1,1,108,97,0.031000," ","int(x^3*(d+I*c*d*x)*(a+b*arctan(c*x)),x)","\frac{i c d a \,x^{5}}{5}+\frac{d a \,x^{4}}{4}+\frac{i c d b \arctan \left(c x \right) x^{5}}{5}+\frac{d b \arctan \left(c x \right) x^{4}}{4}+\frac{b d x}{4 c^{3}}-\frac{i b d \,x^{4}}{20}-\frac{b d \,x^{3}}{12 c}+\frac{i b d \,x^{2}}{10 c^{2}}-\frac{i b d \ln \left(c^{2} x^{2}+1\right)}{10 c^{4}}-\frac{b d \arctan \left(c x \right)}{4 c^{4}}"," ",0,"1/5*I*c*d*a*x^5+1/4*d*a*x^4+1/5*I*c*d*b*arctan(c*x)*x^5+1/4*d*b*arctan(c*x)*x^4+1/4*b*d*x/c^3-1/20*I*b*d*x^4-1/12*b*d*x^3/c+1/10*I*b*d*x^2/c^2-1/10*I*b*d*ln(c^2*x^2+1)/c^4-1/4*b*d*arctan(c*x)/c^4","A"
2,1,98,87,0.032000," ","int(x^2*(d+I*c*d*x)*(a+b*arctan(c*x)),x)","\frac{i c d a \,x^{4}}{4}+\frac{d a \,x^{3}}{3}+\frac{i c d b \arctan \left(c x \right) x^{4}}{4}+\frac{d b \arctan \left(c x \right) x^{3}}{3}+\frac{i b d x}{4 c^{2}}-\frac{i b d \,x^{3}}{12}-\frac{b d \,x^{2}}{6 c}+\frac{b d \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}-\frac{i b d \arctan \left(c x \right)}{4 c^{3}}"," ",0,"1/4*I*c*d*a*x^4+1/3*d*a*x^3+1/4*I*c*d*b*arctan(c*x)*x^4+1/3*d*b*arctan(c*x)*x^3+1/4*I*b*d*x/c^2-1/12*I*b*d*x^3-1/6*b*d*x^2/c+1/6*b*d*ln(c^2*x^2+1)/c^3-1/4*I*b*d*arctan(c*x)/c^3","A"
3,1,87,76,0.031000," ","int(x*(d+I*c*d*x)*(a+b*arctan(c*x)),x)","\frac{i c d a \,x^{3}}{3}+\frac{d a \,x^{2}}{2}+\frac{i c d b \arctan \left(c x \right) x^{3}}{3}+\frac{d b \arctan \left(c x \right) x^{2}}{2}-\frac{i b d \,x^{2}}{6}-\frac{b d x}{2 c}+\frac{i b d \ln \left(c^{2} x^{2}+1\right)}{6 c^{2}}+\frac{b d \arctan \left(c x \right)}{2 c^{2}}"," ",0,"1/3*I*c*d*a*x^3+1/2*d*a*x^2+1/3*I*c*d*b*arctan(c*x)*x^3+1/2*d*b*arctan(c*x)*x^2-1/6*I*b*d*x^2-1/2*b*d*x/c+1/6*I*b*d*ln(c^2*x^2+1)/c^2+1/2*b*d*arctan(c*x)/c^2","A"
4,1,71,45,0.028000," ","int((d+I*c*d*x)*(a+b*arctan(c*x)),x)","a d x +\frac{i c d a \,x^{2}}{2}+d b \arctan \left(c x \right) x +\frac{i c d b \arctan \left(c x \right) x^{2}}{2}-\frac{i b d x}{2}-\frac{b d \ln \left(c^{2} x^{2}+1\right)}{2 c}+\frac{i d b \arctan \left(c x \right)}{2 c}"," ",0,"a*d*x+1/2*I*c*d*a*x^2+d*b*arctan(c*x)*x+1/2*I*c*d*b*arctan(c*x)*x^2-1/2*I*b*d*x-1/2*b*d*ln(c^2*x^2+1)/c+1/2*I/c*d*b*arctan(c*x)","A"
5,1,113,63,0.047000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))/x,x)","i a c d x +d a \ln \left(c x \right)+i b c d x \arctan \left(c x \right)+d b \ln \left(c x \right) \arctan \left(c x \right)+\frac{i d b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i d b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{i d b \dilog \left(i c x +1\right)}{2}-\frac{i d b \dilog \left(-i c x +1\right)}{2}-\frac{i b d \ln \left(c^{2} x^{2}+1\right)}{2}"," ",0,"I*a*c*d*x+d*a*ln(c*x)+I*b*c*d*x*arctan(c*x)+d*b*ln(c*x)*arctan(c*x)+1/2*I*d*b*ln(c*x)*ln(1+I*c*x)-1/2*I*d*b*ln(c*x)*ln(1-I*c*x)+1/2*I*d*b*dilog(1+I*c*x)-1/2*I*d*b*dilog(1-I*c*x)-1/2*I*b*d*ln(c^2*x^2+1)","A"
6,1,127,68,0.055000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))/x^2,x)","i c d a \ln \left(c x \right)-\frac{d a}{x}+i c d b \arctan \left(c x \right) \ln \left(c x \right)-\frac{d b \arctan \left(c x \right)}{x}-\frac{c d b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}+\frac{c d b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}-\frac{c d b \dilog \left(i c x +1\right)}{2}+\frac{c d b \dilog \left(-i c x +1\right)}{2}+c d b \ln \left(c x \right)-\frac{b c d \ln \left(c^{2} x^{2}+1\right)}{2}"," ",0,"I*c*d*a*ln(c*x)-d*a/x+I*c*d*b*arctan(c*x)*ln(c*x)-d*b*arctan(c*x)/x-1/2*c*d*b*ln(c*x)*ln(1+I*c*x)+1/2*c*d*b*ln(c*x)*ln(1-I*c*x)-1/2*c*d*b*dilog(1+I*c*x)+1/2*c*d*b*dilog(1-I*c*x)+c*d*b*ln(c*x)-1/2*b*c*d*ln(c^2*x^2+1)","A"
7,1,91,57,0.043000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))/x^3,x)","-\frac{i c d a}{x}-\frac{d a}{2 x^{2}}-\frac{i c d b \arctan \left(c x \right)}{x}-\frac{d b \arctan \left(c x \right)}{2 x^{2}}+i c^{2} d b \ln \left(c x \right)-\frac{b c d}{2 x}-\frac{i c^{2} d b \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{b \,c^{2} d \arctan \left(c x \right)}{2}"," ",0,"-I*c*d*a/x-1/2*d*a/x^2-I*c*d*b*arctan(c*x)/x-1/2*d*b*arctan(c*x)/x^2+I*c^2*d*b*ln(c*x)-1/2*b*c*d/x-1/2*I*c^2*d*b*ln(c^2*x^2+1)-1/2*b*c^2*d*arctan(c*x)","A"
8,1,101,88,0.042000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))/x^4,x)","-\frac{d a}{3 x^{3}}-\frac{i c d a}{2 x^{2}}-\frac{d b \arctan \left(c x \right)}{3 x^{3}}-\frac{i c d b \arctan \left(c x \right)}{2 x^{2}}-\frac{i b \,c^{2} d}{2 x}-\frac{b c d}{6 x^{2}}-\frac{c^{3} d b \ln \left(c x \right)}{3}+\frac{c^{3} d b \ln \left(c^{2} x^{2}+1\right)}{6}-\frac{i c^{3} d b \arctan \left(c x \right)}{2}"," ",0,"-1/3*d*a/x^3-1/2*I*c*d*a/x^2-1/3*d*b*arctan(c*x)/x^3-1/2*I*c*d*b*arctan(c*x)/x^2-1/2*I*b*c^2*d/x-1/6*b*c*d/x^2-1/3*c^3*d*b*ln(c*x)+1/6*c^3*d*b*ln(c^2*x^2+1)-1/2*I*c^3*d*b*arctan(c*x)","A"
9,1,112,101,0.046000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))/x^5,x)","-\frac{i c d a}{3 x^{3}}-\frac{d a}{4 x^{4}}-\frac{i c d b \arctan \left(c x \right)}{3 x^{3}}-\frac{d b \arctan \left(c x \right)}{4 x^{4}}-\frac{i b \,c^{2} d}{6 x^{2}}-\frac{i c^{4} d b \ln \left(c x \right)}{3}-\frac{b c d}{12 x^{3}}+\frac{b \,c^{3} d}{4 x}+\frac{i c^{4} d b \ln \left(c^{2} x^{2}+1\right)}{6}+\frac{c^{4} d b \arctan \left(c x \right)}{4}"," ",0,"-1/3*I*c*d*a/x^3-1/4*d*a/x^4-1/3*I*c*d*b*arctan(c*x)/x^3-1/4*d*b*arctan(c*x)/x^4-1/6*I*b*c^2*d/x^2-1/3*I*c^4*d*b*ln(c*x)-1/12*b*c*d/x^3+1/4*b*c^3*d/x+1/6*I*c^4*d*b*ln(c^2*x^2+1)+1/4*c^4*d*b*arctan(c*x)","A"
10,1,166,142,0.030000," ","int(x^3*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x)","-\frac{c^{2} d^{2} a \,x^{6}}{6}+\frac{2 i c \,d^{2} a \,x^{5}}{5}+\frac{d^{2} a \,x^{4}}{4}-\frac{c^{2} d^{2} b \arctan \left(c x \right) x^{6}}{6}+\frac{2 i c \,d^{2} b \arctan \left(c x \right) x^{5}}{5}+\frac{d^{2} b \arctan \left(c x \right) x^{4}}{4}+\frac{5 b \,d^{2} x}{12 c^{3}}+\frac{b c \,d^{2} x^{5}}{30}-\frac{i b \,d^{2} x^{4}}{10}-\frac{5 b \,d^{2} x^{3}}{36 c}+\frac{i b \,d^{2} x^{2}}{5 c^{2}}-\frac{i b \,d^{2} \ln \left(c^{2} x^{2}+1\right)}{5 c^{4}}-\frac{5 b \,d^{2} \arctan \left(c x \right)}{12 c^{4}}"," ",0,"-1/6*c^2*d^2*a*x^6+2/5*I*c*d^2*a*x^5+1/4*d^2*a*x^4-1/6*c^2*d^2*b*arctan(c*x)*x^6+2/5*I*c*d^2*b*arctan(c*x)*x^5+1/4*d^2*b*arctan(c*x)*x^4+5/12*b*d^2*x/c^3+1/30*b*c*d^2*x^5-1/10*I*b*d^2*x^4-5/36*b*d^2*x^3/c+1/5*I*b*d^2*x^2/c^2-1/5*I*b*d^2*ln(c^2*x^2+1)/c^4-5/12*b*d^2*arctan(c*x)/c^4","A"
11,1,154,130,0.029000," ","int(x^2*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x)","-\frac{c^{2} d^{2} a \,x^{5}}{5}+\frac{i c \,d^{2} a \,x^{4}}{2}+\frac{d^{2} a \,x^{3}}{3}-\frac{c^{2} d^{2} b \arctan \left(c x \right) x^{5}}{5}+\frac{i c \,d^{2} b \arctan \left(c x \right) x^{4}}{2}+\frac{d^{2} b \arctan \left(c x \right) x^{3}}{3}+\frac{i b \,d^{2} x}{2 c^{2}}+\frac{b c \,d^{2} x^{4}}{20}-\frac{i b \,d^{2} x^{3}}{6}-\frac{4 b \,d^{2} x^{2}}{15 c}+\frac{4 b \,d^{2} \ln \left(c^{2} x^{2}+1\right)}{15 c^{3}}-\frac{i b \,d^{2} \arctan \left(c x \right)}{2 c^{3}}"," ",0,"-1/5*c^2*d^2*a*x^5+1/2*I*c*d^2*a*x^4+1/3*d^2*a*x^3-1/5*c^2*d^2*b*arctan(c*x)*x^5+1/2*I*c*d^2*b*arctan(c*x)*x^4+1/3*d^2*b*arctan(c*x)*x^3+1/2*I*b*d^2*x/c^2+1/20*b*c*d^2*x^4-1/6*I*b*d^2*x^3-4/15*b*d^2*x^2/c+4/15*b*d^2*ln(c^2*x^2+1)/c^3-1/2*I*b*d^2*arctan(c*x)/c^3","A"
12,1,141,117,0.031000," ","int(x*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x)","-\frac{c^{2} d^{2} a \,x^{4}}{4}+\frac{2 i c \,d^{2} a \,x^{3}}{3}+\frac{d^{2} a \,x^{2}}{2}-\frac{c^{2} d^{2} b \arctan \left(c x \right) x^{4}}{4}+\frac{2 i c \,d^{2} b \arctan \left(c x \right) x^{3}}{3}+\frac{d^{2} b \arctan \left(c x \right) x^{2}}{2}-\frac{3 b \,d^{2} x}{4 c}+\frac{b c \,d^{2} x^{3}}{12}-\frac{i b \,d^{2} x^{2}}{3}+\frac{i b \,d^{2} \ln \left(c^{2} x^{2}+1\right)}{3 c^{2}}+\frac{3 b \,d^{2} \arctan \left(c x \right)}{4 c^{2}}"," ",0,"-1/4*c^2*d^2*a*x^4+2/3*I*c*d^2*a*x^3+1/2*d^2*a*x^2-1/4*c^2*d^2*b*arctan(c*x)*x^4+2/3*I*c*d^2*b*arctan(c*x)*x^3+1/2*d^2*b*arctan(c*x)*x^2-3/4*b*d^2*x/c+1/12*b*c*d^2*x^3-1/3*I*b*d^2*x^2+1/3*I*b*d^2*ln(c^2*x^2+1)/c^2+3/4*b*d^2*arctan(c*x)/c^2","A"
13,1,133,70,0.034000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x)),x)","-\frac{c^{2} d^{2} a \,x^{3}}{3}+i c \,x^{2} a \,d^{2}+a x \,d^{2}-\frac{i d^{2} a}{3 c}-\frac{c^{2} d^{2} b \arctan \left(c x \right) x^{3}}{3}+i c \,d^{2} b \arctan \left(c x \right) x^{2}+b \arctan \left(c x \right) d^{2} x +\frac{i d^{2} b \arctan \left(c x \right)}{c}-i d^{2} b x +\frac{c \,d^{2} b \,x^{2}}{6}-\frac{2 d^{2} b \ln \left(c^{2} x^{2}+1\right)}{3 c}"," ",0,"-1/3*c^2*d^2*a*x^3+I*c*x^2*a*d^2+a*x*d^2-1/3*I/c*d^2*a-1/3*c^2*d^2*b*arctan(c*x)*x^3+I*c*d^2*b*arctan(c*x)*x^2+b*arctan(c*x)*d^2*x+I/c*d^2*b*arctan(c*x)-I*d^2*b*x+1/6*c*d^2*b*x^2-2/3/c*d^2*b*ln(c^2*x^2+1)","A"
14,1,177,112,0.054000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))/x,x)","2 i a c \,d^{2} x -\frac{d^{2} a \,c^{2} x^{2}}{2}+a \,d^{2} \ln \left(c x \right)+2 i b c \,d^{2} x \arctan \left(c x \right)-\frac{d^{2} b \arctan \left(c x \right) c^{2} x^{2}}{2}+d^{2} b \ln \left(c x \right) \arctan \left(c x \right)+\frac{b c \,d^{2} x}{2}-i b \,d^{2} \ln \left(c^{2} x^{2}+1\right)-\frac{b \,d^{2} \arctan \left(c x \right)}{2}+\frac{i d^{2} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i d^{2} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{i d^{2} b \dilog \left(i c x +1\right)}{2}-\frac{i d^{2} b \dilog \left(-i c x +1\right)}{2}"," ",0,"2*I*a*c*d^2*x-1/2*d^2*a*c^2*x^2+a*d^2*ln(c*x)+2*I*b*c*d^2*x*arctan(c*x)-1/2*d^2*b*arctan(c*x)*c^2*x^2+d^2*b*ln(c*x)*arctan(c*x)+1/2*b*c*d^2*x-I*b*d^2*ln(c^2*x^2+1)-1/2*b*d^2*arctan(c*x)+1/2*I*d^2*b*ln(c*x)*ln(1+I*c*x)-1/2*I*d^2*b*ln(c*x)*ln(1-I*c*x)+1/2*I*d^2*b*dilog(1+I*c*x)-1/2*I*d^2*b*dilog(1-I*c*x)","A"
15,1,152,86,0.053000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^2,x)","-a \,c^{2} d^{2} x +2 i c \,d^{2} a \ln \left(c x \right)-\frac{d^{2} a}{x}-b \,c^{2} d^{2} x \arctan \left(c x \right)+2 i c \,d^{2} b \arctan \left(c x \right) \ln \left(c x \right)-\frac{d^{2} b \arctan \left(c x \right)}{x}-c \,d^{2} b \ln \left(c x \right) \ln \left(i c x +1\right)+c \,d^{2} b \ln \left(c x \right) \ln \left(-i c x +1\right)-c \,d^{2} b \dilog \left(i c x +1\right)+c \,d^{2} b \dilog \left(-i c x +1\right)+c \,d^{2} b \ln \left(c x \right)"," ",0,"-a*c^2*d^2*x+2*I*c*d^2*a*ln(c*x)-d^2*a/x-b*c^2*d^2*x*arctan(c*x)+2*I*c*d^2*b*arctan(c*x)*ln(c*x)-d^2*b*arctan(c*x)/x-c*d^2*b*ln(c*x)*ln(1+I*c*x)+c*d^2*b*ln(c*x)*ln(1-I*c*x)-c*d^2*b*dilog(1+I*c*x)+c*d^2*b*dilog(1-I*c*x)+c*d^2*b*ln(c*x)","A"
16,1,217,135,0.069000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^3,x)","-c^{2} d^{2} a \ln \left(c x \right)-\frac{2 i c \,d^{2} a}{x}-\frac{d^{2} a}{2 x^{2}}-c^{2} d^{2} b \ln \left(c x \right) \arctan \left(c x \right)-\frac{2 i c \,d^{2} b \arctan \left(c x \right)}{x}-\frac{d^{2} b \arctan \left(c x \right)}{2 x^{2}}-\frac{i c^{2} d^{2} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}+\frac{i c^{2} d^{2} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}-\frac{i c^{2} d^{2} b \dilog \left(i c x +1\right)}{2}+\frac{i c^{2} d^{2} b \dilog \left(-i c x +1\right)}{2}-\frac{b c \,d^{2}}{2 x}+2 i c^{2} d^{2} b \ln \left(c x \right)-i b \,c^{2} d^{2} \ln \left(c^{2} x^{2}+1\right)-\frac{b \,c^{2} d^{2} \arctan \left(c x \right)}{2}"," ",0,"-c^2*d^2*a*ln(c*x)-2*I*c*d^2*a/x-1/2*d^2*a/x^2-c^2*d^2*b*ln(c*x)*arctan(c*x)-2*I*c*d^2*b*arctan(c*x)/x-1/2*d^2*b*arctan(c*x)/x^2-1/2*I*c^2*d^2*b*ln(c*x)*ln(1+I*c*x)+1/2*I*c^2*d^2*b*ln(c*x)*ln(1-I*c*x)-1/2*I*c^2*d^2*b*dilog(1+I*c*x)+1/2*I*c^2*d^2*b*dilog(1-I*c*x)-1/2*b*c*d^2/x+2*I*c^2*d^2*b*ln(c*x)-I*b*c^2*d^2*ln(c^2*x^2+1)-1/2*b*c^2*d^2*arctan(c*x)","A"
17,1,145,76,0.044000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^4,x)","-\frac{d^{2} a}{3 x^{3}}+\frac{c^{2} d^{2} a}{x}-\frac{i c \,d^{2} a}{x^{2}}-\frac{d^{2} b \arctan \left(c x \right)}{3 x^{3}}+\frac{c^{2} d^{2} b \arctan \left(c x \right)}{x}-\frac{i c \,d^{2} b \arctan \left(c x \right)}{x^{2}}-\frac{i b \,c^{2} d^{2}}{x}-\frac{b c \,d^{2}}{6 x^{2}}-\frac{4 c^{3} d^{2} b \ln \left(c x \right)}{3}+\frac{2 c^{3} d^{2} b \ln \left(c^{2} x^{2}+1\right)}{3}-i c^{3} d^{2} b \arctan \left(c x \right)"," ",0,"-1/3*d^2*a/x^3+c^2*d^2*a/x-I*c*d^2*a/x^2-1/3*d^2*b*arctan(c*x)/x^3+c^2*d^2*b*arctan(c*x)/x-I*c*d^2*b*arctan(c*x)/x^2-I*b*c^2*d^2/x-1/6*b*c*d^2/x^2-4/3*c^3*d^2*b*ln(c*x)+2/3*c^3*d^2*b*ln(c^2*x^2+1)-I*c^3*d^2*b*arctan(c*x)","A"
18,1,160,136,0.039000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^5,x)","-\frac{2 i c \,d^{2} a}{3 x^{3}}-\frac{d^{2} a}{4 x^{4}}+\frac{c^{2} d^{2} a}{2 x^{2}}-\frac{2 i c \,d^{2} b \arctan \left(c x \right)}{3 x^{3}}-\frac{d^{2} b \arctan \left(c x \right)}{4 x^{4}}+\frac{c^{2} d^{2} b \arctan \left(c x \right)}{2 x^{2}}-\frac{i b \,c^{2} d^{2}}{3 x^{2}}-\frac{2 i c^{4} d^{2} b \ln \left(c x \right)}{3}-\frac{b c \,d^{2}}{12 x^{3}}+\frac{3 b \,c^{3} d^{2}}{4 x}+\frac{i c^{4} d^{2} b \ln \left(c^{2} x^{2}+1\right)}{3}+\frac{3 b \,c^{4} d^{2} \arctan \left(c x \right)}{4}"," ",0,"-2/3*I*c*d^2*a/x^3-1/4*d^2*a/x^4+1/2*c^2*d^2*a/x^2-2/3*I*c*d^2*b*arctan(c*x)/x^3-1/4*d^2*b*arctan(c*x)/x^4+1/2*c^2*d^2*b*arctan(c*x)/x^2-1/3*I*b*c^2*d^2/x^2-2/3*I*c^4*d^2*b*ln(c*x)-1/12*b*c*d^2/x^3+3/4*b*c^3*d^2/x+1/3*I*c^4*d^2*b*ln(c^2*x^2+1)+3/4*b*c^4*d^2*arctan(c*x)","A"
19,1,172,146,0.039000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^6,x)","\frac{c^{2} d^{2} a}{3 x^{3}}-\frac{i c \,d^{2} a}{2 x^{4}}-\frac{d^{2} a}{5 x^{5}}+\frac{c^{2} d^{2} b \arctan \left(c x \right)}{3 x^{3}}-\frac{i c \,d^{2} b \arctan \left(c x \right)}{2 x^{4}}-\frac{d^{2} b \arctan \left(c x \right)}{5 x^{5}}-\frac{i b \,c^{2} d^{2}}{6 x^{3}}+\frac{i b \,c^{4} d^{2}}{2 x}-\frac{b c \,d^{2}}{20 x^{4}}+\frac{4 b \,c^{3} d^{2}}{15 x^{2}}+\frac{8 c^{5} d^{2} b \ln \left(c x \right)}{15}-\frac{4 c^{5} d^{2} b \ln \left(c^{2} x^{2}+1\right)}{15}+\frac{i c^{5} d^{2} b \arctan \left(c x \right)}{2}"," ",0,"1/3*c^2*d^2*a/x^3-1/2*I*c*d^2*a/x^4-1/5*d^2*a/x^5+1/3*c^2*d^2*b*arctan(c*x)/x^3-1/2*I*c*d^2*b*arctan(c*x)/x^4-1/5*d^2*b*arctan(c*x)/x^5-1/6*I*b*c^2*d^2/x^3+1/2*I*b*c^4*d^2/x-1/20*b*c*d^2/x^4+4/15*b*c^3*d^2/x^2+8/15*c^5*d^2*b*ln(c*x)-4/15*c^5*d^2*b*ln(c^2*x^2+1)+1/2*I*c^5*d^2*b*arctan(c*x)","A"
20,1,209,175,0.031000," ","int(x^3*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x)","\frac{3 i c \,d^{3} b \arctan \left(c x \right) x^{5}}{5}-\frac{c^{2} d^{3} a \,x^{6}}{2}-\frac{i c^{3} d^{3} b \arctan \left(c x \right) x^{7}}{7}+\frac{d^{3} a \,x^{4}}{4}+\frac{13 i b \,d^{3} x^{2}}{35 c^{2}}-\frac{c^{2} d^{3} b \arctan \left(c x \right) x^{6}}{2}+\frac{3 i c \,d^{3} a \,x^{5}}{5}+\frac{d^{3} b \arctan \left(c x \right) x^{4}}{4}+\frac{3 b \,d^{3} x}{4 c^{3}}-\frac{13 i b \,d^{3} x^{4}}{70}+\frac{b c \,d^{3} x^{5}}{10}-\frac{i c^{3} d^{3} a \,x^{7}}{7}-\frac{b \,d^{3} x^{3}}{4 c}+\frac{i b \,c^{2} d^{3} x^{6}}{42}-\frac{13 i b \,d^{3} \ln \left(c^{2} x^{2}+1\right)}{35 c^{4}}-\frac{3 b \,d^{3} \arctan \left(c x \right)}{4 c^{4}}"," ",0,"3/5*I*c*d^3*b*arctan(c*x)*x^5-1/2*c^2*d^3*a*x^6-1/7*I*c^3*d^3*b*arctan(c*x)*x^7+1/4*d^3*a*x^4+13/35*I*b*d^3*x^2/c^2-1/2*c^2*d^3*b*arctan(c*x)*x^6+3/5*I*c*d^3*a*x^5+1/4*d^3*b*arctan(c*x)*x^4+3/4*b*d^3*x/c^3-13/70*I*b*d^3*x^4+1/10*b*c*d^3*x^5-1/7*I*c^3*d^3*a*x^7-1/4*b*d^3*x^3/c+1/42*I*b*c^2*d^3*x^6-13/35*I*b*d^3*ln(c^2*x^2+1)/c^4-3/4*b*d^3*arctan(c*x)/c^4","A"
21,1,197,163,0.032000," ","int(x^2*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x)","-\frac{i c^{3} d^{3} a \,x^{6}}{6}-\frac{3 c^{2} d^{3} a \,x^{5}}{5}+\frac{3 i c \,d^{3} a \,x^{4}}{4}+\frac{d^{3} a \,x^{3}}{3}-\frac{i c^{3} d^{3} b \arctan \left(c x \right) x^{6}}{6}-\frac{3 c^{2} d^{3} b \arctan \left(c x \right) x^{5}}{5}+\frac{3 i c \,d^{3} b \arctan \left(c x \right) x^{4}}{4}+\frac{d^{3} b \arctan \left(c x \right) x^{3}}{3}+\frac{11 i b \,d^{3} x}{12 c^{2}}+\frac{i b \,c^{2} d^{3} x^{5}}{30}+\frac{3 b c \,d^{3} x^{4}}{20}-\frac{11 i b \,d^{3} x^{3}}{36}-\frac{7 b \,d^{3} x^{2}}{15 c}+\frac{7 b \,d^{3} \ln \left(c^{2} x^{2}+1\right)}{15 c^{3}}-\frac{11 i b \,d^{3} \arctan \left(c x \right)}{12 c^{3}}"," ",0,"-1/6*I*c^3*d^3*a*x^6-3/5*c^2*d^3*a*x^5+3/4*I*c*d^3*a*x^4+1/3*d^3*a*x^3-1/6*I*c^3*d^3*b*arctan(c*x)*x^6-3/5*c^2*d^3*b*arctan(c*x)*x^5+3/4*I*c*d^3*b*arctan(c*x)*x^4+1/3*d^3*b*arctan(c*x)*x^3+11/12*I*b*d^3*x/c^2+1/30*I*b*c^2*d^3*x^5+3/20*b*c*d^3*x^4-11/36*I*b*d^3*x^3-7/15*b*d^3*x^2/c+7/15*b*d^3*ln(c^2*x^2+1)/c^3-11/12*I*b*d^3*arctan(c*x)/c^3","A"
22,1,184,134,0.032000," ","int(x*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x)","-\frac{i c^{3} d^{3} a \,x^{5}}{5}-\frac{3 c^{2} d^{3} a \,x^{4}}{4}+i c \,d^{3} a \,x^{3}+\frac{d^{3} a \,x^{2}}{2}-\frac{i c^{3} d^{3} b \arctan \left(c x \right) x^{5}}{5}-\frac{3 c^{2} d^{3} b \arctan \left(c x \right) x^{4}}{4}+i c \,d^{3} b \arctan \left(c x \right) x^{3}+\frac{d^{3} b \arctan \left(c x \right) x^{2}}{2}-\frac{5 b \,d^{3} x}{4 c}+\frac{i c^{2} d^{3} b \,x^{4}}{20}+\frac{c \,d^{3} b \,x^{3}}{4}-\frac{3 i d^{3} b \,x^{2}}{5}+\frac{3 i d^{3} b \ln \left(c^{2} x^{2}+1\right)}{5 c^{2}}+\frac{5 d^{3} b \arctan \left(c x \right)}{4 c^{2}}"," ",0,"-1/5*I*c^3*d^3*a*x^5-3/4*c^2*d^3*a*x^4+I*c*d^3*a*x^3+1/2*d^3*a*x^2-1/5*I*c^3*d^3*b*arctan(c*x)*x^5-3/4*c^2*d^3*b*arctan(c*x)*x^4+I*c*d^3*b*arctan(c*x)*x^3+1/2*d^3*b*arctan(c*x)*x^2-5/4*b*d^3*x/c+1/20*I*c^2*d^3*b*x^4+1/4*c*d^3*b*x^3-3/5*I*d^3*b*x^2+3/5*I/c^2*d^3*b*ln(c^2*x^2+1)+5/4/c^2*d^3*b*arctan(c*x)","A"
23,1,176,88,0.030000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x)),x)","-\frac{i c^{3} x^{4} a \,d^{3}}{4}-c^{2} d^{3} a \,x^{3}+\frac{3 i c \,x^{2} a \,d^{3}}{2}+x a \,d^{3}-\frac{i d^{3} a}{4 c}-\frac{i c^{3} d^{3} b \arctan \left(c x \right) x^{4}}{4}-c^{2} d^{3} b \arctan \left(c x \right) x^{3}+\frac{3 i c \,d^{3} b \arctan \left(c x \right) x^{2}}{2}+d^{3} b \arctan \left(c x \right) x +\frac{7 i d^{3} b \arctan \left(c x \right)}{4 c}-\frac{7 i d^{3} b x}{4}+\frac{i c^{2} d^{3} b \,x^{3}}{12}+\frac{c \,d^{3} b \,x^{2}}{2}-\frac{d^{3} b \ln \left(c^{2} x^{2}+1\right)}{c}"," ",0,"-1/4*I*c^3*x^4*a*d^3-c^2*d^3*a*x^3+3/2*I*c*x^2*a*d^3+x*a*d^3-1/4*I/c*d^3*a-1/4*I*c^3*d^3*b*arctan(c*x)*x^4-c^2*d^3*b*arctan(c*x)*x^3+3/2*I*c*d^3*b*arctan(c*x)*x^2+d^3*b*arctan(c*x)*x+7/4*I/c*d^3*b*arctan(c*x)-7/4*I*d^3*b*x+1/12*I*c^2*d^3*b*x^3+1/2*c*d^3*b*x^2-1/c*d^3*b*ln(c^2*x^2+1)","A"
