(d*x^n + c) - sin(d*x^n + c)) + (b*d*e^(2*n - 1)*x^n + b*c*e^(2*n - 1))*log(I*cos(d*x^n + c) + sin(d*x^n + c) + 1) - (b*d*e^(2*n - 1)*x^n + b*c*e^(2*n - 1))*log(I*cos(d*x^n + c) - sin(d*x^n + c) + 1) + (b*d*e^(2*n - 1)*x^n + b*c*e^(2*n - 1))*log(-I*cos(d*x^n + c) + sin(d*x^n + c) + 1) - (b*d*e^(2*n - 1)*x^n + b*c*e^(2*n - 1))*log(-I*cos(d*x^n + c) - sin(d*x^n + c) + 1))/(d^2*n)","B",0
74,1,655,0,0.826028," ","integrate((e*x)^(-1+3*n)*(a+b*sec(c+d*x^n)),x, algorithm=""fricas"")","\frac{2 \, a d^{3} e^{3 \, n - 1} x^{3 \, n} - 6 i \, b d e^{3 \, n - 1} x^{n} {\rm Li}_2\left(i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) - 6 i \, b d e^{3 \, n - 1} x^{n} {\rm Li}_2\left(i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right)\right) + 6 i \, b d e^{3 \, n - 1} x^{n} {\rm Li}_2\left(-i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) + 6 i \, b d e^{3 \, n - 1} x^{n} {\rm Li}_2\left(-i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right)\right) + 3 \, b c^{2} e^{3 \, n - 1} \log\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + i\right) - 3 \, b c^{2} e^{3 \, n - 1} \log\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + i\right) + 3 \, b c^{2} e^{3 \, n - 1} \log\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + i\right) - 3 \, b c^{2} e^{3 \, n - 1} \log\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + i\right) - 6 \, b e^{3 \, n - 1} {\rm polylog}\left(3, i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) + 6 \, b e^{3 \, n - 1} {\rm polylog}\left(3, i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right)\right) - 6 \, b e^{3 \, n - 1} {\rm polylog}\left(3, -i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) + 6 \, b e^{3 \, n - 1} {\rm polylog}\left(3, -i \, \cos\left(d x^{n} + c\right) - \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(i \, \cos\left(d x^{n} + c\right) + \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(i \, \cos\left(d x^{n} + c\right) - \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(-i \, \cos\left(d x^{n} + c\right) + \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(-i \, \cos\left(d x^{n} + c\right) - \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) - 6*I*b*d*e^(3*n - 1)*x^n*dilog(I*cos(d*x^n + c) + sin(d*x^n + c)) - 6*I*b*d*e^(3*n - 1)*x^n*dilog(I*cos(d*x^n + c) - sin(d*x^n + c)) + 6*I*b*d*e^(3*n - 1)*x^n*dilog(-I*cos(d*x^n + c) + sin(d*x^n + c)) + 6*I*b*d*e^(3*n - 1)*x^n*dilog(-I*cos(d*x^n + c) - sin(d*x^n + c)) + 3*b*c^2*e^(3*n - 1)*log(cos(d*x^n + c) + I*sin(d*x^n + c) + I) - 3*b*c^2*e^(3*n - 1)*log(cos(d*x^n + c) - I*sin(d*x^n + c) + I) + 3*b*c^2*e^(3*n - 1)*log(-cos(d*x^n + c) + I*sin(d*x^n + c) + I) - 3*b*c^2*e^(3*n - 1)*log(-cos(d*x^n + c) - I*sin(d*x^n + c) + I) - 6*b*e^(3*n - 1)*polylog(3, I*cos(d*x^n + c) + sin(d*x^n + c)) + 6*b*e^(3*n - 1)*polylog(3, I*cos(d*x^n + c) - sin(d*x^n + c)) - 6*b*e^(3*n - 1)*polylog(3, -I*cos(d*x^n + c) + sin(d*x^n + c)) + 6*b*e^(3*n - 1)*polylog(3, -I*cos(d*x^n + c) - sin(d*x^n + c)) + 3*(b*d^2*e^(3*n - 1)*x^(2*n) - b*c^2*e^(3*n - 1))*log(I*cos(d*x^n + c) + 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(I*cos(d*x^n + c) - 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(-I*cos(d*x^n + c) + 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(-I*cos(d*x^n + c) - sin(d*x^n + c) + 1))/(d^3*n)","C",0
75,1,113,0,0.580993," ","integrate((e*x)^(-1+n)*(a+b*sec(c+d*x^n))^2,x, algorithm=""fricas"")","\frac{a^{2} d e^{n - 1} x^{n} \cos\left(d x^{n} + c\right) + a b e^{n - 1} \cos\left(d x^{n} + c\right) \log\left(\sin\left(d x^{n} + c\right) + 1\right) - a b e^{n - 1} \cos\left(d x^{n} + c\right) \log\left(-\sin\left(d x^{n} + c\right) + 1\right) + b^{2} e^{n - 1} \sin\left(d x^{n} + c\right)}{d n \cos\left(d x^{n} + c\right)}"," ",0,"(a^2*d*e^(n - 1)*x^n*cos(d*x^n + c) + a*b*e^(n - 1)*cos(d*x^n + c)*log(sin(d*x^n + c) + 1) - a*b*e^(n - 1)*cos(d*x^n + c)*log(-sin(d*x^n + c) + 1) + b^2*e^(n - 1)*sin(d*x^n + c))/(d*n*cos(d*x^n + c))","A",0
76,1,656,0,0.935555," ","integrate((e*x)^(-1+2*n)*(a+b*sec(c+d*x^n))^2,x, algorithm=""fricas"")","\frac{a^{2} d^{2} e^{2 \, n - 1} x^{2 \, n} \cos\left(d x^{n} + c\right) + 2 \, b^{2} d e^{2 \, n - 1} x^{n} \sin\left(d x^{n} + c\right) - 2 i \, a b e^{2 \, n - 1} \cos\left(d x^{n} + c\right) {\rm Li}_2\left(i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) - 2 i \, a b e^{2 \, n - 1} \cos\left(d x^{n} + c\right) {\rm Li}_2\left(i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right)\right) + 2 i \, a b e^{2 \, n - 1} \cos\left(d x^{n} + c\right) {\rm Li}_2\left(-i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) + 2 i \, a b e^{2 \, n - 1} \cos\left(d x^{n} + c\right) {\rm Li}_2\left(-i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right)\right) - {\left(2 \, a b c - b^{2}\right)} e^{2 \, n - 1} \cos\left(d x^{n} + c\right) \log\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + i\right) + {\left(2 \, a b c + b^{2}\right)} e^{2 \, n - 1} \cos\left(d x^{n} + c\right) \log\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + i\right) - {\left(2 \, a b c - b^{2}\right)} e^{2 \, n - 1} \cos\left(d x^{n} + c\right) \log\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + i\right) + {\left(2 \, a b c + b^{2}\right)} e^{2 \, n - 1} \cos\left(d x^{n} + c\right) \log\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + i\right) + 2 \, {\left(a b d e^{2 \, n - 1} x^{n} + a b c e^{2 \, n - 1}\right)} \cos\left(d x^{n} + c\right) \log\left(i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right) + 1\right) - 2 \, {\left(a b d e^{2 \, n - 1} x^{n} + a b c e^{2 \, n - 1}\right)} \cos\left(d x^{n} + c\right) \log\left(i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right) + 1\right) + 2 \, {\left(a b d e^{2 \, n - 1} x^{n} + a b c e^{2 \, n - 1}\right)} \cos\left(d x^{n} + c\right) \log\left(-i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right) + 1\right) - 2 \, {\left(a b d e^{2 \, n - 1} x^{n} + a b c e^{2 \, n - 1}\right)} \cos\left(d x^{n} + c\right) \log\left(-i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right) + 1\right)}{2 \, d^{2} n \cos\left(d x^{n} + c\right)}"," ",0,"1/2*(a^2*d^2*e^(2*n - 1)*x^(2*n)*cos(d*x^n + c) + 2*b^2*d*e^(2*n - 1)*x^n*sin(d*x^n + c) - 2*I*a*b*e^(2*n - 1)*cos(d*x^n + c)*dilog(I*cos(d*x^n + c) + sin(d*x^n + c)) - 2*I*a*b*e^(2*n - 1)*cos(d*x^n + c)*dilog(I*cos(d*x^n + c) - sin(d*x^n + c)) + 2*I*a*b*e^(2*n - 1)*cos(d*x^n + c)*dilog(-I*cos(d*x^n + c) + sin(d*x^n + c)) + 2*I*a*b*e^(2*n - 1)*cos(d*x^n + c)*dilog(-I*cos(d*x^n + c) - sin(d*x^n + c)) - (2*a*b*c - b^2)*e^(2*n - 1)*cos(d*x^n + c)*log(cos(d*x^n + c) + I*sin(d*x^n + c) + I) + (2*a*b*c + b^2)*e^(2*n - 1)*cos(d*x^n + c)*log(cos(d*x^n + c) - I*sin(d*x^n + c) + I) - (2*a*b*c - b^2)*e^(2*n - 1)*cos(d*x^n + c)*log(-cos(d*x^n + c) + I*sin(d*x^n + c) + I) + (2*a*b*c + b^2)*e^(2*n - 1)*cos(d*x^n + c)*log(-cos(d*x^n + c) - I*sin(d*x^n + c) + I) + 2*(a*b*d*e^(2*n - 1)*x^n + a*b*c*e^(2*n - 1))*cos(d*x^n + c)*log(I*cos(d*x^n + c) + sin(d*x^n + c) + 1) - 2*(a*b*d*e^(2*n - 1)*x^n + a*b*c*e^(2*n - 1))*cos(d*x^n + c)*log(I*cos(d*x^n + c) - sin(d*x^n + c) + 1) + 2*(a*b*d*e^(2*n - 1)*x^n + a*b*c*e^(2*n - 1))*cos(d*x^n + c)*log(-I*cos(d*x^n + c) + sin(d*x^n + c) + 1) - 2*(a*b*d*e^(2*n - 1)*x^n + a*b*c*e^(2*n - 1))*cos(d*x^n + c)*log(-I*cos(d*x^n + c) - sin(d*x^n + c) + 1))/(d^2*n*cos(d*x^n + c))","B",0
77,1,1028,0,1.276549," ","integrate((e*x)^(-1+3*n)*(a+b*sec(c+d*x^n))^2,x, algorithm=""fricas"")","\frac{a^{2} d^{3} e^{3 \, n - 1} x^{3 \, n} \cos\left(d x^{n} + c\right) + 3 \, b^{2} d^{2} e^{3 \, n - 1} x^{2 \, n} \sin\left(d x^{n} + c\right) - 6 \, a b e^{3 \, n - 1} \cos\left(d x^{n} + c\right) {\rm polylog}\left(3, i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) + 6 \, a b e^{3 \, n - 1} \cos\left(d x^{n} + c\right) {\rm polylog}\left(3, i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right)\right) - 6 \, a b e^{3 \, n - 1} \cos\left(d x^{n} + c\right) {\rm polylog}\left(3, -i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) + 6 \, a b e^{3 \, n - 1} \cos\left(d x^{n} + c\right) {\rm polylog}\left(3, -i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right)\right) + 3 \, {\left(a b c^{2} - b^{2} c\right)} e^{3 \, n - 1} \cos\left(d x^{n} + c\right) \log\left(\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + i\right) - 3 \, {\left(a b c^{2} + b^{2} c\right)} e^{3 \, n - 1} \cos\left(d x^{n} + c\right) \log\left(\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + i\right) + 3 \, {\left(a b c^{2} - b^{2} c\right)} e^{3 \, n - 1} \cos\left(d x^{n} + c\right) \log\left(-\cos\left(d x^{n} + c\right) + i \, \sin\left(d x^{n} + c\right) + i\right) - 3 \, {\left(a b c^{2} + b^{2} c\right)} e^{3 \, n - 1} \cos\left(d x^{n} + c\right) \log\left(-\cos\left(d x^{n} + c\right) - i \, \sin\left(d x^{n} + c\right) + i\right) + {\left(-6 i \, a b d e^{3 \, n - 1} x^{n} + 3 i \, b^{2} e^{3 \, n - 1}\right)} \cos\left(d x^{n} + c\right) {\rm Li}_2\left(i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) + {\left(-6 i \, a b d e^{3 \, n - 1} x^{n} - 3 i \, b^{2} e^{3 \, n - 1}\right)} \cos\left(d x^{n} + c\right) {\rm Li}_2\left(i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right)\right) + {\left(6 i \, a b d e^{3 \, n - 1} x^{n} - 3 i \, b^{2} e^{3 \, n - 1}\right)} \cos\left(d x^{n} + c\right) {\rm Li}_2\left(-i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right)\right) + {\left(6 i \, a b d e^{3 \, n - 1} x^{n} + 3 i \, b^{2} e^{3 \, n - 1}\right)} \cos\left(d x^{n} + c\right) {\rm Li}_2\left(-i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right)\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)} \cos\left(d x^{n} + c\right) \log\left(i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right) + 1\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)} \cos\left(d x^{n} + c\right) \log\left(i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right) + 1\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)} \cos\left(d x^{n} + c\right) \log\left(-i \, \cos\left(d x^{n} + c\right) + \sin\left(d x^{n} + c\right) + 1\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)} \cos\left(d x^{n} + c\right) \log\left(-i \, \cos\left(d x^{n} + c\right) - \sin\left(d x^{n} + c\right) + 1\right)}{3 \, d^{3} n \cos\left(d x^{n} + c\right)}"," ",0,"1/3*(a^2*d^3*e^(3*n - 1)*x^(3*n)*cos(d*x^n + c) + 3*b^2*d^2*e^(3*n - 1)*x^(2*n)*sin(d*x^n + c) - 6*a*b*e^(3*n - 1)*cos(d*x^n + c)*polylog(3, I*cos(d*x^n + c) + sin(d*x^n + c)) + 6*a*b*e^(3*n - 1)*cos(d*x^n + c)*polylog(3, I*cos(d*x^n + c) - sin(d*x^n + c)) - 6*a*b*e^(3*n - 1)*cos(d*x^n + c)*polylog(3, -I*cos(d*x^n + c) + sin(d*x^n + c)) + 6*a*b*e^(3*n - 1)*cos(d*x^n + c)*polylog(3, -I*cos(d*x^n + c) - sin(d*x^n + c)) + 3*(a*b*c^2 - b^2*c)*e^(3*n - 1)*cos(d*x^n + c)*log(cos(d*x^n + c) + I*sin(d*x^n + c) + I) - 3*(a*b*c^2 + b^2*c)*e^(3*n - 1)*cos(d*x^n + c)*log(cos(d*x^n + c) - I*sin(d*x^n + c) + I) + 3*(a*b*c^2 - b^2*c)*e^(3*n - 1)*cos(d*x^n + c)*log(-cos(d*x^n + c) + I*sin(d*x^n + c) + I) - 3*(a*b*c^2 + b^2*c)*e^(3*n - 1)*cos(d*x^n + c)*log(-cos(d*x^n + c) - I*sin(d*x^n + c) + I) + (-6*I*a*b*d*e^(3*n - 1)*x^n + 3*I*b^2*e^(3*n - 1))*cos(d*x^n + c)*dilog(I*cos(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))*cos(d*x^n + c)*dilog(I*cos(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))*cos(d*x^n + c)*dilog(-I*cos(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))*cos(d*x^n + c)*dilog(-I*cos(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 - (a*b*c^2 - b^2*c)*e^(3*n - 1))*cos(d*x^n + c)*log(I*cos(d*x^n + c) + sin(d*x^n + c) + 1) - 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))*cos(d*x^n + c)*log(I*cos(d*x^n + c) - sin(d*x^n + c) + 1) + 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))*cos(d*x^n + c)*log(-I*cos(d*x^n + c) + sin(d*x^n + c) + 1) - 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))*cos(d*x^n + c)*log(-I*cos(d*x^n + c) - sin(d*x^n + c) + 1))/(d^3*n*cos(d*x^n + c))","C",0
78,1,300,0,0.638132," ","integrate((e*x)^(-1+n)/(a+b*sec(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{2 \, a b \cos\left(d x^{n} + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x^{n} + c\right)^{2} + 2 \, a^{2} - b^{2} - 2 \, {\left(\sqrt{a^{2} - b^{2}} b \cos\left(d x^{n} + c\right) + \sqrt{a^{2} - b^{2}} a\right)} \sin\left(d x^{n} + c\right)}{a^{2} \cos\left(d x^{n} + c\right)^{2} + 2 \, a b \cos\left(d x^{n} + c\right) + 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 \cos\left(d x^{n} + c\right) + \sqrt{-a^{2} + b^{2}} a}{{\left(a^{2} - b^{2}\right)} \sin\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((2*a*b*cos(d*x^n + c) - (a^2 - 2*b^2)*cos(d*x^n + c)^2 + 2*a^2 - b^2 - 2*(sqrt(a^2 - b^2)*b*cos(d*x^n + c) + sqrt(a^2 - b^2)*a)*sin(d*x^n + c))/(a^2*cos(d*x^n + c)^2 + 2*a*b*cos(d*x^n + c) + 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*cos(d*x^n + c) + sqrt(-a^2 + b^2)*a)/((a^2 - b^2)*sin(d*x^n + c))))/((a^3 - a*b^2)*d*n)]","A",0
79,1,1291,0,0.706868," ","integrate((e*x)^(-1+2*n)/(a+b*sec(c+d*x^n)),x, algorithm=""fricas"")","-\frac{2 i \, 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 \, b\right) - 2 i \, 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 \, b\right) + 2 i \, 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 \, b\right) - 2 i \, 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 \, b\right) - 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2 \, n - 1} x^{2 \, n} + 2 \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) + 2 \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) - 2 \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) - 2 \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + {\left(2 i \, a b d e^{2 \, n - 1} x^{n} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + {\left(-2 i \, a b d e^{2 \, n - 1} x^{n} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + {\left(2 i \, a b d e^{2 \, n - 1} x^{n} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right) + {\left(-2 i \, a b d e^{2 \, n - 1} x^{n} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, 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*I*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*b) - 2*I*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*b) + 2*I*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*b) - 2*I*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*b) - 2*(a^2 - b^2)*d^2*e^(2*n - 1)*x^(2*n) + 2*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) + b)*cos(d*x^n + c) + (2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) + 2*a)/a + 1) + 2*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) + b)*cos(d*x^n + c) + (-2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) + 2*a)/a + 1) - 2*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) - b)*cos(d*x^n + c) - (2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) - 2*a)/a + 1) - 2*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) - b)*cos(d*x^n + c) - (-2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) - 2*a)/a + 1) + (2*I*a*b*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) + 2*I*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) + b)*cos(d*x^n + c) + (2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) + 2*a)/a) + (-2*I*a*b*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) - 2*I*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) + b)*cos(d*x^n + c) + (-2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) + 2*a)/a) + (2*I*a*b*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) + 2*I*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) - b)*cos(d*x^n + c) - (2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) - 2*a)/a) + (-2*I*a*b*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) - 2*I*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) - b)*cos(d*x^n + c) - (-2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) - 2*a)/a))/((a^3 - a*b^2)*d^2*n)","B",0
