1,1,283,172,0.031000," ","int((e*x+d)^4*(a+b*arctan(c*x)),x)","\frac{a \,e^{4} x^{5}}{5}+a \,e^{3} x^{4} d +2 a \,e^{2} x^{3} d^{2}+2 a e \,x^{2} d^{3}+a x \,d^{4}+\frac{a \,d^{5}}{5 e}+\frac{b \,e^{4} \arctan \left(c x \right) x^{5}}{5}+b \,e^{3} \arctan \left(c x \right) x^{4} d +2 b \,e^{2} \arctan \left(c x \right) x^{3} d^{2}+2 b e \arctan \left(c x \right) x^{2} d^{3}+b \arctan \left(c x \right) x \,d^{4}-\frac{b \,e^{4} x^{4}}{20 c}-\frac{b d \,e^{3} x^{3}}{3 c}-\frac{b \,e^{2} x^{2} d^{2}}{c}-\frac{2 b e \,d^{3} x}{c}+\frac{b \,e^{4} x^{2}}{10 c^{3}}+\frac{b \,e^{3} d x}{c^{3}}-\frac{b \ln \left(c^{2} x^{2}+1\right) d^{4}}{2 c}+\frac{b \,e^{2} \ln \left(c^{2} x^{2}+1\right) d^{2}}{c^{3}}-\frac{b \,e^{4} \ln \left(c^{2} x^{2}+1\right)}{10 c^{5}}+\frac{2 b e \arctan \left(c x \right) d^{3}}{c^{2}}-\frac{b \,e^{3} \arctan \left(c x \right) d}{c^{4}}"," ",0,"1/5*a*e^4*x^5+a*e^3*x^4*d+2*a*e^2*x^3*d^2+2*a*e*x^2*d^3+a*x*d^4+1/5*a/e*d^5+1/5*b*e^4*arctan(c*x)*x^5+b*e^3*arctan(c*x)*x^4*d+2*b*e^2*arctan(c*x)*x^3*d^2+2*b*e*arctan(c*x)*x^2*d^3+b*arctan(c*x)*x*d^4-1/20*b*e^4*x^4/c-1/3*b*d*e^3*x^3/c-1/c*b*e^2*x^2*d^2-2*b/c*e*d^3*x+1/10/c^3*b*e^4*x^2+b/c^3*e^3*d*x-1/2/c*b*ln(c^2*x^2+1)*d^4+1/c^3*b*e^2*ln(c^2*x^2+1)*d^2-1/10/c^5*b*e^4*ln(c^2*x^2+1)+2/c^2*b*e*arctan(c*x)*d^3-1/c^4*b*e^3*arctan(c*x)*d","A"
2,1,207,132,0.034000," ","int((e*x+d)^3*(a+b*arctan(c*x)),x)","\frac{a \,e^{3} x^{4}}{4}+a \,e^{2} x^{3} d +\frac{3 a e \,x^{2} d^{2}}{2}+a x \,d^{3}+\frac{a \,d^{4}}{4 e}+\frac{b \,e^{3} \arctan \left(c x \right) x^{4}}{4}+b \,e^{2} \arctan \left(c x \right) d \,x^{3}+\frac{3 b e \arctan \left(c x \right) x^{2} d^{2}}{2}+b \arctan \left(c x \right) d^{3} x -\frac{b \,e^{3} x^{3}}{12 c}-\frac{b d \,e^{2} x^{2}}{2 c}-\frac{3 b e \,d^{2} x}{2 c}+\frac{b \,e^{3} x}{4 c^{3}}-\frac{b \ln \left(c^{2} x^{2}+1\right) d^{3}}{2 c}+\frac{b \,e^{2} \ln \left(c^{2} x^{2}+1\right) d}{2 c^{3}}+\frac{3 b e \arctan \left(c x \right) d^{2}}{2 c^{2}}-\frac{b \,e^{3} \arctan \left(c x \right)}{4 c^{4}}"," ",0,"1/4*a*e^3*x^4+a*e^2*x^3*d+3/2*a*e*x^2*d^2+a*x*d^3+1/4*a/e*d^4+1/4*b*e^3*arctan(c*x)*x^4+b*e^2*arctan(c*x)*d*x^3+3/2*b*e*arctan(c*x)*x^2*d^2+b*arctan(c*x)*d^3*x-1/12*b*e^3*x^3/c-1/2*b*d*e^2*x^2/c-3/2*b/c*e*d^2*x+1/4*b/c^3*e^3*x-1/2/c*b*ln(c^2*x^2+1)*d^3+1/2/c^3*b*e^2*ln(c^2*x^2+1)*d+3/2/c^2*b*e*arctan(c*x)*d^2-1/4/c^4*b*e^3*arctan(c*x)","A"
3,1,137,95,0.033000," ","int((e*x+d)^2*(a+b*arctan(c*x)),x)","\frac{a \,e^{2} x^{3}}{3}+a e d \,x^{2}+a x \,d^{2}+\frac{a \,d^{3}}{3 e}+\frac{b \,e^{2} \arctan \left(c x \right) x^{3}}{3}+b e \arctan \left(c x \right) d \,x^{2}+b \arctan \left(c x \right) d^{2} x -\frac{b \,e^{2} x^{2}}{6 c}-\frac{b d e x}{c}-\frac{b \ln \left(c^{2} x^{2}+1\right) d^{2}}{2 c}+\frac{b \,e^{2} \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}+\frac{b e \arctan \left(c x \right) d}{c^{2}}"," ",0,"1/3*a*e^2*x^3+a*e*d*x^2+a*x*d^2+1/3*a/e*d^3+1/3*b*e^2*arctan(c*x)*x^3+b*e*arctan(c*x)*d*x^2+b*arctan(c*x)*d^2*x-1/6*b*e^2*x^2/c-b*d*e*x/c-1/2/c*b*ln(c^2*x^2+1)*d^2+1/6/c^3*b*e^2*ln(c^2*x^2+1)+1/c^2*b*e*arctan(c*x)*d","A"
4,1,68,68,0.033000," ","int((e*x+d)*(a+b*arctan(c*x)),x)","\frac{a \,x^{2} e}{2}+a d x +\frac{b \arctan \left(c x \right) x^{2} e}{2}+b \arctan \left(c x \right) x d -\frac{b e x}{2 c}-\frac{b d \ln \left(c^{2} x^{2}+1\right)}{2 c}+\frac{b e \arctan \left(c x \right)}{2 c^{2}}"," ",0,"1/2*a*x^2*e+a*d*x+1/2*b*arctan(c*x)*x^2*e+b*arctan(c*x)*x*d-1/2*b*e*x/c-1/2*b*d*ln(c^2*x^2+1)/c+1/2/c^2*b*e*arctan(c*x)","A"
5,1,168,126,0.061000," ","int((a+b*arctan(c*x))/(e*x+d),x)","\frac{a \ln \left(c e x +d c \right)}{e}+\frac{b \ln \left(c e x +d c \right) \arctan \left(c x \right)}{e}+\frac{i b \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e}-\frac{i b \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e}+\frac{i b \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e}-\frac{i b \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e}"," ",0,"a*ln(c*e*x+c*d)/e+b*ln(c*e*x+c*d)/e*arctan(c*x)+1/2*I*b*ln(c*e*x+c*d)/e*ln((I*e-c*e*x)/(d*c+I*e))-1/2*I*b*ln(c*e*x+c*d)/e*ln((I*e+c*e*x)/(I*e-d*c))+1/2*I*b/e*dilog((I*e-c*e*x)/(d*c+I*e))-1/2*I*b/e*dilog((I*e+c*e*x)/(I*e-d*c))","A"
6,1,118,98,0.036000," ","int((a+b*arctan(c*x))/(e*x+d)^2,x)","-\frac{c a}{\left(c e x +d c \right) e}-\frac{c b \arctan \left(c x \right)}{\left(c e x +d c \right) e}+\frac{c b \ln \left(c e x +d c \right)}{c^{2} d^{2}+e^{2}}-\frac{b c \ln \left(c^{2} x^{2}+1\right)}{2 \left(c^{2} d^{2}+e^{2}\right)}+\frac{b \,c^{2} d \arctan \left(c x \right)}{e \left(c^{2} d^{2}+e^{2}\right)}"," ",0,"-c*a/(c*e*x+c*d)/e-c*b/(c*e*x+c*d)/e*arctan(c*x)+c*b/(c^2*d^2+e^2)*ln(c*e*x+c*d)-1/2*b*c*ln(c^2*x^2+1)/(c^2*d^2+e^2)+b*c^2*d*arctan(c*x)/e/(c^2*d^2+e^2)","A"
7,1,184,141,0.040000," ","int((a+b*arctan(c*x))/(e*x+d)^3,x)","-\frac{c^{2} a}{2 \left(c e x +d c \right)^{2} e}-\frac{c^{2} b \arctan \left(c x \right)}{2 \left(c e x +d c \right)^{2} e}-\frac{c^{2} b}{2 \left(c^{2} d^{2}+e^{2}\right) \left(c e x +d c \right)}+\frac{c^{3} b d \ln \left(c e x +d c \right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{c^{4} b \arctan \left(c x \right) d^{2}}{2 e \left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{b \,c^{3} d \ln \left(c^{2} x^{2}+1\right)}{2 \left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{c^{2} b e \arctan \left(c x \right)}{2 \left(c^{2} d^{2}+e^{2}\right)^{2}}"," ",0,"-1/2*c^2*a/(c*e*x+c*d)^2/e-1/2*c^2*b/(c*e*x+c*d)^2/e*arctan(c*x)-1/2*c^2*b/(c^2*d^2+e^2)/(c*e*x+c*d)+c^3*b*d/(c^2*d^2+e^2)^2*ln(c*e*x+c*d)+1/2*c^4*b/e/(c^2*d^2+e^2)^2*arctan(c*x)*d^2-1/2*b*c^3*d*ln(c^2*x^2+1)/(c^2*d^2+e^2)^2-1/2*c^2*b*e/(c^2*d^2+e^2)^2*arctan(c*x)","A"
8,1,282,197,0.040000," ","int((a+b*arctan(c*x))/(e*x+d)^4,x)","-\frac{c^{3} a}{3 \left(c e x +d c \right)^{3} e}-\frac{c^{3} b \arctan \left(c x \right)}{3 \left(c e x +d c \right)^{3} e}-\frac{c^{3} b}{6 \left(c^{2} d^{2}+e^{2}\right) \left(c e x +d c \right)^{2}}+\frac{c^{5} b \ln \left(c e x +d c \right) d^{2}}{\left(c^{2} d^{2}+e^{2}\right)^{3}}-\frac{c^{3} b \,e^{2} \ln \left(c e x +d c \right)}{3 \left(c^{2} d^{2}+e^{2}\right)^{3}}-\frac{2 c^{4} b d}{3 \left(c^{2} d^{2}+e^{2}\right)^{2} \left(c e x +d c \right)}-\frac{c^{5} b \ln \left(c^{2} x^{2}+1\right) d^{2}}{2 \left(c^{2} d^{2}+e^{2}\right)^{3}}+\frac{c^{3} b \,e^{2} \ln \left(c^{2} x^{2}+1\right)}{6 \left(c^{2} d^{2}+e^{2}\right)^{3}}+\frac{c^{6} b \arctan \left(c x \right) d^{3}}{3 e \left(c^{2} d^{2}+e^{2}\right)^{3}}-\frac{c^{4} b e \arctan \left(c x \right) d}{\left(c^{2} d^{2}+e^{2}\right)^{3}}"," ",0,"-1/3*c^3*a/(c*e*x+c*d)^3/e-1/3*c^3*b/(c*e*x+c*d)^3/e*arctan(c*x)-1/6*c^3*b/(c^2*d^2+e^2)/(c*e*x+c*d)^2+c^5*b/(c^2*d^2+e^2)^3*ln(c*e*x+c*d)*d^2-1/3*c^3*b*e^2/(c^2*d^2+e^2)^3*ln(c*e*x+c*d)-2/3*c^4*b*d/(c^2*d^2+e^2)^2/(c*e*x+c*d)-1/2*c^5*b/(c^2*d^2+e^2)^3*ln(c^2*x^2+1)*d^2+1/6*c^3*b*e^2/(c^2*d^2+e^2)^3*ln(c^2*x^2+1)+1/3*c^6*b/e/(c^2*d^2+e^2)^3*arctan(c*x)*d^3-c^4*b*e/(c^2*d^2+e^2)^3*arctan(c*x)*d","A"