24,1,220,145,0.055000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))/x,x)","\frac{i d^{3} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}+\frac{i d^{3} b \dilog \left(i c x +1\right)}{2}-\frac{3 d^{3} a \,c^{2} x^{2}}{2}+d^{3} a \ln \left(c x \right)-\frac{i d^{3} b \arctan \left(c x \right) c^{3} x^{3}}{3}-\frac{5 i b \,d^{3} \ln \left(c^{2} x^{2}+1\right)}{3}-\frac{3 d^{3} b \arctan \left(c x \right) c^{2} x^{2}}{2}+d^{3} b \ln \left(c x \right) \arctan \left(c x \right)+3 i a c \,d^{3} x +3 i b c \,d^{3} x \arctan \left(c x \right)+\frac{i b \,c^{2} d^{3} x^{2}}{6}-\frac{i d^{3} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{3 b c \,d^{3} x}{2}-\frac{i d^{3} a \,c^{3} x^{3}}{3}-\frac{i d^{3} b \dilog \left(-i c x +1\right)}{2}-\frac{3 b \,d^{3} \arctan \left(c x \right)}{2}"," ",0,"1/2*I*d^3*b*ln(c*x)*ln(1+I*c*x)-1/3*I*d^3*b*arctan(c*x)*c^3*x^3-3/2*d^3*a*c^2*x^2+d^3*a*ln(c*x)-5/3*I*b*d^3*ln(c^2*x^2+1)+3*I*a*c*d^3*x-3/2*d^3*b*arctan(c*x)*c^2*x^2+d^3*b*ln(c*x)*arctan(c*x)+3*I*b*c*d^3*x*arctan(c*x)+1/6*I*b*c^2*d^3*x^2-1/2*I*d^3*b*ln(c*x)*ln(1-I*c*x)-1/3*I*d^3*a*c^3*x^3+3/2*b*c*d^3*x-1/2*I*d^3*b*dilog(1-I*c*x)+1/2*I*d^3*b*dilog(1+I*c*x)-3/2*b*d^3*arctan(c*x)","A"
25,1,223,146,0.064000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^2,x)","-3 a \,c^{2} d^{3} x +3 i c \,d^{3} a \ln \left(c x \right)-\frac{i d^{3} a \,c^{3} x^{2}}{2}-\frac{d^{3} a}{x}-3 b \,c^{2} d^{3} x \arctan \left(c x \right)-\frac{i d^{3} b \arctan \left(c x \right) c^{3} x^{2}}{2}+3 i c \,d^{3} b \arctan \left(c x \right) \ln \left(c x \right)-\frac{d^{3} b \arctan \left(c x \right)}{x}-\frac{3 c \,d^{3} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}+\frac{3 c \,d^{3} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}-\frac{3 c \,d^{3} b \dilog \left(i c x +1\right)}{2}+\frac{3 c \,d^{3} b \dilog \left(-i c x +1\right)}{2}-\frac{i b c \,d^{3} \arctan \left(c x \right)}{2}+c \,d^{3} b \ln \left(c x \right)+b c \,d^{3} \ln \left(c^{2} x^{2}+1\right)+\frac{i b \,c^{2} d^{3} x}{2}"," ",0,"-3*a*c^2*d^3*x+3*I*c*d^3*a*ln(c*x)-1/2*I*d^3*a*c^3*x^2-d^3*a/x-3*b*c^2*d^3*x*arctan(c*x)-1/2*I*d^3*b*arctan(c*x)*c^3*x^2+3*I*c*d^3*b*arctan(c*x)*ln(c*x)-d^3*b*arctan(c*x)/x-3/2*c*d^3*b*ln(c*x)*ln(1+I*c*x)+3/2*c*d^3*b*ln(c*x)*ln(1-I*c*x)-3/2*c*d^3*b*dilog(1+I*c*x)+3/2*c*d^3*b*dilog(1-I*c*x)-1/2*I*b*c*d^3*arctan(c*x)+c*d^3*b*ln(c*x)+b*c*d^3*ln(c^2*x^2+1)+1/2*I*b*c^2*d^3*x","A"
26,1,243,161,0.063000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^3,x)","-\frac{3 i c^{2} d^{3} b \dilog \left(i c x +1\right)}{2}-3 c^{2} d^{3} a \ln \left(c x \right)-i a \,c^{3} d^{3} x -\frac{d^{3} a}{2 x^{2}}+3 i c^{2} d^{3} b \ln \left(c x \right)-3 c^{2} d^{3} b \ln \left(c x \right) \arctan \left(c x \right)-\frac{3 i c^{2} d^{3} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{d^{3} b \arctan \left(c x \right)}{2 x^{2}}+\frac{3 i c^{2} d^{3} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}-i b \,c^{3} d^{3} x \arctan \left(c x \right)-\frac{3 i c \,d^{3} b \arctan \left(c x \right)}{x}-\frac{3 i c \,d^{3} a}{x}-\frac{b c \,d^{3}}{2 x}+\frac{3 i c^{2} d^{3} b \dilog \left(-i c x +1\right)}{2}-i b \,c^{2} d^{3} \ln \left(c^{2} x^{2}+1\right)-\frac{b \,c^{2} d^{3} \arctan \left(c x \right)}{2}"," ",0,"-I*a*c^3*d^3*x-3*c^2*d^3*a*ln(c*x)-3/2*I*c^2*d^3*b*dilog(1+I*c*x)-1/2*d^3*a/x^2+3*I*c^2*d^3*b*ln(c*x)-3*c^2*d^3*b*ln(c*x)*arctan(c*x)-3/2*I*c^2*d^3*b*ln(c*x)*ln(1+I*c*x)-1/2*d^3*b*arctan(c*x)/x^2+3/2*I*c^2*d^3*b*ln(c*x)*ln(1-I*c*x)-I*b*c^3*d^3*x*arctan(c*x)-3*I*c*d^3*b*arctan(c*x)/x-3*I*c*d^3*a/x-1/2*b*c*d^3/x+3/2*I*c^2*d^3*b*dilog(1-I*c*x)-I*b*c^2*d^3*ln(c^2*x^2+1)-1/2*b*c^2*d^3*arctan(c*x)","A"
27,1,255,165,0.066000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^4,x)","-\frac{d^{3} a}{3 x^{3}}-i c^{3} d^{3} b \arctan \left(c x \right) \ln \left(c x \right)+\frac{3 c^{2} d^{3} a}{x}-\frac{3 i b \,c^{3} d^{3} \arctan \left(c x \right)}{2}-\frac{d^{3} b \arctan \left(c x \right)}{3 x^{3}}-\frac{3 i c \,d^{3} a}{2 x^{2}}+\frac{3 c^{2} d^{3} b \arctan \left(c x \right)}{x}-\frac{3 i c \,d^{3} b \arctan \left(c x \right)}{2 x^{2}}+\frac{c^{3} d^{3} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{c^{3} d^{3} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{c^{3} d^{3} b \dilog \left(i c x +1\right)}{2}-\frac{c^{3} d^{3} b \dilog \left(-i c x +1\right)}{2}-i c^{3} d^{3} a \ln \left(c x \right)-\frac{b c \,d^{3}}{6 x^{2}}-\frac{10 c^{3} d^{3} b \ln \left(c x \right)}{3}+\frac{5 b \,c^{3} d^{3} \ln \left(c^{2} x^{2}+1\right)}{3}-\frac{3 i b \,c^{2} d^{3}}{2 x}"," ",0,"-1/3*d^3*a/x^3-I*c^3*d^3*b*arctan(c*x)*ln(c*x)+3*c^2*d^3*a/x-3/2*I*b*c^3*d^3*arctan(c*x)-1/3*d^3*b*arctan(c*x)/x^3-3/2*I*c*d^3*a/x^2+3*c^2*d^3*b*arctan(c*x)/x-3/2*I*c*d^3*b*arctan(c*x)/x^2+1/2*c^3*d^3*b*ln(c*x)*ln(1+I*c*x)-1/2*c^3*d^3*b*ln(c*x)*ln(1-I*c*x)+1/2*c^3*d^3*b*dilog(1+I*c*x)-1/2*c^3*d^3*b*dilog(1-I*c*x)-I*c^3*d^3*a*ln(c*x)-1/6*b*c*d^3/x^2-10/3*c^3*d^3*b*ln(c*x)+5/3*b*c^3*d^3*ln(c^2*x^2+1)-3/2*I*b*c^2*d^3/x","A"
28,1,190,90,0.044000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^5,x)","-\frac{i c \,d^{3} a}{x^{3}}+\frac{i c^{3} d^{3} a}{x}-\frac{d^{3} a}{4 x^{4}}+\frac{3 c^{2} d^{3} a}{2 x^{2}}-\frac{i c \,d^{3} b \arctan \left(c x \right)}{x^{3}}+\frac{i c^{3} d^{3} b \arctan \left(c x \right)}{x}-\frac{d^{3} b \arctan \left(c x \right)}{4 x^{4}}+\frac{3 c^{2} d^{3} b \arctan \left(c x \right)}{2 x^{2}}-\frac{i b \,c^{2} d^{3}}{2 x^{2}}-2 i c^{4} d^{3} b \ln \left(c x \right)-\frac{b c \,d^{3}}{12 x^{3}}+\frac{7 b \,c^{3} d^{3}}{4 x}+i c^{4} d^{3} b \ln \left(c^{2} x^{2}+1\right)+\frac{7 b \,c^{4} d^{3} \arctan \left(c x \right)}{4}"," ",0,"-I*c*d^3*a/x^3+I*c^3*d^3*a/x-1/4*d^3*a/x^4+3/2*c^2*d^3*a/x^2-I*c*d^3*b*arctan(c*x)/x^3+I*c^3*d^3*b*arctan(c*x)/x-1/4*d^3*b*arctan(c*x)/x^4+3/2*c^2*d^3*b*arctan(c*x)/x^2-1/2*I*b*c^2*d^3/x^2-2*I*c^4*d^3*b*ln(c*x)-1/12*b*c*d^3/x^3+7/4*b*c^3*d^3/x+I*c^4*d^3*b*ln(c^2*x^2+1)+7/4*b*c^4*d^3*arctan(c*x)","B"
29,1,200,128,0.056000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^6,x)","\frac{c^{2} d^{3} a}{x^{3}}-\frac{3 i c \,d^{3} a}{4 x^{4}}-\frac{d^{3} a}{5 x^{5}}+\frac{i c^{3} d^{3} a}{2 x^{2}}+\frac{c^{2} d^{3} b \arctan \left(c x \right)}{x^{3}}-\frac{3 i c \,d^{3} b \arctan \left(c x \right)}{4 x^{4}}-\frac{d^{3} b \arctan \left(c x \right)}{5 x^{5}}+\frac{i c^{3} d^{3} b \arctan \left(c x \right)}{2 x^{2}}-\frac{i b \,c^{2} d^{3}}{4 x^{3}}+\frac{5 i b \,c^{4} d^{3}}{4 x}-\frac{b c \,d^{3}}{20 x^{4}}+\frac{3 b \,c^{3} d^{3}}{5 x^{2}}+\frac{6 c^{5} d^{3} b \ln \left(c x \right)}{5}-\frac{3 c^{5} d^{3} b \ln \left(c^{2} x^{2}+1\right)}{5}+\frac{5 i c^{5} d^{3} b \arctan \left(c x \right)}{4}"," ",0,"c^2*d^3*a/x^3-3/4*I*c*d^3*a/x^4-1/5*d^3*a/x^5+1/2*I*c^3*d^3*a/x^2+c^2*d^3*b*arctan(c*x)/x^3-3/4*I*c*d^3*b*arctan(c*x)/x^4-1/5*d^3*b*arctan(c*x)/x^5+1/2*I*c^3*d^3*b*arctan(c*x)/x^2-1/4*I*b*c^2*d^3/x^3+5/4*I*b*c^4*d^3/x-1/20*b*c*d^3/x^4+3/5*b*c^3*d^3/x^2+6/5*c^5*d^3*b*ln(c*x)-3/5*c^5*d^3*b*ln(c^2*x^2+1)+5/4*I*c^5*d^3*b*arctan(c*x)","A"
30,1,215,181,0.047000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^7,x)","-\frac{7 i c^{6} d^{3} b \ln \left(c^{2} x^{2}+1\right)}{15}+\frac{3 c^{2} d^{3} a}{4 x^{4}}-\frac{3 i c \,d^{3} b \arctan \left(c x \right)}{5 x^{5}}-\frac{d^{3} a}{6 x^{6}}+\frac{i c^{3} d^{3} b \arctan \left(c x \right)}{3 x^{3}}+\frac{3 c^{2} d^{3} b \arctan \left(c x \right)}{4 x^{4}}+\frac{i c^{3} d^{3} a}{3 x^{3}}-\frac{d^{3} b \arctan \left(c x \right)}{6 x^{6}}-\frac{3 i b \,c^{2} d^{3}}{20 x^{4}}+\frac{14 i c^{6} d^{3} b \ln \left(c x \right)}{15}+\frac{7 i b \,c^{4} d^{3}}{15 x^{2}}-\frac{b c \,d^{3}}{30 x^{5}}+\frac{11 b \,c^{3} d^{3}}{36 x^{3}}-\frac{11 b \,c^{5} d^{3}}{12 x}-\frac{3 i c \,d^{3} a}{5 x^{5}}-\frac{11 b \,c^{6} d^{3} \arctan \left(c x \right)}{12}"," ",0,"-7/15*I*c^6*d^3*b*ln(c^2*x^2+1)+3/4*c^2*d^3*a/x^4-3/5*I*c*d^3*b*arctan(c*x)/x^5-1/6*d^3*a/x^6+1/3*I*c^3*d^3*b*arctan(c*x)/x^3+3/4*c^2*d^3*b*arctan(c*x)/x^4+1/3*I*c^3*d^3*a/x^3-1/6*d^3*b*arctan(c*x)/x^6-3/20*I*b*c^2*d^3/x^4+14/15*I*c^6*d^3*b*ln(c*x)+7/15*I*b*c^4*d^3/x^2-1/30*b*c*d^3/x^5+11/36*b*c^3*d^3/x^3-11/12*b*c^5*d^3/x-3/5*I*c*d^3*a/x^5-11/12*b*c^6*d^3*arctan(c*x)","A"
31,1,249,206,0.038000," ","int(x^3*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x)","\frac{c^{4} d^{4} a \,x^{8}}{8}-\frac{4 i c^{3} d^{4} b \arctan \left(c x \right) x^{7}}{7}-c^{2} d^{4} a \,x^{6}+\frac{4 i c \,d^{4} b \arctan \left(c x \right) x^{5}}{5}+\frac{d^{4} a \,x^{4}}{4}+\frac{c^{4} d^{4} b \arctan \left(c x \right) x^{8}}{8}+\frac{24 i b \,d^{4} x^{2}}{35 c^{2}}-c^{2} d^{4} b \arctan \left(c x \right) x^{6}-\frac{12 i b \,d^{4} x^{4}}{35}+\frac{d^{4} b \arctan \left(c x \right) x^{4}}{4}+\frac{11 b \,d^{4} x}{8 c^{3}}-\frac{b \,c^{3} d^{4} x^{7}}{56}+\frac{2 i b \,c^{2} d^{4} x^{6}}{21}+\frac{9 b c \,d^{4} x^{5}}{40}+\frac{4 i c \,d^{4} a \,x^{5}}{5}-\frac{11 b \,d^{4} x^{3}}{24 c}-\frac{4 i c^{3} d^{4} a \,x^{7}}{7}-\frac{24 i b \,d^{4} \ln \left(c^{2} x^{2}+1\right)}{35 c^{4}}-\frac{11 b \,d^{4} \arctan \left(c x \right)}{8 c^{4}}"," ",0,"1/8*c^4*d^4*a*x^8-4/7*I*c^3*d^4*b*arctan(c*x)*x^7-c^2*d^4*a*x^6+4/5*I*c*d^4*b*arctan(c*x)*x^5+1/4*d^4*a*x^4+1/8*c^4*d^4*b*arctan(c*x)*x^8+24/35*I*b*d^4*x^2/c^2-c^2*d^4*b*arctan(c*x)*x^6-12/35*I*b*d^4*x^4+1/4*d^4*b*arctan(c*x)*x^4+11/8*b*d^4*x/c^3-1/56*b*c^3*d^4*x^7+2/21*I*b*c^2*d^4*x^6+9/40*b*c*d^4*x^5+4/5*I*c*d^4*a*x^5-11/24*b*d^4*x^3/c-4/7*I*c^3*d^4*a*x^7-24/35*I*b*d^4*ln(c^2*x^2+1)/c^4-11/8*b*d^4*arctan(c*x)/c^4","A"
32,1,237,163,0.046000," ","int(x^2*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x)","\frac{c^{4} d^{4} a \,x^{7}}{7}-\frac{5 i d^{4} b \arctan \left(c x \right)}{3 c^{3}}-\frac{6 c^{2} d^{4} a \,x^{5}}{5}-\frac{2 i c^{3} d^{4} b \arctan \left(c x \right) x^{6}}{3}+\frac{d^{4} a \,x^{3}}{3}+\frac{c^{4} d^{4} b \arctan \left(c x \right) x^{7}}{7}+i c \,d^{4} a \,x^{4}-\frac{6 c^{2} d^{4} b \arctan \left(c x \right) x^{5}}{5}-\frac{5 i b \,d^{4} x^{3}}{9}+\frac{d^{4} b \arctan \left(c x \right) x^{3}}{3}+i c \,d^{4} b \arctan \left(c x \right) x^{4}-\frac{b \,c^{3} d^{4} x^{6}}{42}+\frac{5 i b \,d^{4} x}{3 c^{2}}+\frac{47 b c \,d^{4} x^{4}}{140}-\frac{2 i c^{3} d^{4} a \,x^{6}}{3}-\frac{88 b \,d^{4} x^{2}}{105 c}+\frac{88 d^{4} b \ln \left(c^{2} x^{2}+1\right)}{105 c^{3}}+\frac{2 i b \,c^{2} d^{4} x^{5}}{15}"," ",0,"1/7*c^4*d^4*a*x^7-5/3*I/c^3*d^4*b*arctan(c*x)-6/5*c^2*d^4*a*x^5-2/3*I*c^3*d^4*b*arctan(c*x)*x^6+1/3*d^4*a*x^3+1/7*c^4*d^4*b*arctan(c*x)*x^7+I*c*d^4*a*x^4-6/5*c^2*d^4*b*arctan(c*x)*x^5-5/9*I*b*d^4*x^3+1/3*d^4*b*arctan(c*x)*x^3+I*c*d^4*b*arctan(c*x)*x^4-1/42*b*c^3*d^4*x^6+5/3*I*b*d^4*x/c^2+47/140*b*c*d^4*x^4-2/3*I*c^3*d^4*a*x^6-88/105*b*d^4*x^2/c+88/105/c^3*d^4*b*ln(c^2*x^2+1)+2/15*I*b*c^2*d^4*x^5","A"
33,1,224,152,0.034000," ","int(x*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x)","\frac{c^{4} d^{4} a \,x^{6}}{6}-\frac{4 i c^{3} d^{4} b \arctan \left(c x \right) x^{5}}{5}-\frac{3 c^{2} d^{4} a \,x^{4}}{2}-\frac{4 i c^{3} d^{4} a \,x^{5}}{5}+\frac{d^{4} a \,x^{2}}{2}+\frac{c^{4} d^{4} b \arctan \left(c x \right) x^{6}}{6}+\frac{4 i c \,d^{4} b \arctan \left(c x \right) x^{3}}{3}-\frac{3 c^{2} d^{4} b \arctan \left(c x \right) x^{4}}{2}+\frac{i c^{2} d^{4} b \,x^{4}}{5}+\frac{d^{4} b \arctan \left(c x \right) x^{2}}{2}-\frac{13 b \,d^{4} x}{6 c}-\frac{c^{3} d^{4} b \,x^{5}}{30}+\frac{4 i c \,d^{4} a \,x^{3}}{3}+\frac{5 c \,d^{4} b \,x^{3}}{9}-\frac{16 i d^{4} b \,x^{2}}{15}+\frac{16 i d^{4} b \ln \left(c^{2} x^{2}+1\right)}{15 c^{2}}+\frac{13 d^{4} b \arctan \left(c x \right)}{6 c^{2}}"," ",0,"1/6*c^4*d^4*a*x^6-4/5*I*c^3*d^4*b*arctan(c*x)*x^5-3/2*c^2*d^4*a*x^4-4/5*I*c^3*d^4*a*x^5+1/2*d^4*a*x^2+1/6*c^4*d^4*b*arctan(c*x)*x^6+4/3*I*c*d^4*b*arctan(c*x)*x^3-3/2*c^2*d^4*b*arctan(c*x)*x^4+1/5*I*c^2*d^4*b*x^4+1/2*d^4*b*arctan(c*x)*x^2-13/6*b*d^4*x/c-1/30*c^3*d^4*b*x^5+4/3*I*c*d^4*a*x^3+5/9*c*d^4*b*x^3-16/15*I*d^4*b*x^2+16/15*I/c^2*d^4*b*ln(c^2*x^2+1)+13/6/c^2*d^4*b*arctan(c*x)","A"
34,1,216,106,0.043000," ","int((d+I*c*d*x)^4*(a+b*arctan(c*x)),x)","\frac{c^{4} d^{4} a \,x^{5}}{5}-i c^{3} x^{4} a \,d^{4}-2 c^{2} d^{4} a \,x^{3}-3 i d^{4} b x +a x \,d^{4}+2 i c \,d^{4} b \arctan \left(c x \right) x^{2}+\frac{c^{4} d^{4} b \arctan \left(c x \right) x^{5}}{5}-\frac{i d^{4} a}{5 c}-2 c^{2} d^{4} b \arctan \left(c x \right) x^{3}-i c^{3} d^{4} b \arctan \left(c x \right) x^{4}+b \arctan \left(c x \right) x \,d^{4}+\frac{3 i d^{4} b \arctan \left(c x \right)}{c}+2 i c \,x^{2} a \,d^{4}-\frac{c^{3} d^{4} b \,x^{4}}{20}+\frac{i c^{2} d^{4} b \,x^{3}}{3}+\frac{11 c \,d^{4} b \,x^{2}}{10}-\frac{8 b \ln \left(c^{2} x^{2}+1\right) d^{4}}{5 c}"," ",0,"1/5*c^4*d^4*a*x^5-I*c^3*x^4*a*d^4-2*c^2*d^4*a*x^3-3*I*d^4*b*x+a*x*d^4+2*I*c*d^4*b*arctan(c*x)*x^2+1/5*c^4*d^4*b*arctan(c*x)*x^5-1/5*I/c*d^4*a-2*c^2*d^4*b*arctan(c*x)*x^3-I*c^3*d^4*b*arctan(c*x)*x^4+b*arctan(c*x)*x*d^4+3*I/c*d^4*b*arctan(c*x)+2*I*c*x^2*a*d^4-1/20*c^3*d^4*b*x^4+1/3*I*c^2*d^4*b*x^3+11/10*c*d^4*b*x^2-8/5/c*b*ln(c^2*x^2+1)*d^4","B"
35,1,260,176,0.066000," ","int((d+I*c*d*x)^4*(a+b*arctan(c*x))/x,x)","\frac{i d^{4} b \dilog \left(i c x +1\right)}{2}+\frac{d^{4} a \,c^{4} x^{4}}{4}+\frac{i d^{4} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-3 d^{4} a \,c^{2} x^{2}+d^{4} a \ln \left(c x \right)-\frac{4 i d^{4} b \arctan \left(c x \right) c^{3} x^{3}}{3}+\frac{d^{4} b \arctan \left(c x \right) c^{4} x^{4}}{4}-\frac{i d^{4} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}-3 d^{4} b \arctan \left(c x \right) c^{2} x^{2}+d^{4} b \ln \left(c x \right) \arctan \left(c x \right)+\frac{2 i b \,c^{2} d^{4} x^{2}}{3}-\frac{i d^{4} b \dilog \left(-i c x +1\right)}{2}-\frac{4 i d^{4} a \,c^{3} x^{3}}{3}+4 i a c \,d^{4} x +\frac{13 b c \,d^{4} x}{4}-\frac{b \,c^{3} d^{4} x^{3}}{12}+4 i b c \,d^{4} x \arctan \left(c x \right)-\frac{8 i b \,d^{4} \ln \left(c^{2} x^{2}+1\right)}{3}-\frac{13 b \,d^{4} \arctan \left(c x \right)}{4}"," ",0,"1/2*I*d^4*b*dilog(1+I*c*x)+1/4*d^4*a*c^4*x^4-1/2*I*d^4*b*dilog(1-I*c*x)-3*d^4*a*c^2*x^2+d^4*a*ln(c*x)+1/2*I*d^4*b*ln(c*x)*ln(1+I*c*x)+1/4*d^4*b*arctan(c*x)*c^4*x^4-4/3*I*d^4*b*arctan(c*x)*c^3*x^3-3*d^4*b*arctan(c*x)*c^2*x^2+d^4*b*ln(c*x)*arctan(c*x)-1/2*I*d^4*b*ln(c*x)*ln(1-I*c*x)+2/3*I*b*c^2*d^4*x^2-4/3*I*d^4*a*c^3*x^3+4*I*a*c*d^4*x+13/4*b*c*d^4*x-1/12*b*c^3*d^4*x^3+4*I*b*c*d^4*x*arctan(c*x)-8/3*I*b*d^4*ln(c^2*x^2+1)-13/4*b*d^4*arctan(c*x)","A"
36,1,264,178,0.063000," ","int((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^2,x)","-6 a \,c^{2} d^{4} x +\frac{d^{4} a \,c^{4} x^{3}}{3}+2 i b \,c^{2} d^{4} x -2 i d^{4} a \,c^{3} x^{2}-\frac{d^{4} a}{x}-6 b \,c^{2} d^{4} x \arctan \left(c x \right)+\frac{d^{4} b \arctan \left(c x \right) c^{4} x^{3}}{3}-2 i b c \,d^{4} \arctan \left(c x \right)+4 i c \,d^{4} b \arctan \left(c x \right) \ln \left(c x \right)-\frac{d^{4} b \arctan \left(c x \right)}{x}-2 c \,d^{4} b \ln \left(c x \right) \ln \left(i c x +1\right)+2 c \,d^{4} b \ln \left(c x \right) \ln \left(-i c x +1\right)-2 c \,d^{4} b \dilog \left(i c x +1\right)+2 c \,d^{4} b \dilog \left(-i c x +1\right)+4 i c \,d^{4} a \ln \left(c x \right)-\frac{b \,c^{3} d^{4} x^{2}}{6}+c \,d^{4} b \ln \left(c x \right)+\frac{8 b c \,d^{4} \ln \left(c^{2} x^{2}+1\right)}{3}-2 i d^{4} b \arctan \left(c x \right) c^{3} x^{2}"," ",0,"-6*a*c^2*d^4*x+1/3*d^4*a*c^4*x^3+2*I*b*c^2*d^4*x-2*I*d^4*a*c^3*x^2-d^4*a/x-6*b*c^2*d^4*x*arctan(c*x)+1/3*d^4*b*arctan(c*x)*c^4*x^3-2*I*b*c*d^4*arctan(c*x)+4*I*c*d^4*b*arctan(c*x)*ln(c*x)-d^4*b*arctan(c*x)/x-2*c*d^4*b*ln(c*x)*ln(1+I*c*x)+2*c*d^4*b*ln(c*x)*ln(1-I*c*x)-2*c*d^4*b*dilog(1+I*c*x)+2*c*d^4*b*dilog(1-I*c*x)+4*I*c*d^4*a*ln(c*x)-1/6*b*c^3*d^4*x^2+c*d^4*b*ln(c*x)+8/3*b*c*d^4*ln(c^2*x^2+1)-2*I*d^4*b*arctan(c*x)*c^3*x^2","A"
37,1,248,157,0.070000," ","int((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^3,x)","-4 i b \,c^{3} d^{4} x \arctan \left(c x \right)+\frac{c^{4} d^{4} a \,x^{2}}{2}-6 c^{2} d^{4} a \ln \left(c x \right)-4 i a \,c^{3} d^{4} x -\frac{d^{4} a}{2 x^{2}}-\frac{4 i c \,d^{4} b \arctan \left(c x \right)}{x}+\frac{c^{4} d^{4} b \arctan \left(c x \right) x^{2}}{2}-6 c^{2} d^{4} b \ln \left(c x \right) \arctan \left(c x \right)+4 i c^{2} d^{4} b \ln \left(c x \right)-\frac{d^{4} b \arctan \left(c x \right)}{2 x^{2}}-\frac{b \,c^{3} d^{4} x}{2}-3 i c^{2} d^{4} b \dilog \left(i c x +1\right)-\frac{b c \,d^{4}}{2 x}+3 i c^{2} d^{4} b \ln \left(c x \right) \ln \left(-i c x +1\right)-3 i c^{2} d^{4} b \ln \left(c x \right) \ln \left(i c x +1\right)-\frac{4 i c \,d^{4} a}{x}+3 i c^{2} d^{4} b \dilog \left(-i c x +1\right)"," ",0,"-4*I*b*c^3*d^4*x*arctan(c*x)+1/2*c^4*d^4*a*x^2-6*c^2*d^4*a*ln(c*x)-4*I*a*c^3*d^4*x-1/2*d^4*a/x^2-4*I*c*d^4*b*arctan(c*x)/x+1/2*c^4*d^4*b*arctan(c*x)*x^2-6*c^2*d^4*b*ln(c*x)*arctan(c*x)+4*I*c^2*d^4*b*ln(c*x)-1/2*d^4*b*arctan(c*x)/x^2-1/2*b*c^3*d^4*x+3*I*c^2*d^4*b*ln(c*x)*ln(1-I*c*x)-1/2*b*c*d^4/x-3*I*c^2*d^4*b*ln(c*x)*ln(1+I*c*x)+3*I*c^2*d^4*b*dilog(1-I*c*x)-4*I*c*d^4*a/x-3*I*c^2*d^4*b*dilog(1+I*c*x)","A"
38,1,277,187,0.070000," ","int((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^4,x)","a \,c^{4} d^{4} x -\frac{d^{4} a}{3 x^{3}}-\frac{2 i b \,c^{2} d^{4}}{x}+\frac{6 c^{2} d^{4} a}{x}-4 i c^{3} d^{4} a \ln \left(c x \right)+b \,c^{4} d^{4} x \arctan \left(c x \right)-\frac{d^{4} b \arctan \left(c x \right)}{3 x^{3}}-2 i b \,c^{3} d^{4} \arctan \left(c x \right)+\frac{6 c^{2} d^{4} b \arctan \left(c x \right)}{x}-\frac{2 i c \,d^{4} a}{x^{2}}+2 c^{3} d^{4} b \ln \left(c x \right) \ln \left(i c x +1\right)-2 c^{3} d^{4} b \ln \left(c x \right) \ln \left(-i c x +1\right)+2 c^{3} d^{4} b \dilog \left(i c x +1\right)-2 c^{3} d^{4} b \dilog \left(-i c x +1\right)-\frac{b c \,d^{4}}{6 x^{2}}-\frac{2 i c \,d^{4} b \arctan \left(c x \right)}{x^{2}}-\frac{19 c^{3} d^{4} b \ln \left(c x \right)}{3}+\frac{8 b \,c^{3} d^{4} \ln \left(c^{2} x^{2}+1\right)}{3}-4 i c^{3} d^{4} b \arctan \left(c x \right) \ln \left(c x \right)"," ",0,"a*c^4*d^4*x-1/3*d^4*a/x^3-2*I*b*c^2*d^4/x+6*c^2*d^4*a/x-4*I*c^3*d^4*a*ln(c*x)+b*c^4*d^4*x*arctan(c*x)-1/3*d^4*b*arctan(c*x)/x^3-2*I*b*c^3*d^4*arctan(c*x)+6*c^2*d^4*b*arctan(c*x)/x-2*I*c*d^4*a/x^2+2*c^3*d^4*b*ln(c*x)*ln(1+I*c*x)-2*c^3*d^4*b*ln(c*x)*ln(1-I*c*x)+2*c^3*d^4*b*dilog(1+I*c*x)-2*c^3*d^4*b*dilog(1-I*c*x)-1/6*b*c*d^4/x^2-2*I*c*d^4*b*arctan(c*x)/x^2-19/3*c^3*d^4*b*ln(c*x)+8/3*b*c^3*d^4*ln(c^2*x^2+1)-4*I*c^3*d^4*b*arctan(c*x)*ln(c*x)","A"
