1,1,225,64,0.038000," ","int((d*e*x+c*e)^3*(a+b*arctan(d*x+c)),x)","\frac{d^{3} x^{4} a \,e^{3}}{4}+d^{2} x^{3} a c \,e^{3}+\frac{3 d \,x^{2} a \,c^{2} e^{3}}{2}+x a \,c^{3} e^{3}+\frac{a \,c^{4} e^{3}}{4 d}+\frac{d^{3} \arctan \left(d x +c \right) x^{4} b \,e^{3}}{4}+d^{2} \arctan \left(d x +c \right) x^{3} b c \,e^{3}+\frac{3 d \arctan \left(d x +c \right) x^{2} b \,c^{2} e^{3}}{2}+\arctan \left(d x +c \right) x b \,c^{3} e^{3}+\frac{\arctan \left(d x +c \right) b \,c^{4} e^{3}}{4 d}-\frac{d^{2} x^{3} b \,e^{3}}{12}-\frac{d \,x^{2} b c \,e^{3}}{4}-\frac{x b \,c^{2} e^{3}}{4}-\frac{b \,c^{3} e^{3}}{12 d}+\frac{b \,e^{3} x}{4}+\frac{b c \,e^{3}}{4 d}-\frac{b \,e^{3} \arctan \left(d x +c \right)}{4 d}"," ",0,"1/4*d^3*x^4*a*e^3+d^2*x^3*a*c*e^3+3/2*d*x^2*a*c^2*e^3+x*a*c^3*e^3+1/4/d*a*c^4*e^3+1/4*d^3*arctan(d*x+c)*x^4*b*e^3+d^2*arctan(d*x+c)*x^3*b*c*e^3+3/2*d*arctan(d*x+c)*x^2*b*c^2*e^3+arctan(d*x+c)*x*b*c^3*e^3+1/4/d*arctan(d*x+c)*b*c^4*e^3-1/12*d^2*x^3*b*e^3-1/4*d*x^2*b*c*e^3-1/4*x*b*c^2*e^3-1/12/d*b*c^3*e^3+1/4*b*e^3*x+1/4/d*b*c*e^3-1/4*b*e^3*arctan(d*x+c)/d","B"
2,1,161,61,0.040000," ","int((d*e*x+c*e)^2*(a+b*arctan(d*x+c)),x)","\frac{d^{2} x^{3} a \,e^{2}}{3}+d \,x^{2} a c \,e^{2}+x a \,c^{2} e^{2}+\frac{a \,c^{3} e^{2}}{3 d}+\frac{d^{2} \arctan \left(d x +c \right) x^{3} b \,e^{2}}{3}+d \arctan \left(d x +c \right) x^{2} b c \,e^{2}+\arctan \left(d x +c \right) x b \,c^{2} e^{2}+\frac{\arctan \left(d x +c \right) b \,c^{3} e^{2}}{3 d}-\frac{d \,x^{2} b \,e^{2}}{6}-\frac{x b c \,e^{2}}{3}-\frac{b \,c^{2} e^{2}}{6 d}+\frac{b \,e^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{6 d}"," ",0,"1/3*d^2*x^3*a*e^2+d*x^2*a*c*e^2+x*a*c^2*e^2+1/3/d*a*c^3*e^2+1/3*d^2*arctan(d*x+c)*x^3*b*e^2+d*arctan(d*x+c)*x^2*b*c*e^2+arctan(d*x+c)*x*b*c^2*e^2+1/3/d*arctan(d*x+c)*b*c^3*e^2-1/6*d*x^2*b*e^2-1/3*x*b*c*e^2-1/6/d*b*c^2*e^2+1/6*b*e^2*ln(1+(d*x+c)^2)/d","B"
3,1,92,42,0.038000," ","int((d*e*x+c*e)*(a+b*arctan(d*x+c)),x)","\frac{a e d \,x^{2}}{2}+x a c e +\frac{a \,c^{2} e}{2 d}+\frac{d \arctan \left(d x +c \right) x^{2} b e}{2}+\arctan \left(d x +c \right) x b c e +\frac{\arctan \left(d x +c \right) b \,c^{2} e}{2 d}-\frac{b e x}{2}-\frac{b c e}{2 d}+\frac{b e \arctan \left(d x +c \right)}{2 d}"," ",0,"1/2*a*e*d*x^2+x*a*c*e+1/2/d*a*c^2*e+1/2*d*arctan(d*x+c)*x^2*b*e+arctan(d*x+c)*x*b*c*e+1/2/d*arctan(d*x+c)*b*c^2*e-1/2*b*e*x-1/2/d*b*c*e+1/2*b*e*arctan(d*x+c)/d","B"
4,1,132,55,0.058000," ","int((a+b*arctan(d*x+c))/(d*e*x+c*e),x)","\frac{a \ln \left(d x +c \right)}{d e}+\frac{b \ln \left(d x +c \right) \arctan \left(d x +c \right)}{d e}+\frac{i b \ln \left(d x +c \right) \ln \left(1+i \left(d x +c \right)\right)}{2 d e}-\frac{i b \ln \left(d x +c \right) \ln \left(1-i \left(d x +c \right)\right)}{2 d e}+\frac{i b \dilog \left(1+i \left(d x +c \right)\right)}{2 d e}-\frac{i b \dilog \left(1-i \left(d x +c \right)\right)}{2 d e}"," ",0,"a*ln(d*x+c)/d/e+1/d*b/e*ln(d*x+c)*arctan(d*x+c)+1/2*I/d*b/e*ln(d*x+c)*ln(1+I*(d*x+c))-1/2*I/d*b/e*ln(d*x+c)*ln(1-I*(d*x+c))+1/2*I/d*b/e*dilog(1+I*(d*x+c))-1/2*I/d*b/e*dilog(1-I*(d*x+c))","B"
5,1,73,61,0.044000," ","int((a+b*arctan(d*x+c))/(d*e*x+c*e)^2,x)","-\frac{a}{d \,e^{2} \left(d x +c \right)}-\frac{b \arctan \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}+\frac{b \ln \left(d x +c \right)}{d \,e^{2}}-\frac{b \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d \,e^{2}}"," ",0,"-1/d*a/e^2/(d*x+c)-1/d*b/e^2/(d*x+c)*arctan(d*x+c)+b*ln(d*x+c)/d/e^2-1/2*b*ln(1+(d*x+c)^2)/d/e^2","A"
6,1,71,60,0.043000," ","int((a+b*arctan(d*x+c))/(d*e*x+c*e)^3,x)","-\frac{a}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b \arctan \left(d x +c \right)}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b}{2 d \,e^{3} \left(d x +c \right)}-\frac{b \arctan \left(d x +c \right)}{2 d \,e^{3}}"," ",0,"-1/2/d*a/e^3/(d*x+c)^2-1/2/d*b/e^3/(d*x+c)^2*arctan(d*x+c)-1/2*b/d/e^3/(d*x+c)-1/2*b*arctan(d*x+c)/d/e^3","A"
7,1,543,143,0.057000," ","int((d*e*x+c*e)^3*(a+b*arctan(d*x+c))^2,x)","\frac{\arctan \left(d x +c \right) b^{2} c \,e^{3}}{2 d}-\frac{e^{3} a b \arctan \left(d x +c \right)}{2 d}-\frac{\arctan \left(d x +c \right) x \,b^{2} c^{2} e^{3}}{2}-\frac{x a b \,c^{2} e^{3}}{2}-\frac{d^{2} x^{3} a b \,e^{3}}{6}+\frac{3 d \,x^{2} a^{2} c^{2} e^{3}}{2}+d^{2} x^{3} a^{2} c \,e^{3}+\frac{\arctan \left(d x +c \right)^{2} b^{2} c^{4} e^{3}}{4 d}-\frac{\arctan \left(d x +c \right) b^{2} c^{3} e^{3}}{6 d}+\frac{d^{3} \arctan \left(d x +c \right)^{2} x^{4} b^{2} e^{3}}{4}-\frac{d^{2} \arctan \left(d x +c \right) x^{3} b^{2} e^{3}}{6}-\frac{a b \,c^{3} e^{3}}{6 d}+\frac{a b c \,e^{3}}{2 d}+x \,a^{2} c^{3} e^{3}+\frac{d \,x^{2} b^{2} e^{3}}{12}+\frac{\arctan \left(d x +c \right) x \,b^{2} e^{3}}{2}-\frac{e^{3} b^{2} \arctan \left(d x +c \right)^{2}}{4 d}+\frac{d^{3} x^{4} a^{2} e^{3}}{4}+\frac{a^{2} c^{4} e^{3}}{4 d}+\frac{x \,b^{2} c \,e^{3}}{6}+\frac{b^{2} c^{2} e^{3}}{12 d}+\frac{a b \,e^{3} x}{2}-\frac{b^{2} e^{3} \ln \left(1+\left(d x +c \right)^{2}\right)}{3 d}+\frac{d^{3} \arctan \left(d x +c \right) x^{4} a b \,e^{3}}{2}-\frac{d \,x^{2} a b c \,e^{3}}{2}+d^{2} \arctan \left(d x +c \right)^{2} x^{3} b^{2} c \,e^{3}+\frac{\arctan \left(d x +c \right) a b \,c^{4} e^{3}}{2 d}+\frac{3 d \arctan \left(d x +c \right)^{2} x^{2} b^{2} c^{2} e^{3}}{2}-\frac{d \arctan \left(d x +c \right) x^{2} b^{2} c \,e^{3}}{2}+2 \arctan \left(d x +c \right) x a b \,c^{3} e^{3}+2 d^{2} \arctan \left(d x +c \right) x^{3} a b c \,e^{3}+3 d \arctan \left(d x +c \right) x^{2} a b \,c^{2} e^{3}+\arctan \left(d x +c \right)^{2} x \,b^{2} c^{3} e^{3}"," ",0,"1/2/d*arctan(d*x+c)*b^2*c*e^3-1/2/d*e^3*a*b*arctan(d*x+c)-1/2*arctan(d*x+c)*x*b^2*c^2*e^3-1/2*x*a*b*c^2*e^3-1/6*d^2*x^3*a*b*e^3+3/2*d*x^2*a^2*c^2*e^3+d^2*x^3*a^2*c*e^3+1/4/d*arctan(d*x+c)^2*b^2*c^4*e^3-1/6/d*arctan(d*x+c)*b^2*c^3*e^3+1/4*d^3*arctan(d*x+c)^2*x^4*b^2*e^3-1/6*d^2*arctan(d*x+c)*x^3*b^2*e^3-1/6/d*a*b*c^3*e^3+1/2/d*a*b*c*e^3+x*a^2*c^3*e^3+1/12*d*x^2*b^2*e^3+1/2*arctan(d*x+c)*x*b^2*e^3-1/4/d*e^3*b^2*arctan(d*x+c)^2+1/4*d^3*x^4*a^2*e^3+1/4/d*a^2*c^4*e^3+1/6*x*b^2*c*e^3+1/12/d*b^2*c^2*e^3+1/2*a*b*e^3*x-1/3*b^2*e^3*ln(1+(d*x+c)^2)/d+1/2*d^3*arctan(d*x+c)*x^4*a*b*e^3-1/2*d*x^2*a*b*c*e^3+d^2*arctan(d*x+c)^2*x^3*b^2*c*e^3+1/2/d*arctan(d*x+c)*a*b*c^4*e^3+3/2*d*arctan(d*x+c)^2*x^2*b^2*c^2*e^3-1/2*d*arctan(d*x+c)*x^2*b^2*c*e^3+2*arctan(d*x+c)*x*a*b*c^3*e^3+2*d^2*arctan(d*x+c)*x^3*a*b*c*e^3+3*d*arctan(d*x+c)*x^2*a*b*c^2*e^3+arctan(d*x+c)^2*x*b^2*c^3*e^3","B"
8,1,593,165,0.203000," ","int((d*e*x+c*e)^2*(a+b*arctan(d*x+c))^2,x)","\frac{a^{2} c^{3} e^{2}}{3 d}+\frac{b^{2} c \,e^{2}}{3 d}+\arctan \left(d x +c \right)^{2} x \,b^{2} c^{2} e^{2}-\frac{d \,x^{2} a b \,e^{2}}{3}+d \,x^{2} a^{2} c \,e^{2}+\frac{\arctan \left(d x +c \right)^{2} b^{2} c^{3} e^{2}}{3 d}-\frac{\arctan \left(d x +c \right) b^{2} c^{2} e^{2}}{3 d}+\frac{d^{2} \arctan \left(d x +c \right)^{2} x^{3} b^{2} e^{2}}{3}-\frac{d \arctan \left(d x +c \right) x^{2} b^{2} e^{2}}{3}+\frac{e^{2} a b \ln \left(1+\left(d x +c \right)^{2}\right)}{3 d}+\frac{d^{2} x^{3} a^{2} e^{2}}{3}+x \,a^{2} c^{2} e^{2}+\frac{e^{2} b^{2} \arctan \left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{3 d}-\frac{2 \arctan \left(d x +c \right) x \,b^{2} c \,e^{2}}{3}-\frac{2 x a b c \,e^{2}}{3}-\frac{i e^{2} b^{2} \ln \left(d x +c -i\right)^{2}}{12 d}+\frac{i e^{2} b^{2} \ln \left(d x +c +i\right)^{2}}{12 d}+\frac{i e^{2} b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right)}{6 d}-\frac{i e^{2} b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{6 d}-\frac{a b \,c^{2} e^{2}}{3 d}-\frac{b^{2} e^{2} \arctan \left(d x +c \right)}{3 d}+\frac{i e^{2} b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right)}{6 d}+\frac{i e^{2} b^{2} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{6 d}-\frac{i e^{2} b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{6 d}-\frac{i e^{2} b^{2} \ln \left(d x +c +i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{6 d}+\frac{2 \arctan \left(d x +c \right) a b \,c^{3} e^{2}}{3 d}+\frac{2 d^{2} \arctan \left(d x +c \right) x^{3} a b \,e^{2}}{3}+d \arctan \left(d x +c \right)^{2} x^{2} b^{2} c \,e^{2}+2 \arctan \left(d x +c \right) x a b \,c^{2} e^{2}+2 d \arctan \left(d x +c \right) x^{2} a b c \,e^{2}+\frac{b^{2} e^{2} x}{3}"," ",0,"1/3/d*a^2*c^3*e^2+1/3/d*b^2*c*e^2-1/12*I/d*e^2*b^2*ln(d*x+c-I)^2+1/6*I/d*e^2*b^2*dilog(1/2*I*(d*x+c-I))+arctan(d*x+c)^2*x*b^2*c^2*e^2-1/6*I/d*e^2*b^2*dilog(-1/2*I*(I+d*x+c))-1/3*d*x^2*a*b*e^2+d*x^2*a^2*c*e^2+1/3/d*arctan(d*x+c)^2*b^2*c^3*e^2-1/3/d*arctan(d*x+c)*b^2*c^2*e^2+1/3*d^2*arctan(d*x+c)^2*x^3*b^2*e^2-1/3*d*arctan(d*x+c)*x^2*b^2*e^2+1/3/d*e^2*a*b*ln(1+(d*x+c)^2)+1/3*d^2*x^3*a^2*e^2+x*a^2*c^2*e^2+1/12*I/d*e^2*b^2*ln(I+d*x+c)^2+1/3/d*e^2*b^2*arctan(d*x+c)*ln(1+(d*x+c)^2)-2/3*arctan(d*x+c)*x*b^2*c*e^2-2/3*x*a*b*c*e^2-1/3/d*a*b*c^2*e^2-1/3*b^2*e^2*arctan(d*x+c)/d-1/6*I/d*e^2*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))-1/6*I/d*e^2*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)+1/6*I/d*e^2*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)+1/6*I/d*e^2*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))+2/3/d*arctan(d*x+c)*a*b*c^3*e^2+2/3*d^2*arctan(d*x+c)*x^3*a*b*e^2+d*arctan(d*x+c)^2*x^2*b^2*c*e^2+2*arctan(d*x+c)*x*a*b*c^2*e^2+2*d*arctan(d*x+c)*x^2*a*b*c*e^2+1/3*b^2*e^2*x","B"
9,1,220,89,0.056000," ","int((d*e*x+c*e)*(a+b*arctan(d*x+c))^2,x)","\frac{a^{2} e \,x^{2} d}{2}+x \,a^{2} c e +\frac{a^{2} c^{2} e}{2 d}+\frac{d \arctan \left(d x +c \right)^{2} x^{2} b^{2} e}{2}+\arctan \left(d x +c \right)^{2} x \,b^{2} c e +\frac{\arctan \left(d x +c \right)^{2} b^{2} c^{2} e}{2 d}+\frac{e \,b^{2} \arctan \left(d x +c \right)^{2}}{2 d}-\arctan \left(d x +c \right) x \,b^{2} e -\frac{\arctan \left(d x +c \right) b^{2} c e}{d}+\frac{b^{2} e \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}+d \arctan \left(d x +c \right) x^{2} a b e +2 \arctan \left(d x +c \right) x a b c e +\frac{\arctan \left(d x +c \right) a b \,c^{2} e}{d}+\frac{e a b \arctan \left(d x +c \right)}{d}-a b e x -\frac{a b c e}{d}"," ",0,"1/2*a^2*e*x^2*d+x*a^2*c*e+1/2/d*a^2*c^2*e+1/2*d*arctan(d*x+c)^2*x^2*b^2*e+arctan(d*x+c)^2*x*b^2*c*e+1/2/d*arctan(d*x+c)^2*b^2*c^2*e+1/2/d*e*b^2*arctan(d*x+c)^2-arctan(d*x+c)*x*b^2*e-1/d*arctan(d*x+c)*b^2*c*e+1/2*b^2*e*ln(1+(d*x+c)^2)/d+d*arctan(d*x+c)*x^2*a*b*e+2*arctan(d*x+c)*x*a*b*c*e+1/d*arctan(d*x+c)*a*b*c^2*e+1/d*e*a*b*arctan(d*x+c)-a*b*e*x-1/d*a*b*c*e","B"
10,1,1433,172,0.775000," ","int((a+b*arctan(d*x+c))^2/(d*e*x+c*e),x)","\frac{2 a b \ln \left(d x +c \right) \arctan \left(d x +c \right)}{d e}+\frac{i b^{2} \pi  \arctan \left(d x +c \right)^{2}}{2 d e}-\frac{2 i b^{2} \arctan \left(d x +c \right) \polylog \left(2, \frac{1+i \left(d x +c \right)}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d e}-\frac{2 i b^{2} \arctan \left(d x +c \right) \polylog \left(2, -\frac{1+i \left(d x +c \right)}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d e}+\frac{i a b \dilog \left(1+i \left(d x +c \right)\right)}{d e}-\frac{i a b \dilog \left(1-i \left(d x +c \right)\right)}{d e}+\frac{i b^{2} \arctan \left(d x +c \right) \polylog \left(2, -\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{2 b^{2} \polylog \left(3, -\frac{1+i \left(d x +c \right)}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d e}+\frac{2 b^{2} \polylog \left(3, \frac{1+i \left(d x +c \right)}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d e}-\frac{b^{2} \polylog \left(3, -\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}\right)}{2 d e}+\frac{b^{2} \arctan \left(d x +c \right)^{2} \ln \left(1+\frac{1+i \left(d x +c \right)}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d e}+\frac{b^{2} \arctan \left(d x +c \right)^{2} \ln \left(1-\frac{1+i \left(d x +c \right)}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d e}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right)^{2} \arctan \left(d x +c \right)^{2}}{2 d e}+\frac{i a b \ln \left(d x +c \right) \ln \left(1+i \left(d x +c \right)\right)}{d e}-\frac{b^{2} \arctan \left(d x +c \right)^{2} \ln \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1\right)}{d e}-\frac{i a b \ln \left(d x +c \right) \ln \left(1-i \left(d x +c \right)\right)}{d e}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1\right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right)^{2} \arctan \left(d x +c \right)^{2}}{2 d e}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1\right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right)^{2} \arctan \left(d x +c \right)^{2}}{2 d e}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1\right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right) \arctan \left(d x +c \right)^{2}}{2 d e}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1\right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right)^{2} \arctan \left(d x +c \right)^{2}}{2 d e}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1\right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right)^{3} \arctan \left(d x +c \right)^{2}}{2 d e}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right)^{3} \arctan \left(d x +c \right)^{2}}{2 d e}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-1\right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right) \arctan \left(d x +c \right)^{2}}{2 d e}+\frac{a^{2} \ln \left(d x +c \right)}{d e}+\frac{b^{2} \ln \left(d x +c \right) \arctan \left(d x +c \right)^{2}}{d e}"," ",0,"-2*I/d*b^2/e*arctan(d*x+c)*polylog(2,(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))-2*I/d*b^2/e*arctan(d*x+c)*polylog(2,-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+I/d*a*b/e*dilog(1+I*(d*x+c))+2/d*a*b/e*ln(d*x+c)*arctan(d*x+c)-I/d*a*b/e*dilog(1-I*(d*x+c))+1/2*I/d*b^2/e*Pi*arctan(d*x+c)^2+I/d*b^2/e*arctan(d*x+c)*polylog(2,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))-I/d*a*b/e*ln(d*x+c)*ln(1-I*(d*x+c))+I/d*a*b/e*ln(d*x+c)*ln(1+I*(d*x+c))+1/2*I/d*b^2/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1))*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^2+1/2*I/d*b^2/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*arctan(d*x+c)^2+1/2*I/d*b^2/e*Pi*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*arctan(d*x+c)^2-1/2*I/d*b^2/e*Pi*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2-1/2*I/d*b^2/e*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2-1/2*I/d*b^2/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2+1/2*I/d*b^2/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^2-1/2*I/d*b^2/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2+2/d*b^2/e*polylog(3,-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+2/d*b^2/e*polylog(3,(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+1/d*a^2/e*ln(d*x+c)-1/2/d*b^2/e*polylog(3,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))+1/d*b^2/e*arctan(d*x+c)^2*ln(1+(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+1/d*b^2/e*arctan(d*x+c)^2*ln(1-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+1/d*b^2/e*ln(d*x+c)*arctan(d*x+c)^2-1/d*b^2/e*arctan(d*x+c)^2*ln((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)","C"
