1,1,465,153,0.145000," ","int(x/(a+b*sin(x)^2),x)","-\frac{i x \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 \sqrt{a \left(a +b \right)}}-\frac{x^{2}}{2 \sqrt{a \left(a +b \right)}}-\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{4 \sqrt{a \left(a +b \right)}}+\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) x}{2 \sqrt{a \left(a +b \right)}+2 a +b}+\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) a x}{\sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) b x}{2 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{x^{2}}{2 \sqrt{a \left(a +b \right)}+2 a +b}+\frac{a \,x^{2}}{\sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{b \,x^{2}}{2 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{4 \sqrt{a \left(a +b \right)}+4 a +2 b}+\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) a}{2 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) b}{4 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}"," ",0,"-1/2*I/(a*(a+b))^(1/2)*x*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)+2*a+b))-1/2/(a*(a+b))^(1/2)*x^2-1/4/(a*(a+b))^(1/2)*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)+2*a+b))+I/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*x+I/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*a*x+1/2*I/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*b*x+1/(2*(a*(a+b))^(1/2)+2*a+b)*x^2+1/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*a*x^2+1/2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*b*x^2+1/2/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))+1/2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*a+1/4/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*b","B"
2,1,660,233,0.201000," ","int(x^2/(a+b*sin(x)^2),x)","\frac{x \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 \sqrt{a \left(a +b \right)}+2 a +b}+\frac{i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{4 \sqrt{a \left(a +b \right)}+4 a +2 b}+\frac{a x \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{\sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i x^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 \sqrt{a \left(a +b \right)}+2 a +b}+\frac{2 x^{3}}{3 \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{4 \sqrt{a \left(a +b \right)}}+\frac{b \,x^{3}}{3 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i b \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{4 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{x \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 \sqrt{a \left(a +b \right)}}+\frac{i b \,x^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{x^{3}}{3 \sqrt{a \left(a +b \right)}}+\frac{i a \,x^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{\sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{b x \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i a \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{2 a \,x^{3}}{3 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{i x^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 \sqrt{a \left(a +b \right)}}"," ",0,"1/(2*(a*(a+b))^(1/2)+2*a+b)*x*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))+I/(2*(a*(a+b))^(1/2)+2*a+b)*x^2*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))+1/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*a*x*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))-1/4*I/(a*(a+b))^(1/2)*polylog(3,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)+2*a+b))+2/3/(2*(a*(a+b))^(1/2)+2*a+b)*x^3+1/2*I/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(3,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))+1/3/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*b*x^3+1/2*I/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*b*x^2*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))-1/2/(a*(a+b))^(1/2)*x*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)+2*a+b))+I/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*a*x^2*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))-1/3/(a*(a+b))^(1/2)*x^3+1/2*I/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*a*polylog(3,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))+1/2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*b*x*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))+1/4*I/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*b*polylog(3,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))+2/3/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*a*x^3-1/2*I/(a*(a+b))^(1/2)*x^2*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)+2*a+b))","B"
3,1,853,311,0.139000," ","int(x^3/(a+b*sin(x)^2),x)","-\frac{3 i x \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{4 \sqrt{a \left(a +b \right)}}-\frac{x^{4}}{4 \sqrt{a \left(a +b \right)}}-\frac{3 x^{2} \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{4 \sqrt{a \left(a +b \right)}}-\frac{i x^{3} \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 \sqrt{a \left(a +b \right)}}+\frac{3 \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{8 \sqrt{a \left(a +b \right)}}+\frac{3 i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) b x}{4 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) b \,x^{3}}{2 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{3 i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) x}{2 \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{x^{4}}{4 \sqrt{a \left(a +b \right)}+4 a +2 b}+\frac{a \,x^{4}}{2 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{b \,x^{4}}{4 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{3 