39,1,298,198,0.066000," ","int((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^5,x)","\frac{4 i c^{3} d^{4} b \arctan \left(c x \right)}{x}+c^{4} d^{4} a \ln \left(c x \right)-\frac{4 i c \,d^{4} b \arctan \left(c x \right)}{3 x^{3}}-\frac{d^{4} a}{4 x^{4}}+\frac{3 c^{2} d^{4} a}{x^{2}}-\frac{4 i c \,d^{4} a}{3 x^{3}}+c^{4} d^{4} b \ln \left(c x \right) \arctan \left(c x \right)+\frac{i c^{4} d^{4} b \dilog \left(i c x +1\right)}{2}-\frac{d^{4} b \arctan \left(c x \right)}{4 x^{4}}+\frac{3 c^{2} d^{4} b \arctan \left(c x \right)}{x^{2}}+\frac{4 i c^{3} d^{4} a}{x}-\frac{2 i b \,c^{2} d^{4}}{3 x^{2}}-\frac{b c \,d^{4}}{12 x^{3}}+\frac{13 b \,c^{3} d^{4}}{4 x}-\frac{16 i c^{4} d^{4} b \ln \left(c x \right)}{3}+\frac{13 b \,c^{4} d^{4} \arctan \left(c x \right)}{4}+\frac{8 i b \,c^{4} d^{4} \ln \left(c^{2} x^{2}+1\right)}{3}+\frac{i c^{4} d^{4} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i c^{4} d^{4} b \dilog \left(-i c x +1\right)}{2}-\frac{i c^{4} d^{4} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}"," ",0,"4*I*c^3*d^4*b*arctan(c*x)/x+c^4*d^4*a*ln(c*x)-4/3*I*c*d^4*b*arctan(c*x)/x^3-1/4*d^4*a/x^4+3*c^2*d^4*a/x^2-4/3*I*c*d^4*a/x^3+c^4*d^4*b*ln(c*x)*arctan(c*x)-1/2*I*c^4*d^4*b*dilog(1-I*c*x)-1/4*d^4*b*arctan(c*x)/x^4+3*c^2*d^4*b*arctan(c*x)/x^2+1/2*I*c^4*d^4*b*dilog(1+I*c*x)+4*I*c^3*d^4*a/x-1/12*b*c*d^4/x^3+13/4*b*c^3*d^4/x-2/3*I*b*c^2*d^4/x^2+13/4*b*c^4*d^4*arctan(c*x)-16/3*I*c^4*d^4*b*ln(c*x)+8/3*I*b*c^4*d^4*ln(c^2*x^2+1)+1/2*I*c^4*d^4*b*ln(c*x)*ln(1+I*c*x)-1/2*I*c^4*d^4*b*ln(c*x)*ln(1-I*c*x)","A"
40,1,230,101,0.046000," ","int((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^6,x)","\frac{2 c^{2} d^{4} a}{x^{3}}-\frac{c^{4} d^{4} a}{x}+\frac{3 i b \,c^{4} d^{4}}{x}-\frac{d^{4} a}{5 x^{5}}+\frac{2 i c^{3} d^{4} a}{x^{2}}+\frac{2 c^{2} d^{4} b \arctan \left(c x \right)}{x^{3}}-\frac{c^{4} d^{4} b \arctan \left(c x \right)}{x}-\frac{i b \,c^{2} d^{4}}{3 x^{3}}-\frac{d^{4} b \arctan \left(c x \right)}{5 x^{5}}+3 i c^{5} d^{4} b \arctan \left(c x \right)-\frac{i c \,d^{4} a}{x^{4}}+\frac{2 i c^{3} d^{4} b \arctan \left(c x \right)}{x^{2}}-\frac{b c \,d^{4}}{20 x^{4}}+\frac{11 b \,c^{3} d^{4}}{10 x^{2}}+\frac{16 c^{5} d^{4} b \ln \left(c x \right)}{5}-\frac{8 c^{5} d^{4} b \ln \left(c^{2} x^{2}+1\right)}{5}-\frac{i c \,d^{4} b \arctan \left(c x \right)}{x^{4}}"," ",0,"2*c^2*d^4*a/x^3-c^4*d^4*a/x+3*I*b*c^4*d^4/x-1/5*d^4*a/x^5+2*I*c^3*d^4*a/x^2+2*c^2*d^4*b*arctan(c*x)/x^3-c^4*d^4*b*arctan(c*x)/x-1/3*I*b*c^2*d^4/x^3-1/5*d^4*b*arctan(c*x)/x^5+3*I*c^5*d^4*b*arctan(c*x)-I*c*d^4*a/x^4+2*I*c^3*d^4*b*arctan(c*x)/x^2-1/20*b*c*d^4/x^4+11/10*b*c^3*d^4/x^2+16/5*c^5*d^4*b*ln(c*x)-8/5*c^5*d^4*b*ln(c^2*x^2+1)-I*c*d^4*b*arctan(c*x)/x^4","B"
41,1,243,142,0.067000," ","int((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^7,x)","\frac{4 i c^{3} d^{4} a}{3 x^{3}}+\frac{3 c^{2} d^{4} a}{2 x^{4}}-\frac{4 i c \,d^{4} b \arctan \left(c x \right)}{5 x^{5}}-\frac{c^{4} d^{4} a}{2 x^{2}}-\frac{d^{4} a}{6 x^{6}}-\frac{4 i c \,d^{4} a}{5 x^{5}}+\frac{3 c^{2} d^{4} b \arctan \left(c x \right)}{2 x^{4}}+\frac{4 i c^{3} d^{4} b \arctan \left(c x \right)}{3 x^{3}}-\frac{c^{4} d^{4} b \arctan \left(c x \right)}{2 x^{2}}-\frac{d^{4} b \arctan \left(c x \right)}{6 x^{6}}+\frac{16 i b \,c^{4} d^{4}}{15 x^{2}}-\frac{16 i c^{6} d^{4} b \ln \left(c^{2} x^{2}+1\right)}{15}-\frac{i b \,c^{2} d^{4}}{5 x^{4}}-\frac{b c \,d^{4}}{30 x^{5}}+\frac{5 b \,c^{3} d^{4}}{9 x^{3}}-\frac{13 b \,c^{5} d^{4}}{6 x}+\frac{32 i c^{6} d^{4} b \ln \left(c x \right)}{15}-\frac{13 c^{6} d^{4} b \arctan \left(c x \right)}{6}"," ",0,"4/3*I*c^3*d^4*a/x^3+3/2*c^2*d^4*a/x^4-4/5*I*c*d^4*b*arctan(c*x)/x^5-1/2*c^4*d^4*a/x^2-1/6*d^4*a/x^6-4/5*I*c*d^4*a/x^5+3/2*c^2*d^4*b*arctan(c*x)/x^4+4/3*I*c^3*d^4*b*arctan(c*x)/x^3-1/2*c^4*d^4*b*arctan(c*x)/x^2-1/6*d^4*b*arctan(c*x)/x^6+16/15*I*b*c^4*d^4/x^2-16/15*I*c^6*d^4*b*ln(c^2*x^2+1)-1/5*I*b*c^2*d^4/x^4-1/30*b*c*d^4/x^5+5/9*b*c^3*d^4/x^3-13/6*b*c^5*d^4/x+32/15*I*c^6*d^4*b*ln(c*x)-13/6*c^6*d^4*b*arctan(c*x)","A"
42,1,255,210,0.052000," ","int((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^8,x)","-\frac{d^{4} a}{7 x^{7}}-\frac{c^{4} d^{4} a}{3 x^{3}}+\frac{i c^{3} d^{4} b \arctan \left(c x \right)}{x^{4}}+\frac{6 c^{2} d^{4} a}{5 x^{5}}-\frac{5 i c^{7} d^{4} b \arctan \left(c x \right)}{3}-\frac{d^{4} b \arctan \left(c x \right)}{7 x^{7}}-\frac{c^{4} d^{4} b \arctan \left(c x \right)}{3 x^{3}}+\frac{i c^{3} d^{4} a}{x^{4}}+\frac{6 c^{2} d^{4} b \arctan \left(c x \right)}{5 x^{5}}-\frac{2 i c \,d^{4} b \arctan \left(c x \right)}{3 x^{6}}+\frac{5 i b \,c^{4} d^{4}}{9 x^{3}}-\frac{2 i c \,d^{4} a}{3 x^{6}}-\frac{2 i b \,c^{2} d^{4}}{15 x^{5}}-\frac{b c \,d^{4}}{42 x^{6}}+\frac{47 b \,c^{3} d^{4}}{140 x^{4}}-\frac{88 b \,c^{5} d^{4}}{105 x^{2}}-\frac{176 c^{7} d^{4} b \ln \left(c x \right)}{105}+\frac{88 c^{7} d^{4} b \ln \left(c^{2} x^{2}+1\right)}{105}-\frac{5 i b \,c^{6} d^{4}}{3 x}"," ",0,"-1/7*d^4*a/x^7-1/3*c^4*d^4*a/x^3+I*c^3*d^4*b*arctan(c*x)/x^4+6/5*c^2*d^4*a/x^5-5/3*I*c^7*d^4*b*arctan(c*x)-1/7*d^4*b*arctan(c*x)/x^7-1/3*c^4*d^4*b*arctan(c*x)/x^3+I*c^3*d^4*a/x^4+6/5*c^2*d^4*b*arctan(c*x)/x^5-2/3*I*c*d^4*b*arctan(c*x)/x^6+5/9*I*b*c^4*d^4/x^3-2/3*I*c*d^4*a/x^6-2/15*I*b*c^2*d^4/x^5-1/42*b*c*d^4/x^6+47/140*b*c^3*d^4/x^4-88/105*b*c^5*d^4/x^2-176/105*c^7*d^4*b*ln(c*x)+88/105*c^7*d^4*b*ln(c^2*x^2+1)-5/3*I*b*c^6*d^4/x","A"
43,1,353,174,0.102000," ","int(x^3*(a+b*arctan(c*x))/(d+I*c*d*x),x)","\frac{i b x \arctan \left(c x \right)}{c^{3} d}-\frac{i b \arctan \left(c x \right) x^{3}}{3 c d}+\frac{a \,x^{2}}{2 c^{2} d}-\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 c^{4} d}-\frac{5 i b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{48 c^{4} d}+\frac{i b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{4} d}+\frac{i b \,x^{2}}{6 c^{2} d}+\frac{b \arctan \left(c x \right) x^{2}}{2 c^{2} d}-\frac{b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{4} d}+\frac{i a x}{c^{3} d}-\frac{i a \arctan \left(c x \right)}{c^{4} d}-\frac{11 i b \ln \left(c^{2} x^{2}+1\right)}{24 c^{4} d}-\frac{b x}{2 c^{3} d}+\frac{i b \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right)}{2 c^{4} d}+\frac{2 i b}{3 c^{4} d}-\frac{i a \,x^{3}}{3 c d}-\frac{5 b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{24 c^{4} d}+\frac{5 b \arctan \left(\frac{c x}{2}\right)}{24 c^{4} d}-\frac{5 b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{12 c^{4} d}-\frac{i b \ln \left(c x -i\right)^{2}}{4 c^{4} d}+\frac{11 b \arctan \left(c x \right)}{12 d \,c^{4}}"," ",0,"I*b*x*arctan(c*x)/c^3/d-1/3*I/c*b/d*arctan(c*x)*x^3+1/2/c^2*a/d*x^2-1/2/c^4*a/d*ln(c^2*x^2+1)-5/48*I/c^4*b/d*ln(c^4*x^4+10*c^2*x^2+9)+1/6*I*b*x^2/c^2/d+I*a*x/c^3/d+1/2/c^2*b/d*arctan(c*x)*x^2-1/c^4*b/d*arctan(c*x)*ln(c*x-I)-I/c^4*a/d*arctan(c*x)-11/24*I/c^4*b/d*ln(c^2*x^2+1)+1/2*I/c^4*b/d*ln(-1/2*I*(I+c*x))*ln(c*x-I)-1/2*b*x/c^3/d+2/3*I/c^4*b/d+1/2*I/c^4*b/d*dilog(-1/2*I*(I+c*x))-1/3*I/c*a/d*x^3-5/24/c^4*b/d*arctan(1/6*c^3*x^3+7/6*c*x)+5/24/c^4*b/d*arctan(1/2*c*x)-5/12/c^4*b/d*arctan(1/2*c*x-1/2*I)-1/4*I/c^4*b/d*ln(c*x-I)^2+11/12*b*arctan(c*x)/d/c^4","B"
44,1,308,140,0.081000," ","int(x^2*(a+b*arctan(c*x))/(d+I*c*d*x),x)","\frac{a x}{c^{2} d}-\frac{i b \arctan \left(c x \right) x^{2}}{2 c d}+\frac{i b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{3} d}-\frac{a \arctan \left(c x \right)}{c^{3} d}+\frac{b x \arctan \left(c x \right)}{c^{2} d}+\frac{i b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{8 c^{3} d}-\frac{i a \,x^{2}}{2 c d}+\frac{b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{3} d}+\frac{b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{3} d}-\frac{b \ln \left(c x -i\right)^{2}}{4 c^{3} d}+\frac{i b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{4 c^{3} d}+\frac{b}{2 c^{3} d}-\frac{b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{16 c^{3} d}-\frac{3 i b \arctan \left(c x \right)}{4 c^{3} d}+\frac{i a \ln \left(c^{2} x^{2}+1\right)}{2 c^{3} d}-\frac{i b \arctan \left(\frac{c x}{2}\right)}{8 c^{3} d}-\frac{3 b \ln \left(c^{2} x^{2}+1\right)}{8 c^{3} d}+\frac{i b x}{2 c^{2} d}"," ",0,"1/c^2*a/d*x-1/2*I/c*b/d*arctan(c*x)*x^2+I/c^3*b/d*arctan(c*x)*ln(c*x-I)-1/c^3*a/d*arctan(c*x)+b*x*arctan(c*x)/c^2/d+1/8*I/c^3*b/d*arctan(1/6*c^3*x^3+7/6*c*x)-1/2*I/c*a/d*x^2+1/2/c^3*b/d*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/2/c^3*b/d*dilog(-1/2*I*(I+c*x))-1/4/c^3*b/d*ln(c*x-I)^2+1/4*I/c^3*b/d*arctan(1/2*c*x-1/2*I)+1/2/c^3*b/d-1/16/c^3*b/d*ln(c^4*x^4+10*c^2*x^2+9)-3/4*I/c^3*b/d*arctan(c*x)+1/2*I/c^3*a/d*ln(c^2*x^2+1)-1/8*I/c^3*b/d*arctan(1/2*c*x)-3/8*b*ln(c^2*x^2+1)/c^3/d+1/2*I*b*x/c^2/d","B"
45,1,244,100,0.069000," ","int(x*(a+b*arctan(c*x))/(d+I*c*d*x),x)","-\frac{i a x}{d c}+\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 c^{2} d}+\frac{i a \arctan \left(c x \right)}{c^{2} d}-\frac{i b x \arctan \left(c x \right)}{d c}+\frac{b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{2} d}-\frac{i b \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right)}{2 c^{2} d}-\frac{i b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{2} d}+\frac{i b \ln \left(c x -i\right)^{2}}{4 c^{2} d}+\frac{i b \ln \left(c^{8} x^{8}+12 c^{6} x^{6}+30 c^{4} x^{4}+28 c^{2} x^{2}+9\right)}{8 c^{2} d}-\frac{b \arctan \left(\frac{1}{12} c^{3} x^{3}+\frac{13}{12} c x \right)}{4 c^{2} d}-\frac{b \arctan \left(\frac{c x}{4}\right)}{4 c^{2} d}+\frac{b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{2 c^{2} d}"," ",0,"-I*a*x/d/c+1/2/c^2*a/d*ln(c^2*x^2+1)+I/c^2*a/d*arctan(c*x)-I*b*x*arctan(c*x)/d/c+1/c^2*b/d*arctan(c*x)*ln(c*x-I)-1/2*I/c^2*b/d*ln(-1/2*I*(I+c*x))*ln(c*x-I)-1/2*I/c^2*b/d*dilog(-1/2*I*(I+c*x))+1/4*I/c^2*b/d*ln(c*x-I)^2+1/8*I/c^2*b/d*ln(c^8*x^8+12*c^6*x^6+30*c^4*x^4+28*c^2*x^2+9)-1/4/c^2*b/d*arctan(1/12*c^3*x^3+13/12*c*x)-1/4/c^2*b/d*arctan(1/4*c*x)+1/2/c^2*b/d*arctan(1/2*c*x-1/2*I)","B"
46,1,142,54,0.045000," ","int((a+b*arctan(c*x))/(d+I*c*d*x),x)","-\frac{i a \ln \left(c^{2} x^{2}+1\right)}{2 c d}+\frac{a \arctan \left(c x \right)}{c d}-\frac{i b \ln \left(i c x +1\right) \arctan \left(c x \right)}{c d}-\frac{b \ln \left(\frac{1}{2}-\frac{i c x}{2}\right) \ln \left(i c x +1\right)}{2 c d}+\frac{b \ln \left(\frac{1}{2}-\frac{i c x}{2}\right) \ln \left(\frac{i c x}{2}+\frac{1}{2}\right)}{2 c d}+\frac{b \dilog \left(\frac{i c x}{2}+\frac{1}{2}\right)}{2 c d}+\frac{b \ln \left(i c x +1\right)^{2}}{4 c d}"," ",0,"-1/2*I/c*a/d*ln(c^2*x^2+1)+1/c*a/d*arctan(c*x)-I/c*b/d*ln(1+I*c*x)*arctan(c*x)-1/2/c*b/d*ln(1/2-1/2*I*c*x)*ln(1+I*c*x)+1/2/c*b/d*ln(1/2-1/2*I*c*x)*ln(1/2*I*c*x+1/2)+1/2/c*b/d*dilog(1/2*I*c*x+1/2)+1/4/c*b/d*ln(1+I*c*x)^2","B"
47,1,193,49,0.061000," ","int((a+b*arctan(c*x))/x/(d+I*c*d*x),x)","\frac{a \ln \left(c x \right)}{d}-\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 d}-\frac{i a \arctan \left(c x \right)}{d}-\frac{b \arctan \left(c x \right) \ln \left(c x -i\right)}{d}+\frac{b \ln \left(c x \right) \arctan \left(c x \right)}{d}+\frac{i b \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d}-\frac{i b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d}+\frac{i b \dilog \left(i c x +1\right)}{2 d}-\frac{i b \dilog \left(-i c x +1\right)}{2 d}+\frac{i b \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right)}{2 d}+\frac{i b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d}-\frac{i b \ln \left(c x -i\right)^{2}}{4 d}"," ",0,"a/d*ln(c*x)-1/2*a/d*ln(c^2*x^2+1)-I*a/d*arctan(c*x)-b/d*arctan(c*x)*ln(c*x-I)+b/d*ln(c*x)*arctan(c*x)+1/2*I*b/d*ln(c*x)*ln(1+I*c*x)-1/2*I*b/d*ln(c*x)*ln(1-I*c*x)+1/2*I*b/d*dilog(1+I*c*x)-1/2*I*b/d*dilog(1-I*c*x)+1/2*I*b/d*ln(-1/2*I*(I+c*x))*ln(c*x-I)+1/2*I*b/d*dilog(-1/2*I*(I+c*x))-1/4*I*b/d*ln(c*x-I)^2","B"
48,1,252,95,0.066000," ","int((a+b*arctan(c*x))/x^2/(d+I*c*d*x),x)","-\frac{a}{d x}-\frac{i c a \ln \left(c x \right)}{d}-\frac{i c b \arctan \left(c x \right) \ln \left(c x \right)}{d}-\frac{c a \arctan \left(c x \right)}{d}-\frac{b \arctan \left(c x \right)}{d x}+\frac{i c a \ln \left(c^{2} x^{2}+1\right)}{2 d}+\frac{i c b \arctan \left(c x \right) \ln \left(c x -i\right)}{d}+\frac{c b \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d}-\frac{c b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d}+\frac{c b \dilog \left(i c x +1\right)}{2 d}-\frac{c b \dilog \left(-i c x +1\right)}{2 d}+\frac{c b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d}+\frac{c b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d}-\frac{c b \ln \left(c x -i\right)^{2}}{4 d}+\frac{c b \ln \left(c x \right)}{d}-\frac{b c \ln \left(c^{2} x^{2}+1\right)}{2 d}"," ",0,"-a/d/x-I*c*a/d*ln(c*x)-I*c*b/d*arctan(c*x)*ln(c*x)-c*a/d*arctan(c*x)-b/d*arctan(c*x)/x+1/2*I*c*a/d*ln(c^2*x^2+1)+I*c*b/d*arctan(c*x)*ln(c*x-I)+1/2*c*b/d*ln(c*x)*ln(1+I*c*x)-1/2*c*b/d*ln(c*x)*ln(1-I*c*x)+1/2*c*b/d*dilog(1+I*c*x)-1/2*c*b/d*dilog(1-I*c*x)+1/2*c*b/d*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/2*c*b/d*dilog(-1/2*I*(I+c*x))-1/4*c*b/d*ln(c*x-I)^2+c*b/d*ln(c*x)-1/2*b*c*ln(c^2*x^2+1)/d","B"
49,1,335,148,0.068000," ","int((a+b*arctan(c*x))/x^3/(d+I*c*d*x),x)","-\frac{a}{2 d \,x^{2}}-\frac{i c^{2} b \dilog \left(i c x +1\right)}{2 d}-\frac{c^{2} a \ln \left(c x \right)}{d}+\frac{c^{2} a \ln \left(c^{2} x^{2}+1\right)}{2 d}+\frac{i c^{2} a \arctan \left(c x \right)}{d}-\frac{b \arctan \left(c x \right)}{2 d \,x^{2}}+\frac{i c^{2} b \dilog \left(-i c x +1\right)}{2 d}-\frac{c^{2} b \ln \left(c x \right) \arctan \left(c x \right)}{d}+\frac{c^{2} b \arctan \left(c x \right) \ln \left(c x -i\right)}{d}+\frac{i b \,c^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d}-\frac{b c}{2 d x}+\frac{i c b \arctan \left(c x \right)}{d x}-\frac{b \,c^{2} \arctan \left(c x \right)}{2 d}-\frac{i c^{2} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d}-\frac{i c^{2} b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d}-\frac{i c^{2} b \ln \left(c x \right)}{d}-\frac{i c^{2} b \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right)}{2 d}+\frac{i c^{2} b \ln \left(c x -i\right)^{2}}{4 d}+\frac{i c a}{d x}+\frac{i c^{2} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d}"," ",0,"-1/2*a/d/x^2+I*c^2*a/d*arctan(c*x)-c^2*a/d*ln(c*x)+1/2*c^2*a/d*ln(c^2*x^2+1)+1/2*I*b*c^2*ln(c^2*x^2+1)/d-1/2*b/d*arctan(c*x)/x^2+I*c*b/d*arctan(c*x)/x-c^2*b/d*ln(c*x)*arctan(c*x)+c^2*b/d*arctan(c*x)*ln(c*x-I)-1/2*I*c^2*b/d*dilog(-1/2*I*(I+c*x))-1/2*b*c/d/x-1/2*I*c^2*b/d*dilog(1+I*c*x)-1/2*b*c^2*arctan(c*x)/d-1/2*I*c^2*b/d*ln(c*x)*ln(1+I*c*x)-I*c^2*b/d*ln(c*x)-1/2*I*c^2*b/d*ln(-1/2*I*(I+c*x))*ln(c*x-I)+1/2*I*c^2*b/d*dilog(1-I*c*x)+1/4*I*c^2*b/d*ln(c*x-I)^2+I*c*a/d/x+1/2*I*c^2*b/d*ln(c*x)*ln(1-I*c*x)","B"
50,1,369,178,0.075000," ","int((a+b*arctan(c*x))/x^4/(d+I*c*d*x),x)","-\frac{a}{3 d \,x^{3}}+\frac{i c a}{2 d \,x^{2}}+\frac{i c b \arctan \left(c x \right)}{2 d \,x^{2}}+\frac{c^{2} a}{d x}+\frac{i c^{3} b \arctan \left(c x \right) \ln \left(c x \right)}{d}+\frac{c^{3} a \arctan \left(c x \right)}{d}-\frac{b \arctan \left(c x \right)}{3 d \,x^{3}}+\frac{i b \,c^{2}}{2 d x}+\frac{i b \,c^{3} \arctan \left(c x \right)}{2 d}+\frac{c^{2} b \arctan \left(c x \right)}{d x}+\frac{i c^{3} a \ln \left(c x \right)}{d}-\frac{c^{3} b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d}-\frac{c^{3} b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d}+\frac{c^{3} b \ln \left(c x -i\right)^{2}}{4 d}-\frac{c^{3} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d}+\frac{c^{3} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d}-\frac{c^{3} b \dilog \left(i c x +1\right)}{2 d}+\frac{c^{3} b \dilog \left(-i c x +1\right)}{2 d}-\frac{i c^{3} b \arctan \left(c x \right) \ln \left(c x -i\right)}{d}-\frac{b c}{6 d \,x^{2}}-\frac{4 c^{3} b \ln \left(c x \right)}{3 d}+\frac{2 b \,c^{3} \ln \left(c^{2} x^{2}+1\right)}{3 d}-\frac{i c^{3} a \ln \left(c^{2} x^{2}+1\right)}{2 d}"," ",0,"-1/3*a/d/x^3+1/2*I*c*a/d/x^2+1/2*I*c*b/d*arctan(c*x)/x^2+c^2*a/d/x+I*c^3*b/d*arctan(c*x)*ln(c*x)+c^3*a/d*arctan(c*x)-1/3*b/d*arctan(c*x)/x^3+1/2*I*b*c^2/d/x+1/2*I*b*c^3*arctan(c*x)/d+c^2*b/d*arctan(c*x)/x+I*c^3*a/d*ln(c*x)-1/2*c^3*b/d*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*c^3*b/d*dilog(-1/2*I*(I+c*x))+1/4*c^3*b/d*ln(c*x-I)^2-1/2*c^3*b/d*ln(c*x)*ln(1+I*c*x)+1/2*c^3*b/d*ln(c*x)*ln(1-I*c*x)-1/2*c^3*b/d*dilog(1+I*c*x)+1/2*c^3*b/d*dilog(1-I*c*x)-I*c^3*b/d*arctan(c*x)*ln(c*x-I)-1/6*b*c/d/x^2-4/3*c^3*b/d*ln(c*x)+2/3*b*c^3*ln(c^2*x^2+1)/d-1/2*I*c^3*a/d*ln(c^2*x^2+1)","B"
51,1,367,186,0.069000," ","int(x^3*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x)","-\frac{2 i a x}{c^{3} d^{2}}-\frac{a \,x^{2}}{2 c^{2} d^{2}}-\frac{3 i b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{4} d^{2}}+\frac{3 a \ln \left(c^{2} x^{2}+1\right)}{2 c^{4} d^{2}}+\frac{3 i a \arctan \left(c x \right)}{c^{4} d^{2}}-\frac{i b}{2 c^{4} d^{2}}-\frac{b \arctan \left(c x \right) x^{2}}{2 c^{2} d^{2}}-\frac{2 i b x \arctan \left(c x \right)}{c^{3} d^{2}}+\frac{3 b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{4} d^{2}}+\frac{3 i b \ln \left(c x -i\right)^{2}}{4 c^{4} d^{2}}-\frac{i b \arctan \left(c x \right)}{c^{4} d^{2} \left(c x -i\right)}+\frac{i b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{8 c^{4} d^{2}}+\frac{b x}{2 c^{3} d^{2}}+\frac{3 i b \ln \left(c^{2} x^{2}+1\right)}{4 c^{4} d^{2}}-\frac{i a}{c^{4} d^{2} \left(c x -i\right)}-\frac{b \arctan \left(\frac{c x}{2}\right)}{4 c^{4} d^{2}}+\frac{b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{4 c^{4} d^{2}}+\frac{b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{2 c^{4} d^{2}}-\frac{b}{2 c^{4} d^{2} \left(c x -i\right)}-\frac{3 i b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{4} d^{2}}-\frac{3 b \arctan \left(c x \right)}{2 d^{2} c^{4}}"," ",0,"-3/2*I/c^4*b/d^2*dilog(-1/2*I*(I+c*x))-1/2/c^2*a/d^2*x^2-2*I*a*x/c^3/d^2+3/2/c^4*a/d^2*ln(c^2*x^2+1)+3*I/c^4*a/d^2*arctan(c*x)-1/2*I/c^4*b/d^2-1/2/c^2*b/d^2*arctan(c*x)*x^2-2*I*b*x*arctan(c*x)/c^3/d^2+3/c^4*b/d^2*arctan(c*x)*ln(c*x-I)+3/4*I/c^4*b/d^2*ln(c*x-I)^2-I/c^4*b/d^2*arctan(c*x)/(c*x-I)+1/8*I/c^4*b/d^2*ln(c^4*x^4+10*c^2*x^2+9)+1/2*b*x/c^3/d^2+3/4*I/c^4*b/d^2*ln(c^2*x^2+1)-I/c^4*a/d^2/(c*x-I)-1/4/c^4*b/d^2*arctan(1/2*c*x)+1/4/c^4*b/d^2*arctan(1/6*c^3*x^3+7/6*c*x)+1/2/c^4*b/d^2*arctan(1/2*c*x-1/2*I)-1/2/c^4*b/d^2/(c*x-I)-3/2*I/c^4*b/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-3/2*b*arctan(c*x)/d^2/c^4","A"