11,1,471,115,0.172000," ","int((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^2,x)","-\frac{a^{2}}{d \,e^{2} \left(d x +c \right)}-\frac{b^{2} \arctan \left(d x +c \right)^{2}}{d \,e^{2} \left(d x +c \right)}+\frac{2 b^{2} \ln \left(d x +c \right) \arctan \left(d x +c \right)}{d \,e^{2}}-\frac{b^{2} \arctan \left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{d \,e^{2}}-\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d \,e^{2}}-\frac{i b^{2} \ln \left(d x +c +i\right)^{2}}{4 d \,e^{2}}+\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{2 d \,e^{2}}-\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right)}{2 d \,e^{2}}+\frac{i b^{2} \dilog \left(1+i \left(d x +c \right)\right)}{d \,e^{2}}-\frac{i b^{2} \dilog \left(1-i \left(d x +c \right)\right)}{d \,e^{2}}+\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{2 d \,e^{2}}-\frac{i b^{2} \ln \left(d x +c \right) \ln \left(1-i \left(d x +c \right)\right)}{d \,e^{2}}+\frac{i b^{2} \ln \left(d x +c \right) \ln \left(1+i \left(d x +c \right)\right)}{d \,e^{2}}+\frac{i b^{2} \ln \left(d x +c -i\right)^{2}}{4 d \,e^{2}}-\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right)}{2 d \,e^{2}}+\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d \,e^{2}}-\frac{2 a b \arctan \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}+\frac{2 a b \ln \left(d x +c \right)}{d \,e^{2}}-\frac{a b \ln \left(1+\left(d x +c \right)^{2}\right)}{d \,e^{2}}"," ",0,"-1/d*a^2/e^2/(d*x+c)-1/d*b^2/e^2/(d*x+c)*arctan(d*x+c)^2+2/d*b^2/e^2*ln(d*x+c)*arctan(d*x+c)-1/d*b^2/e^2*arctan(d*x+c)*ln(1+(d*x+c)^2)-1/2*I/d*b^2/e^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)-1/4*I/d*b^2/e^2*ln(I+d*x+c)^2+1/2*I/d*b^2/e^2*dilog(-1/2*I*(I+d*x+c))+1/2*I/d*b^2/e^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))-I/d*b^2/e^2*dilog(1-I*(d*x+c))+I/d*b^2/e^2*dilog(1+I*(d*x+c))-I/d*b^2/e^2*ln(d*x+c)*ln(1-I*(d*x+c))+I/d*b^2/e^2*ln(d*x+c)*ln(1+I*(d*x+c))+1/4*I/d*b^2/e^2*ln(d*x+c-I)^2-1/2*I/d*b^2/e^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))-1/2*I/d*b^2/e^2*dilog(1/2*I*(d*x+c-I))+1/2*I/d*b^2/e^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)-2/d*a*b/e^2/(d*x+c)*arctan(d*x+c)+2/d*a*b/e^2*ln(d*x+c)-1/d*a*b/e^2*ln(1+(d*x+c)^2)","B"
12,1,182,111,0.057000," ","int((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^3,x)","-\frac{a^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b^{2} \arctan \left(d x +c \right)^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b^{2} \arctan \left(d x +c \right)}{d \,e^{3} \left(d x +c \right)}-\frac{b^{2} \arctan \left(d x +c \right)^{2}}{2 d \,e^{3}}+\frac{b^{2} \ln \left(d x +c \right)}{d \,e^{3}}-\frac{b^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d \,e^{3}}-\frac{a b \arctan \left(d x +c \right)}{d \,e^{3} \left(d x +c \right)^{2}}-\frac{a b}{d \,e^{3} \left(d x +c \right)}-\frac{a b \arctan \left(d x +c \right)}{d \,e^{3}}"," ",0,"-1/2/d*a^2/e^3/(d*x+c)^2-1/2/d*b^2/e^3/(d*x+c)^2*arctan(d*x+c)^2-1/d*b^2/e^3*arctan(d*x+c)/(d*x+c)-1/2/d*b^2/e^3*arctan(d*x+c)^2+b^2*ln(d*x+c)/d/e^3-1/2*b^2*ln(1+(d*x+c)^2)/d/e^3-1/d*a*b/e^3/(d*x+c)^2*arctan(d*x+c)-1/d*a*b/e^3/(d*x+c)-1/d*a*b/e^3*arctan(d*x+c)","A"
13,1,547,176,0.143000," ","int((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^4,x)","-\frac{a^{2}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b^{2} \arctan \left(d x +c \right)^{2}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b^{2} \arctan \left(d x +c \right)}{3 d \,e^{4} \left(d x +c \right)^{2}}-\frac{2 b^{2} \ln \left(d x +c \right) \arctan \left(d x +c \right)}{3 d \,e^{4}}+\frac{b^{2} \arctan \left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{3 d \,e^{4}}+\frac{i b^{2} \ln \left(d x +c +i\right)^{2}}{12 d \,e^{4}}-\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{6 d \,e^{4}}+\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right)}{6 d \,e^{4}}-\frac{i b^{2} \ln \left(d x +c -i\right)^{2}}{12 d \,e^{4}}+\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right)}{6 d \,e^{4}}-\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{6 d \,e^{4}}-\frac{i b^{2} \dilog \left(1+i \left(d x +c \right)\right)}{3 d \,e^{4}}-\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{6 d \,e^{4}}-\frac{b^{2}}{3 d \,e^{4} \left(d x +c \right)}-\frac{b^{2} \arctan \left(d x +c \right)}{3 d \,e^{4}}-\frac{i b^{2} \ln \left(d x +c \right) \ln \left(1+i \left(d x +c \right)\right)}{3 d \,e^{4}}+\frac{i b^{2} \dilog \left(1-i \left(d x +c \right)\right)}{3 d \,e^{4}}+\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{6 d \,e^{4}}+\frac{i b^{2} \ln \left(d x +c \right) \ln \left(1-i \left(d x +c \right)\right)}{3 d \,e^{4}}-\frac{2 a b \arctan \left(d x +c \right)}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{a b}{3 d \,e^{4} \left(d x +c \right)^{2}}-\frac{2 a b \ln \left(d x +c \right)}{3 d \,e^{4}}+\frac{a b \ln \left(1+\left(d x +c \right)^{2}\right)}{3 d \,e^{4}}"," ",0,"-1/3/d*a^2/e^4/(d*x+c)^3-1/3/d*b^2/e^4/(d*x+c)^3*arctan(d*x+c)^2-1/3/d*b^2/e^4*arctan(d*x+c)/(d*x+c)^2-2/3/d*b^2/e^4*ln(d*x+c)*arctan(d*x+c)+1/3/d*b^2/e^4*arctan(d*x+c)*ln(1+(d*x+c)^2)+1/12*I/d*b^2/e^4*ln(I+d*x+c)^2-1/6*I/d*b^2/e^4*ln(I+d*x+c)*ln(1+(d*x+c)^2)-1/12*I/d*b^2/e^4*ln(d*x+c-I)^2-1/3*I/d*b^2/e^4*dilog(1+I*(d*x+c))+1/6*I/d*b^2/e^4*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))-1/6*I/d*b^2/e^4*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))+1/6*I/d*b^2/e^4*dilog(1/2*I*(d*x+c-I))-1/6*I/d*b^2/e^4*dilog(-1/2*I*(I+d*x+c))-1/3*b^2/d/e^4/(d*x+c)-1/3*b^2*arctan(d*x+c)/d/e^4-1/3*I/d*b^2/e^4*ln(d*x+c)*ln(1+I*(d*x+c))+1/3*I/d*b^2/e^4*dilog(1-I*(d*x+c))+1/6*I/d*b^2/e^4*ln(d*x+c-I)*ln(1+(d*x+c)^2)+1/3*I/d*b^2/e^4*ln(d*x+c)*ln(1-I*(d*x+c))-2/3/d*a*b/e^4/(d*x+c)^3*arctan(d*x+c)-1/3/d*a*b/e^4/(d*x+c)^2-2/3/d*a*b/e^4*ln(d*x+c)+1/3/d*a*b/e^4*ln(1+(d*x+c)^2)","B"
14,1,242,156,0.065000," ","int((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^5,x)","-\frac{a^{2}}{4 d \,e^{5} \left(d x +c \right)^{4}}-\frac{b^{2} \arctan \left(d x +c \right)^{2}}{4 d \,e^{5} \left(d x +c \right)^{4}}-\frac{b^{2} \arctan \left(d x +c \right)}{6 d \,e^{5} \left(d x +c \right)^{3}}+\frac{b^{2} \arctan \left(d x +c \right)}{2 d \,e^{5} \left(d x +c \right)}+\frac{b^{2} \arctan \left(d x +c \right)^{2}}{4 d \,e^{5}}-\frac{b^{2}}{12 d \,e^{5} \left(d x +c \right)^{2}}-\frac{2 b^{2} \ln \left(d x +c \right)}{3 d \,e^{5}}+\frac{b^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{3 d \,e^{5}}-\frac{a b \arctan \left(d x +c \right)}{2 d \,e^{5} \left(d x +c \right)^{4}}-\frac{a b}{6 d \,e^{5} \left(d x +c \right)^{3}}+\frac{a b}{2 d \,e^{5} \left(d x +c \right)}+\frac{a b \arctan \left(d x +c \right)}{2 d \,e^{5}}"," ",0,"-1/4/d*a^2/e^5/(d*x+c)^4-1/4/d*b^2/e^5/(d*x+c)^4*arctan(d*x+c)^2-1/6/d*b^2/e^5*arctan(d*x+c)/(d*x+c)^3+1/2/d*b^2/e^5*arctan(d*x+c)/(d*x+c)+1/4/d*b^2/e^5*arctan(d*x+c)^2-1/12*b^2/d/e^5/(d*x+c)^2-2/3*b^2*ln(d*x+c)/d/e^5+1/3*b^2*ln(1+(d*x+c)^2)/d/e^5-1/2/d*a*b/e^5/(d*x+c)^4*arctan(d*x+c)-1/6/d*a*b/e^5/(d*x+c)^3+1/2/d*a*b/e^5/(d*x+c)+1/2/d*a*b/e^5*arctan(d*x+c)","A"
15,1,3242,254,2.247000," ","int((d*e*x+c*e)^2*(a+b*arctan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"1/4/d*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2*arctan(d*x+c)^2*Pi*b^3*c*e^2+1/4*I/d*e^2*b^3*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^2*Pi-1/8*I/d*e^2*b^3*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2*Pi-1/4*I/d*e^2*b^3*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)*arctan(d*x+c)^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2*Pi-1/2*I/d*e^2*b^3*arctan(d*x+c)^2*csgn(I*(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))^2*Pi+1/4*I/d*e^2*b^3*csgn(I*(1+I*(d*x+c))^4/(1+(d*x+c)^2)^2+2*I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)*arctan(d*x+c)^2*Pi-1/4/d*csgn(I*(1+I*(d*x+c))^4/(1+(d*x+c)^2)^2+2*I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)*arctan(d*x+c)^2*Pi*b^3*c*e^2-1/4*I/d*e^2*b^3*arctan(d*x+c)^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))*Pi-1/8*I/d*e^2*b^3*csgn(I*(1+I*(d*x+c))^4/(1+(d*x+c)^2)^2+2*I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)^2*arctan(d*x+c)^2*Pi+1/4*I/d*e^2*b^3*arctan(d*x+c)^2*csgn(I*(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))*Pi-1/2*d*x^2*a^2*b*e^2+d*x^2*a^3*c*e^2+arctan(d*x+c)^3*x*b^3*c^2*e^2-arctan(d*x+c)^2*x*b^3*c*e^2-1/d*e^2*b^3*arctan(d*x+c)^2*ln((1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+1/2/d*e^2*b^3*arctan(d*x+c)^2*ln(1+(d*x+c)^2)+1/d*arctan(d*x+c)*b^3*c*e^2+1/3/d*arctan(d*x+c)^3*b^3*c^3*e^2-1/2/d*arctan(d*x+c)^2*b^3*c^2*e^2-1/d*e^2*b^3*ln(2)*arctan(d*x+c)^2-1/d*e^2*a*b^2*arctan(d*x+c)+1/3*d^2*arctan(d*x+c)^3*x^3*b^3*e^2-1/2*d*arctan(d*x+c)^2*x^2*b^3*e^2+1/2/d*e^2*a^2*b*ln(1+(d*x+c)^2)+1/3*I/d*e^2*b^3*arctan(d*x+c)^3-I/d*e^2*b^3*arctan(d*x+c)-d*arctan(d*x+c)*x^2*a*b^2*e^2+d^2*arctan(d*x+c)*x^3*a^2*b*e^2+1/d*arctan(d*x+c)^2*a*b^2*c^3*e^2-1/d*arctan(d*x+c)*a*b^2*c^2*e^2+d^2*arctan(d*x+c)^2*x^3*a*b^2*e^2+d*arctan(d*x+c)^3*x^2*b^3*c*e^2+1/3*d^2*x^3*a^3*e^2+1/d*e^2*b^3*ln((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)-1/2/d*e^2*b^3*arctan(d*x+c)^2-1/2/d*e^2*b^3*polylog(3,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))+arctan(d*x+c)*x*b^3*e^2+x*a^3*c^2*e^2+1/d*a*b^2*c*e^2-x*a^2*b*c*e^2+a*b^2*e^2*x-1/8*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)*arctan(d*x+c)^2*Pi*x*b^3*e^2-1/4*csgn(I*(1+I*(d*x+c))^4/(1+(d*x+c)^2)^2+2*I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)*arctan(d*x+c)^2*Pi*x*b^3*e^2+1/8*csgn(I*(1+I*(d*x+c))^4/(1+(d*x+c)^2)^2+2*I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)^2*arctan(d*x+c)^2*Pi*x*b^3*e^2+3*d*arctan(d*x+c)^2*x^2*a*b^2*c*e^2-1/8/d*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^3*arctan(d*x+c)^2*Pi*b^3*c*e^2+1/8/d*csgn(I*(1+I*(d*x+c))^4/(1+(d*x+c)^2)^2+2*I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)^3*arctan(d*x+c)^2*Pi*b^3*c*e^2-1/2*I/d*e^2*a*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)+1/2*I/d*e^2*a*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))-1/8*I/d*e^2*b^3*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^3*arctan(d*x+c)^2*Pi-1/8*I/d*e^2*b^3*csgn(I*(1+I*(d*x+c))^4/(1+(d*x+c)^2)^2+2*I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)^3*arctan(d*x+c)^2*Pi+1/4*I/d*e^2*b^3*arctan(d*x+c)^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^3*Pi+1/4*I/d*e^2*b^3*arctan(d*x+c)^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))^3*Pi+3*d*arctan(d*x+c)*x^2*a^2*b*c*e^2+1/2*I/d*e^2*a*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)-1/2*I/d*e^2*a*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))+1/3/d*a^3*c^3*e^2+1/d*arctan(d*x+c)*a^2*b*c^3*e^2+1/d*e^2*a*b^2*arctan(d*x+c)*ln(1+(d*x+c)^2)+I/d*e^2*b^3*arctan(d*x+c)*polylog(2,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))-1/8*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^3*arctan(d*x+c)^2*Pi*x*b^3*e^2+3*arctan(d*x+c)^2*x*a*b^2*c^2*e^2+3*arctan(d*x+c)*x*a^2*b*c^2*e^2+1/8*csgn(I*(1+I*(d*x+c))^4/(1+(d*x+c)^2)^2+2*I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)^3*arctan(d*x+c)^2*Pi*x*b^3*e^2-2*arctan(d*x+c)*x*a*b^2*c*e^2+1/4*I/d*e^2*a*b^2*ln(I+d*x+c)^2+1/2*I/d*e^2*a*b^2*dilog(1/2*I*(d*x+c-I))-1/4*I/d*e^2*a*b^2*ln(d*x+c-I)^2-1/2*I/d*e^2*a*b^2*dilog(-1/2*I*(I+d*x+c))+1/4*I/d*e^2*b^3*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)*arctan(d*x+c)^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))*Pi-1/2/d*a^2*b*c^2*e^2+1/4*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2*arctan(d*x+c)^2*Pi*x*b^3*e^2+1/8/d*csgn(I*(1+I*(d*x+c))^4/(1+(d*x+c)^2)^2+2*I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+I)^2*arctan(d*x+c)^2*Pi*b^3*c*e^2-1/8/d*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)*arctan(d*x+c)^2*Pi*b^3*c*e^2","C"
16,1,567,150,0.145000," ","int((d*e*x+c*e)*(a+b*arctan(d*x+c))^3,x)","\frac{3 i e \,b^{3} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right)}{4 d}-\frac{3 i e \,b^{3} \ln \left(d x +c -i\right)^{2}}{8 d}+\frac{3 i e \,b^{3} \ln \left(d x +c +i\right)^{2}}{8 d}-\frac{3 i e \,b^{3} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{4 d}+\frac{3 e a \,b^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}-3 \arctan \left(d x +c \right) x a \,b^{2} e +\arctan \left(d x +c \right)^{3} x \,b^{3} c e +\frac{\arctan \left(d x +c \right)^{3} b^{3} c^{2} e}{2 d}-\frac{3 \arctan \left(d x +c \right)^{2} b^{3} c e}{2 d}+\frac{3 e \,a^{2} b \arctan \left(d x +c \right)}{2 d}+\frac{3 e \,b^{3} \arctan \left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}+\frac{3 e a \,b^{2} \arctan \left(d x +c \right)^{2}}{2 d}-\frac{3 a^{2} b c e}{2 d}+\frac{3 i e \,b^{3} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{4 d}+\frac{3 i e \,b^{3} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right)}{4 d}-\frac{3 i e \,b^{3} \ln \left(d x +c +i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{4 d}-\frac{3 i e \,b^{3} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{4 d}+\frac{d \arctan \left(d x +c \right)^{3} x^{2} b^{3} e}{2}+3 \arctan \left(d x +c \right)^{2} x a \,b^{2} c e +\frac{3 \arctan \left(d x +c \right)^{2} a \,b^{2} c^{2} e}{2 d}+\frac{a^{3} c^{2} e}{2 d}-\frac{3 e x \,a^{2} b}{2}+x \,a^{3} c e +\frac{d \,x^{2} a^{3} e}{2}-\frac{3 \arctan \left(d x +c \right)^{2} x \,b^{3} e}{2}+\frac{e \,b^{3} \arctan \left(d x +c \right)^{3}}{2 d}+3 \arctan \left(d x +c \right) x \,a^{2} b c e +\frac{3 \arctan \left(d x +c \right) a^{2} b \,c^{2} e}{2 d}-\frac{3 \arctan \left(d x +c \right) a \,b^{2} c e}{d}+\frac{3 d \arctan \left(d x +c \right)^{2} x^{2} a \,b^{2} e}{2}+\frac{3 d \arctan \left(d x +c \right) x^{2} a^{2} b e}{2}"," ",0,"3/2/d*e*a*b^2*ln(1+(d*x+c)^2)-3/4*I/d*e*b^3*dilog(-1/2*I*(I+d*x+c))-3/8*I/d*e*b^3*ln(d*x+c-I)^2+3/4*I/d*e*b^3*dilog(1/2*I*(d*x+c-I))+3/8*I/d*e*b^3*ln(I+d*x+c)^2-3*arctan(d*x+c)*x*a*b^2*e+arctan(d*x+c)^3*x*b^3*c*e+1/2/d*arctan(d*x+c)^3*b^3*c^2*e-3/2/d*arctan(d*x+c)^2*b^3*c*e+3/2/d*e*a^2*b*arctan(d*x+c)+3/2/d*e*b^3*arctan(d*x+c)*ln(1+(d*x+c)^2)+3/2/d*e*a*b^2*arctan(d*x+c)^2-3/2/d*a^2*b*c*e+1/2*d*arctan(d*x+c)^3*x^2*b^3*e+3*arctan(d*x+c)^2*x*a*b^2*c*e-3/4*I/d*e*b^3*ln(I+d*x+c)*ln(1+(d*x+c)^2)-3/4*I/d*e*b^3*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))+3/4*I/d*e*b^3*ln(d*x+c-I)*ln(1+(d*x+c)^2)+3/2/d*arctan(d*x+c)^2*a*b^2*c^2*e+3/4*I/d*e*b^3*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))+1/2/d*a^3*c^2*e-3/2*e*x*a^2*b+x*a^3*c*e+1/2*d*x^2*a^3*e-3/2*arctan(d*x+c)^2*x*b^3*e+1/2/d*e*b^3*arctan(d*x+c)^3+3*arctan(d*x+c)*x*a^2*b*c*e+3/2/d*arctan(d*x+c)*a^2*b*c^2*e-3/d*arctan(d*x+c)*a*b^2*c*e+3/2*d*arctan(d*x+c)^2*x^2*a*b^2*e+3/2*d*arctan(d*x+c)*x^2*a^2*b*e","B"
17,1,2894,256,0.280000," ","int((a+b*arctan(d*x+c))^3/(d*e*x+c*e),x)","\text{output too large to display}"," ",0,"1/d*a^3/e*ln(d*x+c)+1/2*I/d*b^3/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1))*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^3-3/2*I/d*a*b^2/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2+3/2*I/d*a*b^2/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^2-3/2*I/d*a*b^2/e*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2-3/2*I/d*a*b^2/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2-3/2*I/d*a^2*b/e*dilog(1-I*(d*x+c))+3/2*I/d*a^2*b/e*dilog(1+I*(d*x+c))+1/2*I/d*b^3/e*Pi*arctan(d*x+c)^3+3/d*a*b^2/e*ln(d*x+c)*arctan(d*x+c)^2-3/d*a*b^2/e*arctan(d*x+c)^2*ln((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)+3/d*a*b^2/e*arctan(d*x+c)^2*ln(1+(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+3/d*a*b^2/e*arctan(d*x+c)^2*ln(1-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))-3*I/d*b^3/e*arctan(d*x+c)^2*polylog(2,(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+3/2*I/d*b^3/e*arctan(d*x+c)^2*polylog(2,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))-3*I/d*b^3/e*arctan(d*x+c)^2*polylog(2,-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+3/d*a^2*b/e*ln(d*x+c)*arctan(d*x+c)-6*I/d*a*b^2/e*arctan(d*x+c)*polylog(2,(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+3*I/d*a*b^2/e*arctan(d*x+c)*polylog(2,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))-1/2*I/d*b^3/e*Pi*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^3+1/2*I/d*b^3/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*arctan(d*x+c)^3+1/2*I/d*b^3/e*Pi*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*arctan(d*x+c)^3-3/2*I/d*a^2*b/e*ln(d*x+c)*ln(1-I*(d*x+c))-6*I/d*a*b^2/e*arctan(d*x+c)*polylog(2,-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+3/2*I/d*a^2*b/e*ln(d*x+c)*ln(1+I*(d*x+c))+3/2*I/d*a*b^2/e*Pi*arctan(d*x+c)^2-1/2*I/d*b^3/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^3-3/2*I/d*a*b^2/e*Pi*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2-1/2*I/d*b^3/e*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^3-1/2*I/d*b^3/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^3+3/2*I/d*a*b^2/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*arctan(d*x+c)^2+1/2*I/d*b^3/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^3+6*I/d*b^3/e*polylog(4,(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+6*I/d*b^3/e*polylog(4,-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))-3/4*I/d*b^3/e*polylog(4,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))-3/2/d*b^3/e*arctan(d*x+c)*polylog(3,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))+1/d*b^3/e*ln(d*x+c)*arctan(d*x+c)^3-1/d*b^3/e*arctan(d*x+c)^3*ln((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)+1/d*b^3/e*arctan(d*x+c)^3*ln(1+(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+3/2*I/d*a*b^2/e*Pi*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*arctan(d*x+c)^2+6/d*b^3/e*arctan(d*x+c)*polylog(3,-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+1/d*b^3/e*arctan(d*x+c)^3*ln(1-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+6/d*b^3/e*arctan(d*x+c)*polylog(3,(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+6/d*a*b^2/e*polylog(3,-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+6/d*a*b^2/e*polylog(3,(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))-3/2/d*a*b^2/e*polylog(3,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))+3/2*I/d*a*b^2/e*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1))*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^2","C"