9,1,948,356,0.108000," ","int((e*x+d)^3*(a+b*arctan(c*x))^2,x)","\frac{a^{2} e^{3} x^{4}}{4}+a^{2} x \,d^{3}-\frac{i b^{2} e^{2} d \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right)}{2 c^{3}}+\frac{i b^{2} e^{2} d \ln \left(\frac{i \left(c x -i\right)}{2}\right) \ln \left(c x +i\right)}{2 c^{3}}+\frac{i b^{2} e^{2} d \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right)}{2 c^{3}}-\frac{i b^{2} e^{2} d \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right)}{2 c^{3}}+2 a b \,e^{2} \arctan \left(c x \right) x^{3} d +3 a b e \arctan \left(c x \right) x^{2} d^{2}+\frac{b^{2} e^{3} x^{2}}{12 c^{2}}-\frac{i b^{2} d^{3} \ln \left(c x +i\right)^{2}}{4 c}+\frac{i b^{2} d^{3} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c}-\frac{i b^{2} d^{3} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2 c}+\frac{i b^{2} d^{3} \ln \left(c x -i\right)^{2}}{4 c}+\frac{b^{2} d \,e^{2} x}{c^{2}}-\frac{b^{2} d \,e^{2} \arctan \left(c x \right)}{c^{3}}-\frac{a b \,e^{2} d \,x^{2}}{c}-\frac{3 b^{2} e \arctan \left(c x \right) d^{2} x}{c}-\frac{b^{2} e^{2} \arctan \left(c x \right) d \,x^{2}}{c}+\frac{b^{2} e^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d}{c^{3}}+\frac{a b \,e^{2} \ln \left(c^{2} x^{2}+1\right) d}{c^{3}}+\frac{3 a b e \arctan \left(c x \right) d^{2}}{c^{2}}-\frac{3 a b e \,d^{2} x}{c}+\frac{3 b^{2} e \arctan \left(c x \right)^{2} d^{2}}{2 c^{2}}-\frac{a b \,e^{3} \arctan \left(c x \right)}{2 c^{4}}-\frac{b^{2} e^{3} \arctan \left(c x \right) x^{3}}{6 c}-\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d^{3}}{c}-\frac{a b \ln \left(c^{2} x^{2}+1\right) d^{3}}{c}-\frac{a b \,e^{3} x^{3}}{6 c}+\frac{a b \,e^{3} x}{2 c^{3}}+\frac{a b \,e^{3} \arctan \left(c x \right) x^{4}}{2}+b^{2} e^{2} \arctan \left(c x \right)^{2} x^{3} d +\frac{3 b^{2} e \arctan \left(c x \right)^{2} x^{2} d^{2}}{2}+2 a b \arctan \left(c x \right) x \,d^{3}+\frac{b^{2} e^{3} \arctan \left(c x \right) x}{2 c^{3}}+\frac{a^{2} d^{4}}{4 e}-\frac{b^{2} e^{3} \arctan \left(c x \right)^{2}}{4 c^{4}}+\frac{b^{2} e^{3} \arctan \left(c x \right)^{2} x^{4}}{4}+b^{2} \arctan \left(c x \right)^{2} x \,d^{3}+a^{2} e^{2} x^{3} d +\frac{3 a^{2} e \,x^{2} d^{2}}{2}+\frac{3 b^{2} e \ln \left(c^{2} x^{2}+1\right) d^{2}}{2 c^{2}}-\frac{i b^{2} d^{3} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right)}{2 c}-\frac{i b^{2} d^{3} \ln \left(\frac{i \left(c x -i\right)}{2}\right) \ln \left(c x +i\right)}{2 c}-\frac{i b^{2} e^{2} d \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{3}}+\frac{i b^{2} e^{2} d \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2 c^{3}}+\frac{i b^{2} d^{3} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right)}{2 c}+\frac{i b^{2} d^{3} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right)}{2 c}+\frac{i b^{2} e^{2} d \ln \left(c x +i\right)^{2}}{4 c^{3}}-\frac{i b^{2} e^{2} d \ln \left(c x -i\right)^{2}}{4 c^{3}}-\frac{b^{2} e^{3} \ln \left(c^{2} x^{2}+1\right)}{3 c^{4}}"," ",0,"1/4*a^2*e^3*x^4+a^2*x*d^3+2*a*b*e^2*arctan(c*x)*x^3*d+3*a*b*e*arctan(c*x)*x^2*d^2+1/2*I/c*b^2*d^3*ln(c^2*x^2+1)*ln(I+c*x)+1/12*b^2*e^3*x^2/c^2+b^2*d*e^2*x/c^2-b^2*d*e^2*arctan(c*x)/c^3+1/2*I/c*b^2*d^3*ln(-1/2*I*(I+c*x))*ln(c*x-I)-1/2*I/c^3*b^2*e^2*d*dilog(-1/2*I*(I+c*x))+1/4*I/c^3*b^2*e^2*d*ln(I+c*x)^2+1/2*I/c^3*b^2*e^2*d*dilog(1/2*I*(c*x-I))-1/4*I/c^3*b^2*e^2*d*ln(c*x-I)^2-1/2*I/c*b^2*d^3*ln(c^2*x^2+1)*ln(c*x-I)-1/2*I/c*b^2*d^3*ln(1/2*I*(c*x-I))*ln(I+c*x)-1/c*a*b*e^2*d*x^2-3/c*b^2*e*arctan(c*x)*d^2*x-1/c*b^2*e^2*arctan(c*x)*d*x^2+1/c^3*b^2*e^2*arctan(c*x)*ln(c^2*x^2+1)*d+1/c^3*a*b*e^2*ln(c^2*x^2+1)*d+3/c^2*a*b*e*arctan(c*x)*d^2-3*a*b/c*e*d^2*x+3/2/c^2*b^2*e*arctan(c*x)^2*d^2-1/2/c^4*a*b*e^3*arctan(c*x)-1/6/c*b^2*e^3*arctan(c*x)*x^3-1/c*b^2*arctan(c*x)*ln(c^2*x^2+1)*d^3-1/c*a*b*ln(c^2*x^2+1)*d^3-1/6/c*a*b*e^3*x^3+1/2*a*b/c^3*e^3*x+1/4*I/c*b^2*d^3*ln(c*x-I)^2-1/4*I/c*b^2*d^3*ln(I+c*x)^2-1/2*I/c*b^2*d^3*dilog(1/2*I*(c*x-I))+1/2*a*b*e^3*arctan(c*x)*x^4+b^2*e^2*arctan(c*x)^2*x^3*d+3/2*b^2*e*arctan(c*x)^2*x^2*d^2+2*a*b*arctan(c*x)*x*d^3+1/2/c^3*b^2*e^3*arctan(c*x)*x+1/2*I/c*b^2*d^3*dilog(-1/2*I*(I+c*x))+1/4*a^2/e*d^4-1/4/c^4*b^2*e^3*arctan(c*x)^2+1/4*b^2*e^3*arctan(c*x)^2*x^4+b^2*arctan(c*x)^2*x*d^3+a^2*e^2*x^3*d+3/2*a^2*e*x^2*d^2+3/2/c^2*b^2*e*ln(c^2*x^2+1)*d^2-1/3*b^2*e^3*ln(c^2*x^2+1)/c^4-1/2*I/c^3*b^2*e^2*d*ln(c^2*x^2+1)*ln(I+c*x)-1/2*I/c^3*b^2*e^2*d*ln(-1/2*I*(I+c*x))*ln(c*x-I)+1/2*I/c^3*b^2*e^2*d*ln(1/2*I*(c*x-I))*ln(I+c*x)+1/2*I/c^3*b^2*e^2*d*ln(c^2*x^2+1)*ln(c*x-I)","B"
10,1,750,250,0.109000," ","int((e*x+d)^2*(a+b*arctan(c*x))^2,x)","-\frac{b^{2} e^{2} \arctan \left(c x \right)}{3 c^{3}}+\frac{b^{2} d e \ln \left(c^{2} x^{2}+1\right)}{c^{2}}-\frac{2 a b d e x}{c}-\frac{2 b^{2} d e x \arctan \left(c x \right)}{c}+2 a b e \arctan \left(c x \right) x^{2} d +\frac{2 a b e \arctan \left(c x \right) d}{c^{2}}+\frac{a^{2} e^{2} x^{3}}{3}+a^{2} x \,d^{2}+\frac{i b^{2} \ln \left(c x -i\right)^{2} d^{2}}{4 c}+\frac{i b^{2} \ln \left(c x +i\right)^{2} e^{2}}{12 c^{3}}-\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d^{2}}{2 c}+\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) e^{2}}{6 c^{3}}-\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) e^{2}}{6 c^{3}}+\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d^{2}}{2 c}+\frac{a b \,e^{2} \ln \left(c^{2} x^{2}+1\right)}{3 c^{3}}-\frac{b^{2} e^{2} \arctan \left(c x \right) x^{2}}{3 c}-\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d^{2}}{c}+2 a b \arctan \left(c x \right) x \,d^{2}+\frac{2 a b \,e^{2} \arctan \left(c x \right) x^{3}}{3}+\frac{b^{2} e^{2} x}{3 c^{2}}+\frac{b^{2} e \arctan \left(c x \right)^{2} d}{c^{2}}-\frac{a b \ln \left(c^{2} x^{2}+1\right) d^{2}}{c}+\frac{b^{2} e^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{3 c^{3}}-\frac{i b^{2} \ln \left(c x +i\right)^{2} d^{2}}{4 c}-\frac{i b^{2} \ln \left(c x -i\right)^{2} e^{2}}{12 c^{3}}+\frac{b^{2} e^{2} \arctan \left(c x \right)^{2} x^{3}}{3}+b^{2} \arctan \left(c x \right)^{2} x \,d^{2}+a^{2} e \,x^{2} d -\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) e^{2}}{6 c^{3}}+\frac{i b^{2} \ln \left(\frac{i \left(c x -i\right)}{2}\right) \ln \left(c x +i\right) e^{2}}{6 c^{3}}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d^{2}}{2 c}+\frac{i b^{2} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right) d^{2}}{2 c}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) d^{2}}{2 c}-\frac{i b^{2} \ln \left(\frac{i \left(c x -i\right)}{2}\right) \ln \left(c x +i\right) d^{2}}{2 c}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) e^{2}}{6 c^{3}}-\frac{i b^{2} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right) e^{2}}{6 c^{3}}+\frac{a^{2} d^{3}}{3 e}-\frac{a b \,x^{2} e^{2}}{3 c}+b^{2} e \arctan \left(c x \right)^{2} x^{2} d"," ",0,"-1/3*b^2*e^2*arctan(c*x)/c^3+b^2*d*e*ln(c^2*x^2+1)/c^2-2*a*b*d*e*x/c-2*b^2*d*e*x*arctan(c*x)/c+1/2*I/c*b^2*ln(-1/2*I*(I+c*x))*ln(c*x-I)*d^2+2*a*b*e*arctan(c*x)*x^2*d+1/2*I/c*b^2*ln(c^2*x^2+1)*ln(I+c*x)*d^2-1/2*I/c*b^2*ln(1/2*I*(c*x-I))*ln(I+c*x)*d^2+1/6*I/c^3*b^2*ln(c^2*x^2+1)*ln(c*x-I)*e^2-1/6*I/c^3*b^2*ln(-1/2*I*(I+c*x))*ln(c*x-I)*e^2-1/6*I/c^3*b^2*ln(c^2*x^2+1)*ln(I+c*x)*e^2+2/c^2*a*b*e*arctan(c*x)*d+1/3*a^2*e^2*x^3+a^2*x*d^2+1/6*I/c^3*b^2*ln(1/2*I*(c*x-I))*ln(I+c*x)*e^2-1/2*I/c*b^2*ln(c^2*x^2+1)*ln(c*x-I)*d^2+1/3/c^3*a*b*e^2*ln(c^2*x^2+1)-1/2*I/c*b^2*dilog(1/2*I*(c*x-I))*d^2-1/3/c*b^2*e^2*arctan(c*x)*x^2-1/c*b^2*arctan(c*x)*ln(c^2*x^2+1)*d^2+2*a*b*arctan(c*x)*x*d^2+2/3*a*b*e^2*arctan(c*x)*x^3+1/3*b^2*e^2*x/c^2+1/c^2*b^2*e*arctan(c*x)^2*d+1/6*I/c^3*b^2*dilog(1/2*I*(c*x-I))*e^2-1/12*I/c^3*b^2*ln(c*x-I)^2*e^2-1/6*I/c^3*b^2*dilog(-1/2*I*(I+c*x))*e^2-1/c*a*b*ln(c^2*x^2+1)*d^2+1/3/c^3*b^2*e^2*arctan(c*x)*ln(c^2*x^2+1)+1/2*I/c*b^2*dilog(-1/2*I*(I+c*x))*d^2-1/4*I/c*b^2*ln(I+c*x)^2*d^2+1/12*I/c^3*b^2*ln(I+c*x)^2*e^2+1/3*b^2*e^2*arctan(c*x)^2*x^3+b^2*arctan(c*x)^2*x*d^2+a^2*e*x^2*d+1/3*a^2/e*d^3+1/4*I/c*b^2*ln(c*x-I)^2*d^2-1/3/c*a*b*x^2*e^2+b^2*e*arctan(c*x)^2*x^2*d","B"
11,1,360,161,0.101000," ","int((e*x+d)*(a+b*arctan(c*x))^2,x)","\frac{a^{2} x^{2} e}{2}+a^{2} d x +\frac{b^{2} \arctan \left(c x \right)^{2} x^{2} e}{2}+b^{2} \arctan \left(c x \right)^{2} x d -\frac{b^{2} \ln \left(c^{2} x^{2}+1\right) \arctan \left(c x \right) d}{c}+\frac{b^{2} \arctan \left(c x \right)^{2} e}{2 c^{2}}-\frac{b^{2} e x \arctan \left(c x \right)}{c}+\frac{b^{2} e \ln \left(c^{2} x^{2}+1\right)}{2 c^{2}}+\frac{i b^{2} d \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c}-\frac{i b^{2} d \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2 c}+\frac{i b^{2} d \ln \left(c x -i\right)^{2}}{4 c}+\frac{i b^{2} d \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{2 c}-\frac{i b^{2} d \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{2 c}-\frac{i b^{2} d \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{2 c}-\frac{i b^{2} d \ln \left(c x +i\right)^{2}}{4 c}+\frac{i b^{2} d \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c}+a b \arctan \left(c x \right) x^{2} e +2 a b \arctan \left(c x \right) x d -\frac{a b e x}{c}-\frac{a b d \ln \left(c^{2} x^{2}+1\right)}{c}+\frac{a b e \arctan \left(c x \right)}{c^{2}}"," ",0,"1/2*a^2*x^2*e+a^2*d*x+1/2*b^2*arctan(c*x)^2*x^2*e+b^2*arctan(c*x)^2*x*d-1/c*b^2*ln(c^2*x^2+1)*arctan(c*x)*d+1/2/c^2*b^2*arctan(c*x)^2*e-b^2*e*x*arctan(c*x)/c+1/2*b^2*e*ln(c^2*x^2+1)/c^2+1/2*I/c*b^2*d*dilog(-1/2*I*(I+c*x))+1/4*I/c*b^2*d*ln(c*x-I)^2+1/2*I/c*b^2*d*ln(I+c*x)*ln(c^2*x^2+1)-1/2*I/c*b^2*d*ln(c*x-I)*ln(c^2*x^2+1)-1/2*I/c*b^2*d*ln(I+c*x)*ln(1/2*I*(c*x-I))-1/4*I/c*b^2*d*ln(I+c*x)^2-1/2*I/c*b^2*d*dilog(1/2*I*(c*x-I))+1/2*I/c*b^2*d*ln(c*x-I)*ln(-1/2*I*(I+c*x))+a*b*arctan(c*x)*x^2*e+2*a*b*arctan(c*x)*x*d-a*b*e*x/c-1/c*a*b*d*ln(c^2*x^2+1)+1/c^2*a*b*e*arctan(c*x)","B"