52,1,316,154,0.082000," ","int(x^2*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x)","-\frac{a x}{c^{2} d^{2}}-\frac{a}{c^{3} d^{2} \left(c x -i\right)}+\frac{2 a \arctan \left(c x \right)}{c^{3} d^{2}}-\frac{i b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{8 c^{3} d^{2}}-\frac{b x \arctan \left(c x \right)}{c^{2} d^{2}}-\frac{b \arctan \left(c x \right)}{c^{3} d^{2} \left(c x -i\right)}-\frac{2 i b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{3} d^{2}}-\frac{b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{3} d^{2}}-\frac{b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{3} d^{2}}+\frac{b \ln \left(c x -i\right)^{2}}{2 c^{3} d^{2}}+\frac{b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{16 c^{3} d^{2}}+\frac{i b \arctan \left(\frac{c x}{2}\right)}{8 c^{3} d^{2}}-\frac{i b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{4 c^{3} d^{2}}+\frac{i b}{2 c^{3} d^{2} \left(c x -i\right)}-\frac{i a \ln \left(c^{2} x^{2}+1\right)}{c^{3} d^{2}}+\frac{3 b \ln \left(c^{2} x^{2}+1\right)}{8 c^{3} d^{2}}+\frac{3 i b \arctan \left(c x \right)}{4 c^{3} d^{2}}"," ",0,"-a*x/c^2/d^2-1/c^3*a/d^2/(c*x-I)+2/c^3*a/d^2*arctan(c*x)-1/8*I/c^3*b/d^2*arctan(1/6*c^3*x^3+7/6*c*x)-b*x*arctan(c*x)/c^2/d^2-1/c^3*b/d^2*arctan(c*x)/(c*x-I)-2*I/c^3*b/d^2*arctan(c*x)*ln(c*x-I)-1/c^3*b/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/c^3*b/d^2*dilog(-1/2*I*(I+c*x))+1/2/c^3*b/d^2*ln(c*x-I)^2+1/16/c^3*b/d^2*ln(c^4*x^4+10*c^2*x^2+9)+1/8*I/c^3*b/d^2*arctan(1/2*c*x)-1/4*I/c^3*b/d^2*arctan(1/2*c*x-1/2*I)+1/2*I/c^3*b/d^2/(c*x-I)-I/c^3*a/d^2*ln(c^2*x^2+1)+3/8*b*ln(c^2*x^2+1)/c^3/d^2+3/4*I/c^3*b/d^2*arctan(c*x)","B"
53,1,293,110,0.063000," ","int(x*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x)","\frac{i a}{c^{2} d^{2} \left(c x -i\right)}-\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 c^{2} d^{2}}-\frac{i a \arctan \left(c x \right)}{c^{2} d^{2}}+\frac{i b \arctan \left(c x \right)}{c^{2} d^{2} \left(c x -i\right)}-\frac{b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{2} d^{2}}+\frac{i b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{16 c^{2} d^{2}}-\frac{b \arctan \left(\frac{c x}{2}\right)}{8 c^{2} d^{2}}+\frac{b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{8 c^{2} d^{2}}+\frac{b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{4 c^{2} d^{2}}+\frac{b}{2 c^{2} d^{2} \left(c x -i\right)}-\frac{i b \ln \left(c^{2} x^{2}+1\right)}{8 c^{2} d^{2}}+\frac{b \arctan \left(c x \right)}{4 c^{2} d^{2}}+\frac{i b \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right)}{2 c^{2} d^{2}}+\frac{i b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{2} d^{2}}-\frac{i b \ln \left(c x -i\right)^{2}}{4 c^{2} d^{2}}"," ",0,"I/c^2*a/d^2/(c*x-I)-1/2/c^2*a/d^2*ln(c^2*x^2+1)-I/c^2*a/d^2*arctan(c*x)+I/c^2*b/d^2*arctan(c*x)/(c*x-I)-1/c^2*b/d^2*arctan(c*x)*ln(c*x-I)+1/16*I/c^2*b/d^2*ln(c^4*x^4+10*c^2*x^2+9)-1/8/c^2*b/d^2*arctan(1/2*c*x)+1/8/c^2*b/d^2*arctan(1/6*c^3*x^3+7/6*c*x)+1/4/c^2*b/d^2*arctan(1/2*c*x-1/2*I)+1/2/c^2*b/d^2/(c*x-I)-1/8*I/c^2*b/d^2*ln(c^2*x^2+1)+1/4*b*arctan(c*x)/c^2/d^2+1/2*I/c^2*b/d^2*ln(-1/2*I*(I+c*x))*ln(c*x-I)+1/2*I/c^2*b/d^2*dilog(-1/2*I*(I+c*x))-1/4*I/c^2*b/d^2*ln(c*x-I)^2","B"
54,1,76,60,0.046000," ","int((a+b*arctan(c*x))/(d+I*c*d*x)^2,x)","\frac{i a}{c \,d^{2} \left(i c x +1\right)}+\frac{i b \arctan \left(c x \right)}{c \,d^{2} \left(i c x +1\right)}-\frac{i b \arctan \left(c x \right)}{2 c \,d^{2}}-\frac{i b}{2 c \,d^{2} \left(c x -i\right)}"," ",0,"I/c*a/d^2/(1+I*c*x)+I/c*b/d^2/(1+I*c*x)*arctan(c*x)-1/2*I*b*arctan(c*x)/c/d^2-1/2*I/c*b/d^2/(c*x-I)","A"
55,1,251,130,0.076000," ","int((a+b*arctan(c*x))/x/(d+I*c*d*x)^2,x)","\frac{a \ln \left(c x \right)}{d^{2}}-\frac{i b \arctan \left(c x \right)}{d^{2} \left(c x -i\right)}-\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 d^{2}}+\frac{i b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d^{2}}+\frac{b \ln \left(c x \right) \arctan \left(c x \right)}{d^{2}}+\frac{i b \dilog \left(i c x +1\right)}{2 d^{2}}-\frac{b \arctan \left(c x \right) \ln \left(c x -i\right)}{d^{2}}+\frac{i b \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right)}{2 d^{2}}+\frac{i b \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d^{2}}-\frac{i a \arctan \left(c x \right)}{d^{2}}-\frac{i b \ln \left(c x -i\right)^{2}}{4 d^{2}}-\frac{b \arctan \left(c x \right)}{2 d^{2}}-\frac{b}{2 d^{2} \left(c x -i\right)}-\frac{i b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d^{2}}-\frac{i b \dilog \left(-i c x +1\right)}{2 d^{2}}-\frac{i a}{d^{2} \left(c x -i\right)}"," ",0,"a/d^2*ln(c*x)-I*b/d^2*arctan(c*x)/(c*x-I)-1/2*a/d^2*ln(c^2*x^2+1)+1/2*I*b/d^2*dilog(1+I*c*x)+b/d^2*ln(c*x)*arctan(c*x)+1/2*I*b/d^2*ln(-1/2*I*(I+c*x))*ln(c*x-I)-b/d^2*arctan(c*x)*ln(c*x-I)+1/2*I*b/d^2*ln(c*x)*ln(1+I*c*x)-I*a/d^2*arctan(c*x)-1/4*I*b/d^2*ln(c*x-I)^2-1/2*I*b/d^2*ln(c*x)*ln(1-I*c*x)-1/2*b*arctan(c*x)/d^2-1/2*b/d^2/(c*x-I)+1/2*I*b/d^2*dilog(-1/2*I*(I+c*x))-1/2*I*b/d^2*dilog(1-I*c*x)-I*a/d^2/(c*x-I)","A"
56,1,340,180,0.079000," ","int((a+b*arctan(c*x))/x^2/(d+I*c*d*x)^2,x)","-\frac{a}{d^{2} x}+\frac{i c a \ln \left(c^{2} x^{2}+1\right)}{d^{2}}-\frac{c a}{d^{2} \left(c x -i\right)}-\frac{2 c a \arctan \left(c x \right)}{d^{2}}+\frac{i c b}{2 d^{2} \left(c x -i\right)}-\frac{b \arctan \left(c x \right)}{d^{2} x}+\frac{i b c \arctan \left(c x \right)}{2 d^{2}}-\frac{c b \arctan \left(c x \right)}{d^{2} \left(c x -i\right)}-\frac{2 i c a \ln \left(c x \right)}{d^{2}}-\frac{c b \dilog \left(-i \left(c x +i\right)\right)}{d^{2}}-\frac{c b \ln \left(c x \right) \ln \left(-i \left(c x +i\right)\right)}{d^{2}}+\frac{c b \ln \left(-i \left(-c x +i\right)\right) \ln \left(c x \right)}{d^{2}}-\frac{c b \ln \left(-i \left(-c x +i\right)\right) \ln \left(-i c x \right)}{d^{2}}-\frac{c b \dilog \left(-i c x \right)}{d^{2}}+\frac{c b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{d^{2}}+\frac{c b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{d^{2}}-\frac{c b \ln \left(c x -i\right)^{2}}{2 d^{2}}+\frac{c b \ln \left(c x \right)}{d^{2}}-\frac{b c \ln \left(c^{2} x^{2}+1\right)}{2 d^{2}}+\frac{2 i c b \arctan \left(c x \right) \ln \left(c x -i\right)}{d^{2}}-\frac{2 i c b \arctan \left(c x \right) \ln \left(c x \right)}{d^{2}}"," ",0,"-a/d^2/x+I*c*a/d^2*ln(c^2*x^2+1)-c*a/d^2/(c*x-I)-2*c*a/d^2*arctan(c*x)+1/2*I*c*b/d^2/(c*x-I)-b/d^2*arctan(c*x)/x+1/2*I*b*c*arctan(c*x)/d^2-c*b/d^2*arctan(c*x)/(c*x-I)-2*I*c*a/d^2*ln(c*x)-c*b/d^2*dilog(-I*(I+c*x))-c*b/d^2*ln(c*x)*ln(-I*(I+c*x))+c*b/d^2*ln(-I*(-c*x+I))*ln(c*x)-c*b/d^2*ln(-I*(-c*x+I))*ln(-I*c*x)-c*b/d^2*dilog(-I*c*x)+c*b/d^2*dilog(-1/2*I*(I+c*x))+c*b/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*c*b/d^2*ln(c*x-I)^2+c*b/d^2*ln(c*x)-1/2*b*c*ln(c^2*x^2+1)/d^2+2*I*c*b/d^2*arctan(c*x)*ln(c*x-I)-2*I*c*b/d^2*arctan(c*x)*ln(c*x)","A"
57,1,380,222,0.082000," ","int((a+b*arctan(c*x))/x^3/(d+I*c*d*x)^2,x)","-\frac{a}{2 d^{2} x^{2}}-\frac{3 i c^{2} b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d^{2}}-\frac{3 c^{2} a \ln \left(c x \right)}{d^{2}}+\frac{i b \,c^{2} \ln \left(c^{2} x^{2}+1\right)}{d^{2}}+\frac{3 c^{2} a \ln \left(c^{2} x^{2}+1\right)}{2 d^{2}}-\frac{3 i c^{2} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d^{2}}-\frac{b \arctan \left(c x \right)}{2 d^{2} x^{2}}-\frac{2 i c^{2} b \ln \left(c x \right)}{d^{2}}-\frac{3 c^{2} b \ln \left(c x \right) \arctan \left(c x \right)}{d^{2}}+\frac{2 i c a}{d^{2} x}+\frac{3 c^{2} b \arctan \left(c x \right) \ln \left(c x -i\right)}{d^{2}}+\frac{3 i c^{2} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d^{2}}-\frac{3 i c^{2} b \dilog \left(i c x +1\right)}{2 d^{2}}+\frac{2 i c b \arctan \left(c x \right)}{d^{2} x}+\frac{3 i c^{2} b \ln \left(c x -i\right)^{2}}{4 d^{2}}-\frac{3 i c^{2} b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d^{2}}+\frac{3 i c^{2} b \dilog \left(-i c x +1\right)}{2 d^{2}}+\frac{i c^{2} b \arctan \left(c x \right)}{d^{2} \left(c x -i\right)}-\frac{b c}{2 d^{2} x}+\frac{3 i c^{2} a \arctan \left(c x \right)}{d^{2}}+\frac{i c^{2} a}{d^{2} \left(c x -i\right)}+\frac{c^{2} b}{2 d^{2} \left(c x -i\right)}"," ",0,"-1/2*a/d^2/x^2+I*b*c^2*ln(c^2*x^2+1)/d^2-3*c^2*a/d^2*ln(c*x)-3/2*I*c^2*b/d^2*ln(c*x)*ln(1+I*c*x)+3/2*c^2*a/d^2*ln(c^2*x^2+1)-2*I*c^2*b/d^2*ln(c*x)-1/2*b/d^2*arctan(c*x)/x^2+2*I*c*a/d^2/x-3*c^2*b/d^2*ln(c*x)*arctan(c*x)+3/2*I*c^2*b/d^2*ln(c*x)*ln(1-I*c*x)+3*c^2*b/d^2*arctan(c*x)*ln(c*x-I)+2*I*c*b/d^2*arctan(c*x)/x+3/4*I*c^2*b/d^2*ln(c*x-I)^2-3/2*I*c^2*b/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+3/2*I*c^2*b/d^2*dilog(1-I*c*x)+I*c^2*b/d^2*arctan(c*x)/(c*x-I)-3/2*I*c^2*b/d^2*dilog(1+I*c*x)-3/2*I*c^2*b/d^2*dilog(-1/2*I*(I+c*x))-1/2*b*c/d^2/x+3*I*c^2*a/d^2*arctan(c*x)+I*c^2*a/d^2/(c*x-I)+1/2*c^2*b/d^2/(c*x-I)","A"
58,1,423,230,0.072000," ","int(x^4*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x)","-\frac{3 a x}{c^{4} d^{3}}-\frac{3 i a \ln \left(c^{2} x^{2}+1\right)}{c^{5} d^{3}}-\frac{4 a}{c^{5} d^{3} \left(c x -i\right)}-\frac{i b \arctan \left(c x \right)}{2 c^{5} d^{3} \left(c x -i\right)^{2}}+\frac{6 a \arctan \left(c x \right)}{c^{5} d^{3}}+\frac{i a \,x^{2}}{2 c^{3} d^{3}}-\frac{3 b x \arctan \left(c x \right)}{c^{4} d^{3}}+\frac{5 i b \arctan \left(\frac{c x}{2}\right)}{32 c^{5} d^{3}}-\frac{4 b \arctan \left(c x \right)}{c^{5} d^{3} \left(c x -i\right)}+\frac{15 i b}{8 c^{5} d^{3} \left(c x -i\right)}-\frac{5 i b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{32 c^{5} d^{3}}-\frac{b}{2 c^{5} d^{3}}-\frac{5 i b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{16 c^{5} d^{3}}+\frac{5 b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{64 c^{5} d^{3}}-\frac{i b x}{2 c^{4} d^{3}}-\frac{i a}{2 c^{5} d^{3} \left(c x -i\right)^{2}}+\frac{i b \arctan \left(c x \right) x^{2}}{2 c^{3} d^{3}}-\frac{6 i b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{5} d^{3}}-\frac{b}{8 c^{5} d^{3} \left(c x -i\right)^{2}}+\frac{43 b \ln \left(c^{2} x^{2}+1\right)}{32 c^{5} d^{3}}+\frac{43 i b \arctan \left(c x \right)}{16 c^{5} d^{3}}+\frac{3 b \ln \left(c x -i\right)^{2}}{2 c^{5} d^{3}}-\frac{3 b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{5} d^{3}}-\frac{3 b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{5} d^{3}}"," ",0,"-3*a*x/c^4/d^3-3*I/c^5*a/d^3*ln(c^2*x^2+1)-4/c^5*a/d^3/(c*x-I)-1/2*I/c^5*b/d^3*arctan(c*x)/(c*x-I)^2+6/c^5*a/d^3*arctan(c*x)+1/2*I/c^3*a/d^3*x^2-3*b*x*arctan(c*x)/c^4/d^3+5/32*I/c^5*b/d^3*arctan(1/2*c*x)-4/c^5*b/d^3*arctan(c*x)/(c*x-I)+15/8*I/c^5*b/d^3/(c*x-I)-5/32*I/c^5*b/d^3*arctan(1/6*c^3*x^3+7/6*c*x)-1/2/c^5*b/d^3-5/16*I/c^5*b/d^3*arctan(1/2*c*x-1/2*I)+5/64/c^5*b/d^3*ln(c^4*x^4+10*c^2*x^2+9)-1/2*I*b*x/c^4/d^3-1/2*I/c^5*a/d^3/(c*x-I)^2+1/2*I/c^3*b/d^3*arctan(c*x)*x^2-6*I/c^5*b/d^3*arctan(c*x)*ln(c*x-I)-1/8/c^5*b/d^3/(c*x-I)^2+43/32*b*ln(c^2*x^2+1)/c^5/d^3+43/16*I/c^5*b/d^3*arctan(c*x)+3/2/c^5*b/d^3*ln(c*x-I)^2-3/c^5*b/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))-3/c^5*b/d^3*dilog(-1/2*I*(I+c*x))","A"
59,1,375,204,0.066000," ","int(x^3*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x)","-\frac{3 i a \arctan \left(c x \right)}{c^{4} d^{3}}+\frac{3 i b \arctan \left(c x \right)}{c^{4} d^{3} \left(c x -i\right)}-\frac{3 a \ln \left(c^{2} x^{2}+1\right)}{2 c^{4} d^{3}}+\frac{i b x \arctan \left(c x \right)}{c^{3} d^{3}}-\frac{a}{2 c^{4} d^{3} \left(c x -i\right)^{2}}+\frac{3 i b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{4} d^{3}}+\frac{i a x}{c^{3} d^{3}}-\frac{3 b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{4} d^{3}}-\frac{b \arctan \left(c x \right)}{2 c^{4} d^{3} \left(c x -i\right)^{2}}+\frac{3 i b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{64 c^{4} d^{3}}+\frac{3 b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{32 c^{4} d^{3}}-\frac{3 b \arctan \left(\frac{c x}{2}\right)}{32 c^{4} d^{3}}+\frac{3 b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{16 c^{4} d^{3}}-\frac{19 i b \ln \left(c^{2} x^{2}+1\right)}{32 c^{4} d^{3}}-\frac{3 i b \ln \left(c x -i\right)^{2}}{4 c^{4} d^{3}}+\frac{19 b \arctan \left(c x \right)}{16 c^{4} d^{3}}+\frac{11 b}{8 c^{4} d^{3} \left(c x -i\right)}+\frac{3 i a}{c^{4} d^{3} \left(c x -i\right)}+\frac{3 i b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{4} d^{3}}+\frac{i b}{8 c^{4} d^{3} \left(c x -i\right)^{2}}"," ",0,"-3*I/c^4*a/d^3*arctan(c*x)+3*I/c^4*b/d^3*arctan(c*x)/(c*x-I)-3/2/c^4*a/d^3*ln(c^2*x^2+1)+I*b*x*arctan(c*x)/c^3/d^3-1/2/c^4*a/d^3/(c*x-I)^2+3/2*I/c^4*b/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))+I*a*x/c^3/d^3-3/c^4*b/d^3*arctan(c*x)*ln(c*x-I)-1/2/c^4*b/d^3*arctan(c*x)/(c*x-I)^2+3/64*I/c^4*b/d^3*ln(c^4*x^4+10*c^2*x^2+9)+3/32/c^4*b/d^3*arctan(1/6*c^3*x^3+7/6*c*x)-3/32/c^4*b/d^3*arctan(1/2*c*x)+3/16/c^4*b/d^3*arctan(1/2*c*x-1/2*I)-19/32*I/c^4*b/d^3*ln(c^2*x^2+1)-3/4*I/c^4*b/d^3*ln(c*x-I)^2+19/16*b*arctan(c*x)/c^4/d^3+11/8/c^4*b/d^3/(c*x-I)+3*I/c^4*a/d^3/(c*x-I)+1/8*I/c^4*b/d^3/(c*x-I)^2+3/2*I/c^4*b/d^3*dilog(-1/2*I*(I+c*x))","A"
60,1,349,156,0.067000," ","int(x^2*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x)","\frac{2 a}{c^{3} d^{3} \left(c x -i\right)}+\frac{i a \ln \left(c^{2} x^{2}+1\right)}{2 c^{3} d^{3}}-\frac{a \arctan \left(c x \right)}{c^{3} d^{3}}-\frac{7 i b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{32 c^{3} d^{3}}+\frac{2 b \arctan \left(c x \right)}{c^{3} d^{3} \left(c x -i\right)}-\frac{7 i b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{16 c^{3} d^{3}}-\frac{7 i b \arctan \left(c x \right)}{16 c^{3} d^{3}}+\frac{7 b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{64 c^{3} d^{3}}-\frac{7 i b}{8 c^{3} d^{3} \left(c x -i\right)}+\frac{i b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{3} d^{3}}+\frac{i b \arctan \left(c x \right)}{2 c^{3} d^{3} \left(c x -i\right)^{2}}+\frac{i a}{2 c^{3} d^{3} \left(c x -i\right)^{2}}+\frac{b}{8 c^{3} d^{3} \left(c x -i\right)^{2}}-\frac{7 b \ln \left(c^{2} x^{2}+1\right)}{32 c^{3} d^{3}}+\frac{7 i b \arctan \left(\frac{c x}{2}\right)}{32 c^{3} d^{3}}+\frac{b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{3} d^{3}}+\frac{b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{3} d^{3}}-\frac{b \ln \left(c x -i\right)^{2}}{4 c^{3} d^{3}}"," ",0,"2/c^3*a/d^3/(c*x-I)+1/2*I/c^3*a/d^3*ln(c^2*x^2+1)-1/c^3*a/d^3*arctan(c*x)-7/32*I/c^3*b/d^3*arctan(1/6*c^3*x^3+7/6*c*x)+2/c^3*b/d^3*arctan(c*x)/(c*x-I)-7/16*I/c^3*b/d^3*arctan(1/2*c*x-1/2*I)-7/16*I/c^3*b/d^3*arctan(c*x)+7/64/c^3*b/d^3*ln(c^4*x^4+10*c^2*x^2+9)-7/8*I/c^3*b/d^3/(c*x-I)+I/c^3*b/d^3*arctan(c*x)*ln(c*x-I)+1/2*I/c^3*b/d^3*arctan(c*x)/(c*x-I)^2+1/2*I/c^3*a/d^3/(c*x-I)^2+1/8/c^3*b/d^3/(c*x-I)^2-7/32/c^3*b/d^3*ln(c^2*x^2+1)+7/32*I/c^3*b/d^3*arctan(1/2*c*x)+1/2/c^3*b/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/2/c^3*b/d^3*dilog(-1/2*I*(I+c*x))-1/4/c^3*b/d^3*ln(c*x-I)^2","B"
61,1,128,76,0.056000," ","int(x*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x)","-\frac{i a}{c^{2} d^{3} \left(c x -i\right)}+\frac{a}{2 c^{2} d^{3} \left(c x -i\right)^{2}}-\frac{i b \arctan \left(c x \right)}{c^{2} d^{3} \left(c x -i\right)}+\frac{b \arctan \left(c x \right)}{2 c^{2} d^{3} \left(c x -i\right)^{2}}-\frac{3 b \arctan \left(c x \right)}{8 c^{2} d^{3}}-\frac{i b}{8 c^{2} d^{3} \left(c x -i\right)^{2}}-\frac{3 b}{8 c^{2} d^{3} \left(c x -i\right)}"," ",0,"-I/c^2*a/d^3/(c*x-I)+1/2/c^2*a/d^3/(c*x-I)^2-I/c^2*b/d^3*arctan(c*x)/(c*x-I)+1/2/c^2*b/d^3*arctan(c*x)/(c*x-I)^2-3/8*b*arctan(c*x)/c^2/d^3-1/8*I/c^2*b/d^3/(c*x-I)^2-3/8/c^2*b/d^3/(c*x-I)","A"
62,1,93,78,0.052000," ","int((a+b*arctan(c*x))/(d+I*c*d*x)^3,x)","\frac{i a}{2 c \,d^{3} \left(i c x +1\right)^{2}}+\frac{i b \arctan \left(c x \right)}{2 c \,d^{3} \left(i c x +1\right)^{2}}-\frac{i b \arctan \left(c x \right)}{8 c \,d^{3}}-\frac{b}{8 c \,d^{3} \left(c x -i\right)^{2}}-\frac{i b}{8 c \,d^{3} \left(c x -i\right)}"," ",0,"1/2*I/c*a/d^3/(1+I*c*x)^2+1/2*I/c*b/d^3/(1+I*c*x)^2*arctan(c*x)-1/8*I*b*arctan(c*x)/c/d^3-1/8/c*b/d^3/(c*x-I)^2-1/8*I/c*b/d^3/(c*x-I)","A"
63,1,327,171,0.073000," ","int((a+b*arctan(c*x))/x/(d+I*c*d*x)^3,x)","\frac{a \ln \left(c x \right)}{d^{3}}-\frac{a}{2 d^{3} \left(c x -i\right)^{2}}-\frac{i a}{d^{3} \left(c x -i\right)}-\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 d^{3}}+\frac{i b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d^{3}}+\frac{b \ln \left(c x \right) \arctan \left(c x \right)}{d^{3}}-\frac{b \arctan \left(c x \right)}{2 d^{3} \left(c x -i\right)^{2}}+\frac{i b}{8 d^{3} \left(c x -i\right)^{2}}-\frac{b \arctan \left(c x \right) \ln \left(c x -i\right)}{d^{3}}-\frac{5 b \arctan \left(c x \right)}{8 d^{3}}-\frac{i b \arctan \left(c x \right)}{d^{3} \left(c x -i\right)}-\frac{5 b}{8 d^{3} \left(c x -i\right)}-\frac{i b \dilog \left(-i c x \right)}{2 d^{3}}+\frac{i b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d^{3}}-\frac{i b \ln \left(c x -i\right)^{2}}{4 d^{3}}-\frac{i b \dilog \left(-i \left(c x +i\right)\right)}{2 d^{3}}-\frac{i b \ln \left(c x \right) \ln \left(-i \left(c x +i\right)\right)}{2 d^{3}}+\frac{i b \ln \left(c x \right) \ln \left(-i \left(-c x +i\right)\right)}{2 d^{3}}-\frac{i a \arctan \left(c x \right)}{d^{3}}-\frac{i b \ln \left(-i c x \right) \ln \left(-i \left(-c x +i\right)\right)}{2 d^{3}}"," ",0,"a/d^3*ln(c*x)-1/2*a/d^3/(c*x-I)^2-I*a/d^3/(c*x-I)-1/2*a/d^3*ln(c^2*x^2+1)+1/2*I*b/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))+b/d^3*ln(c*x)*arctan(c*x)-1/2*b/d^3*arctan(c*x)/(c*x-I)^2+1/8*I*b/d^3/(c*x-I)^2-b/d^3*arctan(c*x)*ln(c*x-I)-5/8*b*arctan(c*x)/d^3-I*b/d^3*arctan(c*x)/(c*x-I)-5/8*b/d^3/(c*x-I)-1/4*I*b/d^3*ln(c*x-I)^2-1/2*I*b/d^3*ln(c*x)*ln(-I*(I+c*x))-1/2*I*b/d^3*dilog(-I*c*x)+1/2*I*b/d^3*dilog(-1/2*I*(I+c*x))+1/2*I*b/d^3*ln(c*x)*ln(-I*(-c*x+I))-I*a/d^3*arctan(c*x)-1/2*I*b/d^3*dilog(-I*(I+c*x))-1/2*I*b/d^3*ln(-I*c*x)*ln(-I*(-c*x+I))","A"