18,1,2696,156,0.442000," ","int((a+b*arctan(d*x+c))^3/(d*e*x+c*e)^2,x)","\text{Expression too large to display}"," ",0,"-3/2*I/d*a*b^2/e^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))+3*I/d*a*b^2/e^2*ln(d*x+c)*ln(1+I*(d*x+c))-3/2*I/d*a*b^2/e^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)-3*I/d*a*b^2/e^2*ln(d*x+c)*ln(1-I*(d*x+c))-1/d*b^3/e^2/(d*x+c)*arctan(d*x+c)^3-3/d*b^3/e^2*arctan(d*x+c)^2*ln((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)+3/d*b^3/e^2*arctan(d*x+c)^2*ln(1+(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+3/d*b^3/e^2*arctan(d*x+c)^2*ln((1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+3/d*b^3/e^2*arctan(d*x+c)^2*ln(1-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+3/d*b^3/e^2*ln(d*x+c)*arctan(d*x+c)^2-3/2/d*b^3/e^2*arctan(d*x+c)^2*ln(1+(d*x+c)^2)+3/d*a^2*b/e^2*ln(d*x+c)-3/2/d*a^2*b/e^2*ln(1+(d*x+c)^2)+3/d*b^3/e^2*arctan(d*x+c)^2*ln(2)-I/d*b^3/e^2*arctan(d*x+c)^3+3/2*I/d*a*b^2/e^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)-3/2*I/d*b^3/e^2*Pi*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2+3/2*I/d*b^3/e^2*Pi*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*arctan(d*x+c)^2+3/4*I/d*b^3/e^2*arctan(d*x+c)^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^3-3/4*I/d*b^3/e^2*arctan(d*x+c)^2*Pi*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))^3-3/4*I/d*b^3/e^2*arctan(d*x+c)^2*Pi*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^3+3/2*I/d*b^3/e^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*arctan(d*x+c)^2+3/2*I/d*a*b^2/e^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))-1/d*a^3/e^2/(d*x+c)+6/d*b^3/e^2*polylog(3,(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))+6/d*b^3/e^2*polylog(3,-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))-3/d*a*b^2/e^2/(d*x+c)*arctan(d*x+c)^2+6/d*a*b^2/e^2*arctan(d*x+c)*ln(d*x+c)-3/d*a*b^2/e^2*arctan(d*x+c)*ln(1+(d*x+c)^2)-3/d*a^2*b/e^2/(d*x+c)*arctan(d*x+c)-6*I/d*b^3/e^2*arctan(d*x+c)*polylog(2,-(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))-3/4*I/d*b^3/e^2*arctan(d*x+c)^2*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)+3/2*I/d*b^3/e^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1))*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^2-3/4*I/d*b^3/e^2*arctan(d*x+c)^2*Pi*csgn(I*(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))+3/4*I/d*b^3/e^2*arctan(d*x+c)^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)+3/2*I/d*b^3/e^2*arctan(d*x+c)^2*Pi*csgn(I*(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))^2+3/4*I/d*b^3/e^2*arctan(d*x+c)^2*Pi*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2-3/2*I/d*b^3/e^2*arctan(d*x+c)^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2+3/2*I/d*b^3/e^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^2+3*I/d*a*b^2/e^2*dilog(1+I*(d*x+c))+3/4*I/d*a*b^2/e^2*ln(d*x+c-I)^2+3/2*I/d*a*b^2/e^2*dilog(-1/2*I*(I+d*x+c))-6*I/d*b^3/e^2*arctan(d*x+c)*polylog(2,(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))-3/4*I/d*a*b^2/e^2*ln(I+d*x+c)^2-3/2*I/d*a*b^2/e^2*dilog(1/2*I*(d*x+c-I))+3/2*I/d*b^3/e^2*Pi*arctan(d*x+c)^2-3*I/d*a*b^2/e^2*dilog(1-I*(d*x+c))-3/2*I/d*b^3/e^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2+3/4*I/d*b^3/e^2*arctan(d*x+c)^2*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2-3/2*I/d*b^3/e^2*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2-3/2*I/d*b^3/e^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(((1+I*(d*x+c))^2/(1+(d*x+c)^2)-1)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2","C"
19,1,631,166,0.159000," ","int((a+b*arctan(d*x+c))^3/(d*e*x+c*e)^3,x)","\frac{3 i b^{3} \ln \left(d x +c +i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{4 d \,e^{3}}+\frac{3 i b^{3} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{4 d \,e^{3}}+\frac{3 i b^{3} \ln \left(d x +c \right) \ln \left(1+i \left(d x +c \right)\right)}{2 d \,e^{3}}-\frac{3 a \,b^{2} \arctan \left(d x +c \right)^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{3 a^{2} b \arctan \left(d x +c \right)}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{3 a \,b^{2} \arctan \left(d x +c \right)}{d \,e^{3} \left(d x +c \right)}-\frac{3 i b^{3} \ln \left(d x +c +i\right)^{2}}{8 d \,e^{3}}+\frac{3 i b^{3} \ln \left(d x +c -i\right)^{2}}{8 d \,e^{3}}+\frac{3 i b^{3} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{4 d \,e^{3}}-\frac{3 i b^{3} \dilog \left(1-i \left(d x +c \right)\right)}{2 d \,e^{3}}+\frac{3 i b^{3} \dilog \left(1+i \left(d x +c \right)\right)}{2 d \,e^{3}}-\frac{3 i b^{3} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right)}{4 d \,e^{3}}-\frac{3 b^{3} \arctan \left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d \,e^{3}}-\frac{3 a^{2} b}{2 d \,e^{3} \left(d x +c \right)}-\frac{3 a \,b^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d \,e^{3}}-\frac{3 a^{2} b \arctan \left(d x +c \right)}{2 d \,e^{3}}-\frac{3 a \,b^{2} \arctan \left(d x +c \right)^{2}}{2 d \,e^{3}}+\frac{3 a \,b^{2} \ln \left(d x +c \right)}{d \,e^{3}}-\frac{3 b^{3} \arctan \left(d x +c \right)^{2}}{2 d \,e^{3} \left(d x +c \right)}+\frac{3 b^{3} \ln \left(d x +c \right) \arctan \left(d x +c \right)}{d \,e^{3}}-\frac{b^{3} \arctan \left(d x +c \right)^{3}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{3 i b^{3} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right)}{4 d \,e^{3}}-\frac{3 i b^{3} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{4 d \,e^{3}}-\frac{3 i b^{3} \ln \left(d x +c \right) \ln \left(1-i \left(d x +c \right)\right)}{2 d \,e^{3}}-\frac{a^{3}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b^{3} \arctan \left(d x +c \right)^{3}}{2 d \,e^{3}}"," ",0,"3/4*I/d*b^3/e^3*ln(I+d*x+c)*ln(1+(d*x+c)^2)+3/4*I/d*b^3/e^3*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))-3/2/d*a*b^2/e^3/(d*x+c)^2*arctan(d*x+c)^2-3/2/d*a^2*b/e^3/(d*x+c)^2*arctan(d*x+c)+3/2*I/d*b^3/e^3*ln(d*x+c)*ln(1+I*(d*x+c))-3/2*I/d*b^3/e^3*ln(d*x+c)*ln(1-I*(d*x+c))-3/4*I/d*b^3/e^3*ln(d*x+c-I)*ln(1+(d*x+c)^2)-3/4*I/d*b^3/e^3*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))-3/d*a*b^2/e^3*arctan(d*x+c)/(d*x+c)-3/2/d*b^3/e^3*arctan(d*x+c)*ln(1+(d*x+c)^2)+3/8*I/d*b^3/e^3*ln(d*x+c-I)^2-3/8*I/d*b^3/e^3*ln(I+d*x+c)^2+3/2*I/d*b^3/e^3*dilog(1+I*(d*x+c))-3/4*I/d*b^3/e^3*dilog(1/2*I*(d*x+c-I))+3/4*I/d*b^3/e^3*dilog(-1/2*I*(I+d*x+c))-3/2*I/d*b^3/e^3*dilog(1-I*(d*x+c))-3/2/d*a^2*b/e^3/(d*x+c)-3/2/d*a*b^2/e^3*ln(1+(d*x+c)^2)-3/2/d*a^2*b/e^3*arctan(d*x+c)-3/2/d*a*b^2/e^3*arctan(d*x+c)^2+3/d*a*b^2/e^3*ln(d*x+c)-3/2/d*b^3/e^3*arctan(d*x+c)^2/(d*x+c)+3/d*b^3/e^3*ln(d*x+c)*arctan(d*x+c)-1/2/d*b^3/e^3/(d*x+c)^2*arctan(d*x+c)^3-1/2/d*a^3/e^3/(d*x+c)^2-1/2/d*b^3/e^3*arctan(d*x+c)^3","B"
20,1,7083,270,1.626000," ","int((a+b*arctan(d*x+c))^3/(d*e*x+c*e)^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
21,1,68,23,0.062000," ","int(arctan(x+1)/(2+2*x),x)","\frac{\ln \left(x +1\right) \arctan \left(x +1\right)}{2}+\frac{i \ln \left(x +1\right) \ln \left(1+i \left(x +1\right)\right)}{4}-\frac{i \ln \left(x +1\right) \ln \left(1-i \left(x +1\right)\right)}{4}+\frac{i \dilog \left(1+i \left(x +1\right)\right)}{4}-\frac{i \dilog \left(1-i \left(x +1\right)\right)}{4}"," ",0,"1/2*ln(x+1)*arctan(x+1)+1/4*I*ln(x+1)*ln(1+I*(x+1))-1/4*I*ln(x+1)*ln(1-I*(x+1))+1/4*I*dilog(1+I*(x+1))-1/4*I*dilog(1-I*(x+1))","B"
22,1,98,33,0.061000," ","int(arctan(b*x+a)/(a*d/b+d*x),x)","\frac{\ln \left(b x +a \right) \arctan \left(b x +a \right)}{d}+\frac{i \ln \left(b x +a \right) \ln \left(1+i \left(b x +a \right)\right)}{2 d}-\frac{i \ln \left(b x +a \right) \ln \left(1-i \left(b x +a \right)\right)}{2 d}+\frac{i \dilog \left(1+i \left(b x +a \right)\right)}{2 d}-\frac{i \dilog \left(1-i \left(b x +a \right)\right)}{2 d}"," ",0,"1/d*ln(b*x+a)*arctan(b*x+a)+1/2*I/d*ln(b*x+a)*ln(1+I*(b*x+a))-1/2*I/d*ln(b*x+a)*ln(1-I*(b*x+a))+1/2*I/d*dilog(1+I*(b*x+a))-1/2*I/d*dilog(1-I*(b*x+a))","B"
23,0,0,18,3.232000," ","int((b*x+a)^2*arctan(b*x+a)^(1/2),x)","\int \left(b x +a \right)^{2} \sqrt{\arctan \left(b x +a \right)}\, dx"," ",0,"int((b*x+a)^2*arctan(b*x+a)^(1/2),x)","F"
24,1,494,221,0.047000," ","int((f*x+e)^3*(a+b*arctan(d*x+c)),x)","\frac{b \,f^{3} \ln \left(1+\left(d x +c \right)^{2}\right) c^{3}}{2 d^{4}}+\frac{5 b \,f^{2} c^{2} e}{2 d^{3}}-\frac{3 b f \,e^{2} c}{2 d^{2}}+\frac{3 a f \,x^{2} e^{2}}{2}+\frac{b \,f^{3} \arctan \left(d x +c \right) x^{4}}{4}+\arctan \left(d x +c \right) x b \,e^{3}-\frac{b \ln \left(1+\left(d x +c \right)^{2}\right) e^{3}}{2 d}-\frac{b \,f^{3} \arctan \left(d x +c \right)}{4 d^{4}}-\frac{b \,f^{3} x^{3}}{12 d}+\frac{b \,f^{3} x}{4 d^{3}}+a \,f^{2} x^{3} e +\frac{b \,f^{3} c}{4 d^{4}}-\frac{13 b \,f^{3} c^{3}}{12 d^{4}}+\frac{a \,e^{4}}{4 f}-\frac{3 b \,f^{2} \arctan \left(d x +c \right) c e}{d^{3}}-\frac{3 b f \arctan \left(d x +c \right) e^{2} c^{2}}{2 d^{2}}+\frac{b \,f^{2} \arctan \left(d x +c \right) c^{3} e}{d^{3}}+\frac{3 b f \ln \left(1+\left(d x +c \right)^{2}\right) c \,e^{2}}{2 d^{2}}-\frac{3 b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right) c^{2} e}{2 d^{3}}+\frac{2 b \,f^{2} c e x}{d^{2}}+\frac{\arctan \left(d x +c \right) b c \,e^{3}}{d}+\frac{b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right) e}{2 d^{3}}+\frac{3 b \,f^{3} \arctan \left(d x +c \right) c^{2}}{2 d^{4}}-\frac{b \,f^{3} \ln \left(1+\left(d x +c \right)^{2}\right) c}{2 d^{4}}-\frac{b \,f^{2} e \,x^{2}}{2 d}+\frac{b \,f^{3} x^{2} c}{4 d^{2}}-\frac{3 b \,f^{3} c^{2} x}{4 d^{3}}-\frac{3 b f \,e^{2} x}{2 d}-\frac{b \,f^{3} \arctan \left(d x +c \right) c^{4}}{4 d^{4}}+\frac{3 b f \arctan \left(d x +c \right) e^{2}}{2 d^{2}}+\frac{3 b f \arctan \left(d x +c \right) e^{2} x^{2}}{2}+b \,f^{2} \arctan \left(d x +c \right) e \,x^{3}+a x \,e^{3}+\frac{a \,f^{3} x^{4}}{4}"," ",0,"1/2/d^4*b*f^3*ln(1+(d*x+c)^2)*c^3+5/2/d^3*b*f^2*c^2*e-3/2/d^2*b*f*e^2*c+3/2*a*f*x^2*e^2+1/4*b*f^3*arctan(d*x+c)*x^4+arctan(d*x+c)*x*b*e^3-1/2/d*b*ln(1+(d*x+c)^2)*e^3-1/4/d^4*b*f^3*arctan(d*x+c)-1/12/d*b*f^3*x^3+1/4*b/d^3*f^3*x+a*f^2*x^3*e+1/4/d^4*b*f^3*c-13/12/d^4*b*f^3*c^3+1/4*a/f*e^4-3/d^3*b*f^2*arctan(d*x+c)*c*e-3/2/d^2*b*f*arctan(d*x+c)*e^2*c^2+1/d^3*b*f^2*arctan(d*x+c)*c^3*e+3/2/d^2*b*f*ln(1+(d*x+c)^2)*c*e^2-3/2/d^3*b*f^2*ln(1+(d*x+c)^2)*c^2*e+2*b/d^2*f^2*c*e*x+1/d*arctan(d*x+c)*b*c*e^3+1/2/d^3*b*f^2*ln(1+(d*x+c)^2)*e+3/2/d^4*b*f^3*arctan(d*x+c)*c^2-1/2/d^4*b*f^3*ln(1+(d*x+c)^2)*c-1/2/d*b*f^2*e*x^2+1/4/d^2*b*f^3*x^2*c-3/4*b/d^3*f^3*c^2*x-3/2*b/d*f*e^2*x-1/4/d^4*b*f^3*arctan(d*x+c)*c^4+3/2/d^2*b*f*arctan(d*x+c)*e^2+3/2*b*f*arctan(d*x+c)*e^2*x^2+b*f^2*arctan(d*x+c)*e*x^3+a*x*e^3+1/4*a*f^3*x^4","B"
25,1,283,147,0.054000," ","int((f*x+e)^2*(a+b*arctan(d*x+c)),x)","\frac{\arctan \left(d x +c \right) b c \,e^{2}}{d}+\frac{b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{6 d^{3}}+\frac{b \,f^{2} \arctan \left(d x +c \right) x^{3}}{3}+\frac{b \,f^{2} \arctan \left(d x +c \right) c^{3}}{3 d^{3}}+\frac{a \,f^{2} x^{3}}{3}+\frac{a \,e^{3}}{3 f}-\frac{b \,f^{2} x^{2}}{6 d}-\frac{b \,f^{2} \arctan \left(d x +c \right) c}{d^{3}}+\arctan \left(d x +c \right) x b \,e^{2}+\frac{b f \ln \left(1+\left(d x +c \right)^{2}\right) c e}{d^{2}}+\frac{5 b \,f^{2} c^{2}}{6 d^{3}}+b f \arctan \left(d x +c \right) e \,x^{2}-\frac{b f \arctan \left(d x +c \right) e \,c^{2}}{d^{2}}+\frac{b f \arctan \left(d x +c \right) e}{d^{2}}-\frac{b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right) c^{2}}{2 d^{3}}-\frac{b f e x}{d}+\frac{2 b \,f^{2} c x}{3 d^{2}}+a x \,e^{2}-\frac{b f c e}{d^{2}}+a f \,x^{2} e -\frac{b \,e^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}"," ",0,"1/d*arctan(d*x+c)*b*c*e^2+1/6/d^3*b*f^2*ln(1+(d*x+c)^2)+1/3*b*f^2*arctan(d*x+c)*x^3+1/3/d^3*b*f^2*arctan(d*x+c)*c^3+1/3*a*f^2*x^3+1/3*a/f*e^3-1/6/d*b*f^2*x^2-1/d^3*b*f^2*arctan(d*x+c)*c+arctan(d*x+c)*x*b*e^2+1/d^2*b*f*ln(1+(d*x+c)^2)*c*e+5/6/d^3*b*f^2*c^2+b*f*arctan(d*x+c)*e*x^2-1/d^2*b*f*arctan(d*x+c)*e*c^2+1/d^2*b*f*arctan(d*x+c)*e-1/2/d^3*b*f^2*ln(1+(d*x+c)^2)*c^2-b/d*f*e*x+2/3*b/d^2*f^2*c*x+a*x*e^2-1/d^2*b*f*c*e+a*f*x^2*e-1/2*b*e^2*ln(1+(d*x+c)^2)/d","A"
26,1,146,89,0.059000," ","int((f*x+e)*(a+b*arctan(d*x+c)),x)","\frac{a \,x^{2} f}{2}-\frac{a f \,c^{2}}{2 d^{2}}+a e x +\frac{a c e}{d}+\frac{b f \arctan \left(d x +c \right) x^{2}}{2}-\frac{b f \arctan \left(d x +c \right) c^{2}}{2 d^{2}}+\arctan \left(d x +c \right) x b e +\frac{\arctan \left(d x +c \right) b c e}{d}-\frac{b f x}{2 d}-\frac{b c f}{2 d^{2}}+\frac{b \ln \left(1+\left(d x +c \right)^{2}\right) c f}{2 d^{2}}-\frac{b \ln \left(1+\left(d x +c \right)^{2}\right) e}{2 d}+\frac{b f \arctan \left(d x +c \right)}{2 d^{2}}"," ",0,"1/2*a*x^2*f-1/2/d^2*a*f*c^2+a*e*x+1/d*a*c*e+1/2*b*f*arctan(d*x+c)*x^2-1/2/d^2*b*f*arctan(d*x+c)*c^2+arctan(d*x+c)*x*b*e+1/d*arctan(d*x+c)*b*c*e-1/2*b*f*x/d-1/2/d^2*b*c*f+1/2/d^2*b*ln(1+(d*x+c)^2)*c*f-1/2/d*b*ln(1+(d*x+c)^2)*e+1/2/d^2*b*f*arctan(d*x+c)","A"
27,1,42,36,0.036000," ","int(a+b*arctan(d*x+c),x)","a x +b \arctan \left(d x +c \right) x +\frac{b \arctan \left(d x +c \right) c}{d}-\frac{b \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}"," ",0,"a*x+b*arctan(d*x+c)*x+b/d*arctan(d*x+c)*c-1/2*b*ln(1+(d*x+c)^2)/d","A"
28,1,224,150,0.099000," ","int((a+b*arctan(d*x+c))/(f*x+e),x)","\frac{a \ln \left(f \left(d x +c \right)-c f +d e \right)}{f}+\frac{b \ln \left(f \left(d x +c \right)-c f +d e \right) \arctan \left(d x +c \right)}{f}+\frac{i b \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{2 f}-\frac{i b \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{2 f}+\frac{i b \dilog \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{2 f}-\frac{i b \dilog \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{2 f}"," ",0,"a*ln(f*(d*x+c)-c*f+d*e)/f+b*ln(f*(d*x+c)-c*f+d*e)/f*arctan(d*x+c)+1/2*I*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f-f*(d*x+c))/(d*e+I*f-c*f))-1/2*I*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f+f*(d*x+c))/(I*f+c*f-d*e))+1/2*I*b/f*dilog((I*f-f*(d*x+c))/(d*e+I*f-c*f))-1/2*I*b/f*dilog((I*f+f*(d*x+c))/(I*f+c*f-d*e))","A"