12,1,1297,208,1.234000," ","int((a+b*arctan(c*x))^2/(e*x+d),x)","\frac{a^{2} \ln \left(c e x +d c \right)}{e}+\frac{b^{2} \ln \left(c e x +d c \right) \arctan \left(c x \right)^{2}}{e}-\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{e}+\frac{i a b \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{e}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 e}-\frac{i a b \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{e}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 e}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \arctan \left(c x \right)^{2}}{2 e}-\frac{b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 e}+\frac{c \,b^{2} d \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e \left(d c -i e \right)}-\frac{i c \,b^{2} d \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e \left(d c -i e \right)}+\frac{c \,b^{2} d \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 e \left(d c -i e \right)}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{i d c +e}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \arctan \left(c x \right)^{2}}{2 e}+\frac{b^{2} \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 i d c +2 e}+\frac{2 a b \ln \left(c e x +d c \right) \arctan \left(c x \right)}{e}+\frac{i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{e}+\frac{i a b \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{e}-\frac{i b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{i d c +e}-\frac{i a b \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{e}"," ",0,"a^2*ln(c*e*x+c*d)/e+b^2*ln(c*e*x+c*d)/e*arctan(c*x)^2-b^2/e*arctan(c*x)^2*ln(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)+I*a*b*ln(c*e*x+c*d)/e*ln((I*e-c*e*x)/(d*c+I*e))-I*a*b/e*dilog((I*e+c*e*x)/(I*e-d*c))+1/2*I*b^2/e*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-I*a*b*ln(c*e*x+c*d)/e*ln((I*e+c*e*x)/(I*e-d*c))-1/2*I*b^2/e*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*b^2/e*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+c*b^2/e*d/(d*c-I*e)*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+1/2*I*b^2/e*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*arctan(c*x)^2+1/2*c*b^2/e*d/(d*c-I*e)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+b^2*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)-I*b^2*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)+1/2*b^2*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)+2*a*b*ln(c*e*x+c*d)/e*arctan(c*x)+I*a*b/e*dilog((I*e-c*e*x)/(d*c+I*e))+I*b^2/e*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-I*c*b^2/e*d/(d*c-I*e)*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))-1/2*I*b^2/e*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*arctan(c*x)^2","C"
13,1,698,329,0.115000," ","int((a+b*arctan(c*x))^2/(e*x+d)^2,x)","-\frac{c \,a^{2}}{\left(c e x +d c \right) e}-\frac{c \,b^{2} \arctan \left(c x \right)^{2}}{\left(c e x +d c \right) e}+\frac{2 c \,b^{2} \arctan \left(c x \right) \ln \left(c e x +d c \right)}{c^{2} d^{2}+e^{2}}-\frac{c \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{c^{2} d^{2}+e^{2}}+\frac{c^{2} b^{2} d \arctan \left(c x \right)^{2}}{e \left(c^{2} d^{2}+e^{2}\right)}+\frac{i c \,b^{2} \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{c^{2} d^{2}+e^{2}}+\frac{i c \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{2 c^{2} d^{2}+2 e^{2}}-\frac{i c \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{2 \left(c^{2} d^{2}+e^{2}\right)}+\frac{i c \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{2} d^{2}+2 e^{2}}-\frac{i c \,b^{2} \ln \left(c x +i\right)^{2}}{4 \left(c^{2} d^{2}+e^{2}\right)}-\frac{i c \,b^{2} \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{c^{2} d^{2}+e^{2}}+\frac{i c \,b^{2} \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{c^{2} d^{2}+e^{2}}-\frac{i c \,b^{2} \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{c^{2} d^{2}+e^{2}}+\frac{i c \,b^{2} \ln \left(c x -i\right)^{2}}{4 c^{2} d^{2}+4 e^{2}}-\frac{i c \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{2 \left(c^{2} d^{2}+e^{2}\right)}+\frac{i c \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{2} d^{2}+2 e^{2}}-\frac{i c \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2 \left(c^{2} d^{2}+e^{2}\right)}-\frac{2 c a b \arctan \left(c x \right)}{\left(c e x +d c \right) e}+\frac{2 c a b \ln \left(c e x +d c \right)}{c^{2} d^{2}+e^{2}}-\frac{c a b \ln \left(c^{2} x^{2}+1\right)}{c^{2} d^{2}+e^{2}}+\frac{2 c^{2} a b d \arctan \left(c x \right)}{e \left(c^{2} d^{2}+e^{2}\right)}"," ",0,"-c*a^2/(c*e*x+c*d)/e-c*b^2/(c*e*x+c*d)/e*arctan(c*x)^2+2*c*b^2*arctan(c*x)/(c^2*d^2+e^2)*ln(c*e*x+c*d)-c*b^2*arctan(c*x)/(c^2*d^2+e^2)*ln(c^2*x^2+1)+c^2*b^2/e/(c^2*d^2+e^2)*d*arctan(c*x)^2-1/2*I*c*b^2/(c^2*d^2+e^2)*dilog(1/2*I*(c*x-I))+I*c*b^2/(c^2*d^2+e^2)*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))-I*c*b^2/(c^2*d^2+e^2)*dilog((I*e+c*e*x)/(I*e-d*c))+1/2*I*c*b^2/(c^2*d^2+e^2)*ln(I+c*x)*ln(c^2*x^2+1)+I*c*b^2/(c^2*d^2+e^2)*dilog((I*e-c*e*x)/(d*c+I*e))-1/2*I*c*b^2/(c^2*d^2+e^2)*ln(I+c*x)*ln(1/2*I*(c*x-I))+1/2*I*c*b^2/(c^2*d^2+e^2)*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/4*I*c*b^2/(c^2*d^2+e^2)*ln(I+c*x)^2-I*c*b^2/(c^2*d^2+e^2)*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))+1/4*I*c*b^2/(c^2*d^2+e^2)*ln(c*x-I)^2-1/2*I*c*b^2/(c^2*d^2+e^2)*ln(c*x-I)*ln(c^2*x^2+1)+1/2*I*c*b^2/(c^2*d^2+e^2)*dilog(-1/2*I*(I+c*x))-2*c*a*b/(c*e*x+c*d)/e*arctan(c*x)+2*c*a*b/(c^2*d^2+e^2)*ln(c*e*x+c*d)-c*a*b/(c^2*d^2+e^2)*ln(c^2*x^2+1)+2*c^2*a*b/e/(c^2*d^2+e^2)*d*arctan(c*x)","B"
14,1,961,478,0.113000," ","int((a+b*arctan(c*x))^2/(e*x+d)^3,x)","-\frac{b^{2} c^{2} e \ln \left(c^{2} x^{2}+1\right)}{2 \left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{c^{2} b^{2} e \ln \left(c e x +d c \right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{c^{2} b^{2} \arctan \left(c x \right)^{2}}{2 \left(c e x +d c \right)^{2} e}-\frac{c^{2} a b}{\left(c^{2} d^{2}+e^{2}\right) \left(c e x +d c \right)}-\frac{c^{2} b^{2} e \arctan \left(c x \right)^{2}}{2 \left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{c^{2} b^{2} \arctan \left(c x \right)}{\left(c^{2} d^{2}+e^{2}\right) \left(c e x +d c \right)}+\frac{i c^{3} b^{2} d \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{i c^{3} b^{2} d \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{2 \left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{i c^{3} b^{2} d \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{2 \left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{i c^{3} b^{2} d \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{i c^{3} b^{2} d \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 \left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{i c^{3} b^{2} d \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{2 \left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{c^{4} a b \arctan \left(c x \right) d^{2}}{e \left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{b^{2} c^{3} d \arctan \left(c x \right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{c^{2} a^{2}}{2 \left(c e x +d c \right)^{2} e}-\frac{i c^{3} b^{2} d \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2 \left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{i c^{3} b^{2} d \ln \left(c x -i\right)^{2}}{4 \left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{i c^{3} b^{2} d \ln \left(c x +i\right)^{2}}{4 \left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{i c^{3} b^{2} d \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{i c^{3} b^{2} d \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{i c^{3} b^{2} d \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 \left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{2 c^{3} a b d \ln \left(c e x +d c \right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{c^{3} a b d \ln \left(c^{2} x^{2}+1\right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{c^{2} a b e \arctan \left(c x \right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{c^{4} b^{2} \arctan \left(c x \right)^{2} d^{2}}{2 e \left(c^{2} d^{2}+e^{2}\right)^{2}}+\frac{2 c^{3} b^{2} \arctan \left(c x \right) d \ln \left(c e x +d c \right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}-\frac{c^{2} a b \arctan \left(c x \right)}{\left(c e x +d c \right)^{2} e}-\frac{c^{3} b^{2} \arctan \left(c x \right) d \ln \left(c^{2} x^{2}+1\right)}{\left(c^{2} d^{2}+e^{2}\right)^{2}}"," ",0,"-1/2*b^2*c^2*e*ln(c^2*x^2+1)/(c^2*d^2+e^2)^2+c^2*b^2*e/(c^2*d^2+e^2)^2*ln(c*e*x+c*d)-1/2*c^2*b^2/(c*e*x+c*d)^2/e*arctan(c*x)^2-c^2*a*b/(c^2*d^2+e^2)/(c*e*x+c*d)-1/2*c^2*b^2*e/(c^2*d^2+e^2)^2*arctan(c*x)^2-c^2*b^2*arctan(c*x)/(c^2*d^2+e^2)/(c*e*x+c*d)+I*c^3*b^2*d/(c^2*d^2+e^2)^2*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))+1/2*I*c^3*b^2*d/(c^2*d^2+e^2)^2*ln(I+c*x)*ln(c^2*x^2+1)-1/2*I*c^3*b^2*d/(c^2*d^2+e^2)^2*ln(c*x-I)*ln(c^2*x^2+1)-I*c^3*b^2*d/(c^2*d^2+e^2)^2*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))+1/2*I*c^3*b^2*d/(c^2*d^2+e^2)^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*I*c^3*b^2*d/(c^2*d^2+e^2)^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+c^4*a*b/e/(c^2*d^2+e^2)^2*arctan(c*x)*d^2+b^2*c^3*d*arctan(c*x)/(c^2*d^2+e^2)^2-1/2*c^2*a^2/(c*e*x+c*d)^2/e+2*c^3*a*b*d/(c^2*d^2+e^2)^2*ln(c*e*x+c*d)-c^3*a*b/(c^2*d^2+e^2)^2*d*ln(c^2*x^2+1)-c^2*a*b*e/(c^2*d^2+e^2)^2*arctan(c*x)+1/2*c^4*b^2/e/(c^2*d^2+e^2)^2*arctan(c*x)^2*d^2+I*c^3*b^2*d/(c^2*d^2+e^2)^2*dilog((I*e-c*e*x)/(d*c+I*e))-I*c^3*b^2*d/(c^2*d^2+e^2)^2*dilog((I*e+c*e*x)/(I*e-d*c))+1/4*I*c^3*b^2*d/(c^2*d^2+e^2)^2*ln(c*x-I)^2+1/2*I*c^3*b^2*d/(c^2*d^2+e^2)^2*dilog(-1/2*I*(I+c*x))-1/2*I*c^3*b^2*d/(c^2*d^2+e^2)^2*dilog(1/2*I*(c*x-I))-1/4*I*c^3*b^2*d/(c^2*d^2+e^2)^2*ln(I+c*x)^2+2*c^3*b^2*arctan(c*x)*d/(c^2*d^2+e^2)^2*ln(c*e*x+c*d)-c^2*a*b/(c*e*x+c*d)^2/e*arctan(c*x)-c^3*b^2*arctan(c*x)/(c^2*d^2+e^2)^2*d*ln(c^2*x^2+1)","B"
15,1,3577,605,18.815000," ","int((e*x+d)^3*(a+b*arctan(c*x))^3,x)","\text{output too large to display}"," ",0,"-1/4*b^3*e^3*x/c^3+1/4*b^3*e^3*arctan(c*x)/c^4+3*a*b^2*d*e^2*x/c^2+3*b^3*d*e^2*x*arctan(c*x)/c^2+2/c^4*b^3*e^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2/c^4*b^3*e^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*a*b^2*arctan(c*x)^2*x*d^3-I/c*b^3*d^3*arctan(c*x)^3-2*I/c^4*b^3*e^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/4*a^2*b/c^3*e^3*x-1/4/c*a^2*b*x^3*e^3+1/4/c^2*a*b^2*x^2*e^3+a^3*x*d^3+1/4*a^3*e^3*x^4-3/4*I/c*b^3*Pi*d^3*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2-3/4*I/c^3*b^3*e^2*Pi*d*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+3/2*I/c^3*b^3*e^2*Pi*d*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2-3/4*I/c^3*b^3*e^2*Pi*d*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2-3/4*I/c^3*b^3*e^2*Pi*d*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+3/4*I/c^3*b^3*e^2*Pi*d*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^2-3/2*I/c^3*b^3*e^2*Pi*d*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*arctan(c*x)^2-1/4*I/c^4*b^3*e^3+1/4*a^3/e*d^4+a^3*e^2*x^3*d+3/2*a^3*e*x^2*d^2+b^3*arctan(c*x)^3*x*d^3-1/4/c^4*b^3*e^3*arctan(c*x)^3+3/2/c*b^3*d^3*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+1/4*b^3*e^3*arctan(c*x)^3*x^4+3/4*a*b^2*e^3*arctan(c*x)^2*x^4+3/4*a^2*b*e^3*arctan(c*x)*x^4+b^3*e^2*arctan(c*x)^3*x^3*d+3/2*b^3*e*arctan(c*x)^3*x^2*d^2+3*a^2*b*arctan(c*x)*x*d^3-3/4/c^4*a^2*b*e^3*arctan(c*x)+3/4/c^3*b^3*e^3*arctan(c*x)^2*x+1/4/c^2*b^3*e^3*arctan(c*x)*x^2+3/c*b^3*d^3*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))*arctan(c*x)^2-3/2/c*b^3*arctan(c*x)^2*ln(c^2*x^2+1)*d^3-1/4/c*b^3*e^3*arctan(c*x)^2*x^3-3/2/c*a^2*b*ln(c^2*x^2+1)*d^3+3/c*b^3*ln(2)*d^3*arctan(c*x)^2-1/c^4*a*b^2*e^3*ln(c^2*x^2+1)-3/4/c^4*a*b^2*e^3*arctan(c*x)^2-3/2/c^3*b^3*e^2*d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-3/2/c^3*b^3*e^2*d*arctan(c*x)^2+3/c^3*b^3*e^2*d*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+3/2/c^2*b^3*e*arctan(c*x)^3*d^2-I/c^4*b^3*e^3*arctan(c*x)^2-2*I/c^4*b^3*e^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-9/2*a^2*b/c*x*d^2*e-3/2/c*a^2*b*x^2*d*e^2+9/2*a*b^2*e*arctan(c*x)^2*d^2*x^2+3*a^2*b*e^2*arctan(c*x)*d*x^3+9/2*a^2*b*e*arctan(c*x)*d^2*x^2+3*a*b^2*e^2*arctan(c*x)^2*d*x^3-9/c^2*b^3*e*d^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2/c^3*b^3*e^2*arctan(c*x)^2*ln(c^2*x^2+1)*d-3/c^3*b^3*e^2*d*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))*arctan(c*x)^2-9/c^2*b^3*e*d^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2/c^3*a*b^2*e^3*arctan(c*x)*x-9/2/c*b^3*e*arctan(c*x)^2*d^2*x-1/2/c*a*b^2*e^3*arctan(c*x)*x^3-3/c*a*b^2*arctan(c*x)*ln(c^2*x^2+1)*d^3+I/c^3*b^3*e^2*d*arctan(c*x)^3-3/c^3*b^3*e^2*ln(2)*d*arctan(c*x)^2+3/2/c^3*a^2*b*e^2*ln(c^2*x^2+1)*d+9/2/c^2*a^2*b*e*arctan(c*x)*d^2+9/2/c^2*a*b^2*e*ln(c^2*x^2+1)*d^2-3/c^3*a*b^2*e^2*d*arctan(c*x)+9/2/c^2*a*b^2*e*arctan(c*x)^2*d^2-3/2/c*b^3*e^2*arctan(c*x)^2*d*x^2+9/2*I/c^2*b^3*e*d^2*arctan(c*x)^2+9*I/c^2*b^3*e*d^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+9*I/c^2*b^3*e*d^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/4*I/c*a*b^2*d^3*ln(c*x-I)^2-9/c*a*b^2*e*arctan(c*x)*d^2*x-3/c*a*b^2*e^2*arctan(c*x)*d*x^2+3/c^3*a*b^2*e^2*arctan(c*x)*ln(c^2*x^2+1)*d+3/4*I/c^3*a*b^2*e^2*d*ln(I+c*x)^2+3/2*I/c^3*a*b^2*e^2*d*dilog(1/2*I*(c*x-I))-3/2*I/c*a*b^2*d^3*ln(c^2*x^2+1)*ln(c*x-I)+3/2*I/c*a*b^2*d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))+3/2*I/c*a*b^2*d^3*ln(I+c*x)*ln(c^2*x^2+1)-3/2*I/c*a*b^2*d^3*ln(I+c*x)*ln(1/2*I*(c*x-I))-3/4*I/c*b^3*Pi*d^3*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*arctan(c*x)^2-3/4*I/c*b^3*Pi*d^3*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+3/4*I/c*b^3*Pi*d^3*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+3*I/c^3*b^3*e^2*d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-3/4*I/c^3*a*b^2*e^2*d*ln(c*x-I)^2-3/2*I/c^3*a*b^2*e^2*d*dilog(-1/2*I*(I+c*x))+3/2*I/c*a*b^2*d^3*dilog(-1/2*I*(I+c*x))-3/4*I/c*a*b^2*d^3*ln(I+c*x)^2-3/2*I/c*a*b^2*d^3*dilog(1/2*I*(c*x-I))-3*I/c^3*b^3*e^2*arctan(c*x)*d-3*I/c*b^3*d^3*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+3/4*I/c^3*b^3*e^2*Pi*d*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2+3/4*I/c*b^3*Pi*d^3*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+3/4*I/c*b^3*Pi*d^3*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+3/4*I/c*b^3*Pi*d^3*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2-3/2*I/c*b^3*Pi*d^3*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+3/4*I/c^3*b^3*e^2*Pi*d*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*arctan(c*x)^2-3/4*I/c^3*b^3*e^2*Pi*d*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+3/4*I/c^3*b^3*e^2*Pi*d*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+3/2*I/c^3*a*b^2*e^2*d*ln(c^2*x^2+1)*ln(c*x-I)-3/2*I/c^3*a*b^2*e^2*d*ln(c*x-I)*ln(-1/2*I*(I+c*x))-3/2*I/c^3*a*b^2*e^2*d*ln(I+c*x)*ln(c^2*x^2+1)+3/2*I/c^3*a*b^2*e^2*d*ln(I+c*x)*ln(1/2*I*(c*x-I))-3/4*I/c*b^3*Pi*d^3*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^2+3/2*I/c*b^3*Pi*d^3*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*arctan(c*x)^2","C"