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) x^{2}}{2 \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{3 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) a \,x^{2}}{2 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{3 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) b \,x^{2}}{4 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) x^{3}}{2 \sqrt{a \left(a +b \right)}+2 a +b}+\frac{3 i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) a x}{2 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) a \,x^{3}}{\sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{3 \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{4 \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{3 \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) a}{4 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{3 \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) b}{8 \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}"," ",0,"-1/2*I/(a*(a+b))^(1/2)*x^3*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)+2*a+b))-1/4/(a*(a+b))^(1/2)*x^4-3/4/(a*(a+b))^(1/2)*x^2*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)+2*a+b))+3/2*I/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(3,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*x+3/8/(a*(a+b))^(1/2)*polylog(4,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)+2*a+b))+1/2*I/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*b*x^3+I/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*x^3+3/4*I/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(3,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*b*x+1/2/(2*(a*(a+b))^(1/2)+2*a+b)*x^4+1/2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*a*x^4+1/4/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*b*x^4+3/2/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*x^2+3/2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*a*x^2+3/4/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*b*x^2-3/4*I/(a*(a+b))^(1/2)*x*polylog(3,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)+2*a+b))+3/2*I/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(3,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*a*x+I/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*a*x^3-3/4/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(4,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))-3/4/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(4,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*a-3/8/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(4,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)+2*a+b))*b","B"
4,1,2169,275,0.343000," ","int(x/(a+b*sin(d*x+c)^2)^2,x)","\frac{x^{2}}{\left(a +b \right) \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{x^{2}}{2 \left(a +b \right) \sqrt{a \left(a +b \right)}}+\frac{b^{2} \polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{8 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{i x \left(2 a \,{\mathrm e}^{2 i \left(d x +c \right)}+b \,{\mathrm e}^{2 i \left(d x +c \right)}-b \right)}{a \left(a +b \right) d \left(-b \,{\mathrm e}^{4 i \left(d x +c \right)}+4 a \,{\mathrm e}^{2 i \left(d x +c \right)}+2 b \,{\mathrm e}^{2 i \left(d x +c \right)}-b \right)}+\frac{b \,c^{2}}{d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{b^{2} x^{2}}{4 \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{b \,c^{2}}{4 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}}+\frac{b \,c^{2}}{2 d^{2} \left(a +b \right) a \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{a \,c^{2}}{d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{c^{2}}{d^{2} \left(a +b \right) \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{c^{2}}{2 d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}}+\frac{b \,x^{2}}{\left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{c x}{d \left(a +b \right) \sqrt{a \left(a +b \right)}}+\frac{2 c x}{d \left(a +b \right) \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{a \,x^{2}}{\left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{b \,x^{2}}{4 \left(a +b \right) a \sqrt{a \left(a +b \right)}}+\frac{b \,x^{2}}{2 \left(a +b \right) a \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) c}{d^{2} \left(a +b \right) \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right) x}{2 d \left(a +b \right) \sqrt{a \left(a +b \right)}}+\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) x}{d \left(a +b \right) \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right) c}{2 d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{b \polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{8 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}}+\frac{b \polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{4 d^{2} \left(a +b \right) a \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) b}{2 d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{a \polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{i c \arctanh \left(\frac{-2 b \,{\mathrm e}^{2 i \left(d x +c \right)}+4 a +2 b}{4 \sqrt{a^{2}+a b}}\right)}{d^{2} \left(a +b \right) \sqrt{a^{2}+a b}}-\frac{\ln \left(-b \,{\mathrm e}^{4 i \left(d x +c \right)}+4 a \,{\mathrm e}^{2 i \left(d x +c \right)}+2 b \,{\mathrm e}^{2 i \left(d x +c \right)}-b \right)}{4 d^{2} \left(a +b \right) a}+\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} \left(a +b \right) a}-\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{4 d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}}+\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right)}{2 