29,1,205,151,0.049000," ","int((a+b*arctan(d*x+c))/(f*x+e)^2,x)","-\frac{d a}{\left(d f x +d e \right) f}-\frac{d b \arctan \left(d x +c \right)}{\left(d f x +d e \right) f}+\frac{d b \ln \left(f \left(d x +c \right)-c f +d e \right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{d b \ln \left(1+\left(d x +c \right)^{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{d b \arctan \left(d x +c \right) c}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{d^{2} b \arctan \left(d x +c \right) e}{f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}"," ",0,"-d*a/(d*f*x+d*e)/f-d*b/(d*f*x+d*e)/f*arctan(d*x+c)+d*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)-1/2*d*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)-d*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*c+d^2*b/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*e","A"
30,1,438,222,0.051000," ","int((a+b*arctan(d*x+c))/(f*x+e)^3,x)","-\frac{d^{2} a}{2 \left(d f x +d e \right)^{2} f}-\frac{d^{2} b \arctan \left(d x +c \right)}{2 \left(d f x +d e \right)^{2} f}-\frac{d^{2} b}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right) \left(d f x +d e \right)}-\frac{d^{2} b f \ln \left(f \left(d x +c \right)-c f +d e \right) c}{\left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}+\frac{d^{3} b \ln \left(f \left(d x +c \right)-c f +d e \right) e}{\left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}+\frac{d^{2} b f \arctan \left(d x +c \right) c^{2}}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}-\frac{d^{3} b \arctan \left(d x +c \right) c e}{\left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}+\frac{d^{4} b \arctan \left(d x +c \right) e^{2}}{2 f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}+\frac{d^{2} b f \ln \left(1+\left(d x +c \right)^{2}\right) c}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}-\frac{d^{3} b \ln \left(1+\left(d x +c \right)^{2}\right) e}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}-\frac{d^{2} b f \arctan \left(d x +c \right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}"," ",0,"-1/2*d^2*a/(d*f*x+d*e)^2/f-1/2*d^2*b/(d*f*x+d*e)^2/f*arctan(d*x+c)-1/2*d^2*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)/(d*f*x+d*e)-d^2*b*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*ln(f*(d*x+c)-c*f+d*e)*c+d^3*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*ln(f*(d*x+c)-c*f+d*e)*e+1/2*d^2*b*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*arctan(d*x+c)*c^2-d^3*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*arctan(d*x+c)*c*e+1/2*d^4*b/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*arctan(d*x+c)*e^2+1/2*d^2*b*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*ln(1+(d*x+c)^2)*c-1/2*d^3*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*ln(1+(d*x+c)^2)*e-1/2*d^2*b*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*arctan(d*x+c)","A"
31,1,1622,362,0.146000," ","int((f*x+e)^2*(a+b*arctan(d*x+c))^2,x)","a^{2} x \,e^{2}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c -i\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) c^{2} f^{2}}{2 d^{3}}+\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) c^{2} f^{2}}{2 d^{3}}+\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \ln \left(d x +c +i\right)^{2} c^{2} f^{2}}{4 d^{3}}+\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) e^{2}}{2 d}+\frac{i b^{2} \ln \left(d x +c +i\right)^{2} f^{2}}{12 d^{3}}+\frac{i b^{2} \ln \left(d x +c -i\right)^{2} e^{2}}{4 d}-\frac{i b^{2} \ln \left(d x +c -i\right)^{2} f^{2}}{12 d^{3}}+\frac{a b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{3 d^{3}}+\frac{5 a b \,f^{2} c^{2}}{3 d^{3}}+\frac{a^{2} e^{3}}{3 f}+\frac{b^{2} f^{2} c}{3 d^{3}}+a^{2} f \,x^{2} e +\frac{b^{2} f^{2} \arctan \left(d x +c \right)^{2} x^{3}}{3}+\arctan \left(d x +c \right)^{2} x \,b^{2} e^{2}+\frac{2 \arctan \left(d x +c \right) a b c \,e^{2}}{d}-\frac{a b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right) c^{2}}{d^{3}}-\frac{2 a b \,f^{2} \arctan \left(d x +c \right) c}{d^{3}}-\frac{2 b^{2} f \arctan \left(d x +c \right) e x}{d}+\frac{2 a b \,f^{2} \arctan \left(d x +c \right) c^{3}}{3 d^{3}}-\frac{b^{2} f \arctan \left(d x +c \right)^{2} c^{2} e}{d^{2}}+\frac{a^{2} f^{2} x^{3}}{3}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) c^{2} f^{2}}{2 d^{3}}+\frac{i b^{2} \ln \left(d x +c +i\right)^{2} c e f}{2 d^{2}}-\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) c^{2} f^{2}}{2 d^{3}}-\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c -i\right) c^{2} f^{2}}{2 d^{3}}+\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) c^{2} f^{2}}{2 d^{3}}-\frac{i b^{2} \ln \left(d x +c -i\right)^{2} c e f}{2 d^{2}}-\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) c e f}{d^{2}}+\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) c e f}{d^{2}}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) e^{2}}{2 d}-\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) e^{2}}{2 d}+\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) e^{2}}{2 d}+\frac{4 a b \,f^{2} c x}{3 d^{2}}-\frac{2 a b f e x}{d}-\frac{2 b^{2} f \arctan \left(d x +c \right) e c}{d^{2}}+\frac{4 b^{2} f^{2} \arctan \left(d x +c \right) c x}{3 d^{2}}+2 a b f \arctan \left(d x +c \right) e \,x^{2}-\frac{b^{2} f^{2} \arctan \left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right) c^{2}}{d^{3}}+\frac{2 a b f \arctan \left(d x +c \right) e}{d^{2}}-\frac{i e^{2} b^{2} \ln \left(d x +c +i\right)^{2}}{4 d}+\frac{i e^{2} b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{2 d}+\frac{b^{2} f^{2} x}{3 d^{2}}-\frac{b^{2} f^{2} \arctan \left(d x +c \right)}{3 d^{3}}-\frac{i e^{2} b^{2} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}+\frac{i b^{2} \ln \left(d x +c -i\right)^{2} c^{2} f^{2}}{4 d^{3}}-\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) c e f}{d^{2}}+\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) c e f}{d^{2}}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c -i\right) c e f}{d^{2}}-\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) c e f}{d^{2}}-\frac{b^{2} f^{2} \arctan \left(d x +c \right)^{2} c}{d^{3}}+\frac{\arctan \left(d x +c \right)^{2} b^{2} c \,e^{2}}{d}+\frac{b^{2} f^{2} \arctan \left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{3 d^{3}}+\frac{b^{2} f \ln \left(1+\left(d x +c \right)^{2}\right) e}{d^{2}}+\frac{b^{2} f \arctan \left(d x +c \right)^{2} e}{d^{2}}+\frac{b^{2} f^{2} \arctan \left(d x +c \right)^{2} c^{3}}{3 d^{3}}+\frac{5 b^{2} f^{2} \arctan \left(d x +c \right) c^{2}}{3 d^{3}}-\frac{b^{2} f^{2} \arctan \left(d x +c \right) x^{2}}{3 d}-\frac{b^{2} f^{2} \ln \left(1+\left(d x +c \right)^{2}\right) c}{d^{3}}+b^{2} f \arctan \left(d x +c \right)^{2} e \,x^{2}-\frac{a b \,f^{2} x^{2}}{3 d}+\frac{2 a b \,f^{2} \arctan \left(d x +c \right) x^{3}}{3}+2 \arctan \left(d x +c \right) x a b \,e^{2}-\frac{e^{2} a b \ln \left(1+\left(d x +c \right)^{2}\right)}{d}-\frac{e^{2} b^{2} \arctan \left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{d}-\frac{2 a b f c e}{d^{2}}-\frac{2 a b f \arctan \left(d x +c \right) e \,c^{2}}{d^{2}}+\frac{2 a b f \ln \left(1+\left(d x +c \right)^{2}\right) c e}{d^{2}}+\frac{2 b^{2} f \arctan \left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right) c e}{d^{2}}"," ",0,"a^2*x*e^2+1/3/d^3*a*b*f^2*ln(1+(d*x+c)^2)+5/3/d^3*a*b*f^2*c^2+1/3*a^2/f*e^3+1/3/d^3*b^2*f^2*c+a^2*f*x^2*e+1/3*b^2*f^2*arctan(d*x+c)^2*x^3+arctan(d*x+c)^2*x*b^2*e^2-1/2*I/d^3*b^2*dilog(1/2*I*(d*x+c-I))*c^2*f^2+1/6*I/d^3*b^2*ln(1+(d*x+c)^2)*ln(d*x+c-I)*f^2-1/6*I/d^3*b^2*ln(1+(d*x+c)^2)*ln(I+d*x+c)*f^2+2/d*arctan(d*x+c)*a*b*c*e^2-1/d^3*a*b*f^2*ln(1+(d*x+c)^2)*c^2-2/d^3*a*b*f^2*arctan(d*x+c)*c-2/d*b^2*f*arctan(d*x+c)*e*x+2/3/d^3*a*b*f^2*arctan(d*x+c)*c^3-1/d^2*b^2*f*arctan(d*x+c)^2*c^2*e+1/3*a^2*f^2*x^3+4/3*a*b/d^2*f^2*c*x-2*a*b/d*f*e*x+1/6*I/d^3*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*f^2-1/4*I/d^3*b^2*ln(I+d*x+c)^2*c^2*f^2+1/4*I/d^3*b^2*ln(d*x+c-I)^2*c^2*f^2-2/d^2*b^2*f*arctan(d*x+c)*e*c+4/3/d^2*b^2*f^2*arctan(d*x+c)*c*x+2*a*b*f*arctan(d*x+c)*e*x^2-1/d^3*b^2*f^2*arctan(d*x+c)*ln(1+(d*x+c)^2)*c^2+2/d^2*a*b*f*arctan(d*x+c)*e-1/6*I/d^3*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))*f^2+1/2*I/d^3*b^2*dilog(-1/2*I*(I+d*x+c))*c^2*f^2+1/2*I/d*b^2*ln(1+(d*x+c)^2)*ln(I+d*x+c)*e^2-1/2*I/d*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*e^2-1/2*I/d*b^2*ln(1+(d*x+c)^2)*ln(d*x+c-I)*e^2+1/2*I/d*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))*e^2+1/3*b^2*f^2*x/d^2-1/3*b^2*f^2*arctan(d*x+c)/d^3-I/d^2*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))*c*e*f-I/d^2*b^2*ln(1+(d*x+c)^2)*ln(I+d*x+c)*c*e*f+I/d^2*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*c*e*f+I/d^2*b^2*ln(1+(d*x+c)^2)*ln(d*x+c-I)*c*e*f-1/d^3*b^2*f^2*arctan(d*x+c)^2*c+1/d*arctan(d*x+c)^2*b^2*c*e^2+1/3/d^3*b^2*f^2*arctan(d*x+c)*ln(1+(d*x+c)^2)+1/d^2*b^2*f*ln(1+(d*x+c)^2)*e+1/d^2*b^2*f*arctan(d*x+c)^2*e-1/2*I/d^3*b^2*ln(1+(d*x+c)^2)*ln(d*x+c-I)*c^2*f^2+1/2*I/d^3*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))*c^2*f^2-1/2*I/d^2*b^2*ln(d*x+c-I)^2*c*e*f+1/2*I/d^3*b^2*ln(1+(d*x+c)^2)*ln(I+d*x+c)*c^2*f^2-I/d^2*b^2*dilog(-1/2*I*(I+d*x+c))*c*e*f+I/d^2*b^2*dilog(1/2*I*(d*x+c-I))*c*e*f+1/2*I/d^2*b^2*ln(I+d*x+c)^2*c*e*f-1/2*I/d^3*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*c^2*f^2+1/3/d^3*b^2*f^2*arctan(d*x+c)^2*c^3+5/3/d^3*b^2*f^2*arctan(d*x+c)*c^2-1/3/d*b^2*f^2*arctan(d*x+c)*x^2-1/d^3*b^2*f^2*ln(1+(d*x+c)^2)*c+b^2*f*arctan(d*x+c)^2*e*x^2-1/3/d*a*b*f^2*x^2+2/3*a*b*f^2*arctan(d*x+c)*x^3+2*arctan(d*x+c)*x*a*b*e^2+1/6*I/d^3*b^2*dilog(1/2*I*(d*x+c-I))*f^2-1/6*I/d^3*b^2*dilog(-1/2*I*(I+d*x+c))*f^2+1/12*I/d^3*b^2*ln(I+d*x+c)^2*f^2+1/2*I/d*b^2*dilog(-1/2*I*(I+d*x+c))*e^2-1/2*I/d*b^2*dilog(1/2*I*(d*x+c-I))*e^2+1/4*I/d*b^2*ln(d*x+c-I)^2*e^2-1/4*I/d*b^2*ln(I+d*x+c)^2*e^2-1/12*I/d^3*b^2*ln(d*x+c-I)^2*f^2-1/d*e^2*a*b*ln(1+(d*x+c)^2)-1/d*e^2*b^2*arctan(d*x+c)*ln(1+(d*x+c)^2)-2/d^2*a*b*f*c*e-2/d^2*a*b*f*arctan(d*x+c)*e*c^2+2/d^2*a*b*f*ln(1+(d*x+c)^2)*c*e+2/d^2*b^2*f*arctan(d*x+c)*ln(1+(d*x+c)^2)*c*e","B"
32,1,748,212,0.135000," ","int((f*x+e)*(a+b*arctan(d*x+c))^2,x)","-\frac{i b^{2} \ln \left(d x +c -i\right)^{2} c f}{4 d^{2}}+\frac{i b^{2} \ln \left(d x +c +i\right)^{2} c f}{4 d^{2}}-\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c -i\right) e}{2 d}-\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) e}{2 d}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) e}{2 d}+\frac{i b^{2} \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) \ln \left(d x +c -i\right) e}{2 d}-\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) c f}{2 d^{2}}+\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) c f}{2 d^{2}}-\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) c f}{2 d^{2}}+\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) c f}{2 d^{2}}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c -i\right) c f}{2 d^{2}}-\frac{i b^{2} \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) \ln \left(d x +c -i\right) c f}{2 d^{2}}+\frac{i b^{2} \ln \left(d x +c -i\right)^{2} e}{4 d}-\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) e}{2 d}+\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) e}{2 d}-\frac{i b^{2} \ln \left(d x +c +i\right)^{2} e}{4 d}-\frac{a b f x}{d}+\frac{b^{2} f \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d^{2}}+\frac{b^{2} \arctan \left(d x +c \right)^{2} f}{2 d^{2}}+\frac{b^{2} \arctan \left(d x +c \right)^{2} f \,x^{2}}{2}+\arctan \left(d x +c \right)^{2} x \,b^{2} e +\frac{a^{2} c e}{d}-\frac{a^{2} f \,c^{2}}{2 d^{2}}+\frac{a b \ln \left(1+\left(d x +c \right)^{2}\right) c f}{d^{2}}+\frac{2 \arctan \left(d x +c \right) a b c e}{d}+\frac{b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \arctan \left(d x +c \right) c f}{d^{2}}-\frac{a b f \arctan \left(d x +c \right) c^{2}}{d^{2}}+\frac{a b f \arctan \left(d x +c \right)}{d^{2}}+\frac{\arctan \left(d x +c \right)^{2} b^{2} c e}{d}-\frac{b^{2} \arctan \left(d x +c \right)^{2} f \,c^{2}}{2 d^{2}}-\frac{b^{2} \arctan \left(d x +c \right) f x}{d}-\frac{b^{2} \arctan \left(d x +c \right) f c}{d^{2}}+2 \arctan \left(d x +c \right) x a b e +a b f \arctan \left(d x +c \right) x^{2}-\frac{b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \arctan \left(d x +c \right) e}{d}-\frac{a b \ln \left(1+\left(d x +c \right)^{2}\right) e}{d}-\frac{a b c f}{d^{2}}+\frac{a^{2} x^{2} f}{2}+a^{2} x e"," ",0,"-1/2*I/d^2*b^2*ln(1+(d*x+c)^2)*ln(I+d*x+c)*c*f+1/2*I/d^2*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*c*f+1/2*I/d^2*b^2*ln(1+(d*x+c)^2)*ln(d*x+c-I)*c*f-1/2*I/d^2*b^2*ln(-1/2*I*(I+d*x+c))*ln(d*x+c-I)*c*f-a*b*f*x/d+1/2*b^2*f*ln(1+(d*x+c)^2)/d^2+1/2/d^2*b^2*arctan(d*x+c)^2*f+1/2*b^2*arctan(d*x+c)^2*f*x^2+arctan(d*x+c)^2*x*b^2*e+1/d*a^2*c*e-1/2/d^2*a^2*f*c^2-1/2*I/d*b^2*ln(1+(d*x+c)^2)*ln(d*x+c-I)*e-1/2*I/d*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*e-1/2*I/d^2*b^2*dilog(-1/2*I*(I+d*x+c))*c*f+1/2*I/d*b^2*ln(1+(d*x+c)^2)*ln(I+d*x+c)*e+1/2*I/d*b^2*ln(-1/2*I*(I+d*x+c))*ln(d*x+c-I)*e-1/4*I/d^2*b^2*ln(d*x+c-I)^2*c*f+1/2*I/d^2*b^2*dilog(1/2*I*(d*x+c-I))*c*f+1/d^2*a*b*ln(1+(d*x+c)^2)*c*f+2/d*arctan(d*x+c)*a*b*c*e+1/d^2*b^2*ln(1+(d*x+c)^2)*arctan(d*x+c)*c*f-1/d^2*a*b*f*arctan(d*x+c)*c^2+1/4*I/d^2*b^2*ln(I+d*x+c)^2*c*f+1/d^2*a*b*f*arctan(d*x+c)+1/d*arctan(d*x+c)^2*b^2*c*e-1/4*I/d*b^2*ln(I+d*x+c)^2*e-1/2*I/d*b^2*dilog(1/2*I*(d*x+c-I))*e+1/2*I/d*b^2*dilog(-1/2*I*(I+d*x+c))*e+1/4*I/d*b^2*ln(d*x+c-I)^2*e-1/2/d^2*b^2*arctan(d*x+c)^2*f*c^2-1/d*b^2*arctan(d*x+c)*f*x-1/d^2*b^2*arctan(d*x+c)*f*c+2*arctan(d*x+c)*x*a*b*e+a*b*f*arctan(d*x+c)*x^2-1/d*b^2*ln(1+(d*x+c)^2)*arctan(d*x+c)*e-1/d*a*b*ln(1+(d*x+c)^2)*e-1/d^2*a*b*c*f+1/2*a^2*x^2*f+a^2*x*e","B"
33,1,180,98,0.333000," ","int((a+b*arctan(d*x+c))^2,x)","\arctan \left(d x +c \right)^{2} x \,b^{2}-\frac{i \arctan \left(d x +c \right)^{2} b^{2}}{d}+\frac{\arctan \left(d x +c \right)^{2} b^{2} c}{d}+2 \arctan \left(d x +c \right) x a b +\frac{2 \ln \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1\right) \arctan \left(d x +c \right) b^{2}}{d}-\frac{i \polylog \left(2, -\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}\right) b^{2}}{d}+\frac{2 \arctan \left(d x +c \right) a b c}{d}+a^{2} x -\frac{a b \ln \left(1+\left(d x +c \right)^{2}\right)}{d}+\frac{a^{2} c}{d}"," ",0,"arctan(d*x+c)^2*x*b^2-I/d*arctan(d*x+c)^2*b^2+1/d*arctan(d*x+c)^2*b^2*c+2*arctan(d*x+c)*x*a*b+2/d*ln((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)*arctan(d*x+c)*b^2-I/d*polylog(2,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))*b^2+2/d*arctan(d*x+c)*a*b*c+a^2*x-1/d*a*b*ln(1+(d*x+c)^2)+a^2*c/d","A"