16,1,3022,388,9.025000," ","int((e*x+d)^2*(a+b*arctan(c*x))^3,x)","\text{output too large to display}"," ",0,"1/4*I/c^3*b^3*e^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2-3/4*I/c*b^3*d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2-3*a^2*b/c*x*d*e+3/c^2*a^2*b*e*arctan(c*x)*d-3/c*b^3*e*arctan(c*x)^2*d*x-1/c*a*b^2*e^2*arctan(c*x)*x^2-3/c*a*b^2*arctan(c*x)*ln(c^2*x^2+1)*d^2+3/c^2*a*b^2*e*ln(c^2*x^2+1)*d+3/c^2*a*b^2*e*arctan(c*x)^2*d+3*a*b^2*e*arctan(c*x)^2*x^2*d+3*a^2*b*e*arctan(c*x)*x^2*d-1/2*I/c^3*a*b^2*dilog(-1/2*I*(I+c*x))*e^2+1/4*I/c^3*a*b^2*ln(I+c*x)^2*e^2+1/2*I/c^3*a*b^2*dilog(1/2*I*(c*x-I))*e^2+3*I/c^2*b^3*e*d*arctan(c*x)^2+6*I/c^2*b^3*e*d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*I/c*a*b^2*dilog(1/2*I*(c*x-I))*d^2+3/4*I/c*a*b^2*ln(c*x-I)^2*d^2+3/2*I/c*a*b^2*dilog(-1/2*I*(I+c*x))*d^2-3/4*I/c*a*b^2*ln(I+c*x)^2*d^2-1/4*I/c^3*a*b^2*ln(c*x-I)^2*e^2-3*I/c*b^3*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))*d^2+6*I/c^2*b^3*e*d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I/c^3*b^3*e^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-6/c^2*b^3*e*d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-6/c^2*b^3*e*d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/c^3*a*b^2*e^2*arctan(c*x)*ln(c^2*x^2+1)-1/c^3*b^3*e^2*ln(2)*arctan(c*x)^2+1/c^2*b^3*e*arctan(c*x)^3*d+1/2/c^3*a^2*b*e^2*ln(c^2*x^2+1)-1/c^3*a*b^2*e^2*arctan(c*x)+1/2/c^3*b^3*e^2*arctan(c*x)^2*ln(c^2*x^2+1)-1/c^3*b^3*e^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))*arctan(c*x)^2-1/2/c*b^3*e^2*arctan(c*x)^2*x^2-3/2/c*b^3*arctan(c*x)^2*ln(c^2*x^2+1)*d^2+3/c*b^3*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))*arctan(c*x)^2*d^2+3/c*b^3*d^2*ln(2)*arctan(c*x)^2-3/2/c*a^2*b*ln(c^2*x^2+1)*d^2+3*a*b^2*arctan(c*x)^2*x*d^2+a^2*b*e^2*arctan(c*x)*x^3+b^3*e*arctan(c*x)^3*x^2*d+a*b^2*e^2*arctan(c*x)^2*x^3+3*a^2*b*arctan(c*x)*x*d^2-I/c^3*b^3*e^2*arctan(c*x)+1/3*I/c^3*b^3*e^2*arctan(c*x)^3-I/c*b^3*arctan(c*x)^3*d^2-1/2/c*a^2*b*x^2*e^2-1/4*I/c^3*b^3*e^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+1/2*I/c^3*b^3*e^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+1/4*I/c^3*b^3*e^2*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^2+3/4*I/c*b^3*d^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+3/4*I/c*b^3*d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+3/2*I/c*b^3*d^2*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*arctan(c*x)^2-3/2*I/c*b^3*d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2-3/4*I/c*b^3*d^2*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^2+3/4*I/c*b^3*d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2-1/2*I/c^3*b^3*e^2*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*arctan(c*x)^2-1/4*I/c^3*b^3*e^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2-1/4*I/c^3*b^3*e^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2+1/3*b^3*e^2*arctan(c*x)^3*x^3+b^3*arctan(c*x)^3*x*d^2+3/2/c*b^3*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))*d^2+1/c^3*b^3*e^2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/2/c^3*b^3*e^2*arctan(c*x)^2-1/2/c^3*b^3*e^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+1/3*a^3/e*d^3+a^3*e*x^2*d-3/2*I/c*a*b^2*ln(c^2*x^2+1)*ln(c*x-I)*d^2+3/2*I/c*a*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))*d^2+3/2*I/c*a*b^2*ln(c^2*x^2+1)*ln(I+c*x)*d^2-3/2*I/c*a*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*d^2-3/4*I/c*b^3*d^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*arctan(c*x)^2-3/4*I/c*b^3*d^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+3/4*I/c*b^3*d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+1/4*I/c^3*b^3*e^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+1/4*I/c^3*b^3*e^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*arctan(c*x)^2-1/4*I/c^3*b^3*e^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2-1/2*I/c^3*a*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))*e^2-1/2*I/c^3*a*b^2*ln(c^2*x^2+1)*ln(I+c*x)*e^2+1/2*I/c^3*a*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*e^2+1/2*I/c^3*a*b^2*ln(c^2*x^2+1)*ln(c*x-I)*e^2-6/c*a*b^2*e*arctan(c*x)*d*x+a*b^2*e^2*x/c^2+b^3*e^2*x*arctan(c*x)/c^2+a^3*x*d^2+1/3*a^3*e^2*x^3","C"
17,1,7462,243,1.417000," ","int((e*x+d)*(a+b*arctan(c*x))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
18,1,2616,292,0.594000," ","int((a+b*arctan(c*x))^3/(e*x+d),x)","-\frac{3 i c a \,b^{2} d \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e \left(d c -i e \right)}+\frac{3 c a \,b^{2} d \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 e \left(d c -i e \right)}+\frac{3 c \,b^{3} d \arctan \left(c x \right) \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 e \left(d c -i e \right)}+\frac{3 i c \,b^{3} d \polylog \left(4, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{4 e \left(d c -i e \right)}+\frac{3 i a \,b^{2} \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \pi  \arctan \left(c x \right)^{2}}{2 e}-\frac{i b^{3} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \pi  \arctan \left(c x \right)^{3}}{2 e}+\frac{3 a^{2} b \ln \left(c e x +d c \right) \arctan \left(c x \right)}{e}+\frac{3 i a^{2} b \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e}-\frac{3 i a^{2} b \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e}+\frac{3 i a \,b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{e}-\frac{3 i a \,b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{i d c +e}+\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \pi  \arctan \left(c x \right)^{3}}{2 e}+\frac{a^{3} \ln \left(c e x +d c \right)}{e}+\frac{3 a \,b^{2} \ln \left(c e x +d c \right) \arctan \left(c x \right)^{2}}{e}+\frac{c \,b^{3} d \arctan \left(c x \right)^{3} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e \left(d c -i e \right)}-\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \pi  \arctan \left(c x \right)^{3}}{2 e}-\frac{3 a \,b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 e}+\frac{3 a \,b^{2} \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 \left(i d c +e \right)}-\frac{3 b^{3} \arctan \left(c x \right) \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 e}+\frac{3 b^{3} \arctan \left(c x \right) \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 \left(i d c +e \right)}-\frac{3 i b^{3} \polylog \left(4, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{4 e}+\frac{3 i b^{3} \polylog \left(4, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{4 \left(i d c +e \right)}-\frac{b^{3} \arctan \left(c x \right)^{3} \ln \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{e}+\frac{b^{3} \arctan \left(c x \right)^{3} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{i d c +e}+\frac{b^{3} \ln \left(c e x +d c \right) \arctan \left(c x \right)^{3}}{e}-\frac{3 i c \,b^{3} d \arctan \left(c x \right)^{2} \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 e \left(d c -i e \right)}+\frac{3 c a \,b^{2} d \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e \left(d c -i e \right)}+\frac{i b^{3} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \pi  \arctan \left(c x \right)^{3}}{2 e}-\frac{3 i a \,b^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \pi  \arctan \left(c x \right)^{2}}{2 e}-\frac{3 i a \,b^{2} \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \pi  \arctan \left(c x \right)^{2}}{2 e}-\frac{3 a \,b^{2} \arctan \left(c x \right)^{2} \ln \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{e}+\frac{3 a \,b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{i d c +e}-\frac{3 i a^{2} b \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e}+\frac{3 i a^{2} b \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e}+\frac{3 i b^{3} \arctan \left(c x \right)^{2} \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 e}-\frac{3 i b^{3} \arctan \left(c x \right)^{2} \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 \left(i d