d^{2} \left(a +b \right) \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{b c x}{d \left(a +b \right) a \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{b^{2} c^{2}}{4 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{b c x}{2 d \left(a +b \right) a \sqrt{a \left(a +b \right)}}+\frac{2 a c x}{d \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{2 b c x}{d \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{i b c \arctanh \left(\frac{-2 b \,{\mathrm e}^{2 i \left(d x +c \right)}+4 a +2 b}{4 \sqrt{a^{2}+a b}}\right)}{2 d^{2} \left(a +b \right) a \sqrt{a^{2}+a b}}+\frac{i b \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) c}{2 d^{2} \left(a +b \right) a \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{i b \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right) c}{4 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}}+\frac{i a \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) c}{d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i b \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) x}{2 d \left(a +b \right) a \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}-\frac{i b \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}+2 a +b}\right) x}{4 d \left(a +b \right) a \sqrt{a \left(a +b \right)}}+\frac{i a \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) x}{d \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) b x}{d \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) b c}{d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{b^{2} c x}{2 d \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i b^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) c}{4 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}+\frac{i b^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}+2 a +b}\right) x}{4 d \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(2 \sqrt{a \left(a +b \right)}+2 a +b \right)}"," ",0,"1/(a+b)/(2*(a*(a+b))^(1/2)+2*a+b)*x^2-1/2/(a+b)/(a*(a+b))^(1/2)*x^2-1/8/d^2/(a+b)/a*b/(a*(a+b))^(1/2)*polylog(2,b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)+2*a+b))+1/4/d^2/(a+b)/a*b/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))+1/2/d^2/(a+b)/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*b+1/d^2/(a+b)/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*b*c^2+1/4/(a+b)/a*b^2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*x^2+1/2/d^2/(a+b)*a/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))-1/4/d^2/(a+b)/a*b/(a*(a+b))^(1/2)*c^2+1/2/d^2/(a+b)/a*b/(2*(a*(a+b))^(1/2)+2*a+b)*c^2+1/d^2/(a+b)*a/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*c^2+1/d^2/(a+b)/(2*(a*(a+b))^(1/2)+2*a+b)*c^2-1/2/d^2/(a+b)/(a*(a+b))^(1/2)*c^2+1/(a+b)/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*b*x^2-1/d/(a+b)/(a*(a+b))^(1/2)*c*x+2/d/(a+b)/(2*(a*(a+b))^(1/2)+2*a+b)*c*x+1/(a+b)*a/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*x^2-1/4/(a+b)/a*b/(a*(a+b))^(1/2)*x^2+1/2/(a+b)/a*b/(2*(a*(a+b))^(1/2)+2*a+b)*x^2+I/d^2/(a+b)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*c-I/d^2/(a+b)*c/(a^2+a*b)^(1/2)*arctanh(1/4*(-2*b*exp(2*I*(d*x+c))+4*a+2*b)/(a^2+a*b)^(1/2))-1/2*I/d/(a+b)/(a*(a+b))^(1/2)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)+2*a+b))*x+I/d/(a+b)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*x-1/2*I/d^2/(a+b)/(a*(a+b))^(1/2)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)+2*a+b))*c-1/4/d^2/(a+b)/(a*(a+b))^(1/2)*polylog(2,b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)+2*a+b))+1/2/d^2/(a+b)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))-1/4/d^2/(a+b)/a*ln(-b*exp(4*I*(d*x+c))+4*a*exp(2*I*(d*x+c))+2*b*exp(2*I*(d*x+c))-b)+1/d^2/(a+b)/a*ln(exp(I*(d*x+c)))-I*x*(2*a*exp(2*I*(d*x+c))+b*exp(2*I*(d*x+c))-b)/a/(a+b)/d/(-b*exp(4*I*(d*x+c))+4*a*exp(2*I*(d*x+c))+2*b*exp(2*I*(d*x+c))-b)+1/8/d^2/(a+b)/a*b^2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*polylog(2,b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))+1/d/(a+b)/a*b/(2*(a*(a+b))^(1/2)+2*a+b)*c*x+1/4/d^2/(a+b)/a*b^2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*c^2-1/2/d/(a+b)/a*b/(a*(a+b))^(1/2)*c*x+2/d/(a+b)*a/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*c*x+2/d/(a+b)/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*b*c*x+1/2/d/(a+b)/a*b^2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*c*x+1/2*I/d^2/(a+b)/a*b/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*c-1/4*I/d^2/(a+b)/a*b/(a*(a+b))^(1/2)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)+2*a+b))*c-1/2*I/d^2/(a+b)/a*b*c/(a^2+a*b)^(1/2)*arctanh(1/4*(-2*b*exp(2*I*(d*x+c))+4*a+2*b)/(a^2+a*b)^(1/2))+I/d^2/(a+b)*a/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*c+1/2*I/d/(a+b)/a*b/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*x-1/4*I/d/(a+b)/a*b/(a*(a+b))^(1/2)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)+2*a+b))*x+I/d/(a+b)*a/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*x+I/d/(a+b)/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*b*x+I/d^2/(a+b)/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*b*c+1/4*I/d^2/(a+b)/a*b^2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*c+1/4*I/d/(a+b)/a*b^2/(a*(a+b))^(1/2)/(2*(a*(a+b))^(1/2)+2*a+b)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)+2*a+b))*x","B"