34,1,2149,246,2.312000," ","int((a+b*arctan(d*x+c))^2/(f*x+e),x)","\frac{b^{2} \ln \left(f \left(d x +c \right)-c f +d e \right) \arctan \left(d x +c \right)^{2}}{f}-\frac{b^{2} \polylog \left(3, -\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}\right)}{2 f}+\frac{2 i d \,b^{2} e \arctan \left(d x +c \right) \polylog \left(2, \frac{\left(c f -d e +i f \right) \left(1+i \left(d x +c \right)\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(-c f +d e +i f \right)}\right)}{f \left(2 c f -2 d e +2 i f \right)}+\frac{a^{2} \ln \left(f \left(d x +c \right)-c f +d e \right)}{f}+\frac{i b^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right) \mathrm{csgn}\left(i \left(\frac{i f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+\frac{c f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-i f +c f -d e \right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{i f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+\frac{c f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-i f +c f -d e \right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right) \pi  \arctan \left(d x +c \right)^{2}}{2 f}-\frac{b^{2} \arctan \left(d x +c \right)^{2} \ln \left(\frac{i f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+\frac{c f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-i f +c f -d e \right)}{f}+\frac{b^{2} \arctan \left(d x +c \right) \polylog \left(2, \frac{\left(c f -d e +i f \right) \left(1+i \left(d x +c \right)\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(-c f +d e +i f \right)}\right)}{c f -d e +i f}+\frac{2 a b \ln \left(f \left(d x +c \right)-c f +d e \right) \arctan \left(d x +c \right)}{f}-\frac{i a b \dilog \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{f}-\frac{i b^{2} \mathrm{csgn}\left(i \left(\frac{i f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+\frac{c f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-i f +c f -d e \right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{i f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+\frac{c f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-i f +c f -d e \right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right)^{2} \pi  \arctan \left(d x +c \right)^{2}}{2 f}-\frac{d \,b^{2} e \arctan \left(d x +c \right)^{2} \ln \left(1-\frac{\left(c f -d e +i f \right) \left(1+i \left(d x +c \right)\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(-c f +d e +i f \right)}\right)}{f \left(c f -d e +i f \right)}-\frac{i b^{2} \pi  \arctan \left(d x +c \right)^{2}}{f}+\frac{i b^{2} \polylog \left(3, \frac{\left(c f -d e +i f \right) \left(1+i \left(d x +c \right)\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(-c f +d e +i f \right)}\right)}{2 c f -2 d e +2 i f}+\frac{b^{2} c \polylog \left(3, \frac{\left(c f -d e +i f \right) \left(1+i \left(d x +c \right)\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(-c f +d e +i f \right)}\right)}{2 c f -2 d e +2 i f}+\frac{b^{2} c \arctan \left(d x +c \right)^{2} \ln \left(1-\frac{\left(c f -d e +i f \right) \left(1+i \left(d x +c \right)\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(-c f +d e +i f \right)}\right)}{c f -d e +i f}+\frac{i b^{2} \arctan \left(d x +c \right)^{2} \ln \left(1-\frac{\left(c f -d e +i f \right) \left(1+i \left(d x +c \right)\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(-c f +d e +i f \right)}\right)}{c f -d e +i f}+\frac{i a b \dilog \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{f}+\frac{i b^{2} \arctan \left(d x +c \right) \polylog \left(2, -\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}\right)}{f}-\frac{i b^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{i f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+\frac{c f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-i f +c f -d e \right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right)^{2} \pi  \arctan \left(d x +c \right)^{2}}{2 f}+\frac{i a b \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{f}+\frac{i b^{2} \mathrm{csgn}\left(\frac{i \left(\frac{i f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+\frac{c f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-i f +c f -d e \right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right)^{2} \pi  \arctan \left(d x +c \right)^{2}}{f}-\frac{i a b \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{f}-\frac{i b^{2} \mathrm{csgn}\left(\frac{i \left(\frac{i f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+\frac{c f \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}-i f +c f -d e \right)}{\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1}\right)^{3} \pi  \arctan \left(d x +c \right)^{2}}{2 f}-\frac{d \,b^{2} e \polylog \left(3, \frac{\left(c f -d e +i f \right) \left(1+i \left(d x +c \right)\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(-c f +d e +i f \right)}\right)}{2 f \left(c f -d e +i f \right)}-\frac{i b^{2} c \arctan \left(d x +c \right) \polylog \left(2, \frac{\left(c f -d e +i f \right) \left(1+i \left(d x +c \right)\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(-c f +d e +i f \right)}\right)}{c f -d e +i f}"," ",0,"b^2*ln(f*(d*x+c)-c*f+d*e)/f*arctan(d*x+c)^2-b^2/f*arctan(d*x+c)^2*ln(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)+b^2/(I*f+c*f-d*e)*arctan(d*x+c)*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+1/2*b^2*c/(I*f+c*f-d*e)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+1/2*I*b^2/(I*f+c*f-d*e)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-1/2*b^2/f*polylog(3,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))+a^2*ln(f*(d*x+c)-c*f+d*e)/f+I*a*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f-f*(d*x+c))/(d*e+I*f-c*f))+I*b^2/f*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*Pi*arctan(d*x+c)^2+2*I*d*b^2/f*e*arctan(d*x+c)*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))/(2*I*f+2*c*f-2*d*e)+1/2*I*b^2/f*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*Pi*arctan(d*x+c)^2+b^2*c/(I*f+c*f-d*e)*arctan(d*x+c)^2*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+2*a*b*ln(f*(d*x+c)-c*f+d*e)/f*arctan(d*x+c)-1/2*I*b^2/f*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*Pi*arctan(d*x+c)^2-1/2*I*b^2/f*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*Pi*arctan(d*x+c)^2+I*a*b/f*dilog((I*f-f*(d*x+c))/(d*e+I*f-c*f))+I*b^2/(I*f+c*f-d*e)*arctan(d*x+c)^2*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+I*b^2/f*arctan(d*x+c)*polylog(2,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))-I*a*b/f*dilog((I*f+f*(d*x+c))/(I*f+c*f-d*e))-I*b^2/f*Pi*arctan(d*x+c)^2-d*b^2/f*e/(I*f+c*f-d*e)*arctan(d*x+c)^2*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-1/2*d*b^2/f*e/(I*f+c*f-d*e)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-I*a*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f+f*(d*x+c))/(I*f+c*f-d*e))-I*b^2*c/(I*f+c*f-d*e)*arctan(d*x+c)*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-1/2*I*b^2/f*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*Pi*arctan(d*x+c)^2","C"
35,1,1087,556,0.148000," ","int((a+b*arctan(d*x+c))^2/(f*x+e)^2,x)","-\frac{d \,a^{2}}{\left(d f x +d e \right) f}-\frac{d \,b^{2} \arctan \left(d x +c \right)^{2}}{\left(d f x +d e \right) f}+\frac{2 d \,b^{2} \arctan \left(d x +c \right) \ln \left(f \left(d x +c \right)-c f +d e \right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{d \,b^{2} \arctan \left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{d \,b^{2} \arctan \left(d x +c \right)^{2} c}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{d^{2} b^{2} \arctan \left(d x +c \right)^{2} e}{f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}+\frac{i d \,b^{2} \ln \left(d x +c -i\right)^{2}}{4 c^{2} f^{2}-8 c d e f +4 d^{2} e^{2}+4 f^{2}}-\frac{i d \,b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}+\frac{i d \,b^{2} \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{i d \,b^{2} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{i d \,b^{2} \dilog \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{i d \,b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{2 c^{2} f^{2}-4 c d e f +2 d^{2} e^{2}+2 f^{2}}+\frac{i d \,b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{2 c^{2} f^{2}-4 c d e f +2 d^{2} e^{2}+2 f^{2}}-\frac{i d \,b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{i d \,b^{2} \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{i d \,b^{2} \ln \left(d x +c +i\right)^{2}}{4 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}+\frac{i d \,b^{2} \ln \left(d x +c +i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 c^{2} f^{2}-4 c d e f +2 d^{2} e^{2}+2 f^{2}}+\frac{i d \,b^{2} \dilog \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{2 d a b \arctan \left(d x +c \right)}{\left(d f x +d e \right) f}+\frac{2 d a b \ln \left(f \left(d x +c \right)-c f +d e \right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{d a b \ln \left(1+\left(d x +c \right)^{2}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{2 d a b \arctan \left(d x +c \right) c}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{2 d^{2} a b \arctan \left(d x +c \right) e}{f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}"," ",0,"-d*a^2/(d*f*x+d*e)/f-d*b^2/(d*f*x+d*e)/f*arctan(d*x+c)^2+2*d*b^2*arctan(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)-d*b^2*arctan(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)-d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*c+d^2*b^2/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*e+1/4*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)^2-1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog(1/2*I*(d*x+c-I))-I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog((I*f+f*(d*x+c))/(I*f+c*f-d*e))+1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog(-1/2*I*(I+d*x+c))+I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog((I*f-f*(d*x+c))/(d*e+I*f-c*f))-1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))+I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)*ln((I*f-f*(d*x+c))/(d*e+I*f-c*f))-1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)*ln(1+(d*x+c)^2)+1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))-I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)*ln((I*f+f*(d*x+c))/(I*f+c*f-d*e))-1/4*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)^2+1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)*ln(1+(d*x+c)^2)-2*d*a*b/(d*f*x+d*e)/f*arctan(d*x+c)+2*d*a*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)-d*a*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)-2*d*a*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*c+2*d^2*a*b/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*e","A"
36,1,6682,541,10.281000," ","int((f*x+e)^2*(a+b*arctan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
37,1,16362,316,2.493000," ","int((f*x+e)*(a+b*arctan(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
38,1,359,136,0.421000," ","int((a+b*arctan(d*x+c))^3,x)","x \,a^{3}+\frac{a^{3} c}{d}-\frac{i b^{3} \arctan \left(d x +c \right)^{3}}{d}+\arctan \left(d x +c \right)^{3} x \,b^{3}+\frac{\arctan \left(d x +c \right)^{3} b^{3} c}{d}+\frac{3 b^{3} \arctan \left(d x +c \right)^{2} \ln \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1\right)}{d}-\frac{3 i \arctan \left(d x +c \right)^{2} a \,b^{2}}{d}+\frac{3 b^{3} \polylog \left(3, -\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}\right)}{2 d}-\frac{3 i b^{3} \arctan \left(d x +c \right) \polylog \left(2, -\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}\right)}{d}+3 \arctan \left(d x +c \right)^{2} x a \,b^{2}+\frac{3 \arctan \left(d x +c \right)^{2} a \,b^{2} c}{d}+\frac{6 \ln \left(\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}+1\right) \arctan \left(d x +c \right) a \,b^{2}}{d}-\frac{3 i \polylog \left(2, -\frac{\left(1+i \left(d x +c \right)\right)^{2}}{1+\left(d x +c \right)^{2}}\right) a \,b^{2}}{d}+3 \arctan \left(d x +c \right) x \,a^{2} b +\frac{3 \arctan \left(d x +c \right) a^{2} b c}{d}-\frac{3 a^{2} b \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}"," ",0,"x*a^3+1/d*a^3*c-3*I/d*b^3*arctan(d*x+c)*polylog(2,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))+arctan(d*x+c)^3*x*b^3+1/d*arctan(d*x+c)^3*b^3*c+3/d*b^3*arctan(d*x+c)^2*ln((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)-I/d*b^3*arctan(d*x+c)^3+3/2/d*b^3*polylog(3,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))-3*I/d*arctan(d*x+c)^2*a*b^2+3*arctan(d*x+c)^2*x*a*b^2+3/d*arctan(d*x+c)^2*a*b^2*c+6/d*ln((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)*arctan(d*x+c)*a*b^2-3*I/d*polylog(2,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))*a*b^2+3*arctan(d*x+c)*x*a^2*b+3/d*arctan(d*x+c)*a^2*b*c-3/2/d*a^2*b*ln(1+(d*x+c)^2)","B"
39,1,4389,344,0.691000," ","int((a+b*arctan(d*x+c))^3/(f*x+e),x)","\text{output too large to display}"," ",0,"-3*I*a*b^2*c/(I*f+c*f-d*e)*arctan(d*x+c)*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-3/2*I*a*b^2/f*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*arctan(d*x+c)^2-3*I*d*b^3/f*e*polylog(4,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))/(4*I*f+4*c*f-4*d*e)-3*d*a*b^2/f*e/(I*f+c*f-d*e)*arctan(d*x+c)^2*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-3/2*I*a*b^2/f*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2-3/2*I*a*b^2/f*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2+1/2*I*b^3/f*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^3+3*I*d*b^3/f*e*arctan(d*x+c)^2*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))/(2*I*f+2*c*f-2*d*e)+3*a^2*b*ln(f*(d*x+c)-c*f+d*e)/f*arctan(d*x+c)+3*a*b^2*ln(f*(d*x+c)-c*f+d*e)/f*arctan(d*x+c)^2-3*a*b^2/f*arctan(d*x+c)^2*ln(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)-3/4*b^3/(I*f+c*f-d*e)*polylog(4,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+a^3*ln(f*(d*x+c)-c*f+d*e)/f-b^3/f*arctan(d*x+c)^3*ln(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)-3/2*b^3/f*arctan(d*x+c)*polylog(3,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))+3/2*b^3/(I*f+c*f-d*e)*arctan(d*x+c)^2*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+b^3*ln(f*(d*x+c)-c*f+d*e)/f*arctan(d*x+c)^3-3/2*a*b^2/f*polylog(3,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))-3/4*I*b^3/f*polylog(4,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))-3/2*d*a*b^2/f*e/(I*f+c*f-d*e)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-d*b^3/f*e/(I*f+c*f-d*e)*arctan(d*x+c)^3*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-3/2*d*b^3/f*e/(I*f+c*f-d*e)*arctan(d*x+c)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-1/2*I*b^3/f*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^3-1/2*I*b^3/f*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^3+3*I*a*b^2/f*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^2+3*a*b^2*c/(I*f+c*f-d*e)*arctan(d*x+c)^2*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-3/2*I*b^3*c/(I*f+c*f-d*e)*arctan(d*x+c)^2*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3/2*I*a^2*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f-f*(d*x+c))/(d*e+I*f-c*f))-3/2*I*a^2*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f+f*(d*x+c))/(I*f+c*f-d*e))+3*I*a*b^2/(I*f+c*f-d*e)*arctan(d*x+c)^2*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3*I*a*b^2/f*arctan(d*x+c)*polylog(2,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))-3*I*a*b^2/f*Pi*arctan(d*x+c)^2-1/2*I*b^3/f*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3*arctan(d*x+c)^3+6*I*d*a*b^2/f*e*arctan(d*x+c)*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))/(2*I*f+2*c*f-2*d*e)+3/2*I*a*b^2/f*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*arctan(d*x+c)^2-3/2*I*a^2*b/f*dilog((I*f+f*(d*x+c))/(I*f+c*f-d*e))+3/4*I*b^3*c/(I*f+c*f-d*e)*polylog(4,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-I*b^3/f*Pi*arctan(d*x+c)^3+3/2*I*a*b^2/(I*f+c*f-d*e)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+b^3*c/(I*f+c*f-d*e)*arctan(d*x+c)^3*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3/2*b^3*c/(I*f+c*f-d*e)*arctan(d*x+c)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+I*b^3/f*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*arctan(d*x+c)^3+3*a*b^2/(I*f+c*f-d*e)*arctan(d*x+c)*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+I*b^3/(I*f+c*f-d*e)*arctan(d*x+c)^3*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3/2*a*b^2*c/(I*f+c*f-d*e)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3/2*I*b^3/f*arctan(d*x+c)^2*polylog(2,-(1+I*(d*x+c))^2/(1+(d*x+c)^2))+3/2*I*b^3/(I*f+c*f-d*e)*arctan(d*x+c)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3/2*I*a^2*b/f*dilog((I*f-f*(d*x+c))/(d*e+I*f-c*f))","C"