64,1,394,223,0.079000," ","int((a+b*arctan(c*x))/x^2/(d+I*c*d*x)^3,x)","-\frac{a}{d^{3} x}-\frac{3 i c b \arctan \left(c x \right) \ln \left(c x \right)}{d^{3}}+\frac{i c b \arctan \left(c x \right)}{2 d^{3} \left(c x -i\right)^{2}}+\frac{9 i b c \arctan \left(c x \right)}{8 d^{3}}-\frac{3 c a \arctan \left(c x \right)}{d^{3}}-\frac{2 c a}{d^{3} \left(c x -i\right)}-\frac{b \arctan \left(c x \right)}{d^{3} x}+\frac{3 i c b \arctan \left(c x \right) \ln \left(c x -i\right)}{d^{3}}+\frac{9 i c b}{8 d^{3} \left(c x -i\right)}+\frac{3 i c a \ln \left(c^{2} x^{2}+1\right)}{2 d^{3}}-\frac{2 c b \arctan \left(c x \right)}{d^{3} \left(c x -i\right)}+\frac{c b \ln \left(c x \right)}{d^{3}}-\frac{b c \ln \left(c^{2} x^{2}+1\right)}{2 d^{3}}+\frac{i c a}{2 d^{3} \left(c x -i\right)^{2}}-\frac{3 i c a \ln \left(c x \right)}{d^{3}}+\frac{c b}{8 d^{3} \left(c x -i\right)^{2}}-\frac{3 c b \dilog \left(-i \left(c x +i\right)\right)}{2 d^{3}}-\frac{3 c b \ln \left(c x \right) \ln \left(-i \left(c x +i\right)\right)}{2 d^{3}}+\frac{3 c b \ln \left(-i \left(-c x +i\right)\right) \ln \left(c x \right)}{2 d^{3}}-\frac{3 c b \ln \left(-i \left(-c x +i\right)\right) \ln \left(-i c x \right)}{2 d^{3}}-\frac{3 c b \dilog \left(-i c x \right)}{2 d^{3}}+\frac{3 c b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d^{3}}+\frac{3 c b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 d^{3}}-\frac{3 c b \ln \left(c x -i\right)^{2}}{4 d^{3}}"," ",0,"-a/d^3/x-3*I*c*b/d^3*arctan(c*x)*ln(c*x)+1/2*I*c*b/d^3*arctan(c*x)/(c*x-I)^2+9/8*I*b*c*arctan(c*x)/d^3-3*c*a/d^3*arctan(c*x)-2*c*a/d^3/(c*x-I)-b/d^3*arctan(c*x)/x+3*I*c*b/d^3*arctan(c*x)*ln(c*x-I)+9/8*I*c*b/d^3/(c*x-I)+3/2*I*c*a/d^3*ln(c^2*x^2+1)-2*c*b/d^3*arctan(c*x)/(c*x-I)+c*b/d^3*ln(c*x)-1/2*b*c*ln(c^2*x^2+1)/d^3+1/2*I*c*a/d^3/(c*x-I)^2-3*I*c*a/d^3*ln(c*x)+1/8*c*b/d^3/(c*x-I)^2-3/2*c*b/d^3*dilog(-I*(I+c*x))-3/2*c*b/d^3*ln(c*x)*ln(-I*(I+c*x))+3/2*c*b/d^3*ln(-I*(-c*x+I))*ln(c*x)-3/2*c*b/d^3*ln(-I*(-c*x+I))*ln(-I*c*x)-3/2*c*b/d^3*dilog(-I*c*x)+3/2*c*b/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))+3/2*c*b/d^3*dilog(-1/2*I*(I+c*x))-3/4*c*b/d^3*ln(c*x-I)^2","A"
65,1,481,279,0.101000," ","int((a+b*arctan(c*x))/x^3/(d+I*c*d*x)^3,x)","-\frac{a}{2 d^{3} x^{2}}+\frac{13 c^{2} b}{8 d^{3} \left(c x -i\right)}+\frac{c^{2} a}{2 d^{3} \left(c x -i\right)^{2}}+\frac{3 c^{2} a \ln \left(c^{2} x^{2}+1\right)}{d^{3}}-\frac{6 c^{2} a \ln \left(c x \right)}{d^{3}}-\frac{b \arctan \left(c x \right)}{2 d^{3} x^{2}}-\frac{3 i c^{2} b \ln \left(c x \right)}{d^{3}}+\frac{3 i c^{2} a}{d^{3} \left(c x -i\right)}+\frac{3 i c a}{d^{3} x}+\frac{6 c^{2} b \arctan \left(c x \right) \ln \left(c x -i\right)}{d^{3}}+\frac{c^{2} b \arctan \left(c x \right)}{2 d^{3} \left(c x -i\right)^{2}}+\frac{6 i c^{2} a \arctan \left(c x \right)}{d^{3}}-\frac{3 i c^{2} b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{d^{3}}+\frac{3 i c^{2} b \dilog \left(-i \left(c x +i\right)\right)}{d^{3}}+\frac{3 i c^{2} b \dilog \left(-i c x \right)}{d^{3}}-\frac{6 c^{2} b \ln \left(c x \right) \arctan \left(c x \right)}{d^{3}}+\frac{3 i c^{2} b \ln \left(-i c x \right) \ln \left(-i \left(-c x +i\right)\right)}{d^{3}}-\frac{b c}{2 d^{3} x}+\frac{9 b \,c^{2} \arctan \left(c x \right)}{8 d^{3}}+\frac{3 i c^{2} b \ln \left(c x \right) \ln \left(-i \left(c x +i\right)\right)}{d^{3}}-\frac{3 i c^{2} b \ln \left(c x \right) \ln \left(-i \left(-c x +i\right)\right)}{d^{3}}-\frac{3 i c^{2} b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{d^{3}}+\frac{3 i c b \arctan \left(c x \right)}{d^{3} x}+\frac{3 i c^{2} b \arctan \left(c x \right)}{d^{3} \left(c x -i\right)}+\frac{3 i b \,c^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d^{3}}-\frac{i c^{2} b}{8 d^{3} \left(c x -i\right)^{2}}+\frac{3 i c^{2} b \ln \left(c x -i\right)^{2}}{2 d^{3}}"," ",0,"-1/2*a/d^3/x^2+3/2*I*b*c^2*ln(c^2*x^2+1)/d^3+3*c^2*a/d^3*ln(c^2*x^2+1)+13/8*c^2*b/d^3/(c*x-I)-6*c^2*a/d^3*ln(c*x)+1/2*c^2*a/d^3/(c*x-I)^2-1/2*b/d^3*arctan(c*x)/x^2-1/8*I*c^2*b/d^3/(c*x-I)^2-3*I*c^2*b/d^3*dilog(-1/2*I*(I+c*x))+3/2*I*c^2*b/d^3*ln(c*x-I)^2-3*I*c^2*b/d^3*ln(c*x)+3*I*c^2*a/d^3/(c*x-I)+3*I*c*a/d^3/x+3*I*c^2*b/d^3*dilog(-I*(I+c*x))-6*c^2*b/d^3*ln(c*x)*arctan(c*x)+6*c^2*b/d^3*arctan(c*x)*ln(c*x-I)+1/2*c^2*b/d^3*arctan(c*x)/(c*x-I)^2+3*I*c^2*b/d^3*arctan(c*x)/(c*x-I)+3*I*c*b/d^3*arctan(c*x)/x-3*I*c^2*b/d^3*ln(c*x)*ln(-I*(-c*x+I))-3*I*c^2*b/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*b*c/d^3/x+9/8*b*c^2*arctan(c*x)/d^3+3*I*c^2*b/d^3*ln(-I*c*x)*ln(-I*(-c*x+I))+3*I*c^2*b/d^3*ln(c*x)*ln(-I*(I+c*x))+6*I*c^2*a/d^3*arctan(c*x)+3*I*c^2*b/d^3*dilog(-I*c*x)","A"
66,1,93,82,0.054000," ","int((a+b*arctan(c*x))/(1+I*c*x)^4,x)","\frac{i a}{3 c \left(i c x +1\right)^{3}}+\frac{i b \arctan \left(c x \right)}{3 c \left(i c x +1\right)^{3}}-\frac{i b \arctan \left(c x \right)}{24 c}-\frac{b}{24 c \left(c x -i\right)^{2}}+\frac{i b}{18 c \left(c x -i\right)^{3}}-\frac{i b}{24 c \left(c x -i\right)}"," ",0,"1/3*I/c*a/(1+I*c*x)^3+1/3*I/c*b/(1+I*c*x)^3*arctan(c*x)-1/24*I*b*arctan(c*x)/c-1/24/c*b/(c*x-I)^2+1/18*I/c*b/(c*x-I)^3-1/24*I/c*b/(c*x-I)","A"
67,1,148,44,0.060000," ","int(arctan(a*x)/(c*x+I*a*c*x^2),x)","\frac{\arctan \left(a x \right) \ln \left(a x \right)}{c}-\frac{\arctan \left(a x \right) \ln \left(a x -i\right)}{c}+\frac{i \ln \left(a x \right) \ln \left(i a x +1\right)}{2 c}-\frac{i \ln \left(a x \right) \ln \left(-i a x +1\right)}{2 c}+\frac{i \dilog \left(i a x +1\right)}{2 c}-\frac{i \dilog \left(-i a x +1\right)}{2 c}+\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 c}+\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 c}-\frac{i \ln \left(a x -i\right)^{2}}{4 c}"," ",0,"1/c*arctan(a*x)*ln(a*x)-1/c*arctan(a*x)*ln(a*x-I)+1/2*I/c*ln(a*x)*ln(1+I*a*x)-1/2*I/c*ln(a*x)*ln(1-I*a*x)+1/2*I/c*dilog(1+I*a*x)-1/2*I/c*dilog(1-I*a*x)+1/2*I/c*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/2*I/c*dilog(-1/2*I*(I+a*x))-1/4*I/c*ln(a*x-I)^2","B"
68,1,499,248,0.101000," ","int(x^3*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x)","\frac{2 i c d a b \arctan \left(c x \right) x^{5}}{5}+\frac{d \,a^{2} x^{4}}{4}+\frac{d a b \arctan \left(c x \right) x^{4}}{2}-\frac{d \,b^{2} \arctan \left(c x \right) x^{3}}{6 c}-\frac{d a b \arctan \left(c x \right)}{2 c^{4}}-\frac{3 i b^{2} d x}{10 c^{3}}-\frac{d \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{10 c^{4}}-\frac{i d a b \,x^{4}}{10}-\frac{i d \,b^{2} \arctan \left(c x \right) x^{4}}{10}+\frac{d \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{10 c^{4}}+\frac{i b^{2} d \,x^{3}}{30 c}+\frac{3 i b^{2} d \arctan \left(c x \right)}{10 c^{4}}+\frac{d \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{10 c^{4}}-\frac{d \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{10 c^{4}}+\frac{i c d \,a^{2} x^{5}}{5}+\frac{a b d x}{2 c^{3}}+\frac{b^{2} d x \arctan \left(c x \right)}{2 c^{3}}+\frac{b^{2} d \,x^{2}}{12 c^{2}}+\frac{i c d \,b^{2} \arctan \left(c x \right)^{2} x^{5}}{5}-\frac{i d \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{5 c^{4}}-\frac{b^{2} d \ln \left(c^{2} x^{2}+1\right)}{3 c^{4}}+\frac{i d a b \,x^{2}}{5 c^{2}}+\frac{i d \,b^{2} \arctan \left(c x \right) x^{2}}{5 c^{2}}-\frac{i d a b \ln \left(c^{2} x^{2}+1\right)}{5 c^{4}}-\frac{d a b \,x^{3}}{6 c}-\frac{d \,b^{2} \ln \left(c x -i\right)^{2}}{20 c^{4}}+\frac{d \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{10 c^{4}}-\frac{d \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{10 c^{4}}+\frac{d \,b^{2} \ln \left(c x +i\right)^{2}}{20 c^{4}}+\frac{d \,b^{2} \arctan \left(c x \right)^{2} x^{4}}{4}-\frac{d \,b^{2} \arctan \left(c x \right)^{2}}{4 c^{4}}"," ",0,"1/4*d*a^2*x^4+2/5*I*c*d*a*b*arctan(c*x)*x^5+1/5*I/c^2*d*a*b*x^2+1/5*I/c^2*d*b^2*arctan(c*x)*x^2+1/5*I*c*d*b^2*arctan(c*x)^2*x^5-1/5*I/c^4*d*b^2*arctan(c*x)*ln(c^2*x^2+1)+1/10/c^4*d*b^2*ln(c*x-I)*ln(c^2*x^2+1)-1/10/c^4*d*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/2*d*a*b*arctan(c*x)*x^4+1/5*I*c*d*a^2*x^5-1/6/c*d*b^2*arctan(c*x)*x^3-1/10*I*d*b^2*arctan(c*x)*x^4+1/10/c^4*d*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-1/2/c^4*d*a*b*arctan(c*x)+1/30*I*b^2*d*x^3/c+3/10*I*b^2*d*arctan(c*x)/c^4+1/2*a*b*d*x/c^3+1/2*b^2*d*x*arctan(c*x)/c^3-3/10*I*b^2*d*x/c^3+1/12*b^2*d*x^2/c^2-1/3*b^2*d*ln(c^2*x^2+1)/c^4-1/5*I/c^4*d*a*b*ln(c^2*x^2+1)-1/10/c^4*d*b^2*ln(I+c*x)*ln(c^2*x^2+1)-1/6/c*d*a*b*x^3-1/10*I*d*a*b*x^4+1/4*d*b^2*arctan(c*x)^2*x^4+1/10/c^4*d*b^2*dilog(1/2*I*(c*x-I))-1/10/c^4*d*b^2*dilog(-1/2*I*(I+c*x))+1/20/c^4*d*b^2*ln(I+c*x)^2-1/4/c^4*d*b^2*arctan(c*x)^2-1/20/c^4*d*b^2*ln(c*x-I)^2","B"
69,1,467,219,0.108000," ","int(x^2*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x)","\frac{d \,a^{2} x^{3}}{3}+\frac{i c d a b \arctan \left(c x \right) x^{4}}{2}+\frac{i d \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{6 c^{3}}+\frac{i b^{2} d x \arctan \left(c x \right)}{2 c^{2}}-\frac{i d a b \arctan \left(c x \right)}{2 c^{3}}-\frac{i d \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{6 c^{3}}+\frac{i a b d x}{2 c^{2}}+\frac{b^{2} d x}{3 c^{2}}-\frac{b^{2} d \arctan \left(c x \right)}{3 c^{3}}-\frac{i d \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}+\frac{i c d \,a^{2} x^{4}}{4}-\frac{i d a b \,x^{3}}{6}-\frac{i d \,b^{2} \arctan \left(c x \right)^{2}}{4 c^{3}}-\frac{i d \,b^{2} \ln \left(c x -i\right)^{2}}{12 c^{3}}+\frac{i d \,b^{2} \ln \left(c x +i\right)^{2}}{12 c^{3}}+\frac{i b^{2} d \,x^{2}}{12 c}-\frac{i d \,b^{2} \arctan \left(c x \right) x^{3}}{6}-\frac{i b^{2} d \ln \left(c^{2} x^{2}+1\right)}{3 c^{3}}+\frac{i d \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{6 c^{3}}-\frac{i d \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{6 c^{3}}-\frac{d \,b^{2} \arctan \left(c x \right) x^{2}}{3 c}+\frac{d \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{3 c^{3}}+\frac{d a b \ln \left(c^{2} x^{2}+1\right)}{3 c^{3}}+\frac{2 d a b \arctan \left(c x \right) x^{3}}{3}-\frac{d a b \,x^{2}}{3 c}+\frac{d \,b^{2} \arctan \left(c x \right)^{2} x^{3}}{3}+\frac{i c d \,b^{2} \arctan \left(c x \right)^{2} x^{4}}{4}+\frac{i d \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}"," ",0,"1/3*d*a^2*x^3+1/6*I/c^3*d*b^2*ln(c*x-I)*ln(c^2*x^2+1)-1/3*I*b^2*d*ln(c^2*x^2+1)/c^3-1/6*I/c^3*d*b^2*ln(I+c*x)*ln(c^2*x^2+1)+1/4*I*c*d*b^2*arctan(c*x)^2*x^4+1/6*I/c^3*d*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+1/2*I*a*b*d*x/c^2+1/3*b^2*d*x/c^2-1/3*b^2*d*arctan(c*x)/c^3-1/6*I*d*b^2*arctan(c*x)*x^3+1/4*I*c*d*a^2*x^4-1/3/c*d*b^2*arctan(c*x)*x^2+1/3/c^3*d*b^2*arctan(c*x)*ln(c^2*x^2+1)+1/3/c^3*d*a*b*ln(c^2*x^2+1)+2/3*d*a*b*arctan(c*x)*x^3-1/3/c*d*a*b*x^2-1/6*I*d*a*b*x^3-1/4*I/c^3*d*b^2*arctan(c*x)^2-1/12*I/c^3*d*b^2*ln(c*x-I)^2+1/6*I/c^3*d*b^2*dilog(1/2*I*(c*x-I))+1/12*I/c^3*d*b^2*ln(I+c*x)^2+1/3*d*b^2*arctan(c*x)^2*x^3+1/12*I*b^2*d*x^2/c+1/2*I*b^2*d*x*arctan(c*x)/c^2-1/6*I/c^3*d*b^2*dilog(-1/2*I*(I+c*x))-1/2*I/c^3*d*a*b*arctan(c*x)-1/6*I/c^3*d*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/2*I*c*d*a*b*arctan(c*x)*x^4","B"
70,1,416,186,0.107000," ","int(x*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x)","-\frac{a b d x}{c}-\frac{b^{2} d x \arctan \left(c x \right)}{c}+\frac{b^{2} d \ln \left(c^{2} x^{2}+1\right)}{2 c^{2}}+\frac{i d \,b^{2} \ln \left(c^{2} x^{2}+1\right) \arctan \left(c x \right)}{3 c^{2}}+\frac{i d a b \ln \left(c^{2} x^{2}+1\right)}{3 c^{2}}+\frac{i c d \,b^{2} \arctan \left(c x \right)^{2} x^{3}}{3}-\frac{d \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{6 c^{2}}+\frac{d \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{6 c^{2}}-\frac{d \,b^{2} \ln \left(c x +i\right)^{2}}{12 c^{2}}+\frac{d \,b^{2} \ln \left(c x -i\right)^{2}}{12 c^{2}}-\frac{i d \,b^{2} \arctan \left(c x \right) x^{2}}{3}+\frac{i b^{2} d x}{3 c}-\frac{i b^{2} d \arctan \left(c x \right)}{3 c^{2}}-\frac{i d a b \,x^{2}}{3}+\frac{d \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{6 c^{2}}-\frac{d \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{6 c^{2}}-\frac{d \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{6 c^{2}}+\frac{d \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{6 c^{2}}+\frac{i c d \,a^{2} x^{3}}{3}+\frac{d a b \arctan \left(c x \right)}{c^{2}}+d a b \arctan \left(c x \right) x^{2}+\frac{d \,b^{2} \arctan \left(c x \right)^{2} x^{2}}{2}+\frac{d \,b^{2} \arctan \left(c x \right)^{2}}{2 c^{2}}+\frac{d \,a^{2} x^{2}}{2}+\frac{2 i c d a b \arctan \left(c x \right) x^{3}}{3}"," ",0,"-a*b*d*x/c+1/3*I*b^2*d*x/c-b^2*d*x*arctan(c*x)/c+1/2*b^2*d*ln(c^2*x^2+1)/c^2-1/3*I*b^2*d*arctan(c*x)/c^2+1/3*I*c*d*b^2*arctan(c*x)^2*x^3+1/3*I/c^2*d*b^2*ln(c^2*x^2+1)*arctan(c*x)+1/3*I/c^2*d*a*b*ln(c^2*x^2+1)-1/3*I*d*a*b*x^2+1/6/c^2*d*b^2*ln(I+c*x)*ln(c^2*x^2+1)-1/6/c^2*d*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+1/c^2*d*a*b*arctan(c*x)+d*a*b*arctan(c*x)*x^2-1/6/c^2*d*b^2*ln(c*x-I)*ln(c^2*x^2+1)+1/6/c^2*d*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/2*d*b^2*arctan(c*x)^2*x^2-1/6/c^2*d*b^2*dilog(1/2*I*(c*x-I))-1/12/c^2*d*b^2*ln(I+c*x)^2+1/2/c^2*d*b^2*arctan(c*x)^2+1/12/c^2*d*b^2*ln(c*x-I)^2+1/6/c^2*d*b^2*dilog(-1/2*I*(I+c*x))+1/3*I*c*d*a^2*x^3+1/2*d*a^2*x^2-1/3*I*d*b^2*arctan(c*x)*x^2+2/3*I*c*d*a*b*arctan(c*x)*x^3","B"
71,1,367,118,0.109000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))^2,x)","a^{2} d x -\frac{i d \,b^{2} \ln \left(c x +i\right)^{2}}{4 c}+d \,b^{2} \arctan \left(c x \right)^{2} x +\frac{i d \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c}+\frac{i c d \,a^{2} x^{2}}{2}-\frac{i d \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{2 c}-\frac{d \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{c}+\frac{i d \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{2 c}-i a b d x -\frac{i d \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2 c}+\frac{i d \,b^{2} \arctan \left(c x \right)^{2}}{2 c}-i b^{2} d x \arctan \left(c x \right)+\frac{i d \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c}+\frac{i b^{2} d \ln \left(c x -i\right)^{2}}{4 c}-\frac{i d \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{2 c}+\frac{i b^{2} d \ln \left(c^{2} x^{2}+1\right)}{2 c}+\frac{i c d \,b^{2} \arctan \left(c x \right)^{2} x^{2}}{2}+i c d a b \arctan \left(c x \right) x^{2}+2 d a b \arctan \left(c x \right) x +\frac{i d a b \arctan \left(c x \right)}{c}-\frac{d a b \ln \left(c^{2} x^{2}+1\right)}{c}"," ",0,"a^2*d*x-1/4*I/c*d*b^2*ln(I+c*x)^2+d*b^2*arctan(c*x)^2*x+1/2*I/c*d*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/2*I/c*d*b^2*dilog(-1/2*I*(I+c*x))+1/2*I*c*d*a^2*x^2-1/c*d*b^2*arctan(c*x)*ln(c^2*x^2+1)-1/2*I/c*d*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+1/2*I/c*d*b^2*ln(I+c*x)*ln(c^2*x^2+1)-I*a*b*d*x+1/2*I/c*d*b^2*arctan(c*x)^2-I*b^2*d*x*arctan(c*x)+1/4*I/c*d*b^2*ln(c*x-I)^2-1/2*I/c*d*b^2*ln(c*x-I)*ln(c^2*x^2+1)+1/2*I*b^2*d*ln(c^2*x^2+1)/c+1/2*I*c*d*b^2*arctan(c*x)^2*x^2+I*c*d*a*b*arctan(c*x)*x^2+I/c*d*a*b*arctan(c*x)+2*d*a*b*arctan(c*x)*x-1/2*I/c*d*b^2*dilog(1/2*I*(c*x-I))-1/c*d*a*b*ln(c^2*x^2+1)","B"
72,1,7034,201,0.794000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))^2/x,x)","\text{output too large to display}"," ",0,"result too large to display","C"
73,1,5963,212,2.071000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))^2/x^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
74,1,487,149,0.128000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))^2/x^3,x)","2 i c^{2} d a b \ln \left(c x \right)-i c^{2} d a b \ln \left(c^{2} x^{2}+1\right)-\frac{i c d \,b^{2} \arctan \left(c x \right)^{2}}{x}-i c^{2} d \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)+2 i c^{2} d \,b^{2} \arctan \left(c x \right) \ln \left(c x \right)-\frac{b^{2} c^{2} d \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{d \,a^{2}}{2 x^{2}}-c^{2} d \,b^{2} \ln \left(c x \right) \ln \left(i c x +1\right)+c^{2} d \,b^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)-\frac{i c d \,a^{2}}{x}-\frac{c^{2} d \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2}-\frac{c^{2} d \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{2}+\frac{c^{2} d \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{2}+\frac{c^{2} d \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{2}-c^{2} d a b \arctan \left(c x \right)-\frac{c d \,b^{2} \arctan \left(c x \right)}{x}-\frac{c d a b}{x}-\frac{d a b \arctan \left(c x \right)}{x^{2}}-\frac{2 i c d a b \arctan \left(c x \right)}{x}+\frac{c^{2} d \,b^{2} \ln \left(c x +i\right)^{2}}{4}-\frac{c^{2} d \,b^{2} \ln \left(c x -i\right)^{2}}{4}-c^{2} d \,b^{2} \dilog \left(i c x +1\right)+c^{2} d \,b^{2} \dilog \left(-i c x +1\right)-\frac{c^{2} d \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2}+\frac{c^{2} d \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2}-\frac{c^{2} d \,b^{2} \arctan \left(c x \right)^{2}}{2}+c^{2} d \,b^{2} \ln \left(c x \right)-\frac{d \,b^{2} \arctan \left(c x \right)^{2}}{2 x^{2}}"," ",0,"-I*c^2*d*a*b*ln(c^2*x^2+1)-I*c*d*b^2*arctan(c*x)^2/x-I*c^2*d*b^2*arctan(c*x)*ln(c^2*x^2+1)+2*I*c^2*d*b^2*arctan(c*x)*ln(c*x)+2*I*c^2*d*a*b*ln(c*x)-2*I*c*d*a*b*arctan(c*x)/x-1/2*b^2*c^2*d*ln(c^2*x^2+1)-1/2*d*a^2/x^2-c^2*d*b^2*ln(c*x)*ln(1+I*c*x)+c^2*d*b^2*ln(c*x)*ln(1-I*c*x)-c^2*d*a*b*arctan(c*x)-c*d*b^2*arctan(c*x)/x-I*c*d*a^2/x-c*d*a*b/x-d*a*b*arctan(c*x)/x^2-1/2*c^2*d*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*c^2*d*b^2*ln(I+c*x)*ln(c^2*x^2+1)+1/2*c^2*d*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+1/2*c^2*d*b^2*ln(c*x-I)*ln(c^2*x^2+1)-1/2*c^2*d*b^2*arctan(c*x)^2-c^2*d*b^2*dilog(1+I*c*x)+c^2*d*b^2*dilog(1-I*c*x)-1/2*c^2*d*b^2*dilog(-1/2*I*(I+c*x))+1/4*c^2*d*b^2*ln(I+c*x)^2+1/2*c^2*d*b^2*dilog(1/2*I*(c*x-I))+c^2*d*b^2*ln(c*x)-1/4*c^2*d*b^2*ln(c*x-I)^2-1/2*d*b^2*arctan(c*x)^2/x^2","B"