c +e \right)}+\frac{3 i a \,b^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \pi  \arctan \left(c x \right)^{2}}{2 e}"," ",0,"3/2*I*a*b^2/e*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*Pi*arctan(c*x)^2-1/2*I*b^3/e*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*arctan(c*x)^3+3/2*I*a^2*b*ln(c*e*x+c*d)/e*ln((I*e-c*e*x)/(d*c+I*e))-3/2*I*a^2*b*ln(c*e*x+c*d)/e*ln((I*e+c*e*x)/(I*e-d*c))+3*I*a*b^2/e*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-3*I*a*b^2*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)-3*a*b^2/e*arctan(c*x)^2*ln(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)+3*a*b^2*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)+3*a^2*b*ln(c*e*x+c*d)/e*arctan(c*x)-3/2*I*a^2*b/e*dilog((I*e+c*e*x)/(I*e-d*c))+3/2*I*a^2*b/e*dilog((I*e-c*e*x)/(d*c+I*e))+3/2*I*b^3/e*arctan(c*x)^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-3/2*I*b^3*arctan(c*x)^2*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)+3/2*c*a*b^2/e*d/(d*c-I*e)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+c*b^3/e*d/(d*c-I*e)*arctan(c*x)^3*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+3/2*c*b^3/e*d/(d*c-I*e)*arctan(c*x)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+3/4*I*c*b^3/e*d/(d*c-I*e)*polylog(4,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))-1/2*I*b^3/e*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*Pi*arctan(c*x)^3+1/2*I*b^3/e*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*Pi*arctan(c*x)^3+a^3*ln(c*e*x+c*d)/e+3*a*b^2*ln(c*e*x+c*d)/e*arctan(c*x)^2-3/2*a*b^2/e*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+3/2*a*b^2*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)-b^3/e*arctan(c*x)^3*ln(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)-3/2*b^3/e*arctan(c*x)*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+b^3*arctan(c*x)^3*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)+3/2*b^3*arctan(c*x)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)+b^3*ln(c*e*x+c*d)/e*arctan(c*x)^3-3/4*I*b^3/e*polylog(4,-(1+I*c*x)^2/(c^2*x^2+1))+3/4*I*b^3*polylog(4,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)+3*c*a*b^2/e*d/(d*c-I*e)*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))-3/2*I*c*b^3/e*d/(d*c-I*e)*arctan(c*x)^2*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+1/2*I*b^3/e*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*Pi*arctan(c*x)^3-3/2*I*a*b^2/e*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*arctan(c*x)^2-3/2*I*a*b^2/e*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*Pi*arctan(c*x)^2+3/2*I*a*b^2/e*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*Pi*arctan(c*x)^2-3*I*c*a*b^2/e*d/(d*c-I*e)*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))","C"
19,1,2960,477,1.231000," ","int((a+b*arctan(c*x))^3/(e*x+d)^2,x)","\text{output too large to display}"," ",0,"-3/4*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)+3/2*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))+3*c^2*b^3/(c^2*d^2+e^2)*d/(d*c-I*e)*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+3*c*b^3*e*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(c^2*d^2+e^2)/(e+I*d*c)+3*c^2*a^2*b/e/(c^2*d^2+e^2)*d*arctan(c*x)+3*c^2*a*b^2/e/(c^2*d^2+e^2)*d*arctan(c*x)^2+3/2*I*c*a*b^2/(c^2*d^2+e^2)*ln(c*x-I)*ln(-1/2*I*(I+c*x))+3/2*I*c*a*b^2/(c^2*d^2+e^2)*ln(I+c*x)*ln(c^2*x^2+1)-3/4*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3+3/4*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3+3/2*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3+3*I*c*a*b^2/(c^2*d^2+e^2)*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))-3/2*I*c*a*b^2/(c^2*d^2+e^2)*ln(I+c*x)*ln(1/2*I*(c*x-I))-3/4*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-3*I*c*a*b^2/(c^2*d^2+e^2)*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))-3/2*I*c*a*b^2/(c^2*d^2+e^2)*ln(c*x-I)*ln(c^2*x^2+1)+3/4*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)+3/2*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2+3/4*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-3*I*c^2*b^3/(c^2*d^2+e^2)*d/(d*c-I*e)*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))-3*I*c*b^3*e*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(c^2*d^2+e^2)/(e+I*d*c)-3/2*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2-3/2*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2-3/2*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-3/4*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))+3/4*I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-c*a^3/(c*e*x+c*d)/e+3*c*a^2*b/(c^2*d^2+e^2)*ln(c*e*x+c*d)-3/2*c*a^2*b/(c^2*d^2+e^2)*ln(c^2*x^2+1)+3*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*ln(2)+3*c*b^3*arctan(c*x)^2/(c^2*d^2+e^2)*ln(c*e*x+c*d)-3/2*c*b^3*arctan(c*x)^2/(c^2*d^2+e^2)*ln(c^2*x^2+1)-c*b^3/(c*e*x+c*d)/e*arctan(c*x)^3+3*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-3*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^2*ln(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)-I*c*b^3/(c^2*d^2+e^2)*arctan(c*x)^3+c^2*b^3/e*arctan(c*x)^3/(c^2*d^2+e^2)*d-3*c*a*b^2/(c*e*x+c*d)/e*arctan(c*x)^2+6*c*a*b^2*arctan(c*x)/(c^2*d^2+e^2)*ln(c*e*x+c*d)-3*c*a*b^2*arctan(c*x)/(c^2*d^2+e^2)*ln(c^2*x^2+1)-3*c*a^2*b/(c*e*x+c*d)/e*arctan(c*x)+3/2*c^2*b^3/(c^2*d^2+e^2)*d/(d*c-I*e)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+3/2*c*b^3*e*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(c^2*d^2+e^2)/(e+I*d*c)-3*I*c*a*b^2/(c^2*d^2+e^2)*dilog((I*e+c*e*x)/(I*e-d*c))-3/2*I*c*a*b^2/(c^2*d^2+e^2)*dilog(1/2*I*(c*x-I))+3*I*c*a*b^2/(c^2*d^2+e^2)*dilog((I*e-c*e*x)/(d*c+I*e))-3/4*I*c*a*b^2/(c^2*d^2+e^2)*ln(I+c*x)^2+3/4*I*c*a*b^2/(c^2*d^2+e^2)*ln(c*x-I)^2+3/2*I*c*a*b^2/(c^2*d^2+e^2)*dilog(-1/2*I*(I+c*x))","C"
20,1,41269,886,23.156000," ","int((a+b*arctan(c*x))^3/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
21,1,381,201,0.048000," ","int((e*x+d)^2*(a+b*arctan(c*x^2)),x)","\frac{a \,e^{2} x^{3}}{3}+a e d \,x^{2}+a x \,d^{2}+\frac{a \,d^{3}}{3 e}+\frac{b \,e^{2} \arctan \left(c \,x^{2}\right) x^{3}}{3}+b e \arctan \left(c \,x^{2}\right) x^{2} d +b \arctan \left(c \,x^{2}\right) x \,d^{2}+\frac{b \,d^{3} \arctan \left(c \,x^{2}\right)}{3 e}-\frac{2 b \,e^{2} x}{3 c}+\frac{b \,e^{2} \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{6 c}+\frac{b \,e^{2} \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{12 c}+\frac{b \,e^{2} \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{6 c}-\frac{b c \,d^{3} \arctan \left(x^{2} \sqrt{c^{2}}\right)}{3 e \sqrt{c^{2}}}-\frac{b \,d^{2} \sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b \,d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b \,d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b d e \ln \left(c^{2} x^{4}+1\right)}{2 c}"," ",0,"1/3*a*e^2*x^3+a*e*d*x^2+a*x*d^2+1/3*a/e*d^3+1/3*b*e^2*arctan(c*x^2)*x^3+b*e*arctan(c*x^2)*x^2*d+b*arctan(c*x^2)*x*d^2+1/3*b*d^3*arctan(c*x^2)/e-2/3*b*e^2*x/c+1/6*b*e^2/c*(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)+1/12*b*e^2/c*(1/c^2)^(1/4)*2^(1/2)*ln((x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))+1/6*b*e^2/c*(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)-1/3*b/e*c*d^3/(c^2)^(1/2)*arctan(x^2*(c^2)^(1/2))-1/4*b/c*d^2/(1/c^2)^(1/4)*2^(1/2)*ln((x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))-1/2*b/c*d^2/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)-1/2*b/c*d^2/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)-1/2*b*d*e*ln(c^2*x^4+1)/c","A"
22,1,167,150,0.028000," ","int((e*x+d)*(a+b*arctan(c*x^2)),x)","\frac{a \,x^{2} e}{2}+a d x +\frac{b \arctan \left(c \,x^{2}\right) x^{2} e}{2}+b \arctan \left(c \,x^{2}\right) d x -\frac{b d \sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b d \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b e \ln \left(c^{2} x^{4}+1\right)}{4 c}"," ",0,"1/2*a*x^2*e+a*d*x+1/2*b*arctan(c*x^2)*x^2*e+b*arctan(c*x^2)*d*x-1/4*b*d/c/(1/c^2)^(1/4)*2^(1/2)*ln((x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))-1/2*b*d/c/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)-1/2*b*d/c/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)-1/4*b*e*ln(c^2*x^4+1)/c","A"