40,1,4764,1197,1.798000," ","int((a+b*arctan(d*x+c))^3/(f*x+e)^2,x)","\text{output too large to display}"," ",0,"-3/2*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2+3/4*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)-3/2*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2+3*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*ln(2)+3*d*a^2*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)-3/2*d*a^2*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)+3*d*b^3*arctan(d*x+c)^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)-d*b^3*arctan(d*x+c)^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*c-3*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*ln(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)+3*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*ln((1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))-3/2*d*b^3*arctan(d*x+c)^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)-d*b^3/(d*f*x+d*e)/f*arctan(d*x+c)^3-I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^3-d*a^3/(d*f*x+d*e)/f+3*d*b^3*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*c/(I*f+c*f-d*e)*arctan(d*x+c)^2*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3*I*d^2*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*e/(I*f+c*f-d*e)*arctan(d*x+c)*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3*I*d*b^3*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)/(I*f+c*f-d*e)*arctan(d*x+c)^2*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3/4*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2+3/4*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^2-3/4*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))^2*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))-3/2*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))+3/2*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*(1+I*(d*x+c))/(1+(d*x+c)^2)^(1/2))*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))^2-3*I*d*b^3*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*c/(I*f+c*f-d*e)*arctan(d*x+c)*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3/2*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e))*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))-3/4*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)+3*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^2-3/4*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^3-3/2*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*(I*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)+c*f*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-d*e*(1+I*(d*x+c))^2/(1+(d*x+c)^2)-I*f+c*f-d*e)/((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1))^3+3/2*I*d*b^3*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)/(I*f+c*f-d*e)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-3/4*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*(1+I*(d*x+c))^2/(1+(d*x+c)^2))^3-3*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)*ln((I*f+f*(d*x+c))/(I*f+c*f-d*e))-3*d^2*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*e/(I*f+c*f-d*e)*arctan(d*x+c)^2*ln(1-(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3*d*b^3*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)/(I*f+c*f-d*e)*arctan(d*x+c)*polylog(2,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3/2*d*b^3*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*c/(I*f+c*f-d*e)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))+3*d^2*a*b^2/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*e+3*d^2*a^2*b/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*e+3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))-3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))+3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)*ln(1+(d*x+c)^2)+3*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)*ln((I*f-f*(d*x+c))/(d*e+I*f-c*f))-3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)*ln(1+(d*x+c)^2)+3/4*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi*csgn(I*((1+I*(d*x+c))^2/(1+(d*x+c)^2)+1)^2)^3-3*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*c-3*d*a^2*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*c+d^2*b^3/f*arctan(d*x+c)^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*e-3/2*d^2*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*e/(I*f+c*f-d*e)*polylog(3,(I*f+c*f-d*e)*(1+I*(d*x+c))^2/(1+(d*x+c)^2)/(d*e+I*f-c*f))-3*d*a*b^2/(d*f*x+d*e)/f*arctan(d*x+c)^2-3*d*a^2*b/(d*f*x+d*e)/f*arctan(d*x+c)+6*d*a*b^2*arctan(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)-3*d*a*b^2*arctan(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)+3*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog((I*f-f*(d*x+c))/(d*e+I*f-c*f))-3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog(1/2*I*(d*x+c-I))-3/4*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)^2+3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog(-1/2*I*(I+d*x+c))-3*I*d*b^3/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*Pi-3*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog((I*f+f*(d*x+c))/(I*f+c*f-d*e))+3/4*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)^2","C"
41,0,0,171,1.958000," ","int((f*x+e)^m*(a+b*arctan(d*x+c)),x)","\int \left(f x +e \right)^{m} \left(a +b \arctan \left(d x +c \right)\right)\, dx"," ",0,"int((f*x+e)^m*(a+b*arctan(d*x+c)),x)","F"
42,0,0,22,1.479000," ","int((f*x+e)^m*(a+b*arctan(d*x+c))^2,x)","\int \left(f x +e \right)^{m} \left(a +b \arctan \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((f*x+e)^m*(a+b*arctan(d*x+c))^2,x)","F"
43,0,0,22,1.434000," ","int((f*x+e)^m*(a+b*arctan(d*x+c))^3,x)","\int \left(f x +e \right)^{m} \left(a +b \arctan \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((f*x+e)^m*(a+b*arctan(d*x+c))^3,x)","F"
44,1,132,94,0.040000," ","int(x^3*arctan(b*x+a),x)","\frac{x^{4} \arctan \left(b x +a \right)}{4}-\frac{\arctan \left(b x +a \right) a^{4}}{4 b^{4}}-\frac{x^{3}}{12 b}+\frac{x^{2} a}{4 b^{2}}-\frac{3 x \,a^{2}}{4 b^{3}}-\frac{13 a^{3}}{12 b^{4}}+\frac{x}{4 b^{3}}+\frac{a}{4 b^{4}}+\frac{\ln \left(1+\left(b x +a \right)^{2}\right) a^{3}}{2 b^{4}}-\frac{\ln \left(1+\left(b x +a \right)^{2}\right) a}{2 b^{4}}+\frac{3 \arctan \left(b x +a \right) a^{2}}{2 b^{4}}-\frac{\arctan \left(b x +a \right)}{4 b^{4}}"," ",0,"1/4*x^4*arctan(b*x+a)-1/4/b^4*arctan(b*x+a)*a^4-1/12/b*x^3+1/4/b^2*x^2*a-3/4/b^3*x*a^2-13/12/b^4*a^3+1/4/b^3*x+1/4/b^4*a+1/2/b^4*ln(1+(b*x+a)^2)*a^3-1/2/b^4*ln(1+(b*x+a)^2)*a+3/2/b^4*arctan(b*x+a)*a^2-1/4/b^4*arctan(b*x+a)","A"
45,1,95,71,0.043000," ","int(x^2*arctan(b*x+a),x)","\frac{x^{3} \arctan \left(b x +a \right)}{3}+\frac{\arctan \left(b x +a \right) a^{3}}{3 b^{3}}-\frac{x^{2}}{6 b}+\frac{2 a x}{3 b^{2}}+\frac{5 a^{2}}{6 b^{3}}-\frac{\ln \left(1+\left(b x +a \right)^{2}\right) a^{2}}{2 b^{3}}+\frac{\ln \left(1+\left(b x +a \right)^{2}\right)}{6 b^{3}}-\frac{\arctan \left(b x +a \right) a}{b^{3}}"," ",0,"1/3*x^3*arctan(b*x+a)+1/3/b^3*arctan(b*x+a)*a^3-1/6/b*x^2+2/3*a*x/b^2+5/6/b^3*a^2-1/2/b^3*ln(1+(b*x+a)^2)*a^2+1/6/b^3*ln(1+(b*x+a)^2)-1/b^3*arctan(b*x+a)*a","A"
46,1,66,52,0.038000," ","int(x*arctan(b*x+a),x)","\frac{x^{2} \arctan \left(b x +a \right)}{2}-\frac{\arctan \left(b x +a \right) a^{2}}{2 b^{2}}-\frac{x}{2 b}-\frac{a}{2 b^{2}}+\frac{a \ln \left(1+\left(b x +a \right)^{2}\right)}{2 b^{2}}+\frac{\arctan \left(b x +a \right)}{2 b^{2}}"," ",0,"1/2*x^2*arctan(b*x+a)-1/2/b^2*arctan(b*x+a)*a^2-1/2*x/b-1/2/b^2*a+1/2*a*ln(1+(b*x+a)^2)/b^2+1/2/b^2*arctan(b*x+a)","A"
47,1,36,31,0.035000," ","int(arctan(b*x+a),x)","x \arctan \left(b x +a \right)+\frac{\arctan \left(b x +a \right) a}{b}-\frac{\ln \left(1+\left(b x +a \right)^{2}\right)}{2 b}"," ",0,"x*arctan(b*x+a)+1/b*arctan(b*x+a)*a-1/2*ln(1+(b*x+a)^2)/b","A"
48,1,103,108,0.058000," ","int(arctan(b*x+a)/x,x)","\ln \left(b x \right) \arctan \left(b x +a \right)+\frac{i \ln \left(b x \right) \ln \left(\frac{-b x -a +i}{i-a}\right)}{2}-\frac{i \ln \left(b x \right) \ln \left(\frac{b x +a +i}{i+a}\right)}{2}+\frac{i \dilog \left(\frac{-b x -a +i}{i-a}\right)}{2}-\frac{i \dilog \left(\frac{b x +a +i}{i+a}\right)}{2}"," ",0,"ln(b*x)*arctan(b*x+a)+1/2*I*ln(b*x)*ln((I-a-b*x)/(I-a))-1/2*I*ln(b*x)*ln((I+a+b*x)/(I+a))+1/2*I*dilog((I-a-b*x)/(I-a))-1/2*I*dilog((I+a+b*x)/(I+a))","A"
49,1,63,60,0.046000," ","int(arctan(b*x+a)/x^2,x)","-\frac{\arctan \left(b x +a \right)}{x}+\frac{b \ln \left(b x \right)}{a^{2}+1}-\frac{b \ln \left(1+\left(b x +a \right)^{2}\right)}{2 \left(a^{2}+1\right)}-\frac{a b \arctan \left(b x +a \right)}{a^{2}+1}"," ",0,"-arctan(b*x+a)/x+b/(a^2+1)*ln(b*x)-1/2*b*ln(1+(b*x+a)^2)/(a^2+1)-a*b*arctan(b*x+a)/(a^2+1)","A"
50,1,105,88,0.047000," ","int(arctan(b*x+a)/x^3,x)","-\frac{\arctan \left(b x +a \right)}{2 x^{2}}-\frac{b}{2 \left(a^{2}+1\right) x}-\frac{b^{2} a \ln \left(b x \right)}{\left(a^{2}+1\right)^{2}}+\frac{b^{2} \arctan \left(b x +a \right) a^{2}}{2 \left(a^{2}+1\right)^{2}}+\frac{a \,b^{2} \ln \left(1+\left(b x +a \right)^{2}\right)}{2 \left(a^{2}+1\right)^{2}}-\frac{b^{2} \arctan \left(b x +a \right)}{2 \left(a^{2}+1\right)^{2}}"," ",0,"-1/2*arctan(b*x+a)/x^2-1/2*b/(a^2+1)/x-b^2/(a^2+1)^2*a*ln(b*x)+1/2*b^2/(a^2+1)^2*arctan(b*x+a)*a^2+1/2*a*b^2*ln(1+(b*x+a)^2)/(a^2+1)^2-1/2*b^2/(a^2+1)^2*arctan(b*x+a)","A"
51,1,162,117,0.048000," ","int(arctan(b*x+a)/x^4,x)","-\frac{\arctan \left(b x +a \right)}{3 x^{3}}-\frac{b}{6 \left(a^{2}+1\right) x^{2}}+\frac{b^{3} \ln \left(b x \right) a^{2}}{\left(a^{2}+1\right)^{3}}-\frac{b^{3} \ln \left(b x \right)}{3 \left(a^{2}+1\right)^{3}}+\frac{2 a \,b^{2}}{3 \left(a^{2}+1\right)^{2} x}-\frac{b^{3} \ln \left(1+\left(b x +a \right)^{2}\right) a^{2}}{2 \left(a^{2}+1\right)^{3}}+\frac{b^{3} \ln \left(1+\left(b x +a \right)^{2}\right)}{6 \left(a^{2}+1\right)^{3}}-\frac{b^{3} \arctan \left(b x +a \right) a^{3}}{3 \left(a^{2}+1\right)^{3}}+\frac{b^{3} \arctan \left(b x +a \right) a}{\left(a^{2}+1\right)^{3}}"," ",0,"-1/3*arctan(b*x+a)/x^3-1/6*b/(a^2+1)/x^2+b^3/(a^2+1)^3*ln(b*x)*a^2-1/3*b^3/(a^2+1)^3*ln(b*x)+2/3*a*b^2/(a^2+1)^2/x-1/2*b^3/(a^2+1)^3*ln(1+(b*x+a)^2)*a^2+1/6*b^3/(a^2+1)^3*ln(1+(b*x+a)^2)-1/3*b^3/(a^2+1)^3*arctan(b*x+a)*a^3+b^3/(a^2+1)^3*arctan(b*x+a)*a","A"
52,1,631,624,1.312000," ","int(arctan(b*x+a)/(d*x^3+c),x)","\frac{2 b^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(\left(a^{3} d +3 i a^{2} d -c \,b^{3}-3 a d -i d \right) \textit{\_Z}^{6}+\left(3 a^{3} d +3 i a^{2} d -3 c \,b^{3}+3 a d +3 i d \right) \textit{\_Z}^{4}+\left(3 a^{3} d -3 i a^{2} d -3 c \,b^{3}+3 a d -3 i d \right) \textit{\_Z}^{2}-3 i a^{2} d +a^{3} d -c \,b^{3}+i d -3 a d \right)}{\sum}\frac{i \arctan \left(b x +a \right) \ln \left(\frac{\textit{\_R1} -\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)}{a^{3} d \,\textit{\_R1}^{4}+3 i a^{2} d \,\textit{\_R1}^{4}-b^{3} c \,\textit{\_R1}^{4}-3 a d \,\textit{\_R1}^{4}-i d \,\textit{\_R1}^{4}+2 a^{3} d \,\textit{\_R1}^{2}+2 i a^{2} d \,\textit{\_R1}^{2}-2 b^{3} c \,\textit{\_R1}^{2}+2 \textit{\_R1}^{2} a d +2 i d \,\textit{\_R1}^{2}+a^{3} d -i a^{2} d -c \,b^{3}+a d -i d}\right)}{3}+\frac{2 b^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(\left(a^{3} d +3 i a^{2} d -c \,b^{3}-3 a d -i d \right) \textit{\_Z}^{6}+\left(3 a^{3} d +3 i a^{2} d -3 c \,b^{3}+3 a d +3 i d \right) \textit{\_Z}^{4}+\left(3 a^{3} d -3 i a^{2} d -3 c \,b^{3}+3 a d -3 i d \right) \textit{\_Z}^{2}-3 i a^{2} d +a^{3} d -c \,b^{3}+i d -3 a d \right)}{\sum}\frac{\textit{\_R1}^{2} \left(i \arctan \left(b x +a \right) \ln \left(\frac{\textit{\_R1} -\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)\right)}{a^{3} d \,\textit{\_R1}^{4}+3 i a^{2} d \,\textit{\_R1}^{4}-b^{3} c \,\textit{\_R1}^{4}-3 a d \,\textit{\_R1}^{4}-i d \,\textit{\_R1}^{4}+2 a^{3} d \,\textit{\_R1}^{2}+2 i a^{2} d \,\textit{\_R1}^{2}-2 b^{3} c \,\textit{\_R1}^{2}+2 \textit{\_R1}^{2} a d +2 i d \,\textit{\_R1}^{2}+a^{3} d -i a^{2} d -c \,b^{3}+a d -i d}\right)}{3}"," ",0,"2/3*b^2*sum(1/(a^3*d*_R1^4+3*I*a^2*d*_R1^4-b^3*c*_R1^4-3*a*d*_R1^4-I*d*_R1^4+2*a^3*d*_R1^2+2*I*a^2*d*_R1^2-2*b^3*c*_R1^2+2*_R1^2*a*d+2*I*d*_R1^2+a^3*d-I*a^2*d-c*b^3+a*d-I*d)*(I*arctan(b*x+a)*ln((_R1-(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))/_R1)+dilog((_R1-(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))/_R1)),_R1=RootOf((3*I*a^2*d+a^3*d-c*b^3-I*d-3*a*d)*_Z^6+(3*I*a^2*d+3*a^3*d-3*c*b^3+3*I*d+3*a*d)*_Z^4+(-3*I*a^2*d+3*a^3*d-3*c*b^3-3*I*d+3*a*d)*_Z^2-3*I*a^2*d+a^3*d-c*b^3+I*d-3*a*d))+2/3*b^2*sum(_R1^2/(a^3*d*_R1^4+3*I*a^2*d*_R1^4-b^3*c*_R1^4-3*a*d*_R1^4-I*d*_R1^4+2*a^3*d*_R1^2+2*I*a^2*d*_R1^2-2*b^3*c*_R1^2+2*_R1^2*a*d+2*I*d*_R1^2+a^3*d-I*a^2*d-c*b^3+a*d-I*d)*(I*arctan(b*x+a)*ln((_R1-(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))/_R1)+dilog((_R1-(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))/_R1)),_R1=RootOf((3*I*a^2*d+a^3*d-c*b^3-I*d-3*a*d)*_Z^6+(3*I*a^2*d+3*a^3*d-3*c*b^3+3*I*d+3*a*d)*_Z^4+(-3*I*a^2*d+3*a^3*d-3*c*b^3-3*I*d+3*a*d)*_Z^2-3*I*a^2*d+a^3*d-c*b^3+I*d-3*a*d))","C"
53,1,2192,411,1.286000," ","int(arctan(b*x+a)/(d*x^2+c),x)","-\frac{i b \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}+2 \sqrt{b^{2} c d}-d \right)}\right) \arctan \left(b x +a \right)}{2 d \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}+\frac{i b \ln \left(1-\frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}+2 \sqrt{b^{2} c d}-d \right)}\right) \arctan \left(b x +a \right)}{a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d}+\frac{i b \ln \left(1-\frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}-2 \sqrt{b^{2} c d}-d \right)}\right) \arctan \left(b x +a \right)}{a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d}-\frac{i \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}+2 \sqrt{b^{2} c d}-d \right)}\right) \arctan \left(b x +a \right)}{2 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}+\frac{b \sqrt{b^{2} c d}\, \arctan \left(b x +a \right)^{2}}{2 d \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}+\frac{b \arctan \left(b x +a \right)^{2}}{a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d}+\frac{\sqrt{b^{2} c d}\, \arctan \left(b x +a \right)^{2}}{2 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}+\frac{\sqrt{b^{2} c d}\, \arctan \left(b x +a \right)^{2} a^{2}}{2 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}+\frac{b \sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}-2 \sqrt{b^{2} c d}-d \right)}\right)}{4 d \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}+\frac{b \polylog \left(2, \frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}-2 \sqrt{b^{2} c d}-d \right)}\right)}{2 a^{2} d +2 c \,b^{2}+4 \sqrt{b^{2} c d}+2 d}+\frac{\sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}-2 \sqrt{b^{2} c d}-d \right)}\right)}{4 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}+\frac{\sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}-2 \sqrt{b^{2} c d}-d \right)}\right) a^{2}}{4 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}+\frac{i \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}-2 \sqrt{b^{2} c d}-d \right)}\right) \arctan \left(b x +a \right) a^{2}}{2 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}+\frac{i \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}-2 \sqrt{b^{2} c d}-d \right)}\right) \arctan \left(b x +a \right)}{2 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{i \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}+2 \sqrt{b^{2} c d}-d \right)}\right) \arctan \left(b x +a \right) a^{2}}{2 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}+\frac{i b \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}-2 \sqrt{b^{2} c d}-d \right)}\right) \arctan \left(b x +a \right)}{2 d \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{b \sqrt{b^{2} c d}\, \arctan \left(b x +a \right)^{2}}{2 d \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}+\frac{b \arctan \left(b x +a \right)^{2}}{a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d}-\frac{\sqrt{b^{2} c d}\, \arctan \left(b x +a \right)^{2}}{2 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}-\frac{\sqrt{b^{2} c d}\, \arctan \left(b x +a \right)^{2} a^{2}}{2 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}-\frac{b \sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}+2 \sqrt{b^{2} c d}-d \right)}\right)}{4 d \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}+\frac{b \polylog \left(2, \frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}+2 \sqrt{b^{2} c d}-d \right)}\right)}{2 a^{2} d +2 c \,b^{2}-4 \sqrt{b^{2} c d}+2 d}-\frac{\sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}+2 \sqrt{b^{2} c d}-d \right)}\right)}{4 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}-\frac{\sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d +2 i a d +c \,b^{2}-d \right) \left(1+i \left(b x +a \right)\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(-a^{2} d -c \,b^{2}+2 \sqrt{b^{2} c d}-d \right)}\right) a^{2}}{4 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}"," ",0,"-1/2*I*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*ln(1-(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2+2*(b^2*c*d)^(1/2)-d))*arctan(b*x+a)+I*b/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*ln(1-(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2+2*(b^2*c*d)^(1/2)-d))*arctan(b*x+a)+I*b/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*ln(1-(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2-2*(b^2*c*d)^(1/2)-d))*arctan(b*x+a)-1/2*I/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*ln(1-(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2+2*(b^2*c*d)^(1/2)-d))*arctan(b*x+a)+1/2*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*arctan(b*x+a)^2+b/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*arctan(b*x+a)^2+1/2/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*arctan(b*x+a)^2+1/2/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*arctan(b*x+a)^2*a^2+1/4*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*polylog(2,(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2-2*(b^2*c*d)^(1/2)-d))+1/2*b/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*polylog(2,(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2-2*(b^2*c*d)^(1/2)-d))+1/4/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*polylog(2,(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2-2*(b^2*c*d)^(1/2)-d))+1/4/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*polylog(2,(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2-2*(b^2*c*d)^(1/2)-d))*a^2+1/2*I/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*ln(1-(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2-2*(b^2*c*d)^(1/2)-d))*arctan(b*x+a)*a^2+1/2*I/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*ln(1-(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2-2*(b^2*c*d)^(1/2)-d))*arctan(b*x+a)-1/2*I/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*ln(1-(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2+2*(b^2*c*d)^(1/2)-d))*arctan(b*x+a)*a^2+1/2*I*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*ln(1-(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2-2*(b^2*c*d)^(1/2)-d))*arctan(b*x+a)-1/2*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*arctan(b*x+a)^2+b/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*arctan(b*x+a)^2-1/2/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*arctan(b*x+a)^2-1/2/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*arctan(b*x+a)^2*a^2-1/4*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*polylog(2,(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2+2*(b^2*c*d)^(1/2)-d))+1/2*b/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*polylog(2,(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2+2*(b^2*c*d)^(1/2)-d))-1/4/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*polylog(2,(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2+2*(b^2*c*d)^(1/2)-d))-1/4/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*polylog(2,(2*I*a*d+a^2*d+c*b^2-d)*(1+I*(b*x+a))^2/(1+(b*x+a)^2)/(-a^2*d-c*b^2+2*(b^2*c*d)^(1/2)-d))*a^2","B"
54,1,198,140,0.062000," ","int(arctan(b*x+a)/(d*x+c),x)","\frac{\ln \left(d \left(b x +a \right)-a d +b c \right) \arctan \left(b x +a \right)}{d}+\frac{i \ln \left(d \left(b x +a \right)-a d +b c \right) \ln \left(\frac{i d -d \left(b x +a \right)}{-a d +b c +i d}\right)}{2 d}-\frac{i \ln \left(d \left(b x +a \right)-a d +b c \right) \ln \left(\frac{i d +d \left(b x +a \right)}{a d -b c +i d}\right)}{2 d}+\frac{i \dilog \left(\frac{i d -d \left(b x +a \right)}{-a d +b c +i d}\right)}{2 d}-\frac{i \dilog \left(\frac{i d +d \left(b x +a \right)}{a d -b c +i d}\right)}{2 d}"," ",0,"ln(d*(b*x+a)-a*d+b*c)/d*arctan(b*x+a)+1/2*I*ln(d*(b*x+a)-a*d+b*c)/d*ln((I*d-d*(b*x+a))/(b*c+I*d-a*d))-1/2*I*ln(d*(b*x+a)-a*d+b*c)/d*ln((I*d+d*(b*x+a))/(I*d+a*d-b*c))+1/2*I/d*dilog((I*d-d*(b*x+a))/(b*c+I*d-a*d))-1/2*I/d*dilog((I*d+d*(b*x+a))/(I*d+a*d-b*c))","A"
55,1,317,210,0.067000," ","int(arctan(b*x+a)/(c+1/x*d),x)","\frac{\arctan \left(b x +a \right) x}{c}+\frac{\arctan \left(b x +a \right) a}{b c}-\frac{\arctan \left(b x +a \right) d \ln \left(c \left(b x +a \right)-a c +b d \right)}{c^{2}}-\frac{\ln \left(a^{2} c^{2}-2 a b c d +b^{2} d^{2}+2 \left(c \left(b x +a \right)-a c +b d \right) a c -2 \left(c \left(b x +a \right)-a c +b d \right) b d +\left(c \left(b x +a \right)-a c +b d \right)^{2}+c^{2}\right)}{2 b c}-\frac{i d \ln \left(c \left(b x +a \right)-a c +b d \right) \ln \left(\frac{i c -c \left(b x +a \right)}{-a c +b d +i c}\right)}{2 c^{2}}+\frac{i d \ln \left(c \left(b x +a \right)-a c +b d \right) \ln \left(\frac{i c +c \left(b x +a \right)}{a c -b d +i c}\right)}{2 c^{2}}-\frac{i d \dilog \left(\frac{i c -c \left(b x +a \right)}{-a c +b d +i c}\right)}{2 c^{2}}+\frac{i d \dilog \left(\frac{i c +c \left(b x +a \right)}{a c -b d +i c}\right)}{2 c^{2}}"," ",0,"arctan(b*x+a)/c*x+1/b*arctan(b*x+a)/c*a-arctan(b*x+a)*d/c^2*ln(c*(b*x+a)-a*c+b*d)-1/2/b/c*ln(a^2*c^2-2*a*b*c*d+b^2*d^2+2*(c*(b*x+a)-a*c+b*d)*a*c-2*(c*(b*x+a)-a*c+b*d)*b*d+(c*(b*x+a)-a*c+b*d)^2+c^2)-1/2*I/c^2*d*ln(c*(b*x+a)-a*c+b*d)*ln((I*c-c*(b*x+a))/(I*c-a*c+b*d))+1/2*I/c^2*d*ln(c*(b*x+a)-a*c+b*d)*ln((I*c+c*(b*x+a))/(I*c+a*c-b*d))-1/2*I/c^2*d*dilog((I*c-c*(b*x+a))/(I*c-a*c+b*d))+1/2*I/c^2*d*dilog((I*c+c*(b*x+a))/(I*c+a*c-b*d))","A"
56,1,53434,510,2.698000," ","int(arctan(b*x+a)/(c+d/x^2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
57,1,682,682,1.235000," ","int(arctan(b*x+a)/(c+d/x^3),x)","\frac{\arctan \left(b x +a \right) x}{c}+\frac{\arctan \left(b x +a \right) a}{b c}-\frac{\ln \left(1+\left(b x +a \right)^{2}\right)}{2 b c}-\frac{2 b^{2} d \left(\munderset{\textit{\_R1} =\RootOf \left(\left(a^{3} c +3 i a^{2} c -d \,b^{3}-3 a c -i c \right) \textit{\_Z}^{6}+\left(3 a^{3} c +3 i a^{2} c -3 d \,b^{3}+3 a c +3 i c \right) \textit{\_Z}^{4}+\left(3 a^{3} c -3 i a^{2} c -3 d \,b^{3}+3 a c -3 i c \right) \textit{\_Z}^{2}-3 i a^{2} c +a^{3} c -d \,b^{3}+i c -3 a c \right)}{\sum}\frac{i \arctan \left(b x +a \right) \ln \left(\frac{\textit{\_R1} -\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)}{a^{3} c \,\textit{\_R1}^{4}+3 i \textit{\_R1}^{4} a^{2} c -b^{3} d \,\textit{\_R1}^{4}-3 a c \,\textit{\_R1}^{4}-i \textit{\_R1}^{4} c +2 a^{3} c \,\textit{\_R1}^{2}+2 i \textit{\_R1}^{2} a^{2} c -2 b^{3} d \,\textit{\_R1}^{2}+2 \textit{\_R1}^{2} a c +2 i \textit{\_R1}^{2} c +a^{3} c -i a^{2} c -d \,b^{3}+a c -i c}\right)}{3 c}-\frac{2 b^{2} d \left(\munderset{\textit{\_R1} =\RootOf \left(\left(a^{3} c +3 i a^{2} c -d \,b^{3}-3 a c -i c \right) \textit{\_Z}^{6}+\left(3 a^{3} c +3 i a^{2} c -3 d \,b^{3}+3 a c +3 i c \right) \textit{\_Z}^{4}+\left(3 a^{3} c -3 i a^{2} c -3 d \,b^{3}+3 a c -3 i c \right) \textit{\_Z}^{2}-3 i a^{2} c +a^{3} c -d \,b^{3}+i c -3 a c \right)}{\sum}\frac{\textit{\_R1}^{2} \left(i \arctan \left(b x +a \right) \ln \left(\frac{\textit{\_R1} -\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}{\textit{\_R1}}\right)\right)}{a^{3} c \,\textit{\_R1}^{4}+3 i \textit{\_R1}^{4} a^{2} c -b^{3} d \,\textit{\_R1}^{4}-3 a c \,\textit{\_R1}^{4}-i \textit{\_R1}^{4} c +2 a^{3} c \,\textit{\_R1}^{2}+2 i \textit{\_R1}^{2} a^{2} c -2 b^{3} d \,\textit{\_R1}^{2}+2 \textit{\_R1}^{2} a c +2 i \textit{\_R1}^{2} c +a^{3} c -i a^{2} c -d \,b^{3}+a c -i c}\right)}{3 c}"," ",0,"arctan(b*x+a)/c*x+1/b*arctan(b*x+a)/c*a-1/2/b/c*ln(1+(b*x+a)^2)-2/3*b^2/c*d*sum(1/(a^3*c*_R1^4+3*I*_R1^4*a^2*c-b^3*d*_R1^4-3*a*c*_R1^4-I*_R1^4*c+2*a^3*c*_R1^2+2*I*_R1^2*a^2*c-2*b^3*d*_R1^2+2*_R1^2*a*c+2*I*_R1^2*c+a^3*c-I*a^2*c-d*b^3+a*c-I*c)*(I*arctan(b*x+a)*ln((_R1-(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))/_R1)+dilog((_R1-(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))/_R1)),_R1=RootOf((3*I*a^2*c+a^3*c-d*b^3-I*c-3*a*c)*_Z^6+(3*I*a^2*c+3*a^3*c-3*d*b^3+3*I*c+3*a*c)*_Z^4+(-3*I*a^2*c+3*a^3*c-3*d*b^3-3*I*c+3*a*c)*_Z^2-3*I*a^2*c+a^3*c-d*b^3+I*c-3*a*c))-2/3*b^2/c*d*sum(_R1^2/(a^3*c*_R1^4+3*I*_R1^4*a^2*c-b^3*d*_R1^4-3*a*c*_R1^4-I*_R1^4*c+2*a^3*c*_R1^2+2*I*_R1^2*a^2*c-2*b^3*d*_R1^2+2*_R1^2*a*c+2*I*_R1^2*c+a^3*c-I*a^2*c-d*b^3+a*c-I*c)*(I*arctan(b*x+a)*ln((_R1-(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))/_R1)+dilog((_R1-(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))/_R1)),_R1=RootOf((3*I*a^2*c+a^3*c-d*b^3-I*c-3*a*c)*_Z^6+(3*I*a^2*c+3*a^3*c-3*d*b^3+3*I*c+3*a*c)*_Z^4+(-3*I*a^2*c+3*a^3*c-3*d*b^3-3*I*c+3*a*c)*_Z^2-3*I*a^2*c+a^3*c-d*b^3+I*c-3*a*c))","C"
58,1,344,527,0.333000," ","int(arctan(b*x+a)/(c+d*x^(1/2)),x)","\frac{2 \arctan \left(b x +a \right) \sqrt{x}}{d}-\frac{2 \arctan \left(b x +a \right) c \ln \left(c +d \sqrt{x}\right)}{d^{2}}+c \left(\munderset{\textit{\_R1} =\RootOf \left(b^{2} \textit{\_Z}^{4}-4 c \,b^{2} \textit{\_Z}^{3}+\left(2 a b \,d^{2}+6 b^{2} c^{2}\right) \textit{\_Z}^{2}+\left(-4 a b c \,d^{2}-4 b^{2} c^{3}\right) \textit{\_Z} +a^{2} d^{4}+2 a b \,c^{2} d^{2}+b^{2} c^{4}+d^{4}\right)}{\sum}\frac{\ln \left(c +d \sqrt{x}\right) \ln \left(\frac{-d \sqrt{x}+\textit{\_R1} -c}{\textit{\_R1}}\right)+\dilog \left(\frac{-d \sqrt{x}+\textit{\_R1} -c}{\textit{\_R1}}\right)}{\textit{\_R1}^{2} b -2 \textit{\_R1} b c +a \,d^{2}+b \,c^{2}}\right)-\left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{4}-4 c \,b^{2} \textit{\_Z}^{3}+\left(2 a b \,d^{2}+6 b^{2} c^{2}\right) \textit{\_Z}^{2}+\left(-4 a b c \,d^{2}-4 b^{2} c^{3}\right) \textit{\_Z} +a^{2} d^{4}+2 a b \,c^{2} d^{2}+b^{2} c^{4}+d^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{2}-2 \textit{\_R} c +c^{2}\right) \ln \left(d \sqrt{x}-\textit{\_R} +c \right)}{b \,\textit{\_R}^{3}-3 b c \,\textit{\_R}^{2}+a \,d^{2} \textit{\_R} +3 b \,c^{2} \textit{\_R} -a c \,d^{2}-b \,c^{3}}\right)"," ",0,"2*arctan(b*x+a)/d*x^(1/2)-2*arctan(b*x+a)*c/d^2*ln(c+d*x^(1/2))+c*sum(1/(_R1^2*b-2*_R1*b*c+a*d^2+b*c^2)*(ln(c+d*x^(1/2))*ln((-d*x^(1/2)+_R1-c)/_R1)+dilog((-d*x^(1/2)+_R1-c)/_R1)),_R1=RootOf(b^2*_Z^4-4*c*b^2*_Z^3+(2*a*b*d^2+6*b^2*c^2)*_Z^2+(-4*a*b*c*d^2-4*b^2*c^3)*_Z+a^2*d^4+2*a*b*c^2*d^2+b^2*c^4+d^4))-sum((_R^2-2*_R*c+c^2)/(_R^3*b-3*_R^2*b*c+_R*a*d^2+3*_R*b*c^2-a*c*d^2-b*c^3)*ln(d*x^(1/2)-_R+c),_R=RootOf(b^2*_Z^4-4*c*b^2*_Z^3+(2*a*b*d^2+6*b^2*c^2)*_Z^2+(-4*a*b*c*d^2-4*b^2*c^3)*_Z+a^2*d^4+2*a*b*c^2*d^2+b^2*c^4+d^4))","C"
59,1,377,612,0.314000," ","int(arctan(b*x+a)/(c+d/x^(1/2)),x)","\frac{\arctan \left(b x +a \right) x}{c}-\frac{2 \arctan \left(b x +a \right) d \sqrt{x}}{c^{2}}+\frac{2 \arctan \left(b x +a \right) d^{2} \ln \left(d +c \sqrt{x}\right)}{c^{3}}-\frac{d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(b^{2} \textit{\_Z}^{4}-4 b^{2} d \,\textit{\_Z}^{3}+\left(2 c^{2} a b +6 b^{2} d^{2}\right) \textit{\_Z}^{2}+\left(-4 a b \,c^{2} d -4 b^{2} d^{3}\right) \textit{\_Z} +a^{2} c^{4}+2 a b \,c^{2} d^{2}+b^{2} d^{4}+c^{4}\right)}{\sum}\frac{\ln \left(d +c \sqrt{x}\right) \ln \left(\frac{-c \sqrt{x}+\textit{\_R1} -d}{\textit{\_R1}}\right)+\dilog \left(\frac{-c \sqrt{x}+\textit{\_R1} -d}{\textit{\_R1}}\right)}{\textit{\_R1}^{2} b -2 \textit{\_R1} b d +a \,c^{2}+b \,d^{2}}\right)}{c}-\frac{\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{4}-4 b^{2} d \,\textit{\_Z}^{3}+\left(2 c^{2} a b +6 b^{2} d^{2}\right) \textit{\_Z}^{2}+\left(-4 a b \,c^{2} d -4 b^{2} d^{3}\right) \textit{\_Z} +a^{2} c^{4}+2 a b \,c^{2} d^{2}+b^{2} d^{4}+c^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{3}-5 \textit{\_R}^{2} d +7 \textit{\_R} \,d^{2}-3 d^{3}\right) \ln \left(c \sqrt{x}-\textit{\_R} +d \right)}{b \,\textit{\_R}^{3}-3 b d \,\textit{\_R}^{2}+a \,c^{2} \textit{\_R} +3 b \,d^{2} \textit{\_R} -a \,c^{2} d -b \,d^{3}}}{2 c}"," ",0,"arctan(b*x+a)/c*x-2*arctan(b*x+a)/c^2*d*x^(1/2)+2*arctan(b*x+a)/c^3*d^2*ln(d+c*x^(1/2))-1/c*d^2*sum(1/(_R1^2*b-2*_R1*b*d+a*c^2+b*d^2)*(ln(d+c*x^(1/2))*ln((-c*x^(1/2)+_R1-d)/_R1)+dilog((-c*x^(1/2)+_R1-d)/_R1)),_R1=RootOf(b^2*_Z^4-4*b^2*d*_Z^3+(2*a*b*c^2+6*b^2*d^2)*_Z^2+(-4*a*b*c^2*d-4*b^2*d^3)*_Z+a^2*c^4+2*a*b*c^2*d^2+b^2*d^4+c^4))-1/2/c*sum((_R^3-5*_R^2*d+7*_R*d^2-3*d^3)/(_R^3*b-3*_R^2*b*d+_R*a*c^2+3*_R*b*d^2-a*c^2*d-b*d^3)*ln(c*x^(1/2)-_R+d),_R=RootOf(b^2*_Z^4-4*b^2*d*_Z^3+(2*a*b*c^2+6*b^2*d^2)*_Z^2+(-4*a*b*c^2*d-4*b^2*d^3)*_Z+a^2*c^4+2*a*b*c^2*d^2+b^2*d^4+c^4))","C"
60,1,833,225,1.056000," ","int(arctan(b*x+a)/(x^2+1),x)","\arctan \left(x \right) \arctan \left(b x +a \right)+\frac{i \arctan \left(\frac{b x +a}{b}-\frac{a}{b}\right) \ln \left(1-\frac{\left(-i b +a -i\right) \left(1+i \left(\frac{b x +a}{b}-\frac{a}{b}\right)\right)^{2}}{\left(\left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}+1\right) \left(-i b -a +i\right)}\right)}{2}+\frac{\arctan \left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}}{2}+\frac{\polylog \left(2, \frac{\left(-i b +a -i\right) \left(1+i \left(\frac{b x +a}{b}-\frac{a}{b}\right)\right)^{2}}{\left(\left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}+1\right) \left(-i b -a +i\right)}\right)}{4}+\frac{b \ln \left(1-\frac{\left(-i b +a +i\right) \left(1+i \left(\frac{b x +a}{b}-\frac{a}{b}\right)\right)^{2}}{\left(\left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}+1\right) \left(-i b -a -i\right)}\right) \arctan \left(\frac{b x +a}{b}-\frac{a}{b}\right)}{2 i b +2 a +2 i}+\frac{\ln \left(1-\frac{\left(-i b +a +i\right) \left(1+i \left(\frac{b x +a}{b}-\frac{a}{b}\right)\right)^{2}}{\left(\left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}+1\right) \left(-i b -a -i\right)}\right) \arctan \left(\frac{b x +a}{b}-\frac{a}{b}\right)}{2 i b +2 a +2 i}-\frac{i \ln \left(1-\frac{\left(-i b +a +i\right) \left(1+i \left(\frac{b x +a}{b}-\frac{a}{b}\right)\right)^{2}}{\left(\left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}+1\right) \left(-i b -a -i\right)}\right) \arctan \left(\frac{b x +a}{b}-\frac{a}{b}\right) a}{2 \left(i b +a +i\right)}-\frac{i b \arctan \left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}}{2 \left(i b +a +i\right)}-\frac{i b \polylog \left(2, \frac{\left(-i b +a +i\right) \left(1+i \left(\frac{b x +a}{b}-\frac{a}{b}\right)\right)^{2}}{\left(\left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}+1\right) \left(-i b -a -i\right)}\right)}{4 \left(i b +a +i\right)}-\frac{i \arctan \left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}}{2 \left(i b +a +i\right)}-\frac{\arctan \left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2} a}{2 \left(i b +a +i\right)}-\frac{i \polylog \left(2, \frac{\left(-i b +a +i\right) \left(1+i \left(\frac{b x +a}{b}-\frac{a}{b}\right)\right)^{2}}{\left(\left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}+1\right) \left(-i b -a -i\right)}\right)}{4 \left(i b +a +i\right)}-\frac{\polylog \left(2, \frac{\left(-i b +a +i\right) \left(1+i \left(\frac{b x +a}{b}-\frac{a}{b}\right)\right)^{2}}{\left(\left(\frac{b x +a}{b}-\frac{a}{b}\right)^{2}+1\right) \left(-i b -a -i\right)}\right) a}{4 \left(i b +a +i\right)}"," ",0,"arctan(x)*arctan(b*x+a)+1/2*I*arctan((b*x+a)/b-a/b)*ln(1-(-I*b+a-I)*(1+I*((b*x+a)/b-a/b))^2/(((b*x+a)/b-a/b)^2+1)/(-I*b+I-a))+1/2*arctan((b*x+a)/b-a/b)^2+1/4*polylog(2,(-I*b+a-I)*(1+I*((b*x+a)/b-a/b))^2/(((b*x+a)/b-a/b)^2+1)/(-I*b+I-a))+1/2*b/(I*b+I+a)*ln(1-(I+a-I*b)*(1+I*((b*x+a)/b-a/b))^2/(((b*x+a)/b-a/b)^2+1)/(-I*b-I-a))*arctan((b*x+a)/b-a/b)+1/2/(I*b+I+a)*ln(1-(I+a-I*b)*(1+I*((b*x+a)/b-a/b))^2/(((b*x+a)/b-a/b)^2+1)/(-I*b-I-a))*arctan((b*x+a)/b-a/b)-1/2*I/(I*b+I+a)*ln(1-(I+a-I*b)*(1+I*((b*x+a)/b-a/b))^2/(((b*x+a)/b-a/b)^2+1)/(-I*b-I-a))*arctan((b*x+a)/b-a/b)*a-1/2*I*b/(I*b+I+a)*arctan((b*x+a)/b-a/b)^2-1/4*I*b/(I*b+I+a)*polylog(2,(I+a-I*b)*(1+I*((b*x+a)/b-a/b))^2/(((b*x+a)/b-a/b)^2+1)/(-I*b-I-a))-1/2*I/(I*b+I+a)*arctan((b*x+a)/b-a/b)^2-1/2/(I*b+I+a)*arctan((b*x+a)/b-a/b)^2*a-1/4*I/(I*b+I+a)*polylog(2,(I+a-I*b)*(1+I*((b*x+a)/b-a/b))^2/(((b*x+a)/b-a/b)^2+1)/(-I*b-I-a))-1/4/(I*b+I+a)*polylog(2,(I+a-I*b)*(1+I*((b*x+a)/b-a/b))^2/(((b*x+a)/b-a/b)^2+1)/(-I*b-I-a))*a","B"