5,1,75,18,0.098000," ","int(x*(sin(x)^2)^(1/2),x)","-\frac{i \sqrt{-\left({\mathrm e}^{2 i x}-1\right)^{2} {\mathrm e}^{-2 i x}}\, {\mathrm e}^{2 i x} \left(x +i\right)}{2 \left({\mathrm e}^{2 i x}-1\right)}-\frac{i \sqrt{-\left({\mathrm e}^{2 i x}-1\right)^{2} {\mathrm e}^{-2 i x}}\, \left(x -i\right)}{2 \left({\mathrm e}^{2 i x}-1\right)}"," ",0,"-1/2*I*(-(exp(2*I*x)-1)^2*exp(-2*I*x))^(1/2)/(exp(2*I*x)-1)*exp(2*I*x)*(x+I)-1/2*I*(-(exp(2*I*x)-1)^2*exp(-2*I*x))^(1/2)/(exp(2*I*x)-1)*(x-I)","C"
6,1,501,153,0.091000," ","int(x/(a+b*cos(x)^2),x)","-\frac{i x \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 \sqrt{a \left(a +b \right)}}-\frac{x^{2}}{2 \sqrt{a \left(a +b \right)}}-\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{4 \sqrt{a \left(a +b \right)}}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) x}{-2 \sqrt{a \left(a +b \right)}-2 a -b}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) a x}{\sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) b x}{2 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{x^{2}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}-\frac{a \,x^{2}}{\sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b \,x^{2}}{2 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) a}{2 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) b}{4 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}"," ",0,"-1/2*I/(a*(a+b))^(1/2)*x*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)-2*a-b))-1/2/(a*(a+b))^(1/2)*x^2-1/4/(a*(a+b))^(1/2)*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)-2*a-b))-I/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*x-I/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*a*x-1/2*I/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*b*x-1/(-2*(a*(a+b))^(1/2)-2*a-b)*x^2-1/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*a*x^2-1/2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*b*x^2-1/2/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))-1/2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*a-1/4/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*b","B"
7,1,710,235,0.094000," ","int(x^2/(a+b*cos(x)^2),x)","-\frac{x \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{-2 \sqrt{a \left(a +b \right)}-2 a -b}-\frac{i b \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{4 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{x \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 \sqrt{a \left(a +b \right)}}-\frac{i x^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{-2 \sqrt{a \left(a +b \right)}-2 a -b}-\frac{a x \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{\sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i a \,x^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{\sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{2 x^{3}}{3 \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i a \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b \,x^{3}}{3 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b x \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i x^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 \sqrt{a \left(a +b \right)}}-\frac{2 a \,x^{3}}{3 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i b \,x^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{x^{3}}{3 \sqrt{a \left(a +b \right)}}-\frac{i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{4 \sqrt{a \left(a +b \right)}}"," ",0,"-1/(-2*(a*(a+b))^(1/2)-2*a-b)*x*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))-1/2*I/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*a*polylog(3,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))-1/2/(a*(a+b))^(1/2)*x*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)-2*a-b))-1/4*I/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*b*polylog(3,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))-1/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*a*x*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))-1/2*I/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(3,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))-2/3/(-2*(a*(a+b))^(1/2)-2*a-b)*x^3-I/(-2*(a*(a+b))^(1/2)-2*a-b)*x^2*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))-1/3/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*b*x^3-I/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*a*x^2*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))-1/2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*b*x*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))-1/2*I/(a*(a+b))^(1/2)*x^2*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)-2*a-b))-2/3/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*a*x^3-1/2*I/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*b*x^2*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))-1/3/(a*(a+b))^(1/2)*x^3-1/4*I/(a*(a+b))^(1/2)*polylog(3,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)-2*a-b))","B"
8,1,915,315,0.099000," ","int(x^3/(a+b*cos(x)^2),x)","-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) a \,x^{3}}{\sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{x^{4}}{4 \sqrt{a \left(a +b \right)}}-\frac{3 i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) b x}{4 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{3 x^{2} \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{4 \sqrt{a \left(a +b \right)}}+\frac{3 \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{8 \sqrt{a \left(a +b \right)}}-\frac{3 i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) x}{2 \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) b \,x^{3}}{2 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{3 i x \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{4 \sqrt{a \left(a +b \right)}}-\frac{x^{4}}{2 \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{a \,x^{4}}{2 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b \,x^{4}}{4 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{3 i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) a x}{2 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) x^{3}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}-\frac{i x^{3} \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 \sqrt{a \left(a +b \right)}}-\frac{3 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) x^{2}}{2 \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{3 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) a \,x^{2}}{2 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{3 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) b \,x^{2}}{4 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}+\frac{3 \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{4 \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}+\frac{3 \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) a}{4 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}+\frac{3 \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) b}{8 \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}"," ",0,"-I/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*a*x^3-1/4/(a*(a+b))^(1/2)*x^4-3/4*I/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(3,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*b*x-3/4/(a*(a+b))^(1/2)*x^2*polylog(2,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)-2*a-b))+3/8/(a*(a+b))^(1/2)*polylog(4,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)-2*a-b))-1/2*I/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*b*x^3-3/2*I/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(3,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*x-I/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*x^3-1/2/(-2*(a*(a+b))^(1/2)-2*a-b)*x^4-1/2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*a*x^4-1/4/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*b*x^4-3/4*I/(a*(a+b))^(1/2)*x*polylog(3,b*exp(2*I*x)/(2*(a*(a+b))^(1/2)-2*a-b))-1/2*I/(a*(a+b))^(1/2)*x^3*ln(1-b*exp(2*I*x)/(2*(a*(a+b))^(1/2)-2*a-b))-3/2*I/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(3,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*a*x-3/2/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*x^2-3/2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*a*x^2-3/4/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*b*x^2+3/4/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(4,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))+3/4/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(4,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*a+3/8/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(4,b*exp(2*I*x)/(-2*(a*(a+b))^(1/2)-2*a-b))*b","B"
9,1,2270,273,0.279000," ","int(x/(a+b*cos(d*x+c)^2)^2,x)","-\frac{x^{2}}{2 \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{i b^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) c}{4 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i b^{2} \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) x}{4 d \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b \,c^{2}}{4 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}}-\frac{x^{2}}{\left(a +b \right) \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{\ln \left(b \,{\mathrm e}^{4 i \left(d x +c \right)}+4 a \,{\mathrm e}^{2 i \left(d x +c \right)}+2 b \,{\mathrm e}^{2 i \left(d x +c \right)}+b \right)}{4 d^{2} \left(a +b \right) a}-\frac{c^{2}}{d^{2} \left(a +b \right) \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{4 d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 d^{2} \left(a +b \right) \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{c^{2}}{2 d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{b \,x^{2}}{2 \left(a +b \right) a \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{a \,x^{2}}{\left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{2 c x}{d \left(a +b \right) \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b \,x^{2}}{\left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{c x}{d \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{b \,x^{2}}{4 \left(a +b \right) a \sqrt{a \left(a +b \right)}}-\frac{2 b c x}{d \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b^{2} c^{2}}{4 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b c x}{d \left(a +b \right) a \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}+\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} \left(a +b \right) a}-\frac{2 a c x}{d \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b c x}{2 d \left(a +b \right) a \sqrt{a \left(a +b \right)}}-\frac{i b c \arctanh \left(\frac{2 b \,{\mathrm e}^{2 i \left(d x +c \right)}+4 a +2 b}{4 \sqrt{a^{2}+a b}}\right)}{2 d^{2} \left(a +b \right) a \sqrt{a^{2}+a b}}-\frac{i b \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right) c}{4 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}}-\frac{i b \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) c}{2 d^{2} \left(a +b \right) a \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i b \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right) x}{4 d \left(a +b \right) a \sqrt{a \left(a +b \right)}}-\frac{i b \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) x}{2 d \left(a +b \right) a \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i a \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) x}{d \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i