75,1,556,198,0.125000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))^2/x^4,x)","-\frac{i c^{2} d \,b^{2} \arctan \left(c x \right)}{x}-\frac{d \,a^{2}}{3 x^{3}}-\frac{i c d a b \arctan \left(c x \right)}{x^{2}}-\frac{c d a b}{3 x^{2}}-\frac{2 d a b \arctan \left(c x \right)}{3 x^{3}}+\frac{c^{3} d a b \ln \left(c^{2} x^{2}+1\right)}{3}-\frac{c d \,b^{2} \arctan \left(c x \right)}{3 x^{2}}-\frac{2 c^{3} d a b \ln \left(c x \right)}{3}-\frac{2 c^{3} d \,b^{2} \ln \left(c x \right) \arctan \left(c x \right)}{3}+\frac{c^{3} d \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{3}+i c^{3} d \,b^{2} \ln \left(c x \right)+\frac{i c^{3} d \,b^{2} \ln \left(c x +i\right)^{2}}{12}-\frac{i c d \,a^{2}}{2 x^{2}}-\frac{i c^{3} d \,b^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i c^{3} d \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{6}-\frac{i c^{3} d \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{6}-\frac{i c^{3} d \,b^{2} \dilog \left(i c x +1\right)}{3}+\frac{i c^{3} d \,b^{2} \dilog \left(-i c x +1\right)}{3}-\frac{i b^{2} c^{3} d \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{i c^{3} d \,b^{2} \ln \left(c x -i\right)^{2}}{12}-\frac{b^{2} c^{2} d}{3 x}-\frac{b^{2} c^{3} d \arctan \left(c x \right)}{3}-\frac{i c^{3} d \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{6}-\frac{i c d \,b^{2} \arctan \left(c x \right)^{2}}{2 x^{2}}-i c^{3} d a b \arctan \left(c x \right)+\frac{i c^{3} d \,b^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)}{3}-\frac{i c^{3} d \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{6}-\frac{d \,b^{2} \arctan \left(c x \right)^{2}}{3 x^{3}}-\frac{i c^{2} d a b}{x}+\frac{i c^{3} d \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{6}+\frac{i c^{3} d \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{6}-\frac{i c^{3} d \,b^{2} \ln \left(c x \right) \ln \left(i c x +1\right)}{3}"," ",0,"-1/3*d*a^2/x^3-I*c*d*a*b*arctan(c*x)/x^2-1/3*c*d*a*b/x^2-2/3*d*a*b*arctan(c*x)/x^3+1/3*c^3*d*a*b*ln(c^2*x^2+1)-1/3*c*d*b^2*arctan(c*x)/x^2-2/3*c^3*d*a*b*ln(c*x)-2/3*c^3*d*b^2*ln(c*x)*arctan(c*x)+1/3*c^3*d*b^2*arctan(c*x)*ln(c^2*x^2+1)+I*c^3*d*b^2*ln(c*x)+1/6*I*c^3*d*b^2*dilog(1/2*I*(c*x-I))-1/6*I*c^3*d*b^2*dilog(-1/2*I*(I+c*x))-1/3*I*c^3*d*b^2*dilog(1+I*c*x)+1/12*I*c^3*d*b^2*ln(I+c*x)^2-1/2*I*c*d*a^2/x^2-1/2*I*c^3*d*b^2*arctan(c*x)^2+1/3*I*c^3*d*b^2*dilog(1-I*c*x)-1/3*b^2*c^2*d/x-1/2*I*b^2*c^3*d*ln(c^2*x^2+1)-1/3*b^2*c^3*d*arctan(c*x)-1/3*d*b^2*arctan(c*x)^2/x^3-I*c^2*d*a*b/x+1/6*I*c^3*d*b^2*ln(c*x-I)*ln(c^2*x^2+1)+1/6*I*c^3*d*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-I*c^3*d*a*b*arctan(c*x)+1/3*I*c^3*d*b^2*ln(c*x)*ln(1-I*c*x)-1/6*I*c^3*d*b^2*ln(I+c*x)*ln(c^2*x^2+1)-1/6*I*c^3*d*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*I*c*d*b^2*arctan(c*x)^2/x^2-I*c^2*d*b^2*arctan(c*x)/x-1/3*I*c^3*d*b^2*ln(c*x)*ln(1+I*c*x)-1/12*I*c^3*d*b^2*ln(c*x-I)^2","B"
76,1,650,328,0.106000," ","int(x^3*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x)","\frac{d^{2} a^{2} x^{4}}{4}+\frac{4 i c \,d^{2} a b \arctan \left(c x \right) x^{5}}{5}-\frac{c^{2} d^{2} a b \arctan \left(c x \right) x^{6}}{3}+\frac{2 i d^{2} b^{2} \arctan \left(c x \right) x^{2}}{5 c^{2}}+\frac{2 i d^{2} a b \,x^{2}}{5 c^{2}}-\frac{2 i d^{2} a b \ln \left(c^{2} x^{2}+1\right)}{5 c^{4}}+\frac{5 a b \,d^{2} x}{6 c^{3}}+\frac{5 b^{2} d^{2} x \arctan \left(c x \right)}{6 c^{3}}+\frac{31 b^{2} d^{2} x^{2}}{180 c^{2}}-\frac{2 i d^{2} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{5 c^{4}}-\frac{53 b^{2} d^{2} \ln \left(c^{2} x^{2}+1\right)}{90 c^{4}}+\frac{i b^{2} d^{2} x^{3}}{15 c}-\frac{i d^{2} a b \,x^{4}}{5}+\frac{d^{2} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{5 c^{4}}-\frac{d^{2} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{5 c^{4}}-\frac{d^{2} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{5 c^{4}}+\frac{d^{2} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{5 c^{4}}-\frac{i d^{2} b^{2} \arctan \left(c x \right) x^{4}}{5}+\frac{2 i c \,d^{2} a^{2} x^{5}}{5}+\frac{3 i b^{2} d^{2} \arctan \left(c x \right)}{5 c^{4}}-\frac{3 i b^{2} d^{2} x}{5 c^{3}}+\frac{d^{2} a b \arctan \left(c x \right) x^{4}}{2}-\frac{5 d^{2} a b \arctan \left(c x \right)}{6 c^{4}}+\frac{c \,d^{2} b^{2} \arctan \left(c x \right) x^{5}}{15}-\frac{5 d^{2} b^{2} \arctan \left(c x \right) x^{3}}{18 c}-\frac{c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} x^{6}}{6}+\frac{c \,d^{2} a b \,x^{5}}{15}-\frac{5 d^{2} a b \,x^{3}}{18 c}+\frac{d^{2} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{5 c^{4}}-\frac{d^{2} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{5 c^{4}}+\frac{d^{2} b^{2} \ln \left(c x +i\right)^{2}}{10 c^{4}}-\frac{d^{2} b^{2} \ln \left(c x -i\right)^{2}}{10 c^{4}}+\frac{d^{2} b^{2} \arctan \left(c x \right)^{2} x^{4}}{4}-\frac{5 d^{2} b^{2} \arctan \left(c x \right)^{2}}{12 c^{4}}-\frac{c^{2} d^{2} a^{2} x^{6}}{6}-\frac{b^{2} d^{2} x^{4}}{60}+\frac{2 i c \,d^{2} b^{2} \arctan \left(c x \right)^{2} x^{5}}{5}"," ",0,"1/4*d^2*a^2*x^4+4/5*I*c*d^2*a*b*arctan(c*x)*x^5-2/5*I/c^4*d^2*a*b*ln(c^2*x^2+1)+2/5*I/c^2*d^2*a*b*x^2+2/5*I/c^2*d^2*b^2*arctan(c*x)*x^2+2/5*I*c*d^2*b^2*arctan(c*x)^2*x^5-1/3*c^2*d^2*a*b*arctan(c*x)*x^6-2/5*I/c^4*d^2*b^2*arctan(c*x)*ln(c^2*x^2+1)+3/5*I*b^2*d^2*arctan(c*x)/c^4+5/6*a*b*d^2*x/c^3+5/6*b^2*d^2*x*arctan(c*x)/c^3+31/180*b^2*d^2*x^2/c^2-3/5*I*b^2*d^2*x/c^3+1/15*I*b^2*d^2*x^3/c-53/90*b^2*d^2*ln(c^2*x^2+1)/c^4-1/5*I*d^2*a*b*x^4+1/2*d^2*a*b*arctan(c*x)*x^4+1/5/c^4*d^2*b^2*ln(c*x-I)*ln(c^2*x^2+1)-5/6/c^4*d^2*a*b*arctan(c*x)+1/15*c*d^2*b^2*arctan(c*x)*x^5-5/18/c*d^2*b^2*arctan(c*x)*x^3-1/6*c^2*d^2*b^2*arctan(c*x)^2*x^6-1/5/c^4*d^2*b^2*ln(I+c*x)*ln(c^2*x^2+1)-1/5/c^4*d^2*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/5/c^4*d^2*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-1/5*I*d^2*b^2*arctan(c*x)*x^4+2/5*I*c*d^2*a^2*x^5+1/15*c*d^2*a*b*x^5-5/18/c*d^2*a*b*x^3+1/4*d^2*b^2*arctan(c*x)^2*x^4+1/10/c^4*d^2*b^2*ln(I+c*x)^2-1/10/c^4*d^2*b^2*ln(c*x-I)^2+1/5/c^4*d^2*b^2*dilog(1/2*I*(c*x-I))-5/12/c^4*d^2*b^2*arctan(c*x)^2-1/5/c^4*d^2*b^2*dilog(-1/2*I*(I+c*x))-1/6*c^2*d^2*a^2*x^6-1/60*b^2*d^2*x^4","A"
77,1,612,295,0.108000," ","int(x^2*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x)","\frac{d^{2} a^{2} x^{3}}{3}+\frac{i b^{2} d^{2} x \arctan \left(c x \right)}{c^{2}}+\frac{19 b^{2} d^{2} x}{30 c^{2}}+\frac{i c \,d^{2} b^{2} \arctan \left(c x \right)^{2} x^{4}}{2}+\frac{4 i d^{2} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{15 c^{3}}-\frac{i d^{2} a b \arctan \left(c x \right)}{c^{3}}+\frac{i a b \,d^{2} x}{c^{2}}-\frac{4 i d^{2} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{15 c^{3}}-\frac{4 i d^{2} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{15 c^{3}}+\frac{4 i d^{2} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{15 c^{3}}+i c \,d^{2} a b \arctan \left(c x \right) x^{4}-\frac{2 i d^{2} b^{2} \ln \left(c x -i\right)^{2}}{15 c^{3}}-\frac{i d^{2} a b \,x^{3}}{3}-\frac{i d^{2} b^{2} \arctan \left(c x \right)^{2}}{2 c^{3}}+\frac{2 i d^{2} b^{2} \ln \left(c x +i\right)^{2}}{15 c^{3}}-\frac{4 i d^{2} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{15 c^{3}}-\frac{i d^{2} b^{2} \arctan \left(c x \right) x^{3}}{3}+\frac{i c \,d^{2} a^{2} x^{4}}{2}-\frac{2 i b^{2} d^{2} \ln \left(c^{2} x^{2}+1\right)}{3 c^{3}}+\frac{4 i d^{2} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{15 c^{3}}+\frac{i b^{2} d^{2} x^{2}}{6 c}+\frac{8 d^{2} a b \ln \left(c^{2} x^{2}+1\right)}{15 c^{3}}-\frac{8 d^{2} a b \,x^{2}}{15 c}+\frac{c \,d^{2} a b \,x^{4}}{10}+\frac{2 d^{2} a b \arctan \left(c x \right) x^{3}}{3}+\frac{8 d^{2} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{15 c^{3}}-\frac{8 d^{2} b^{2} \arctan \left(c x \right) x^{2}}{15 c}-\frac{c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} x^{5}}{5}+\frac{c \,d^{2} b^{2} \arctan \left(c x \right) x^{4}}{10}-\frac{c^{2} d^{2} a^{2} x^{5}}{5}-\frac{b^{2} d^{2} x^{3}}{30}-\frac{19 b^{2} d^{2} \arctan \left(c x \right)}{30 c^{3}}+\frac{d^{2} b^{2} \arctan \left(c x \right)^{2} x^{3}}{3}-\frac{2 c^{2} d^{2} a b \arctan \left(c x \right) x^{5}}{5}"," ",0,"1/3*d^2*a^2*x^3-4/15*I/c^3*d^2*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-4/15*I/c^3*d^2*b^2*ln(I+c*x)*ln(c^2*x^2+1)+4/15*I/c^3*d^2*b^2*ln(c*x-I)*ln(c^2*x^2+1)+1/2*I*c*d^2*b^2*arctan(c*x)^2*x^4+4/15*I/c^3*d^2*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+1/6*I*b^2*d^2*x^2/c+19/30*b^2*d^2*x/c^2-I/c^3*d^2*a*b*arctan(c*x)+I*a*b*d^2*x/c^2+I*b^2*d^2*x*arctan(c*x)/c^2-2/3*I*b^2*d^2*ln(c^2*x^2+1)/c^3+I*c*d^2*a*b*arctan(c*x)*x^4+8/15/c^3*d^2*a*b*ln(c^2*x^2+1)-8/15/c*d^2*a*b*x^2+4/15*I/c^3*d^2*b^2*dilog(1/2*I*(c*x-I))-1/3*I*d^2*b^2*arctan(c*x)*x^3+1/2*I*c*d^2*a^2*x^4+1/10*c*d^2*a*b*x^4+2/3*d^2*a*b*arctan(c*x)*x^3+8/15/c^3*d^2*b^2*arctan(c*x)*ln(c^2*x^2+1)-8/15/c*d^2*b^2*arctan(c*x)*x^2-1/5*c^2*d^2*b^2*arctan(c*x)^2*x^5+1/10*c*d^2*b^2*arctan(c*x)*x^4-1/2*I/c^3*d^2*b^2*arctan(c*x)^2-4/15*I/c^3*d^2*b^2*dilog(-1/2*I*(I+c*x))+2/15*I/c^3*d^2*b^2*ln(I+c*x)^2-2/15*I/c^3*d^2*b^2*ln(c*x-I)^2-1/5*c^2*d^2*a^2*x^5-1/30*b^2*d^2*x^3-1/3*I*d^2*a*b*x^3-19/30*b^2*d^2*arctan(c*x)/c^3+1/3*d^2*b^2*arctan(c*x)^2*x^3-2/5*c^2*d^2*a*b*arctan(c*x)*x^5","B"
78,1,556,258,0.106000," ","int(x*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x)","\frac{d^{2} b^{2} \arctan \left(c x \right)^{2} x^{2}}{2}-\frac{c^{2} d^{2} a^{2} x^{4}}{4}+\frac{3 d^{2} b^{2} \arctan \left(c x \right)^{2}}{4 c^{2}}+\frac{2 i d^{2} a b \ln \left(c^{2} x^{2}+1\right)}{3 c^{2}}+\frac{2 i c \,d^{2} b^{2} \arctan \left(c x \right)^{2} x^{3}}{3}+\frac{2 i d^{2} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{3 c^{2}}-\frac{3 a b \,d^{2} x}{2 c}-\frac{3 b^{2} d^{2} x \arctan \left(c x \right)}{2 c}+\frac{5 b^{2} d^{2} \ln \left(c^{2} x^{2}+1\right)}{6 c^{2}}-\frac{c^{2} d^{2} a b \arctan \left(c x \right) x^{4}}{2}-\frac{d^{2} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{3 c^{2}}-\frac{d^{2} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{3 c^{2}}-\frac{2 i d^{2} b^{2} \arctan \left(c x \right) x^{2}}{3}+\frac{2 i c \,d^{2} a^{2} x^{3}}{3}-\frac{2 i b^{2} d^{2} \arctan \left(c x \right)}{3 c^{2}}+\frac{2 i b^{2} d^{2} x}{3 c}-\frac{2 i d^{2} a b \,x^{2}}{3}+\frac{d^{2} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{3 c^{2}}+\frac{d^{2} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{3 c^{2}}+\frac{c \,d^{2} a b \,x^{3}}{6}-\frac{c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} x^{4}}{4}+d^{2} a b \arctan \left(c x \right) x^{2}+\frac{3 d^{2} a b \arctan \left(c x \right)}{2 c^{2}}+\frac{c \,d^{2} b^{2} \arctan \left(c x \right) x^{3}}{6}-\frac{d^{2} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{3 c^{2}}+\frac{d^{2} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{3 c^{2}}+\frac{d^{2} b^{2} \ln \left(c x -i\right)^{2}}{6 c^{2}}-\frac{d^{2} b^{2} \ln \left(c x +i\right)^{2}}{6 c^{2}}-\frac{b^{2} d^{2} x^{2}}{12}+\frac{d^{2} a^{2} x^{2}}{2}+\frac{4 i c \,d^{2} a b \arctan \left(c x \right) x^{3}}{3}"," ",0,"1/6/c^2*d^2*b^2*ln(c*x-I)^2+1/2*d^2*b^2*arctan(c*x)^2*x^2-1/4*c^2*d^2*a^2*x^4-1/3/c^2*d^2*b^2*dilog(1/2*I*(c*x-I))+1/3/c^2*d^2*b^2*dilog(-1/2*I*(I+c*x))+3/4/c^2*d^2*b^2*arctan(c*x)^2-1/6/c^2*d^2*b^2*ln(I+c*x)^2-3/2*a*b*d^2*x/c-3/2*b^2*d^2*x*arctan(c*x)/c-2/3*I*b^2*d^2*arctan(c*x)/c^2+2/3*I*b^2*d^2*x/c+5/6*b^2*d^2*ln(c^2*x^2+1)/c^2-1/2*c^2*d^2*a*b*arctan(c*x)*x^4+2/3*I*c*d^2*b^2*arctan(c*x)^2*x^3+2/3*I/c^2*d^2*b^2*arctan(c*x)*ln(c^2*x^2+1)+2/3*I/c^2*d^2*a*b*ln(c^2*x^2+1)+1/6*c*d^2*a*b*x^3-2/3*I*d^2*a*b*x^2-1/4*c^2*d^2*b^2*arctan(c*x)^2*x^4+d^2*a*b*arctan(c*x)*x^2+1/3/c^2*d^2*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/3/c^2*d^2*b^2*ln(I+c*x)*ln(c^2*x^2+1)+3/2/c^2*d^2*a*b*arctan(c*x)+1/6*c*d^2*b^2*arctan(c*x)*x^3-1/3/c^2*d^2*b^2*ln(c*x-I)*ln(c^2*x^2+1)-1/3/c^2*d^2*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-2/3*I*d^2*b^2*arctan(c*x)*x^2+2/3*I*c*d^2*a^2*x^3-1/12*b^2*d^2*x^2+1/2*d^2*a^2*x^2+4/3*I*c*d^2*a*b*arctan(c*x)*x^3","B"
79,1,523,172,0.106000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x)","-\frac{i d^{2} a^{2}}{3 c}-\frac{c^{2} d^{2} a^{2} x^{3}}{3}+a^{2} x \,d^{2}+\frac{i b^{2} \ln \left(c x -i\right)^{2} d^{2}}{3 c}-\frac{2 i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d^{2}}{3 c}+\frac{2 i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d^{2}}{3 c}-\frac{4 b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d^{2}}{3 c}+2 a b \arctan \left(c x \right) x \,d^{2}-\frac{4 a b \ln \left(c^{2} x^{2}+1\right) d^{2}}{3 c}-\frac{i b^{2} \ln \left(c x +i\right)^{2} d^{2}}{3 c}+b^{2} \arctan \left(c x \right)^{2} x \,d^{2}+i c \,d^{2} b^{2} \arctan \left(c x \right)^{2} x^{2}+\frac{2 i d^{2} a b \arctan \left(c x \right)}{c}-\frac{2 i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d^{2}}{3 c}+\frac{2 i b^{2} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right) d^{2}}{3 c}+\frac{2 i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) d^{2}}{3 c}-\frac{2 i b^{2} \ln \left(\frac{i \left(c x -i\right)}{2}\right) \ln \left(c x +i\right) d^{2}}{3 c}+2 i c \,d^{2} a b \arctan \left(c x \right) x^{2}+\frac{b^{2} d^{2} \arctan \left(c x \right)}{3 c}-\frac{2 c^{2} d^{2} a b \arctan \left(c x \right) x^{3}}{3}+\frac{i d^{2} b^{2} \arctan \left(c x \right)^{2}}{c}+i c \,x^{2} a^{2} d^{2}-2 i b^{2} d^{2} x \arctan \left(c x \right)+\frac{i b^{2} d^{2} \ln \left(c^{2} x^{2}+1\right)}{c}-2 i a b \,d^{2} x +\frac{c \,d^{2} a b \,x^{2}}{3}+\frac{c \,d^{2} b^{2} \arctan \left(c x \right) x^{2}}{3}-\frac{c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} x^{3}}{3}-\frac{b^{2} d^{2} x}{3}"," ",0,"-1/3*c^2*d^2*a^2*x^3-1/3*I/c*d^2*a^2+a^2*x*d^2-4/3/c*b^2*arctan(c*x)*ln(c^2*x^2+1)*d^2+2*a*b*arctan(c*x)*x*d^2-4/3/c*a*b*ln(c^2*x^2+1)*d^2+b^2*arctan(c*x)^2*x*d^2-2*I*a*b*d^2*x-2*I*b^2*d^2*x*arctan(c*x)+I*b^2*d^2*ln(c^2*x^2+1)/c+2*I*c*d^2*a*b*arctan(c*x)*x^2+1/3*b^2*d^2*arctan(c*x)/c-2/3*c^2*d^2*a*b*arctan(c*x)*x^3+2/3*I/c*d^2*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+I*c*d^2*b^2*arctan(c*x)^2*x^2+2/3*I/c*d^2*b^2*ln(I+c*x)*ln(c^2*x^2+1)-2/3*I/c*d^2*b^2*ln(c*x-I)*ln(c^2*x^2+1)-2/3*I/c*d^2*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+2*I/c*d^2*a*b*arctan(c*x)+2/3*I/c*d^2*b^2*dilog(-1/2*I*(I+c*x))+1/3*c*d^2*a*b*x^2+1/3*I/c*d^2*b^2*ln(c*x-I)^2+I/c*d^2*b^2*arctan(c*x)^2+I*c*x^2*a^2*d^2+1/3*c*d^2*b^2*arctan(c*x)*x^2-1/3*c^2*d^2*b^2*arctan(c*x)^2*x^3-2/3*I/c*d^2*b^2*dilog(1/2*I*(c*x-I))-1/3*I/c*d^2*b^2*ln(I+c*x)^2-1/3*b^2*d^2*x","B"
80,1,1542,279,3.661000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x,x)","d^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)+a b c \,d^{2} x +b^{2} c \,d^{2} x \arctan \left(c x \right)+d^{2} a^{2} \ln \left(c x \right)+\frac{3 d^{2} b^{2} \arctan \left(c x \right)^{2}}{2}-i d^{2} a b \dilog \left(-i c x +1\right)-2 i d^{2} b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+4 i d^{2} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)-2 i d^{2} a b \ln \left(c^{2} x^{2}+1\right)+2 i d^{2} a^{2} c x +4 i d^{2} b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{i d^{2} b^{2} \pi  \arctan \left(c x \right)^{2}}{2}+i d^{2} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)-2 i d^{2} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+i d^{2} a b \dilog \left(i c x +1\right)-\frac{d^{2} a^{2} c^{2} x^{2}}{2}-d^{2} a b \arctan \left(c x \right)+d^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+d^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-d^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)-i d^{2} b^{2} \arctan \left(c x \right)+\frac{i d^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+i d^{2} a b \ln \left(c x \right) \ln \left(i c x +1\right)-i d^{2} a b \ln \left(c x \right) \ln \left(-i c x +1\right)+2 d^{2} a b \arctan \left(c x \right) \ln \left(c x \right)-\frac{d^{2} b^{2} \arctan \left(c x \right)^{2} c^{2} x^{2}}{2}-\frac{d^{2} b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}+4 d^{2} b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)+4 d^{2} b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)+2 d^{2} b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+2 d^{2} b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+d^{2} b^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)-d^{2} a b \arctan \left(c x \right) c^{2} x^{2}+2 i d^{2} b^{2} \arctan \left(c x \right)^{2} c x -\frac{i d^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i d^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{i d^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}+4 i d^{2} a b \arctan \left(c x \right) c x -\frac{i d^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{i d^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{i d^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i d^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}"," ",0,"d^2*b^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+d^2*b^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+d^2*b^2*arctan(c*x)^2*ln(c*x)-d^2*b^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+a*b*c*d^2*x+b^2*c*d^2*x*arctan(c*x)-1/2*d^2*b^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+4*d^2*b^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+4*d^2*b^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*d^2*b^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*d^2*b^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+d^2*b^2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+d^2*a^2*ln(c*x)+3/2*d^2*b^2*arctan(c*x)^2-1/2*d^2*a^2*c^2*x^2-d^2*a*b*arctan(c*x)+4*I*d^2*a*b*arctan(c*x)*c*x-1/2*I*d^2*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*d^2*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*d^2*b^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-I*d^2*b^2*arctan(c*x)+I*d^2*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+4*I*d^2*b^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*d^2*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+I*d^2*a*b*dilog(1+I*c*x)+2*d^2*a*b*arctan(c*x)*ln(c*x)-I*d^2*a*b*dilog(1-I*c*x)-2*I*d^2*a*b*ln(c^2*x^2+1)+2*I*d^2*a^2*c*x-2*I*d^2*b^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+4*I*d^2*b^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I*d^2*b^2*Pi*arctan(c*x)^2-1/2*d^2*b^2*arctan(c*x)^2*c^2*x^2+1/2*I*d^2*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+2*I*d^2*b^2*arctan(c*x)^2*c*x-1/2*I*d^2*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*d^2*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2*I*d^2*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+I*d^2*a*b*ln(c*x)*ln(1+I*c*x)-I*d^2*a*b*ln(c*x)*ln(1-I*c*x)-d^2*a*b*arctan(c*x)*c^2*x^2+1/2*I*d^2*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2","C"