61,1,2192,411,1.244000," ","int(arctan(e*x+d)/(b*x^2+a),x)","\frac{i \sqrt{a b \,e^{2}}\, \ln \left(1-\frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}-2 \sqrt{a b \,e^{2}}-b \right)}\right) \arctan \left(e x +d \right)}{2 e a \left(a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b \right)}+\frac{i \sqrt{a b \,e^{2}}\, \ln \left(1-\frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}-2 \sqrt{a b \,e^{2}}-b \right)}\right) \arctan \left(e x +d \right) d^{2}}{2 e a \left(a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b \right)}-\frac{i e \sqrt{a b \,e^{2}}\, \ln \left(1-\frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}+2 \sqrt{a b \,e^{2}}-b \right)}\right) \arctan \left(e x +d \right)}{2 b \left(a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b \right)}+\frac{i e \ln \left(1-\frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}-2 \sqrt{a b \,e^{2}}-b \right)}\right) \arctan \left(e x +d \right)}{a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b}-\frac{e \sqrt{a b \,e^{2}}\, \arctan \left(e x +d \right)^{2}}{2 b \left(a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b \right)}+\frac{e \arctan \left(e x +d \right)^{2}}{a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b}-\frac{\sqrt{a b \,e^{2}}\, \arctan \left(e x +d \right)^{2}}{2 e a \left(a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b \right)}-\frac{\sqrt{a b \,e^{2}}\, \arctan \left(e x +d \right)^{2} d^{2}}{2 e a \left(a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b \right)}-\frac{e \sqrt{a b \,e^{2}}\, \polylog \left(2, \frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}+2 \sqrt{a b \,e^{2}}-b \right)}\right)}{4 b \left(a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b \right)}+\frac{e \polylog \left(2, \frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}+2 \sqrt{a b \,e^{2}}-b \right)}\right)}{2 a \,e^{2}+2 b \,d^{2}-4 \sqrt{a b \,e^{2}}+2 b}-\frac{\sqrt{a b \,e^{2}}\, \polylog \left(2, \frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}+2 \sqrt{a b \,e^{2}}-b \right)}\right)}{4 e a \left(a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b \right)}-\frac{\sqrt{a b \,e^{2}}\, \polylog \left(2, \frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}+2 \sqrt{a b \,e^{2}}-b \right)}\right) d^{2}}{4 e a \left(a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b \right)}+\frac{i e \ln \left(1-\frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}+2 \sqrt{a b \,e^{2}}-b \right)}\right) \arctan \left(e x +d \right)}{a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b}-\frac{i \sqrt{a b \,e^{2}}\, \ln \left(1-\frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}+2 \sqrt{a b \,e^{2}}-b \right)}\right) \arctan \left(e x +d \right) d^{2}}{2 e a \left(a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b \right)}-\frac{i \sqrt{a b \,e^{2}}\, \ln \left(1-\frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}+2 \sqrt{a b \,e^{2}}-b \right)}\right) \arctan \left(e x +d \right)}{2 e a \left(a \,e^{2}+b \,d^{2}-2 \sqrt{a b \,e^{2}}+b \right)}+\frac{i e \sqrt{a b \,e^{2}}\, \ln \left(1-\frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}-2 \sqrt{a b \,e^{2}}-b \right)}\right) \arctan \left(e x +d \right)}{2 b \left(a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b \right)}+\frac{e \sqrt{a b \,e^{2}}\, \arctan \left(e x +d \right)^{2}}{2 b \left(a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b \right)}+\frac{e \arctan \left(e x +d \right)^{2}}{a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b}+\frac{\sqrt{a b \,e^{2}}\, \arctan \left(e x +d \right)^{2}}{2 e a \left(a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b \right)}+\frac{\sqrt{a b \,e^{2}}\, \arctan \left(e x +d \right)^{2} d^{2}}{2 e a \left(a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b \right)}+\frac{e \sqrt{a b \,e^{2}}\, \polylog \left(2, \frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}-2 \sqrt{a b \,e^{2}}-b \right)}\right)}{4 b \left(a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b \right)}+\frac{e \polylog \left(2, \frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}-2 \sqrt{a b \,e^{2}}-b \right)}\right)}{2 a \,e^{2}+2 b \,d^{2}+4 \sqrt{a b \,e^{2}}+2 b}+\frac{\sqrt{a b \,e^{2}}\, \polylog \left(2, \frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}-2 \sqrt{a b \,e^{2}}-b \right)}\right)}{4 e a \left(a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b \right)}+\frac{\sqrt{a b \,e^{2}}\, \polylog \left(2, \frac{\left(a \,e^{2}+b \,d^{2}+2 i b d -b \right) \left(1+i \left(e x +d \right)\right)^{2}}{\left(\left(e x +d \right)^{2}+1\right) \left(-a \,e^{2}-b \,d^{2}-2 \sqrt{a b \,e^{2}}-b \right)}\right) d^{2}}{4 e a \left(a \,e^{2}+b \,d^{2}+2 \sqrt{a b \,e^{2}}+b \right)}"," ",0,"1/2*I/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*ln(1-(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2-2*(a*b*e^2)^(1/2)-b))*arctan(e*x+d)+1/2*I/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*ln(1-(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2-2*(a*b*e^2)^(1/2)-b))*arctan(e*x+d)*d^2-1/2*I*e/b*(a*b*e^2)^(1/2)/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*ln(1-(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2+2*(a*b*e^2)^(1/2)-b))*arctan(e*x+d)+I*e/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*ln(1-(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2-2*(a*b*e^2)^(1/2)-b))*arctan(e*x+d)-1/2*e/b*(a*b*e^2)^(1/2)/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*arctan(e*x+d)^2+e/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*arctan(e*x+d)^2-1/2/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*arctan(e*x+d)^2-1/2/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*arctan(e*x+d)^2*d^2-1/4*e/b*(a*b*e^2)^(1/2)/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*polylog(2,(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2+2*(a*b*e^2)^(1/2)-b))+1/2*e/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*polylog(2,(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2+2*(a*b*e^2)^(1/2)-b))-1/4/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*polylog(2,(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2+2*(a*b*e^2)^(1/2)-b))-1/4/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*polylog(2,(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2+2*(a*b*e^2)^(1/2)-b))*d^2+I*e/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*ln(1-(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2+2*(a*b*e^2)^(1/2)-b))*arctan(e*x+d)-1/2*I/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*ln(1-(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2+2*(a*b*e^2)^(1/2)-b))*arctan(e*x+d)*d^2-1/2*I/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2-2*(a*b*e^2)^(1/2)+b)*ln(1-(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2+2*(a*b*e^2)^(1/2)-b))*arctan(e*x+d)+1/2*I*e/b*(a*b*e^2)^(1/2)/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*ln(1-(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2-2*(a*b*e^2)^(1/2)-b))*arctan(e*x+d)+1/2*e/b*(a*b*e^2)^(1/2)/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*arctan(e*x+d)^2+e/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*arctan(e*x+d)^2+1/2/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*arctan(e*x+d)^2+1/2/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*arctan(e*x+d)^2*d^2+1/4*e/b*(a*b*e^2)^(1/2)/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*polylog(2,(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2-2*(a*b*e^2)^(1/2)-b))+1/2*e/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*polylog(2,(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2-2*(a*b*e^2)^(1/2)-b))+1/4/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*polylog(2,(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2-2*(a*b*e^2)^(1/2)-b))+1/4/e*(a*b*e^2)^(1/2)/a/(a*e^2+b*d^2+2*(a*b*e^2)^(1/2)+b)*polylog(2,(2*I*b*d+a*e^2+b*d^2-b)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2-b*d^2-2*(a*b*e^2)^(1/2)-b))*d^2","B"
62,1,4743,329,1.622000," ","int(arctan(e*x+d)/(c*x^2+b*x+a),x)","\text{output too large to display}"," ",0,"1/8*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))*b^2+1/2/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))*d^2-1/4*I*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)+1/4*I*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)-1/2/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))*d^2-1/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2*d^2+1/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2*d^2-1/8*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))*b^2+1/4*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2*b^2-1/4*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2*b^2+1/2*e/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))+1/2*e/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))+e/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2+e/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2-I*(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)*b*d-I/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)-1/8*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))+I*e/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)+1/8*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))-1/4*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2-I/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)*d^2+I/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)*d^2-1/4*I*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)*b^2+1/4*I*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)*b^2+I*e/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)+1/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2+1/2/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))-1/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2-1/2/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))+(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2*b*d-(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2*b*d+1/2*(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))*b*d-1/2*(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))*b*d+1/4*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arctan(e*x+d)^2+I*(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2+(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)*b*d+I/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(-I*b*e+2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(1+I*(e*x+d))^2/((e*x+d)^2+1)/(-a*e^2+b*e*d-c*d^2-(e^2*(4*a*c-b^2))^(1/2)-c))*arctan(e*x+d)","B"
63,1,143,109,0.684000," ","int(arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","-\frac{\arctan \left(b x +a \right) \ln \left(1+\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{b}+\frac{\arctan \left(b x +a \right) \ln \left(1-\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{b}+\frac{i \dilog \left(1+\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{b}-\frac{i \dilog \left(1-\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{b}"," ",0,"-1/b*arctan(b*x+a)*ln(1+I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))+1/b*arctan(b*x+a)*ln(1-I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))+I/b*dilog(1+I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))-I/b*dilog(1-I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))","A"
64,1,176,181,0.927000," ","int(arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/2),x)","\frac{i \left(i \arctan \left(b x +a \right) \ln \left(1+\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)-i \arctan \left(b x +a \right) \ln \left(1-\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)+\dilog \left(1+\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)-\dilog \left(1-\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)\right) \sqrt{c \left(b x +a -i\right) \left(b x +a +i\right)}}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, b c}"," ",0,"I*(I*arctan(b*x+a)*ln(1+I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))-I*arctan(b*x+a)*ln(1-I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))+dilog(1+I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))-dilog(1-I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)))*(c*(-I+a+b*x)*(I+a+b*x))^(1/2)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)/b/c","A"
65,0,0,20,1.473000," ","int(arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x)","\int \frac{\arctan \left(b x +a \right)}{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{1}{3}}}\, dx"," ",0,"int(arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x)","F"
66,0,0,22,1.376000," ","int(arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/3),x)","\int \frac{\arctan \left(b x +a \right)}{\left(\left(a^{2}+1\right) c +2 a b c x +b^{2} c \,x^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/3),x)","F"
67,1,187,152,3.160000," ","int((b*x+a)^2*arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","\frac{\left(\arctan \left(b x +a \right) x b +\arctan \left(b x +a \right) a -1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b}+\frac{\arctan \left(b x +a \right) \ln \left(1+\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{2 b}-\frac{\arctan \left(b x +a \right) \ln \left(1-\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{2 b}-\frac{i \dilog \left(1+\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{2 b}+\frac{i \dilog \left(1-\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{2 b}"," ",0,"1/2*(arctan(b*x+a)*x*b+arctan(b*x+a)*a-1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)/b+1/2/b*arctan(b*x+a)*ln(1+I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))-1/2/b*arctan(b*x+a)*ln(1-I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))-1/2*I/b*dilog(1+I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))+1/2*I/b*dilog(1-I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))","A"
68,1,222,234,4.530000," ","int((b*x+a)^2*arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/2),x)","\frac{\left(\arctan \left(b x +a \right) x b +\arctan \left(b x +a \right) a -1\right) \sqrt{c \left(b x +a -i\right) \left(b x +a +i\right)}}{2 b c}-\frac{i \left(i \arctan \left(b x +a \right) \ln \left(1+\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)-i \arctan \left(b x +a \right) \ln \left(1-\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)+\dilog \left(1+\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)-\dilog \left(1-\frac{i \left(1+i \left(b x +a \right)\right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)\right) \sqrt{c \left(b x +a -i\right) \left(b x +a +i\right)}}{2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, b c}"," ",0,"1/2*(arctan(b*x+a)*x*b+arctan(b*x+a)*a-1)*(c*(-I+a+b*x)*(I+a+b*x))^(1/2)/b/c-1/2*I*(I*arctan(b*x+a)*ln(1+I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))-I*arctan(b*x+a)*ln(1-I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))+dilog(1+I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))-dilog(1-I*(1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)))*(c*(-I+a+b*x)*(I+a+b*x))^(1/2)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)/b/c","A"
69,0,0,27,4.682000," ","int((b*x+a)^2*arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x)","\int \frac{\left(b x +a \right)^{2} \arctan \left(b x +a \right)}{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*x+a)^2*arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x)","F"
70,0,0,29,4.702000," ","int((b*x+a)^2*arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/3),x)","\int \frac{\left(b x +a \right)^{2} \arctan \left(b x +a \right)}{\left(\left(a^{2}+1\right) c +2 a b c x +b^{2} c \,x^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*x+a)^2*arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/3),x)","F"