80,1,1733,0,2.326923," ","integrate((e*x)^(-1+3*n)/(a+b*sec(c+d*x^n)),x, algorithm=""fricas"")","-\frac{12 \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) + 12 \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) - 12 \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) - 12 \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) - 6 i \, 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 \, b\right) + 6 i \, 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 \, b\right) - 6 i \, 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 \, b\right) + 6 i \, 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 \, b\right) - 4 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{3 \, n - 1} x^{3 \, n} - 12 i \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) + 12 i \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) - 12 i \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) + 12 i \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) + {\left(6 i \, a b d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 6 i \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + {\left(-6 i \, a b d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 6 i \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + {\left(6 i \, a b d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 6 i \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right) + {\left(-6 i \, a b d^{2} e^{3 \, n - 1} x^{2 \, n} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 6 i \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, 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*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) + b)*cos(d*x^n + c) + (2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) + 2*a)/a + 1) + 12*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) + b)*cos(d*x^n + c) + (-2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) + 2*a)/a + 1) - 12*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) - b)*cos(d*x^n + c) - (2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) - 2*a)/a + 1) - 12*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) - b)*cos(d*x^n + c) - (-2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) - 2*a)/a + 1) - 6*I*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*b) + 6*I*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*b) - 6*I*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*b) + 6*I*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*b) - 4*(a^2 - b^2)*d^3*e^(3*n - 1)*x^(3*n) - 12*I*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) + b)*cos(d*x^n + c) - (2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c))/a) + 12*I*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) + b)*cos(d*x^n + c) - (-2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c))/a) - 12*I*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) - b)*cos(d*x^n + c) + (2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c))/a) + 12*I*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) - b)*cos(d*x^n + c) + (-2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c))/a) + (6*I*a*b*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) - 6*I*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) + b)*cos(d*x^n + c) + (2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) + 2*a)/a) + (-6*I*a*b*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) + 6*I*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) + b)*cos(d*x^n + c) + (-2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) + 2*a)/a) + (6*I*a*b*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) - 6*I*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) - b)*cos(d*x^n + c) - (2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) - 2*a)/a) + (-6*I*a*b*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) + 6*I*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) - b)*cos(d*x^n + c) - (-2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) - 2*a)/a))/((a^3 - a*b^2)*d^3*n)","C",0
81,1,628,0,0.663106," ","integrate((e*x)^(-1+n)/(a+b*sec(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} \cos\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} \sin\left(d x^{n} + c\right) + {\left({\left(2 \, a^{3} b - a b^{3}\right)} \sqrt{a^{2} - b^{2}} e^{n - 1} \cos\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{2 \, a b \cos\left(d x^{n} + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x^{n} + c\right)^{2} + 2 \, a^{2} - b^{2} - 2 \, {\left(\sqrt{a^{2} - b^{2}} b \cos\left(d x^{n} + c\right) + \sqrt{a^{2} - b^{2}} a\right)} \sin\left(d x^{n} + c\right)}{a^{2} \cos\left(d x^{n} + c\right)^{2} + 2 \, a b \cos\left(d x^{n} + c\right) + b^{2}}\right)}{2 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d n \cos\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} \cos\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} \sin\left(d x^{n} + c\right) - {\left({\left(2 \, a^{3} b - a b^{3}\right)} \sqrt{-a^{2} + b^{2}} e^{n - 1} \cos\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 \cos\left(d