81,1,11959,302,2.584000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
82,1,1647,316,6.408000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^3,x)","-c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)-\frac{d^{2} a^{2}}{2 x^{2}}+i c^{2} d^{2} a b \ln \left(c x \right) \ln \left(-i c x +1\right)-2 c^{2} d^{2} a b \arctan \left(c x \right) \ln \left(c x \right)-2 c^{2} d^{2} b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-4 c^{2} d^{2} b^{2} \dilog \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{c^{2} d^{2} b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}+4 c^{2} d^{2} b^{2} \dilog \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 c^{2} d^{2} b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+c^{2} d^{2} b^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+c^{2} d^{2} b^{2} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}-1\right)+\frac{3 c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2}}{2}-\frac{d^{2} b^{2} \arctan \left(c x \right)^{2}}{2 x^{2}}-c^{2} d^{2} a^{2} \ln \left(c x \right)-i c^{2} d^{2} b^{2} \arctan \left(c x \right)-\frac{2 i c \,d^{2} a^{2}}{x}-\frac{c \,d^{2} a b}{x}-\frac{d^{2} a b \arctan \left(c x \right)}{x^{2}}-c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)-c^{2} d^{2} a b \arctan \left(c x \right)-\frac{c \,d^{2} b^{2} \arctan \left(c x \right)}{x}-\frac{i c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2}-i c^{2} d^{2} a b \ln \left(c x \right) \ln \left(i c x +1\right)+\frac{i c^{2} d^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{i c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3}}{2}-\frac{i c^{2} d^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}-\frac{4 i c \,d^{2} a b \arctan \left(c x \right)}{x}-2 i c^{2} d^{2} a b \ln \left(c^{2} x^{2}+1\right)-\frac{i c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} \pi}{2}-i c^{2} d^{2} a b \dilog \left(i c x +1\right)-i c^{2} d^{2} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)+2 i c^{2} d^{2} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+2 i c^{2} d^{2} b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+i c^{2} d^{2} a b \dilog \left(-i c x +1\right)+4 i c^{2} d^{2} a b \ln \left(c x \right)+4 i c^{2} d^{2} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{2 i c \,d^{2} b^{2} \arctan \left(c x \right)^{2}}{x}+\frac{i c^{2} d^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{i c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2}+\frac{i c^{2} d^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i c^{2} d^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}"," ",0,"-1/2*d^2*a^2/x^2-I*c^2*d^2*a*b*dilog(1+I*c*x)+4*I*c^2*d^2*a*b*ln(c*x)+4*I*c^2*d^2*b^2*arctan(c*x)*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*c*d^2*b^2*arctan(c*x)^2/x-I*c^2*d^2*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+2*I*c^2*d^2*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*I*c^2*d^2*b^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-I*c^2*d^2*b^2*arctan(c*x)-2*I*c*d^2*a^2/x+I*c^2*d^2*a*b*ln(c*x)*ln(1-I*c*x)-2*I*c^2*d^2*a*b*ln(c^2*x^2+1)-2*c^2*d^2*a*b*arctan(c*x)*ln(c*x)+I*c^2*d^2*a*b*dilog(1-I*c*x)-1/2*I*c^2*d^2*b^2*arctan(c*x)^2*Pi-2*c^2*d^2*b^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*c^2*d^2*b^2*arctan(c*x)^2-4*c^2*d^2*b^2*dilog((1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*c^2*d^2*b^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+c^2*d^2*b^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*d^2*b^2/x^2*arctan(c*x)^2-c^2*d^2*a^2*ln(c*x)+c^2*d^2*b^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)+4*c^2*d^2*b^2*dilog(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*c^2*d^2*b^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-c*d^2*a*b/x-d^2*a*b*arctan(c*x)/x^2-c^2*d^2*b^2*arctan(c*x)^2*ln(c*x)-c^2*d^2*b^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-c^2*d^2*b^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+c^2*d^2*b^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)-c^2*d^2*a*b*arctan(c*x)-c*d^2*b^2*arctan(c*x)/x-1/2*I*c^2*d^2*b^2*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+1/2*I*c^2*d^2*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*c^2*d^2*b^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*c^2*d^2*b^2*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+1/2*I*c^2*d^2*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-I*c^2*d^2*a*b*ln(c*x)*ln(1+I*c*x)+1/2*I*c^2*d^2*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*c^2*d^2*b^2*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3-1/2*I*c^2*d^2*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-4*I*c*d^2*a*b*arctan(c*x)/x","C"
83,1,669,238,0.117000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^4,x)","\frac{2 c^{2} d^{2} a b \arctan \left(c x \right)}{x}-\frac{d^{2} a^{2}}{3 x^{3}}-\frac{2 i c \,d^{2} a b \arctan \left(c x \right)}{x^{2}}-\frac{b^{2} c^{2} d^{2}}{3 x}-\frac{b^{2} c^{3} d^{2} \arctan \left(c x \right)}{3}-i b^{2} c^{3} d^{2} \ln \left(c^{2} x^{2}+1\right)+\frac{2 i c^{3} d^{2} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{3}+\frac{4 i c^{3} d^{2} b^{2} \dilog \left(-i c x +1\right)}{3}-\frac{2 i c^{3} d^{2} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{3}-\frac{4 i c^{3} d^{2} b^{2} \dilog \left(i c x +1\right)}{3}-\frac{i c^{3} d^{2} b^{2} \ln \left(c x -i\right)^{2}}{3}-i c^{3} d^{2} b^{2} \arctan \left(c x \right)^{2}+\frac{i c^{3} d^{2} b^{2} \ln \left(c x +i\right)^{2}}{3}-\frac{i c \,d^{2} a^{2}}{x^{2}}+2 i c^{3} d^{2} b^{2} \ln \left(c x \right)+\frac{4 c^{3} d^{2} a b \ln \left(c^{2} x^{2}+1\right)}{3}-\frac{c \,d^{2} b^{2} \arctan \left(c x \right)}{3 x^{2}}+\frac{c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2}}{x}+\frac{4 c^{3} d^{2} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{3}-\frac{8 c^{3} d^{2} a b \ln \left(c x \right)}{3}-\frac{8 c^{3} d^{2} b^{2} \ln \left(c x \right) \arctan \left(c x \right)}{3}-\frac{c \,d^{2} a b}{3 x^{2}}-\frac{2 d^{2} a b \arctan \left(c x \right)}{3 x^{3}}-2 i c^{3} d^{2} a b \arctan \left(c x \right)-\frac{i c \,d^{2} b^{2} \arctan \left(c x \right)^{2}}{x^{2}}-\frac{2 i c^{2} d^{2} b^{2} \arctan \left(c x \right)}{x}-\frac{2 i c^{3} d^{2} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{3}+\frac{4 i c^{3} d^{2} b^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)}{3}-\frac{4 i c^{3} d^{2} b^{2} \ln \left(c x \right) \ln \left(i c x +1\right)}{3}+\frac{2 i c^{3} d^{2} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{3}-\frac{2 i c^{3} d^{2} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{3}-\frac{2 i c^{2} d^{2} a b}{x}+\frac{2 i c^{3} d^{2} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{3}+\frac{c^{2} d^{2} a^{2}}{x}-\frac{d^{2} b^{2} \arctan \left(c x \right)^{2}}{3 x^{3}}"," ",0,"2/3*I*c^3*d^2*b^2*ln(c*x-I)*ln(c^2*x^2+1)+2/3*I*c^3*d^2*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-2/3*I*c^3*d^2*b^2*ln(I+c*x)*ln(c^2*x^2+1)+2*c^2*d^2*a*b*arctan(c*x)/x-2*I*c^2*d^2*a*b/x+4/3*I*c^3*d^2*b^2*ln(c*x)*ln(1-I*c*x)-4/3*I*c^3*d^2*b^2*ln(c*x)*ln(1+I*c*x)-1/3*d^2*a^2/x^3-2*I*c*d^2*a*b*arctan(c*x)/x^2-1/3*b^2*c^2*d^2/x-1/3*b^2*c^3*d^2*arctan(c*x)-I*b^2*c^3*d^2*ln(c^2*x^2+1)+4/3*c^3*d^2*a*b*ln(c^2*x^2+1)-1/3*c*d^2*b^2*arctan(c*x)/x^2+c^2*d^2*b^2*arctan(c*x)^2/x+4/3*c^3*d^2*b^2*arctan(c*x)*ln(c^2*x^2+1)-8/3*c^3*d^2*a*b*ln(c*x)-8/3*c^3*d^2*b^2*ln(c*x)*arctan(c*x)-1/3*I*c^3*d^2*b^2*ln(c*x-I)^2-1/3*c*d^2*a*b/x^2-I*c^3*d^2*b^2*arctan(c*x)^2+2/3*I*c^3*d^2*b^2*dilog(1/2*I*(c*x-I))+1/3*I*c^3*d^2*b^2*ln(I+c*x)^2-I*c*d^2*a^2/x^2+2*I*c^3*d^2*b^2*ln(c*x)+4/3*I*c^3*d^2*b^2*dilog(1-I*c*x)-2/3*I*c^3*d^2*b^2*dilog(-1/2*I*(I+c*x))-2/3*d^2*a*b*arctan(c*x)/x^3-4/3*I*c^3*d^2*b^2*dilog(1+I*c*x)-2*I*c^3*d^2*a*b*arctan(c*x)-I*c*d^2*b^2*arctan(c*x)^2/x^2-2*I*c^2*d^2*b^2*arctan(c*x)/x+c^2*d^2*a^2/x-1/3*d^2*b^2*arctan(c*x)^2/x^3-2/3*I*c^3*d^2*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))","B"
84,1,750,384,0.105000," ","int(x^3*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x)","\frac{d^{3} a^{2} x^{4}}{4}-\frac{2 i c^{3} d^{3} a b \arctan \left(c x \right) x^{7}}{7}+\frac{6 i c \,d^{3} a b \arctan \left(c x \right) x^{5}}{5}+\frac{3 a b \,d^{3} x}{2 c^{3}}+\frac{3 b^{2} d^{3} x \arctan \left(c x \right)}{2 c^{3}}+\frac{i c^{2} d^{3} b^{2} \arctan \left(c x \right) x^{6}}{21}-\frac{26 i d^{3} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{35 c^{4}}-\frac{26 i d^{3} a b \ln \left(c^{2} x^{2}+1\right)}{35 c^{4}}+\frac{3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2} x^{5}}{5}+\frac{7 b^{2} d^{3} x^{2}}{20 c^{2}}+\frac{i c^{2} d^{3} a b \,x^{6}}{21}+\frac{26 i d^{3} a b \,x^{2}}{35 c^{2}}+\frac{26 i d^{3} b^{2} \arctan \left(c x \right) x^{2}}{35 c^{2}}-\frac{11 b^{2} d^{3} \ln \left(c^{2} x^{2}+1\right)}{10 c^{4}}-c^{2} d^{3} a b \arctan \left(c x \right) x^{6}-\frac{13 i d^{3} b^{2} \arctan \left(c x \right) x^{4}}{35}+\frac{44 i b^{2} d^{3} x^{3}}{315 c}+\frac{122 i b^{2} d^{3} \arctan \left(c x \right)}{105 c^{4}}-\frac{13 d^{3} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{35 c^{4}}+\frac{13 d^{3} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{35 c^{4}}+\frac{13 d^{3} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{35 c^{4}}-\frac{13 d^{3} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{35 c^{4}}-\frac{13 i d^{3} a b \,x^{4}}{35}+\frac{3 i c \,d^{3} a^{2} x^{5}}{5}-\frac{i c^{3} d^{3} a^{2} x^{7}}{7}-\frac{122 i b^{2} d^{3} x}{105 c^{3}}-\frac{i b^{2} c \,d^{3} x^{5}}{105}-\frac{d^{3} b^{2} \arctan \left(c x \right) x^{3}}{2 c}-\frac{c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} x^{6}}{2}-\frac{d^{3} a b \,x^{3}}{2 c}+\frac{c \,d^{3} a b \,x^{5}}{5}+\frac{d^{3} a b \arctan \left(c x \right) x^{4}}{2}-\frac{3 d^{3} a b \arctan \left(c x \right)}{2 c^{4}}+\frac{c \,d^{3} b^{2} \arctan \left(c x \right) x^{5}}{5}+\frac{13 d^{3} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{35 c^{4}}-\frac{13 d^{3} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{35 c^{4}}+\frac{13 d^{3} b^{2} \ln \left(c x +i\right)^{2}}{70 c^{4}}-\frac{13 d^{3} b^{2} \ln \left(c x -i\right)^{2}}{70 c^{4}}-\frac{3 d^{3} b^{2} \arctan \left(c x \right)^{2}}{4 c^{4}}-\frac{c^{2} d^{3} a^{2} x^{6}}{2}+\frac{d^{3} b^{2} \arctan \left(c x \right)^{2} x^{4}}{4}-\frac{b^{2} d^{3} x^{4}}{20}-\frac{i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2} x^{7}}{7}"," ",0,"1/4*d^3*a^2*x^4-2/7*I*c^3*d^3*a*b*arctan(c*x)*x^7+6/5*I*c*d^3*a*b*arctan(c*x)*x^5+3/2*a*b*d^3*x/c^3+3/2*b^2*d^3*x*arctan(c*x)/c^3-122/105*I*b^2*d^3*x/c^3-1/105*I*b^2*c*d^3*x^5+7/20*b^2*d^3*x^2/c^2-26/35*I/c^4*d^3*b^2*arctan(c*x)*ln(c^2*x^2+1)-26/35*I/c^4*d^3*a*b*ln(c^2*x^2+1)+3/5*I*c*d^3*b^2*arctan(c*x)^2*x^5-1/7*I*c^3*d^3*b^2*arctan(c*x)^2*x^7+1/21*I*c^2*d^3*b^2*arctan(c*x)*x^6+26/35*I/c^2*d^3*b^2*arctan(c*x)*x^2+44/315*I*b^2*d^3*x^3/c+122/105*I*b^2*d^3*arctan(c*x)/c^4-11/10*b^2*d^3*ln(c^2*x^2+1)/c^4+1/21*I*c^2*d^3*a*b*x^6+26/35*I/c^2*d^3*a*b*x^2-c^2*d^3*a*b*arctan(c*x)*x^6-1/2/c*d^3*b^2*arctan(c*x)*x^3-1/2*c^2*d^3*b^2*arctan(c*x)^2*x^6-1/2/c*d^3*a*b*x^3+1/5*c*d^3*a*b*x^5+1/2*d^3*a*b*arctan(c*x)*x^4-13/35/c^4*d^3*b^2*ln(I+c*x)*ln(c^2*x^2+1)+13/35/c^4*d^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+13/35/c^4*d^3*b^2*ln(c*x-I)*ln(c^2*x^2+1)-13/35/c^4*d^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-3/2/c^4*d^3*a*b*arctan(c*x)+1/5*c*d^3*b^2*arctan(c*x)*x^5-13/35*I*d^3*a*b*x^4+3/5*I*c*d^3*a^2*x^5-1/7*I*c^3*d^3*a^2*x^7-13/35*I*d^3*b^2*arctan(c*x)*x^4+13/35/c^4*d^3*b^2*dilog(1/2*I*(c*x-I))-13/35/c^4*d^3*b^2*dilog(-1/2*I*(I+c*x))-3/4/c^4*d^3*b^2*arctan(c*x)^2+13/70/c^4*d^3*b^2*ln(I+c*x)^2-1/2*c^2*d^3*a^2*x^6+1/4*d^3*b^2*arctan(c*x)^2*x^4-13/70/c^4*d^3*b^2*ln(c*x-I)^2-1/20*b^2*d^3*x^4","A"
85,1,712,351,0.115000," ","int(x^2*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x)","-\frac{6 c^{2} d^{3} a b \arctan \left(c x \right) x^{5}}{5}+\frac{d^{3} a^{2} x^{3}}{3}+\frac{i c^{2} d^{3} a b \,x^{5}}{15}+\frac{3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2} x^{4}}{4}-\frac{i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2} x^{6}}{6}-\frac{11 i d^{3} a b \arctan \left(c x \right)}{6 c^{3}}+\frac{i c^{2} d^{3} b^{2} \arctan \left(c x \right) x^{5}}{15}-\frac{7 i d^{3} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{15 c^{3}}+\frac{7 i d^{3} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{15 c^{3}}+\frac{7 i d^{3} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{15 c^{3}}-\frac{7 i d^{3} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{15 c^{3}}+\frac{37 b^{2} d^{3} x}{30 c^{2}}-\frac{37 b^{2} d^{3} \arctan \left(c x \right)}{30 c^{3}}-\frac{11 i d^{3} b^{2} \arctan \left(c x \right)^{2}}{12 c^{3}}-\frac{7 i d^{3} b^{2} \ln \left(c x -i\right)^{2}}{30 c^{3}}+\frac{7 i d^{3} b^{2} \ln \left(c x +i\right)^{2}}{30 c^{3}}-\frac{11 i d^{3} a b \,x^{3}}{18}-\frac{11 i d^{3} b^{2} \arctan \left(c x \right) x^{3}}{18}-\frac{i c^{3} d^{3} a^{2} x^{6}}{6}+\frac{7 i d^{3} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{15 c^{3}}-\frac{7 i d^{3} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{15 c^{3}}+\frac{3 i c \,d^{3} a^{2} x^{4}}{4}-\frac{i b^{2} c \,d^{3} x^{4}}{60}-\frac{113 i b^{2} d^{3} \ln \left(c^{2} x^{2}+1\right)}{90 c^{3}}+\frac{61 i b^{2} d^{3} x^{2}}{180 c}+\frac{14 d^{3} a b \ln \left(c^{2} x^{2}+1\right)}{15 c^{3}}-\frac{14 d^{3} b^{2} \arctan \left(c x \right) x^{2}}{15 c}-\frac{3 c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} x^{5}}{5}+\frac{3 c \,d^{3} b^{2} \arctan \left(c x \right) x^{4}}{10}+\frac{2 d^{3} a b \arctan \left(c x \right) x^{3}}{3}+\frac{14 d^{3} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{15 c^{3}}+\frac{3 c \,d^{3} a b \,x^{4}}{10}-\frac{14 d^{3} a b \,x^{2}}{15 c}-\frac{3 c^{2} d^{3} a^{2} x^{5}}{5}+\frac{d^{3} b^{2} \arctan \left(c x \right)^{2} x^{3}}{3}+\frac{11 i a b \,d^{3} x}{6 c^{2}}+\frac{11 i b^{2} d^{3} x \arctan \left(c x \right)}{6 c^{2}}-\frac{b^{2} d^{3} x^{3}}{10}-\frac{i c^{3} d^{3} a b \arctan \left(c x \right) x^{6}}{3}+\frac{3 i c \,d^{3} a b \arctan \left(c x \right) x^{4}}{2}"," ",0,"-7/15*I/c^3*d^3*b^2*ln(I+c*x)*ln(c^2*x^2+1)+7/15*I/c^3*d^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+7/15*I/c^3*d^3*b^2*ln(c*x-I)*ln(c^2*x^2+1)-7/15*I/c^3*d^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/15*I*c^2*d^3*a*b*x^5+3/4*I*c*d^3*b^2*arctan(c*x)^2*x^4-1/6*I*c^3*d^3*b^2*arctan(c*x)^2*x^6-6/5*c^2*d^3*a*b*arctan(c*x)*x^5+1/3*d^3*a^2*x^3-11/6*I/c^3*d^3*a*b*arctan(c*x)+1/15*I*c^2*d^3*b^2*arctan(c*x)*x^5-1/60*I*b^2*c*d^3*x^4-113/90*I*b^2*d^3*ln(c^2*x^2+1)/c^3+37/30*b^2*d^3*x/c^2+11/6*I*a*b*d^3*x/c^2+61/180*I*b^2*d^3*x^2/c+11/6*I*b^2*d^3*x*arctan(c*x)/c^2-37/30*b^2*d^3*arctan(c*x)/c^3+3/4*I*c*d^3*a^2*x^4+7/15*I/c^3*d^3*b^2*dilog(1/2*I*(c*x-I))+14/15/c^3*d^3*a*b*ln(c^2*x^2+1)-14/15/c*d^3*b^2*arctan(c*x)*x^2-3/5*c^2*d^3*b^2*arctan(c*x)^2*x^5+3/10*c*d^3*b^2*arctan(c*x)*x^4-11/18*I*d^3*b^2*arctan(c*x)*x^3-1/6*I*c^3*d^3*a^2*x^6-7/15*I/c^3*d^3*b^2*dilog(-1/2*I*(I+c*x))+7/30*I/c^3*d^3*b^2*ln(I+c*x)^2+2/3*d^3*a*b*arctan(c*x)*x^3+14/15/c^3*d^3*b^2*arctan(c*x)*ln(c^2*x^2+1)+3/10*c*d^3*a*b*x^4-14/15/c*d^3*a*b*x^2-11/18*I*d^3*a*b*x^3-11/12*I/c^3*d^3*b^2*arctan(c*x)^2-1/3*I*c^3*d^3*a*b*arctan(c*x)*x^6+3/2*I*c*d^3*a*b*arctan(c*x)*x^4-3/5*c^2*d^3*a^2*x^5+1/3*d^3*b^2*arctan(c*x)^2*x^3-1/10*b^2*d^3*x^3-7/30*I/c^3*d^3*b^2*ln(c*x-I)^2","B"
86,1,656,269,0.122000," ","int(x*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x)","2 i c \,d^{3} a b \arctan \left(c x \right) x^{3}-\frac{2 i c^{3} d^{3} a b \arctan \left(c x \right) x^{5}}{5}-\frac{3 c^{2} d^{3} a b \arctan \left(c x \right) x^{4}}{2}-\frac{5 a b \,d^{3} x}{2 c}-\frac{5 b^{2} d^{3} x \arctan \left(c x \right)}{2 c}+\frac{3 b^{2} d^{3} \ln \left(c^{2} x^{2}+1\right)}{2 c^{2}}-\frac{6 i d^{3} a b \,x^{2}}{5}-\frac{3 d^{3} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{5 c^{2}}+\frac{3 d^{3} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{5 c^{2}}+i c \,d^{3} a^{2} x^{3}+\frac{3 d^{3} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{5 c^{2}}-\frac{3 d^{3} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{5 c^{2}}-\frac{6 i d^{3} b^{2} \arctan \left(c x \right) x^{2}}{5}-\frac{i c^{3} d^{3} a^{2} x^{5}}{5}-\frac{i b^{2} c \,d^{3} x^{3}}{30}-\frac{13 i b^{2} d^{3} \arctan \left(c x \right)}{10 c^{2}}+\frac{13 i b^{2} d^{3} x}{10 c}+\frac{c \,d^{3} b^{2} \arctan \left(c x \right) x^{3}}{2}-\frac{3 c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} x^{4}}{4}+\frac{c \,d^{3} a b \,x^{3}}{2}+d^{3} a b \arctan \left(c x \right) x^{2}+\frac{5 d^{3} a b \arctan \left(c x \right)}{2 c^{2}}+\frac{d^{3} b^{2} \arctan \left(c x \right)^{2} x^{2}}{2}+\frac{5 d^{3} b^{2} \arctan \left(c x \right)^{2}}{4 c^{2}}-\frac{3 c^{2} d^{3} a^{2} x^{4}}{4}+\frac{d^{3} a^{2} x^{2}}{2}+\frac{i c^{2} d^{3} b^{2} \arctan \left(c x \right) x^{4}}{10}+i c \,d^{3} b^{2} \arctan \left(c x \right)^{2} x^{3}-\frac{i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2} x^{5}}{5}+\frac{i c^{2} d^{3} a b \,x^{4}}{10}+\frac{6 i d^{3} b^{2} \ln \left(c^{2} x^{2}+1\right) \arctan \left(c x \right)}{5 c^{2}}+\frac{6 i d^{3} a b \ln \left(c^{2} x^{2}+1\right)}{5 c^{2}}-\frac{b^{2} d^{3} x^{2}}{4}-\frac{3 d^{3} b^{2} \ln \left(c x +i\right)^{2}}{10 c^{2}}+\frac{3 d^{3} b^{2} \ln \left(c x -i\right)^{2}}{10 c^{2}}-\frac{3 d^{3} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{5 c^{2}}+\frac{3 d^{3} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{5 c^{2}}"," ",0,"-2/5*I*c^3*d^3*a*b*arctan(c*x)*x^5-3/2*c^2*d^3*a*b*arctan(c*x)*x^4+1/10*I*c^2*d^3*b^2*arctan(c*x)*x^4+I*c*d^3*b^2*arctan(c*x)^2*x^3-1/5*I*c^3*d^3*b^2*arctan(c*x)^2*x^5+1/10*I*c^2*d^3*a*b*x^4+6/5*I/c^2*d^3*b^2*ln(c^2*x^2+1)*arctan(c*x)+6/5*I/c^2*d^3*a*b*ln(c^2*x^2+1)-5/2*a*b*d^3*x/c-5/2*b^2*d^3*x*arctan(c*x)/c-1/30*I*b^2*c*d^3*x^3-13/10*I*b^2*d^3*arctan(c*x)/c^2+13/10*I*b^2*d^3*x/c+3/2*b^2*d^3*ln(c^2*x^2+1)/c^2+1/2*c*d^3*b^2*arctan(c*x)*x^3-3/4*c^2*d^3*b^2*arctan(c*x)^2*x^4-3/5/c^2*d^3*b^2*ln(c*x-I)*ln(c^2*x^2+1)+3/5/c^2*d^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/2*c*d^3*a*b*x^3+d^3*a*b*arctan(c*x)*x^2+I*c*d^3*a^2*x^3+3/5/c^2*d^3*b^2*ln(I+c*x)*ln(c^2*x^2+1)-3/5/c^2*d^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+5/2/c^2*d^3*a*b*arctan(c*x)-6/5*I*d^3*b^2*arctan(c*x)*x^2-1/5*I*c^3*d^3*a^2*x^5+1/2*d^3*b^2*arctan(c*x)^2*x^2-3/5/c^2*d^3*b^2*dilog(1/2*I*(c*x-I))+3/5/c^2*d^3*b^2*dilog(-1/2*I*(I+c*x))+5/4/c^2*d^3*b^2*arctan(c*x)^2-3/10/c^2*d^3*b^2*ln(I+c*x)^2+3/10/c^2*d^3*b^2*ln(c*x-I)^2-3/4*c^2*d^3*a^2*x^4+1/2*d^3*a^2*x^2-1/4*b^2*d^3*x^2-6/5*I*d^3*a*b*x^2+2*I*c*d^3*a*b*arctan(c*x)*x^3","B"