23,1,138,421,0.139000," ","int((a+b*arctan(c*x^2))/(e*x+d),x)","\frac{a \ln \left(e x +d \right)}{e}+\frac{b \ln \left(e x +d \right) \arctan \left(c \,x^{2}\right)}{e}-\frac{b e \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} \textit{\_Z}^{4}-4 c^{2} d \,\textit{\_Z}^{3}+6 c^{2} d^{2} \textit{\_Z}^{2}-4 c^{2} d^{3} \textit{\_Z} +c^{2} d^{4}+e^{4}\right)}{\sum}\frac{\ln \left(e x +d \right) \ln \left(\frac{-e x +\textit{\_R1} -d}{\textit{\_R1}}\right)+\dilog \left(\frac{-e x +\textit{\_R1} -d}{\textit{\_R1}}\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} d +d^{2}}\right)}{2 c}"," ",0,"a*ln(e*x+d)/e+b*ln(e*x+d)/e*arctan(c*x^2)-1/2*b*e/c*sum(1/(_R1^2-2*_R1*d+d^2)*(ln(e*x+d)*ln((-e*x+_R1-d)/_R1)+dilog((-e*x+_R1-d)/_R1)),_R1=RootOf(_Z^4*c^2-4*_Z^3*c^2*d+6*_Z^2*c^2*d^2-4*_Z*c^2*d^3+c^2*d^4+e^4))","C"
24,1,433,292,0.043000," ","int((a+b*arctan(c*x^2))/(e*x+d)^2,x)","-\frac{a}{\left(e x +d \right) e}-\frac{b \arctan \left(c \,x^{2}\right)}{\left(e x +d \right) e}-\frac{2 b c d e \ln \left(e x +d \right)}{c^{2} d^{4}+e^{4}}+\frac{b \,e^{2} c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{4 c^{2} d^{4}+4 e^{4}}+\frac{b \,e^{2} c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 c^{2} d^{4}+2 e^{4}}+\frac{b \,e^{2} c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 c^{2} d^{4}+2 e^{4}}+\frac{b \,c^{3} d^{3} \arctan \left(x^{2} \sqrt{c^{2}}\right)}{e \left(c^{2} d^{4}+e^{4}\right) \sqrt{c^{2}}}-\frac{b c \,d^{2} \sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{4 \left(c^{2} d^{4}+e^{4}\right) \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b c \,d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 \left(c^{2} d^{4}+e^{4}\right) \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b c \,d^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 \left(c^{2} d^{4}+e^{4}\right) \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+\frac{b c d e \ln \left(c^{2} x^{4}+1\right)}{2 c^{2} d^{4}+2 e^{4}}"," ",0,"-a/(e*x+d)/e-b/(e*x+d)/e*arctan(c*x^2)-2*b*c*d*e*ln(e*x+d)/(c^2*d^4+e^4)+1/4*b*e^2*c/(c^2*d^4+e^4)*(1/c^2)^(1/4)*2^(1/2)*ln((x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))+1/2*b*e^2*c/(c^2*d^4+e^4)*(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)+1/2*b*e^2*c/(c^2*d^4+e^4)*(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)+b/e*c^3/(c^2*d^4+e^4)*d^3/(c^2)^(1/2)*arctan(x^2*(c^2)^(1/2))-1/4*b*c/(c^2*d^4+e^4)*d^2/(1/c^2)^(1/4)*2^(1/2)*ln((x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))-1/2*b*c/(c^2*d^4+e^4)*d^2/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)-1/2*b*c/(c^2*d^4+e^4)*d^2/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)+1/2*b*c*d*e*ln(c^2*x^4+1)/(c^2*d^4+e^4)","A"
25,0,0,1025,0.425000," ","int((e*x+d)*(a+b*arctan(c*x^2))^2,x)","\int \left(e x +d \right) \left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int((e*x+d)*(a+b*arctan(c*x^2))^2,x)","F"
26,0,0,22,1.092000," ","int((a+b*arctan(c*x^2))^2/(e*x+d),x)","\int \frac{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}}{e x +d}\, dx"," ",0,"int((a+b*arctan(c*x^2))^2/(e*x+d),x)","F"
27,0,0,22,0.710000," ","int((a+b*arctan(c*x^2))^2/(e*x+d)^2,x)","\int \frac{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((a+b*arctan(c*x^2))^2/(e*x+d)^2,x)","F"
28,1,536,244,0.175000," ","int((e*x+d)^2*(a+b*arctan(c*x^3)),x)","\frac{a \,e^{2} x^{3}}{3}+a e d \,x^{2}+a x \,d^{2}+\frac{a \,d^{3}}{3 e}+\frac{b \,e^{2} \arctan \left(c \,x^{3}\right) x^{3}}{3}+b e \arctan \left(c \,x^{3}\right) x^{2} d +b \arctan \left(c \,x^{3}\right) x \,d^{2}+\frac{b \,d^{3} \arctan \left(c \,x^{3}\right)}{3 e}+\frac{b c \ln \left(x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} d^{2}}{2}-\frac{b \,e^{2} \ln \left(x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{6 c}+\frac{b c \sqrt{\frac{1}{c^{2}}}\, \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right) d^{3}}{3 e}-\frac{b e \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right) d}{c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\frac{b e c \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} d}{4}-\frac{b c \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} d^{2}}{4}-\frac{b \,e^{2} \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{6 c}-\frac{b e \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) d}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\frac{b c \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) \sqrt{3}\, d^{2}}{2}-\frac{b c \sqrt{\frac{1}{c^{2}}}\, \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) d^{3}}{3 e}+\frac{b e c \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} d}{4}-\frac{b c \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} d^{2}}{4}-\frac{b \,e^{2} \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{6 c}-\frac{b e \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right) d}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\frac{b c \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right) \sqrt{3}\, d^{2}}{2}-\frac{b c \sqrt{\frac{1}{c^{2}}}\, \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right) d^{3}}{3 e}"," ",0,"1/3*a*e^2*x^3+a*e*d*x^2+a*x*d^2+1/3*a/e*d^3+1/3*b*e^2*arctan(c*x^3)*x^3+b*e*arctan(c*x^3)*x^2*d+b*arctan(c*x^3)*x*d^2+1/3*b*d^3*arctan(c*x^3)/e+1/2*b*c*ln(x^2+(1/c^2)^(1/3))*(1/c^2)^(2/3)*d^2-1/6*b*e^2/c*ln(x^2+(1/c^2)^(1/3))+1/3*b/e*c*(1/c^2)^(1/2)*arctan(x/(1/c^2)^(1/6))*d^3-b*e/c/(1/c^2)^(1/6)*arctan(x/(1/c^2)^(1/6))*d-1/4*b*e*c*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*3^(1/2)*(1/c^2)^(5/6)*d-1/4*b*c*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*(1/c^2)^(2/3)*d^2-1/6*b*e^2/c*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))-1/2*b*e/c/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*d-1/2*b*c*(1/c^2)^(2/3)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*3^(1/2)*d^2-1/3*b/e*c*(1/c^2)^(1/2)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*d^3+1/4*b*e*c*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*3^(1/2)*(1/c^2)^(5/6)*d-1/4*b*c*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*(1/c^2)^(2/3)*d^2-1/6*b*e^2/c*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))-1/2*b*e/c/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))*d+1/2*b*c*(1/c^2)^(2/3)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))*3^(1/2)*d^2-1/3*b/e*c*(1/c^2)^(1/2)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))*d^3","B"
29,1,314,214,0.122000," ","int((e*x+d)*(a+b*arctan(c*x^3)),x)","\frac{a \,x^{2} e}{2}+a d x +\frac{b \arctan \left(c \,x^{3}\right) x^{2} e}{2}+b \arctan \left(c \,x^{3}\right) d x +\frac{b c \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} d \ln \left(x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{2}-\frac{b e \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\frac{b \,c^{3} \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} d}{4}-\frac{b c \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} e}{8}-\frac{b \,c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) \sqrt{3}\, d}{2}-\frac{b \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) e}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\frac{b c \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} e}{8}-\frac{b c \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} d}{4}-\frac{b \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right) e}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\frac{b c \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right) \sqrt{3}\, d}{2}"," ",0,"1/2*a*x^2*e+a*d*x+1/2*b*arctan(c*x^3)*x^2*e+b*arctan(c*x^3)*d*x+1/2*b*c*(1/c^2)^(2/3)*d*ln(x^2+(1/c^2)^(1/3))-1/2*b/c*e/(1/c^2)^(1/6)*arctan(x/(1/c^2)^(1/6))-1/4*b*c^3*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*(1/c^2)^(5/3)*d-1/8*b*c*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*3^(1/2)*(1/c^2)^(5/6)*e-1/2*b*c^3*(1/c^2)^(5/3)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*3^(1/2)*d-1/4*b/c/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*e+1/8*b*c*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*3^(1/2)*(1/c^2)^(5/6)*e-1/4*b*c*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*(1/c^2)^(2/3)*d-1/4*b/c/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))*e+1/2*b*c*(1/c^2)^(2/3)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))*3^(1/2)*d","A"