x^{n} + c\right) + \sqrt{-a^{2} + b^{2}} a}{{\left(a^{2} - b^{2}\right)} \sin\left(d x^{n} + c\right)}\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d n \cos\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*cos(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)*sin(d*x^n + c) + ((2*a^3*b - a*b^3)*sqrt(a^2 - b^2)*e^(n - 1)*cos(d*x^n + c) + (2*a^2*b^2 - b^4)*sqrt(a^2 - b^2)*e^(n - 1))*log((2*a*b*cos(d*x^n + c) - (a^2 - 2*b^2)*cos(d*x^n + c)^2 + 2*a^2 - b^2 - 2*(sqrt(a^2 - b^2)*b*cos(d*x^n + c) + sqrt(a^2 - b^2)*a)*sin(d*x^n + c))/(a^2*cos(d*x^n + c)^2 + 2*a*b*cos(d*x^n + c) + b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*n*cos(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*cos(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)*sin(d*x^n + c) - ((2*a^3*b - a*b^3)*sqrt(-a^2 + b^2)*e^(n - 1)*cos(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*cos(d*x^n + c) + sqrt(-a^2 + b^2)*a)/((a^2 - b^2)*sin(d*x^n + c))))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*n*cos(d*x^n + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d*n)]","A",0
82,1,2531,0,1.096344," ","integrate((e*x)^(-1+2*n)/(a+b*sec(c+d*x^n))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2 \, n - 1} x^{2 \, n} \cos\left(d x^{n} + c\right) + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2 \, n - 1} x^{2 \, n} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} d e^{2 \, n - 1} x^{n} \sin\left(d x^{n} + c\right) - 2 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \cos\left(d x^{n} + c\right) + {\left(2 \, a^{3} b^{2} - 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}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) - 2 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \cos\left(d x^{n} + c\right) + {\left(2 \, a^{3} b^{2} - 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}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) + 2 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \cos\left(d x^{n} + c\right) + {\left(2 \, a^{3} b^{2} - 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}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + 2 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \cos\left(d x^{n} + c\right) + {\left(2 \, a^{3} b^{2} - 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}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + {\left(2 \, {\left(a^{3} b^{2} - a b^{4} - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1} \cos\left(d x^{n} + c\right) + {\left(2 \, a^{2} b^{3} - 2 \, b^{5} - 2 i \, {\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 \, b\right) + {\left(2 \, {\left(a^{3} b^{2} - a b^{4} + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1} \cos\left(d x^{n} + c\right) + {\left(2 \, a^{2} b^{3} - 2 \, b^{5} + 2 i \, {\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 \, b\right) + {\left(2 \, {\left(a^{3} b^{2} - a b^{4} - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1} \cos\left(d x^{n} + c\right) + {\left(2 \, a^{2} b^{3} - 2 \, b^{5} - 2 i \, {\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 \, b\right) + {\left(2 \, {\left(a^{3} b^{2} - a b^{4} + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} e^{2 \, n - 1} \cos\left(d x^{n} + c\right) + {\left(2 \, a^{2} b^{3} - 2 \, b^{5} + 2 i \, {\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 \, b\right) + {\left(-2 i \, {\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}}} - 2 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + {\left(-2 i \, {\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}}} - 2 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \cos\left(d x^{n} + c\right)\right)} \log\left(\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + {\left(2 i \, {\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}}} + 2 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + {\left(2 i \, {\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}}} + 2 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \cos\left(d x^{n} + c\right)\right)} \log\left(\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + {\left(-2 i \, {\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}}} - 2 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + {\left(-2 i \, {\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}}} - 2 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \cos\left(d x^{n} + c\right)\right)} \log\left(-\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right) + {\left(2 i \, {\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}}} + 2 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + {\left(2 i \, {\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}}} + 2 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c e^{2 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \cos\left(d x^{n} + c\right)\right)} \log\left(-\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right)}{4 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} n \cos\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,"1/4*(2*(a^5 - 2*a^3*b^2 + a*b^4)*d^2*e^(2*n - 1)*x^(2*n)*cos(d*x^n + c) + 2*(a^4*b - 2*a^2*b^3 + b^5)*d^2*e^(2*n - 1)*x^(2*n) + 4*(a^3*b^2 - a*b^4)*d*e^(2*n - 1)*x^n*sin(d*x^n + c) - 2*((2*a^4*b - a^2*b^3)*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2)*cos(d*x^n + c) + (2*a^3*b^2 - 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) + b)*cos(d*x^n + c) + (2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) + 2*a)/a + 1) - 2*((2*a^4*b - a^2*b^3)*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2)*cos(d*x^n + c) + (2*a^3*b^2 - 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) + b)*cos(d*x^n + c) + (-2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) + 2*a)/a + 1) + 2*((2*a^4*b - a^2*b^3)*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2)*cos(d*x^n + c) + (2*a^3*b^2 - 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) - b)*cos(d*x^n + c) - (2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) - 2*a)/a + 1) + 2*((2*a^4*b - a^2*b^3)*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2)*cos(d*x^n + c) + (2*a^3*b^2 - 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) - b)*cos(d*x^n + c) - (-2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) - 2*a)/a + 1) + (2*(a^3*b^2 - a*b^4 - I*(2*a^4*b - a^2*b^3)*c*sqrt(-(a^2 - b^2)/a^2))*e^(2*n - 1)*cos(d*x^n + c) + (2*a^2*b^3 - 2*b^5 - 2*I*(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*b) + (2*(a^3*b^2 - a*b^4 + I*(2*a^4*b - a^2*b^3)*c*sqrt(-(a^2 - b^2)/a^2))*e^(2*n - 1)*cos(d*x^n + c) + (2*a^2*b^3 - 2*b^5 + 2*I*(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*b) + (2*(a^3*b^2 - a*b^4 - I*(2*a^4*b - a^2*b^3)*c*sqrt(-(a^2 - b^2)/a^2))*e^(2*n - 1)*cos(d*x^n + c) + (2*a^2*b^3 - 2*b^5 - 2*I*(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*b) + (2*(a^3*b^2 - a*b^4 + I*(2*a^4*b - a^2*b^3)*c*sqrt(-(a^2 - b^2)/a^2))*e^(2*n - 1)*cos(d*x^n + c) + (2*a^2*b^3 - 2*b^5 + 2*I*(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*b) + (-2*I*(2*a^3*b^2 - a*b^4)*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) - 2*I*(2*a^3*b^2 - a*b^4)*c*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2) + (-2*I*(2*a^4*b - a^2*b^3)*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) - 2*I*(2*a^4*b - a^2*b^3)*c*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2))*cos(d*x^n + c))*log(1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) + b)*cos(d*x^n + c) + (2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) + 2*a)/a) + (2*I*(2*a^3*b^2 - a*b^4)*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) + 2*I*(2*a^3*b^2 - a*b^4)*c*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2) + (2*I*(2*a^4*b - a^2*b^3)*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) + 2*I*(2*a^4*b - a^2*b^3)*c*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2))*cos(d*x^n + c))*log(1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) + b)*cos(d*x^n + c) + (-2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) + 2*a)/a) + (-2*I*(2*a^3*b^2 - a*b^4)*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) - 2*I*(2*a^3*b^2 - a*b^4)*c*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2) + (-2*I*(2*a^4*b - a^2*b^3)*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) - 2*I*(2*a^4*b - a^2*b^3)*c*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2))*cos(d*x^n + c))*log(-1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) - b)*cos(d*x^n + c) - (2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) - 2*a)/a) + (2*I*(2*a^3*b^2 - a*b^4)*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) + 2*I*(2*a^3*b^2 - a*b^4)*c*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2) + (2*I*(2*a^4*b - a^2*b^3)*d*e^(2*n - 1)*x^n*sqrt(-(a^2 - b^2)/a^2) + 2*I*(2*a^4*b - a^2*b^3)*c*e^(2*n - 1)*sqrt(-(a^2 - b^2)/a^2))*cos(d*x^n + c))*log(-1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) - b)*cos(d*x^n + c) - (-2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) - 2*a)/a))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d^2*n*cos(d*x^n + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^2*n)","B",0
83,1,3855,0,1.313925," ","integrate((e*x)^(-1+3*n)/(a+b*sec(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} \cos\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} \sin\left(d x^{n} + c\right) - {\left(12 \, {\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 \, {\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)} \cos\left(d x^{n} + c\right)\right)} {\rm Li}_2\left(-\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) - {\left(12 \, {\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 \, {\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)} \cos\left(d x^{n} + c\right)\right)} {\rm Li}_2\left(-\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a} + 1\right) + {\left(12 \, {\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 \, {\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)} \cos\left(d x^{n} + c\right)\right)} {\rm Li}_2\left(\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + {\left(12 \, {\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 \, {\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)} \cos\left(d x^{n} + c\right)\right)} {\rm Li}_2\left(\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a} + 1\right) + {\left({\left(6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1} \cos\left(d x^{n} + c\right) + {\left(6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 12 \, {\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 \, b\right) + {\left({\left(-6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1} \cos\left(d x^{n} + c\right) + {\left(-6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 12 \, {\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 \, b\right) + {\left({\left(6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1} \cos\left(d x^{n} + c\right) + {\left(6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 12 \, {\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 \, b\right) + {\left({\left(-6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1} \cos\left(d x^{n} + c\right) + {\left(-6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 12 \, {\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 \, b\right) + {\left(-6 i \, {\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}}} + 12 \, {\left(a^{2} b^{3} - b^{5}\right)} d e^{3 \, n - 1} x^{n} + {\left(6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 12 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1} + {\left(-6 i \, {\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}}} + 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} + {\left(6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1}\right)} \cos\left(d x^{n} + c\right)\right)} \log\left(\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + {\left(6 i \, {\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}}} + 12 \, {\left(a^{2} b^{3} - b^{5}\right)} d e^{3 \, n - 1} x^{n} + {\left(-6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 12 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1} + {\left(6 i \, {\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}}} + 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} + {\left(-6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1}\right)} \cos\left(d x^{n} + c\right)\right)} \log\left(\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) + 2 \, a}{2 \, a}\right) + {\left(-6 i \, {\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}}} + 12 \, {\left(a^{2} b^{3} - b^{5}\right)} d e^{3 \, n - 1} x^{n} + {\left(6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 12 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1} + {\left(-6 i \, {\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}}} + 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} + {\left(6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1}\right)} \cos\left(d x^{n} + c\right)\right)} \log\left(-\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right) + {\left(6 i \, {\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}}} + 12 \, {\left(a^{2} b^{3} - b^{5}\right)} d e^{3 \, n - 1} x^{n} + {\left(-6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 12 \, {\left(a^{2} b^{3} - b^{5}\right)} c\right)} e^{3 \, n - 1} + {\left(6 i \, {\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}}} + 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} d e^{3 \, n - 1} x^{n} + {\left(-6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c\right)} e^{3 \, n - 1}\right)} \cos\left(d x^{n} + c\right)\right)} \log\left(-\frac{2 \, {\left(a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right) - 2 \, a}{2 \, a}\right) + 2 \, {\left({\left(12 i \, a^{4} b - 6 i \, a^{2} b^{3}\right)} e^{3 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \cos\left(d x^{n} + c\right) + {\left(12 i \, a^{3} b^{2} - 6 i \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) - {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) + 2 \, {\left({\left(-12 i \, a^{4} b + 6 i \, a^{2} b^{3}\right)} e^{3 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \cos\left(d x^{n} + c\right) + {\left(-12 i \, a^{3} b^{2} + 6 i \, 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}}} + b\right)} \cos\left(d x^{n} + c\right) - {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) + 2 \, {\left({\left(12 i \, a^{4} b - 6 i \, a^{2} b^{3}\right)} e^{3 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \cos\left(d x^{n} + c\right) + {\left(12 i \, a^{3} b^{2} - 6 i \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) + {\left(2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 i \, b\right)} \sin\left(d x^{n} + c\right)}{2 \, a}\right) + 2 \, {\left({\left(-12 i \, a^{4} b + 6 i \, a^{2} b^{3}\right)} e^{3 \, n - 1} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \cos\left(d x^{n} + c\right) + {\left(-12 i \, a^{3} b^{2} + 6 i \, 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}}} - b\right)} \cos\left(d x^{n} + c\right) + {\left(-2 i \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 i \, 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 \cos\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)*cos(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)*sin(d*x^n + c) - (12*(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*(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))*cos(d*x^n + c))*dilog(-1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) + b)*cos(d*x^n + c) + (2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) + 2*a)/a + 1) - (12*(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*(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))*cos(d*x^n + c))*dilog(-1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) + b)*cos(d*x^n + c) + (-2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) + 2*a)/a + 1) + (12*(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*(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))*cos(d*x^n + c))*dilog(1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) - b)*cos(d*x^n + c) - (2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) - 2*a)/a + 1) + (12*(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*(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))*cos(d*x^n + c))*dilog(1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) - b)*cos(d*x^n + c) - (-2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) - 2*a)/a + 1) + ((6*I*(2*a^4*b - a^2*b^3)*c^2*sqrt(-(a^2 - b^2)/a^2) - 12*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1)*cos(d*x^n + c) + (6*I*(2*a^3*b^2 - a*b^4)*c^2*sqrt(-(a^2 - b^2)/a^2) - 12*(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*b) + ((-6*I*(2*a^4*b - a^2*b^3)*c^2*sqrt(-(a^2 - b^2)/a^2) - 12*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1)*cos(d*x^n + c) + (-6*I*(2*a^3*b^2 - a*b^4)*c^2*sqrt(-(a^2 - b^2)/a^2) - 12*(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*b) + ((6*I*(2*a^4*b - a^2*b^3)*c^2*sqrt(-(a^2 - b^2)/a^2) - 12*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1)*cos(d*x^n + c) + (6*I*(2*a^3*b^2 - a*b^4)*c^2*sqrt(-(a^2 - b^2)/a^2) - 12*(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*b) + ((-6*I*(2*a^4*b - a^2*b^3)*c^2*sqrt(-(a^2 - b^2)/a^2) - 12*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1)*cos(d*x^n + c) + (-6*I*(2*a^3*b^2 - a*b^4)*c^2*sqrt(-(a^2 - b^2)/a^2) - 12*(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*b) + (-6*I*(2*a^3*b^2 - a*b^4)*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) + 12*(a^2*b^3 - b^5)*d*e^(3*n - 1)*x^n + (6*I*(2*a^3*b^2 - a*b^4)*c^2*sqrt(-(a^2 - b^2)/a^2) + 12*(a^2*b^3 - b^5)*c)*e^(3*n - 1) + (-6*I*(2*a^4*b - a^2*b^3)*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) + 12*(a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n + (6*I*(2*a^4*b - a^2*b^3)*c^2*sqrt(-(a^2 - b^2)/a^2) + 12*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1))*cos(d*x^n + c))*log(1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) + b)*cos(d*x^n + c) + (2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) + 2*a)/a) + (6*I*(2*a^3*b^2 - a*b^4)*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) + 12*(a^2*b^3 - b^5)*d*e^(3*n - 1)*x^n + (-6*I*(2*a^3*b^2 - a*b^4)*c^2*sqrt(-(a^2 - b^2)/a^2) + 12*(a^2*b^3 - b^5)*c)*e^(3*n - 1) + (6*I*(2*a^4*b - a^2*b^3)*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) + 12*(a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n + (-6*I*(2*a^4*b - a^2*b^3)*c^2*sqrt(-(a^2 - b^2)/a^2) + 12*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1))*cos(d*x^n + c))*log(1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) + b)*cos(d*x^n + c) + (-2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) + 2*a)/a) + (-6*I*(2*a^3*b^2 - a*b^4)*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) + 12*(a^2*b^3 - b^5)*d*e^(3*n - 1)*x^n + (6*I*(2*a^3*b^2 - a*b^4)*c^2*sqrt(-(a^2 - b^2)/a^2) + 12*(a^2*b^3 - b^5)*c)*e^(3*n - 1) + (-6*I*(2*a^4*b - a^2*b^3)*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) + 12*(a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n + (6*I*(2*a^4*b - a^2*b^3)*c^2*sqrt(-(a^2 - b^2)/a^2) + 12*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1))*cos(d*x^n + c))*log(-1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) - b)*cos(d*x^n + c) - (2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c) - 2*a)/a) + (6*I*(2*a^3*b^2 - a*b^4)*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) + 12*(a^2*b^3 - b^5)*d*e^(3*n - 1)*x^n + (-6*I*(2*a^3*b^2 - a*b^4)*c^2*sqrt(-(a^2 - b^2)/a^2) + 12*(a^2*b^3 - b^5)*c)*e^(3*n - 1) + (6*I*(2*a^4*b - a^2*b^3)*d^2*e^(3*n - 1)*x^(2*n)*sqrt(-(a^2 - b^2)/a^2) + 12*(a^3*b^2 - a*b^4)*d*e^(3*n - 1)*x^n + (-6*I*(2*a^4*b - a^2*b^3)*c^2*sqrt(-(a^2 - b^2)/a^2) + 12*(a^3*b^2 - a*b^4)*c)*e^(3*n - 1))*cos(d*x^n + c))*log(-1/2*(2*(a*sqrt(-(a^2 - b^2)/a^2) - b)*cos(d*x^n + c) - (-2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c) - 2*a)/a) + 2*((12*I*a^4*b - 6*I*a^2*b^3)*e^(3*n - 1)*sqrt(-(a^2 - b^2)/a^2)*cos(d*x^n + c) + (12*I*a^3*b^2 - 6*I*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) + b)*cos(d*x^n + c) - (2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c))/a) + 2*((-12*I*a^4*b + 6*I*a^2*b^3)*e^(3*n - 1)*sqrt(-(a^2 - b^2)/a^2)*cos(d*x^n + c) + (-12*I*a^3*b^2 + 6*I*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) + b)*cos(d*x^n + c) - (-2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c))/a) + 2*((12*I*a^4*b - 6*I*a^2*b^3)*e^(3*n - 1)*sqrt(-(a^2 - b^2)/a^2)*cos(d*x^n + c) + (12*I*a^3*b^2 - 6*I*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) - b)*cos(d*x^n + c) + (2*I*a*sqrt(-(a^2 - b^2)/a^2) - 2*I*b)*sin(d*x^n + c))/a) + 2*((-12*I*a^4*b + 6*I*a^2*b^3)*e^(3*n - 1)*sqrt(-(a^2 - b^2)/a^2)*cos(d*x^n + c) + (-12*I*a^3*b^2 + 6*I*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) - b)*cos(d*x^n + c) + (-2*I*a*sqrt(-(a^2 - b^2)/a^2) + 2*I*b)*sin(d*x^n + c))/a))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d^3*n*cos(d*x^n + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^3*n)","C",0