a \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) c}{d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) b c}{d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) b x}{d \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b^{2} c x}{2 d \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i x \left(2 a \,{\mathrm e}^{2 i \left(d x +c \right)}+b \,{\mathrm e}^{2 i \left(d x +c \right)}+b \right)}{a \left(a +b \right) d \left(b \,{\mathrm e}^{4 i \left(d x +c \right)}+4 a \,{\mathrm e}^{2 i \left(d x +c \right)}+2 b \,{\mathrm e}^{2 i \left(d x +c \right)}+b \right)}-\frac{b^{2} \polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{8 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) x}{d \left(a +b \right) \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right) c}{2 d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right) x}{2 d \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{a \polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{2 d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b \polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{8 d^{2} \left(a +b \right) a \sqrt{a \left(a +b \right)}}-\frac{b \polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right)}{4 d^{2} \left(a +b \right) a \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{\polylog \left(2, \frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) b}{2 d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i c \arctanh \left(\frac{2 b \,{\mathrm e}^{2 i \left(d x +c \right)}+4 a +2 b}{4 \sqrt{a^{2}+a b}}\right)}{d^{2} \left(a +b \right) \sqrt{a^{2}+a b}}-\frac{a \,c^{2}}{d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b \,c^{2}}{2 d^{2} \left(a +b \right) a \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b^{2} x^{2}}{4 \left(a +b \right) a \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{b \,c^{2}}{d^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}\, \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}-\frac{i \ln \left(1-\frac{b \,{\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a \left(a +b \right)}-2 a -b}\right) c}{d^{2} \left(a +b \right) \left(-2 \sqrt{a \left(a +b \right)}-2 a -b \right)}"," ",0,"-1/2/(a+b)/(a*(a+b))^(1/2)*x^2-1/4*I/d^2/(a+b)/a*b^2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*c-1/4*I/d/(a+b)/a*b^2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*x-1/4/d^2/(a+b)/a*b/(a*(a+b))^(1/2)*c^2-1/(a+b)/(-2*(a*(a+b))^(1/2)-2*a-b)*x^2-1/d^2/(a+b)/(-2*(a*(a+b))^(1/2)-2*a-b)*c^2-1/2/d^2/(a+b)/(a*(a+b))^(1/2)*c^2-1/2/(a+b)/a*b/(-2*(a*(a+b))^(1/2)-2*a-b)*x^2-1/(a+b)*a/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*x^2-2/d/(a+b)/(-2*(a*(a+b))^(1/2)-2*a-b)*c*x-1/(a+b)/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*b*x^2-1/d/(a+b)/(a*(a+b))^(1/2)*c*x-1/4/(a+b)/a*b/(a*(a+b))^(1/2)*x^2-2/d/(a+b)/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*b*c*x-1/4/d^2/(a+b)/a*b^2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*c^2-1/d/(a+b)/a*b/(-2*(a*(a+b))^(1/2)-2*a-b)*c*x+1/d^2/(a+b)/a*ln(exp(I*(d*x+c)))-2/d/(a+b)*a/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*c*x-1/8/d^2/(a+b)/a*b^2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))-1/2/d/(a+b)/a*b/(a*(a+b))^(1/2)*c*x-I*x*(2*a*exp(2*I*(d*x+c))+b*exp(2*I*(d*x+c))+b)/a/(a+b)/d/(b*exp(4*I*(d*x+c))+4*a*exp(2*I*(d*x+c))+2*b*exp(2*I*(d*x+c))+b)-1/4*I/d^2/(a+b)/a*b/(a*(a+b))^(1/2)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)-2*a-b))*c-1/2*I/d^2/(a+b)/a*b/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*c-1/4*I/d/(a+b)/a*b/(a*(a+b))^(1/2)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)-2*a-b))*x-1/2*I/d/(a+b)/a*b/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*x-1/2*I/d^2/(a+b)/a*b*c/(a^2+a*b)^(1/2)*arctanh(1/4*(2*b*exp(2*I*(d*x+c))+4*a+2*b)/(a^2+a*b)^(1/2))-I/d/(a+b)*a/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*x-I/d^2/(a+b)*a/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*c-I/d^2/(a+b)/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*b*c-I/d/(a+b)/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*b*x-1/2/d/(a+b)/a*b^2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*c*x-1/4/d^2/(a+b)/a*ln(b*exp(4*I*(d*x+c))+4*a*exp(2*I*(d*x+c))+2*b*exp(2*I*(d*x+c))+b)-1/4/d^2/(a+b)/(a*(a+b))^(1/2)*polylog(2,b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)-2*a-b))-1/2/d^2/(a+b)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))-1/d^2/(a+b)*a/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*c^2-I/d^2/(a+b)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*c-I/d/(a+b)/(-2*(a*(a+b))^(1/2)-2*a-b)*ln(1-b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*x-1/2/d^2/(a+b)*a/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))-1/8/d^2/(a+b)/a*b/(a*(a+b))^(1/2)*polylog(2,b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)-2*a-b))-1/4/d^2/(a+b)/a*b/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))-1/2/d^2/(a+b)/a*b/(-2*(a*(a+b))^(1/2)-2*a-b)*c^2-1/2/d^2/(a+b)/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*polylog(2,b*exp(2*I*(d*x+c))/(-2*(a*(a+b))^(1/2)-2*a-b))*b-1/4/(a+b)/a*b^2/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*x^2-1/d^2/(a+b)/(a*(a+b))^(1/2)/(-2*(a*(a+b))^(1/2)-2*a-b)*b*c^2-1/2*I/d^2/(a+b)/(a*(a+b))^(1/2)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)-2*a-b))*c-1/2*I/d/(a+b)/(a*(a+b))^(1/2)*ln(1-b*exp(2*I*(d*x+c))/(2*(a*(a+b))^(1/2)-2*a-b))*x-I/d^2/(a+b)*c/(a^2+a*b)^(1/2)*arctanh(1/4*(2*b*exp(2*I*(d*x+c))+4*a+2*b)/(a^2+a*b)^(1/2))","B"