30,1,172,615,0.149000," ","int((a+b*arctan(c*x^3))/(e*x+d),x)","\frac{a \ln \left(e x +d \right)}{e}+\frac{b \ln \left(e x +d \right) \arctan \left(c \,x^{3}\right)}{e}-\frac{b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(\textit{\_Z}^{6} c^{2}-6 c^{2} d \,\textit{\_Z}^{5}+15 c^{2} d^{2} \textit{\_Z}^{4}-20 c^{2} d^{3} \textit{\_Z}^{3}+15 c^{2} d^{4} \textit{\_Z}^{2}-6 c^{2} d^{5} \textit{\_Z} +c^{2} d^{6}+e^{6}\right)}{\sum}\frac{\ln \left(e x +d \right) \ln \left(\frac{-e x +\textit{\_R1} -d}{\textit{\_R1}}\right)+\dilog \left(\frac{-e x +\textit{\_R1} -d}{\textit{\_R1}}\right)}{\textit{\_R1}^{3}-3 \textit{\_R1}^{2} d +3 \textit{\_R1} \,d^{2}-d^{3}}\right)}{2 c}"," ",0,"a*ln(e*x+d)/e+b*ln(e*x+d)/e*arctan(c*x^3)-1/2*b*e^2/c*sum(1/(_R1^3-3*_R1^2*d+3*_R1*d^2-d^3)*(ln(e*x+d)*ln((-e*x+_R1-d)/_R1)+dilog((-e*x+_R1-d)/_R1)),_R1=RootOf(_Z^6*c^2-6*_Z^5*c^2*d+15*_Z^4*c^2*d^2-20*_Z^3*c^2*d^3+15*_Z^2*c^2*d^4-6*_Z*c^2*d^5+c^2*d^6+e^6))","C"
31,1,1220,766,0.229000," ","int((a+b*arctan(c*x^3))/(e*x+d)^2,x)","-\frac{b \,e^{4} c \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}{4 \left(c^{2} d^{6}+e^{6}\right)}-\frac{b \,e^{2} c \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) d^{2}}{2 \left(c^{2} d^{6}+e^{6}\right)}-\frac{b \,e^{2} c \ln \left(x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) d^{2}}{2 \left(c^{2} d^{6}+e^{6}\right)}-\frac{b \,e^{4} c \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}{4 \left(c^{2} d^{6}+e^{6}\right)}-\frac{b \,e^{2} c \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) d^{2}}{2 \left(c^{2} d^{6}+e^{6}\right)}-\frac{b \,c^{3} \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} d^{4}}{4 \left(c^{2} d^{6}+e^{6}\right)}-\frac{b \,c^{3} \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} d^{4}}{4 \left(c^{2} d^{6}+e^{6}\right)}-\frac{b \arctan \left(c \,x^{3}\right)}{\left(e x +d \right) e}-\frac{b \,e^{3} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{6}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right) d}{2 \left(c^{2} d^{6}+e^{6}\right)}-\frac{b \,e^{3} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{6}} \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right) d}{c^{2} d^{6}+e^{6}}-\frac{b \,e^{3} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{6}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) d}{2 \left(c^{2} d^{6}+e^{6}\right)}+\frac{b \,e^{4} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{4}{3}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) \sqrt{3}}{c^{2} d^{6}+e^{6}}-\frac{b \,c^{3} \sqrt{\frac{1}{c^{2}}}\, \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right) d^{5}}{e \left(c^{2} d^{6}+e^{6}\right)}+\frac{b e c \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right) d^{3}}{\left(c^{2} d^{6}+e^{6}\right) \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\frac{b e c \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) d^{3}}{2 \left(c^{2} d^{6}+e^{6}\right) \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\frac{b \,c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) \sqrt{3}\, d^{4}}{2 \left(c^{2} d^{6}+e^{6}\right)}-\frac{b \,e^{4} c \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) \sqrt{3}}{2 \left(c^{2} d^{6}+e^{6}\right)}+\frac{b \,c^{3} \sqrt{\frac{1}{c^{2}}}\, \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right) d^{5}}{e \left(c^{2} d^{6}+e^{6}\right)}+\frac{b e c \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right) d^{3}}{2 \left(c^{2} d^{6}+e^{6}\right) \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\frac{b \,e^{4} c \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right) \sqrt{3}}{2 \left(c^{2} d^{6}+e^{6}\right)}+\frac{b \,c^{3} \sqrt{\frac{1}{c^{2}}}\, \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right) d^{5}}{e \left(c^{2} d^{6}+e^{6}\right)}+\frac{b \,e^{4} c \ln \left(x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}{2 c^{2} d^{6}+2 e^{6}}+\frac{b \,c^{3} \ln \left(x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} d^{4}}{2 c^{2} d^{6}+2 e^{6}}+\frac{b e \,c^{3} \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} d^{3}}{4 c^{2} d^{6}+4 e^{6}}+\frac{b \,e^{3} c^{3} \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{7}{6}} d}{4 c^{2} d^{6}+4 e^{6}}+\frac{3 b c \,d^{2} e^{2} \ln \left(e x +d \right)}{c^{2} d^{6}+e^{6}}-\frac{b \,e^{3} c^{3} \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{7}{6}} d}{4 \left(c^{2} d^{6}+e^{6}\right)}-\frac{b e \,c^{3} \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right) \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} d^{3}}{4 \left(c^{2} d^{6}+e^{6}\right)}+\frac{b \,c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right) \sqrt{3}\, d^{4}}{2 c^{2} d^{6}+2 e^{6}}-\frac{a}{\left(e x +d \right) e}"," ",0,"-1/4*b*e^4*c/(c^2*d^6+e^6)*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*(1/c^2)^(1/3)-1/2*b*e^2*c/(c^2*d^6+e^6)*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*d^2+1/2*b*e^4*c/(c^2*d^6+e^6)*ln(x^2+(1/c^2)^(1/3))*(1/c^2)^(1/3)-1/2*b*e^2*c/(c^2*d^6+e^6)*ln(x^2+(1/c^2)^(1/3))*d^2-1/4*b*e^4*c/(c^2*d^6+e^6)*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*(1/c^2)^(1/3)-1/2*b*e^2*c/(c^2*d^6+e^6)*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*d^2+1/2*b*c^3/(c^2*d^6+e^6)*ln(x^2+(1/c^2)^(1/3))*(1/c^2)^(2/3)*d^4-1/4*b*c^3/(c^2*d^6+e^6)*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*(1/c^2)^(2/3)*d^4-1/4*b*c^3/(c^2*d^6+e^6)*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*(1/c^2)^(2/3)*d^4-b/(e*x+d)/e*arctan(c*x^3)+1/2*b*c^3/(c^2*d^6+e^6)*(1/c^2)^(2/3)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))*3^(1/2)*d^4-1/2*b*e^3*c^3/(c^2*d^6+e^6)*(1/c^2)^(7/6)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))*d-b*e^3*c^3/(c^2*d^6+e^6)*(1/c^2)^(7/6)*arctan(x/(1/c^2)^(1/6))*d-1/2*b*e^3*c^3/(c^2*d^6+e^6)*(1/c^2)^(7/6)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*d+b*e^4*c^3/(c^2*d^6+e^6)*(1/c^2)^(4/3)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*3^(1/2)-b/e*c^3/(c^2*d^6+e^6)*(1/c^2)^(1/2)*arctan(x/(1/c^2)^(1/6))*d^5+b*e*c/(c^2*d^6+e^6)/(1/c^2)^(1/6)*arctan(x/(1/c^2)^(1/6))*d^3+1/2*b*e*c/(c^2*d^6+e^6)/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*d^3-1/2*b*c^3/(c^2*d^6+e^6)*(1/c^2)^(2/3)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*3^(1/2)*d^4-1/2*b*e^4*c/(c^2*d^6+e^6)*(1/c^2)^(1/3)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*3^(1/2)+b/e*c^3/(c^2*d^6+e^6)*(1/c^2)^(1/2)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))*d^5+1/2*b*e*c/(c^2*d^6+e^6)/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))*d^3-1/2*b*e^4*c/(c^2*d^6+e^6)*(1/c^2)^(1/3)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))*3^(1/2)+b/e*c^3/(c^2*d^6+e^6)*(1/c^2)^(1/2)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))*d^5+3*b*c*d^2*e^2*ln(e*x+d)/(c^2*d^6+e^6)-1/4*b*e^3*c^3/(c^2*d^6+e^6)*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*3^(1/2)*(1/c^2)^(7/6)*d-1/4*b*e*c^3/(c^2*d^6+e^6)*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*3^(1/2)*(1/c^2)^(5/6)*d^3+1/4*b*e^3*c^3/(c^2*d^6+e^6)*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*3^(1/2)*(1/c^2)^(7/6)*d+1/4*b*e*c^3/(c^2*d^6+e^6)*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))*3^(1/2)*(1/c^2)^(5/6)*d^3-a/(e*x+d)/e","A"