87,1,620,204,0.110000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x)","-\frac{i d^{3} a^{2}}{4 c}+d^{3} b^{2} \arctan \left(c x \right)^{2} x -c^{2} d^{3} a^{2} x^{3}+\frac{i c^{2} d^{3} a b \,x^{3}}{6}+\frac{i c^{2} d^{3} b^{2} \arctan \left(c x \right) x^{3}}{6}+\frac{i d^{3} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{c}-\frac{i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2} x^{4}}{4}+\frac{3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2} x^{2}}{2}-\frac{i d^{3} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{c}+\frac{7 i d^{3} a b \arctan \left(c x \right)}{2 c}+\frac{i d^{3} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c}-\frac{i d^{3} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{c}-2 c^{2} d^{3} a b \arctan \left(c x \right) x^{3}+\frac{b^{2} d^{3} \arctan \left(c x \right)}{c}-\frac{7 i b^{2} d^{3} x \arctan \left(c x \right)}{2}-\frac{i d^{3} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{c}+\frac{i d^{3} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c}+\frac{7 i d^{3} b^{2} \arctan \left(c x \right)^{2}}{4 c}+\frac{i d^{3} b^{2} \ln \left(c x -i\right)^{2}}{2 c}-\frac{i d^{3} b^{2} \ln \left(c x +i\right)^{2}}{2 c}+\frac{3 i c \,x^{2} a^{2} d^{3}}{2}-\frac{i c^{3} x^{4} a^{2} d^{3}}{4}-\frac{7 i a b \,d^{3} x}{2}-\frac{i b^{2} c \,d^{3} x^{2}}{12}+\frac{11 i b^{2} d^{3} \ln \left(c^{2} x^{2}+1\right)}{6 c}-\frac{2 d^{3} a b \ln \left(c^{2} x^{2}+1\right)}{c}-\frac{2 d^{3} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{c}+c \,d^{3} b^{2} \arctan \left(c x \right) x^{2}-c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} x^{3}+2 d^{3} a b \arctan \left(c x \right) x +c \,d^{3} a b \,x^{2}-b^{2} d^{3} x +x \,a^{2} d^{3}+3 i c \,d^{3} a b \arctan \left(c x \right) x^{2}-\frac{i c^{3} d^{3} a b \arctan \left(c x \right) x^{4}}{2}"," ",0,"d^3*b^2*arctan(c*x)^2*x-c^2*d^3*a^2*x^3-1/4*I/c*d^3*a^2-I/c*d^3*b^2*ln(c*x-I)*ln(c^2*x^2+1)-I/c*d^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+7/2*I/c*d^3*a*b*arctan(c*x)+I/c*d^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/6*I*c^2*d^3*a*b*x^3+1/6*I*c^2*d^3*b^2*arctan(c*x)*x^3-2*c^2*d^3*a*b*arctan(c*x)*x^3+I/c*d^3*b^2*ln(I+c*x)*ln(c^2*x^2+1)-1/4*I*c^3*d^3*b^2*arctan(c*x)^2*x^4+3/2*I*c*d^3*b^2*arctan(c*x)^2*x^2+11/6*I*b^2*d^3*ln(c^2*x^2+1)/c+b^2*d^3*arctan(c*x)/c-7/2*I*a*b*d^3*x-1/12*I*b^2*c*d^3*x^2-7/2*I*b^2*d^3*x*arctan(c*x)-2/c*d^3*a*b*ln(c^2*x^2+1)-2/c*d^3*b^2*arctan(c*x)*ln(c^2*x^2+1)+c*d^3*b^2*arctan(c*x)*x^2-c^2*d^3*b^2*arctan(c*x)^2*x^3+2*d^3*a*b*arctan(c*x)*x+c*d^3*a*b*x^2+7/4*I/c*d^3*b^2*arctan(c*x)^2+1/2*I/c*d^3*b^2*ln(c*x-I)^2-1/2*I/c*d^3*b^2*ln(I+c*x)^2-I/c*d^3*b^2*dilog(1/2*I*(c*x-I))+3/2*I*c*x^2*a^2*d^3+I/c*d^3*b^2*dilog(-1/2*I*(I+c*x))-1/4*I*c^3*x^4*a^2*d^3-b^2*d^3*x+x*a^2*d^3+3*I*c*d^3*a*b*arctan(c*x)*x^2-1/2*I*c^3*d^3*a*b*arctan(c*x)*x^4","B"
88,1,1651,348,6.332000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x,x)","\frac{11 d^{3} b^{2} \arctan \left(c x \right)^{2}}{6}+d^{3} a^{2} \ln \left(c x \right)+3 d^{3} b^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)+\frac{20 d^{3} b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3}-\frac{d^{3} b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}+2 d^{3} b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{20 d^{3} b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3}+2 d^{3} b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)-\frac{8 i d^{3} b^{2} \arctan \left(c x \right)}{3}+d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)-\frac{3 d^{3} a^{2} c^{2} x^{2}}{2}-3 d^{3} a b \arctan \left(c x \right)+i d^{3} a b \dilog \left(i c x +1\right)-i d^{3} a b \dilog \left(-i c x +1\right)+i d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)-2 i d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 i d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{i d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{i d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+i d^{3} a b \ln \left(c x \right) \ln \left(i c x +1\right)-i d^{3} a b \ln \left(c x \right) \ln \left(-i c x +1\right)+\frac{i d^{3} a b \,c^{2} x^{2}}{3}+3 i d^{3} b^{2} \arctan \left(c x \right)^{2} c x -\frac{i d^{3} b^{2} \arctan \left(c x \right)^{2} c^{3} x^{3}}{3}+\frac{i d^{3} b^{2} \arctan \left(c x \right) c^{2} x^{2}}{3}-3 d^{3} a b \arctan \left(c x \right) c^{2} x^{2}+3 a b c \,d^{3} x +3 b^{2} c \,d^{3} x \arctan \left(c x \right)-\frac{3 d^{3} b^{2} \arctan \left(c x \right)^{2} c^{2} x^{2}}{2}+2 d^{3} a b \arctan \left(c x \right) \ln \left(c x \right)+\frac{i d^{3} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2}-\frac{i b^{2} c \,d^{3} x}{3}-\frac{i d^{3} a^{2} c^{3} x^{3}}{3}-\frac{10 i d^{3} a b \ln \left(c^{2} x^{2}+1\right)}{3}+\frac{i d^{3} b^{2} \arctan \left(c x \right)^{2} \pi}{2}+\frac{20 i d^{3} b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3}+\frac{20 i d^{3} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3}+3 i d^{3} a^{2} c x -\frac{i d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+6 i d^{3} a b \arctan \left(c x \right) c x -\frac{2 i d^{3} a b \arctan \left(c x \right) c^{3} x^{3}}{3}-\frac{i d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{i d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i d^{3} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2}+\frac{d^{3} b^{2}}{3}"," ",0,"20/3*d^3*b^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*d^3*b^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+3*d^3*b^2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+2*d^3*b^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+20/3*d^3*b^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*d^3*b^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+11/6*d^3*b^2*arctan(c*x)^2+d^3*a^2*ln(c*x)+d^3*b^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+d^3*b^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-d^3*b^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+d^3*b^2*arctan(c*x)^2*ln(c*x)-8/3*I*d^3*b^2*arctan(c*x)-3/2*d^3*a^2*c^2*x^2-3*d^3*a*b*arctan(c*x)-1/2*I*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+6*I*d^3*a*b*arctan(c*x)*c*x-2/3*I*d^3*a*b*arctan(c*x)*c^3*x^3-1/2*I*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*d^3*b^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*d^3*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*d^3*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2*I*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+I*d^3*a*b*ln(c*x)*ln(1+I*c*x)-I*d^3*a*b*ln(c*x)*ln(1-I*c*x)+1/3*I*d^3*a*b*c^2*x^2+3*I*d^3*b^2*arctan(c*x)^2*c*x-1/3*I*d^3*b^2*arctan(c*x)^2*c^3*x^3-3*d^3*a*b*arctan(c*x)*c^2*x^2+1/3*I*d^3*b^2*arctan(c*x)*c^2*x^2+3*a*b*c*d^3*x+3*b^2*c*d^3*x*arctan(c*x)-1/3*I*b^2*c*d^3*x-3/2*d^3*b^2*arctan(c*x)^2*c^2*x^2-1/3*I*d^3*a^2*c^3*x^3+2*d^3*a*b*arctan(c*x)*ln(c*x)+I*d^3*a*b*dilog(1+I*c*x)-I*d^3*a*b*dilog(1-I*c*x)-10/3*I*d^3*a*b*ln(c^2*x^2+1)+I*d^3*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+1/2*I*d^3*b^2*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+1/2*I*d^3*b^2*arctan(c*x)^2*Pi+20/3*I*d^3*b^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+20/3*I*d^3*b^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*d^3*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*d^3*b^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I*d^3*a^2*c*x+1/2*I*d^3*b^2*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+1/3*d^3*b^2","C"
89,1,1739,373,8.250000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^2,x)","-\frac{d^{3} a^{2}}{x}-3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)+3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-3 c \,d^{3} a b \ln \left(c x \right) \ln \left(i c x +1\right)+3 c \,d^{3} a b \ln \left(c x \right) \ln \left(-i c x +1\right)-\frac{3 c \,d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{3 c \,d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{3 c \,d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)-\frac{i d^{3} b^{2} \arctan \left(c x \right)^{2} c^{3} x^{2}}{2}-i c \,d^{3} a b \arctan \left(c x \right)-\frac{3 c \,d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}-\frac{3 c \,d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}-6 d^{3} a b \arctan \left(c x \right) c^{2} x -3 c^{2} x \,a^{2} d^{3}+c \,d^{3} b^{2} \arctan \left(c x \right)-\frac{d^{3} b^{2} \arctan \left(c x \right)^{2}}{x}-3 c \,d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)+6 c \,d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-3 c \,d^{3} a b \dilog \left(i c x +1\right)+3 c \,d^{3} a b \dilog \left(-i c x +1\right)+6 i c \,d^{3} b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 i c \,d^{3} b^{2} \dilog \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+6 i c \,d^{3} b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+6 i c \,d^{3} b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{3 i c \,d^{3} b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}+6 i c \,d^{3} b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)+2 i c \,d^{3} b^{2} \dilog \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+i c \,d^{3} b^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)+2 c \,d^{3} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-6 c \,d^{3} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)-6 c \,d^{3} b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)+3 i c \,d^{3} a^{2} \ln \left(c x \right)-\frac{i d^{3} a^{2} c^{3} x^{2}}{2}+6 c \,d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2}}{2}+\frac{3 c \,d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+6 i c \,d^{3} a b \arctan \left(c x \right) \ln \left(c x \right)+\frac{3 c \,d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-i d^{3} a b \arctan \left(c x \right) c^{3} x^{2}+\frac{3 c \,d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+2 c \,d^{3} a b \ln \left(c x \right)+2 c \,d^{3} a b \ln \left(c^{2} x^{2}+1\right)-\frac{3 c \,d^{3} b^{2} \pi  \arctan \left(c x \right)^{2}}{2}-3 d^{3} b^{2} \arctan \left(c x \right)^{2} c^{2} x -\frac{2 d^{3} a b \arctan \left(c x \right)}{x}+i a b \,c^{2} d^{3} x +i b^{2} c^{2} d^{3} x \arctan \left(c x \right)"," ",0,"-d^3*a^2/x+3/2*c*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*c*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+6*c*d^3*b^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*c*d^3*b^2*arctan(c*x)*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*c*d^3*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-6*c*d^3*b^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*c*d^3*b^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*c*d^3*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*c*d^3*a*b*dilog(1+I*c*x)+3*c*d^3*a*b*dilog(1-I*c*x)+6*I*c*d^3*b^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I*c*d^3*a^2*ln(c*x)-1/2*I*d^3*a^2*c^3*x^2+3/2*c*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+6*I*c*d^3*a*b*arctan(c*x)*ln(c*x)-I*d^3*a*b*arctan(c*x)*c^3*x^2+3/2*c*d^3*b^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3*I*c*d^3*b^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+3*I*c*d^3*b^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*d^3*a*b*arctan(c*x)*c^2*x-3*c*d^3*a*b*ln(c*x)*ln(1+I*c*x)+3*c*d^3*a*b*ln(c*x)*ln(1-I*c*x)-3/2*c*d^3*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+3/2*c*d^3*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*c*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+3*I*c*d^3*b^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I*c*d^3*b^2*arctan(c*x)^2*ln(c*x)-1/2*I*d^3*b^2*arctan(c*x)^2*c^3*x^2-I*c*d^3*a*b*arctan(c*x)-3*c^2*x*a^2*d^3+c*d^3*b^2*arctan(c*x)-d^3*b^2*arctan(c*x)^2/x-3/2*c*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+2*c*d^3*a*b*ln(c*x)+2*c*d^3*a*b*ln(c^2*x^2+1)-3/2*c*d^3*b^2*Pi*arctan(c*x)^2+I*c*d^3*b^2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-3*d^3*b^2*arctan(c*x)^2*c^2*x-2*d^3*a*b*arctan(c*x)/x-2*I*c*d^3*b^2*dilog(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*I*c*d^3*b^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*I*c*d^3*b^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*I*c*d^3*b^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+3/2*I*c*d^3*b^2*arctan(c*x)^2+6*I*c*d^3*b^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*I*c*d^3*b^2*dilog((1+I*c*x)/(c^2*x^2+1)^(1/2))+I*a*b*c^2*d^3*x+I*b^2*c^2*d^3*x*arctan(c*x)","C"
90,1,1840,391,6.753000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^3,x)","-\frac{d^{3} a b \arctan \left(c x \right)}{x^{2}}-\frac{d^{3} a^{2}}{2 x^{2}}-3 c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-3 c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+3 c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)-i c^{3} d^{3} a^{2} x -\frac{3 i c \,d^{3} a^{2}}{x}-\frac{d^{3} b^{2} \arctan \left(c x \right)^{2}}{2 x^{2}}+\frac{3 c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2}}{2}-3 i c^{2} d^{3} a b \dilog \left(i c x +1\right)+3 i c^{2} d^{3} a b \dilog \left(-i c x +1\right)-3 i c^{2} d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)+6 i c^{2} d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+6 i c^{2} d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{3 i c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2}-\frac{c \,d^{3} a b}{x}-3 c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)-c^{2} d^{3} a b \arctan \left(c x \right)+3 i c^{2} d^{3} a b \ln \left(c x \right) \ln \left(-i c x +1\right)-\frac{3 i c^{2} d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{3 i c^{2} d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-2 i c^{3} d^{3} a b \arctan \left(c x \right) x -\frac{6 i c \,d^{3} a b \arctan \left(c x \right)}{x}-\frac{3 i c^{2} d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}-3 i c^{2} d^{3} a b \ln \left(c x \right) \ln \left(i c x +1\right)-6 c^{2} d^{3} b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-6 c^{2} d^{3} b^{2} \dilog \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+6 c^{2} d^{3} b^{2} \dilog \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 c^{2} d^{3} b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)-3 c^{2} d^{3} a^{2} \ln \left(c x \right)+c^{2} d^{3} b^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+c^{2} d^{3} b^{2} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}-1\right)+\frac{3 c^{2} d^{3} b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}-6 c^{2} d^{3} b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 c^{2} d^{3} b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{3 i c^{2} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{3 i c^{2} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{3 i c^{2} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{3 i c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2}+\frac{c \,d^{3} b^{2} \arctan \left(c x \right) \sqrt{c^{2} x^{2}+1}}{x}-6 c^{2} d^{3} a b \arctan \left(c x \right) \ln \left(c x \right)-i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2} x -\frac{3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2}}{x}+6 i c^{2} d^{3} a b \ln \left(c x \right)-2 i c^{2} d^{3} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)-2 i c^{2} d^{3} b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)+6 i c^{2} d^{3} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 i c^{2} d^{3} a b \ln \left(c^{2} x^{2}+1\right)-\frac{3 i c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2} \pi}{2}"," ",0,"-d^3*a*b*arctan(c*x)/x^2+3/2*I*c^2*d^3*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-2*I*c^3*d^3*a*b*arctan(c*x)*x-6*I*c*d^3*a*b*arctan(c*x)/x-1/2*d^3*a^2/x^2+3/2*c^2*d^3*b^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-6*c^2*d^3*b^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*c^2*d^3*b^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*c^2*d^3*b^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+c^2*d^3*b^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*c^2*d^3*b^2*dilog((1+I*c*x)/(c^2*x^2+1)^(1/2))+6*c^2*d^3*b^2*dilog(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+c^2*d^3*b^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)-1/2*d^3*b^2*arctan(c*x)^2/x^2+3/2*c^2*d^3*b^2*arctan(c*x)^2-c*d^3*a*b/x-3*c^2*d^3*b^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*c^2*d^3*b^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*c^2*d^3*b^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)-3*c^2*d^3*b^2*arctan(c*x)^2*ln(c*x)-c^2*d^3*a*b*arctan(c*x)-I*c^3*d^3*a^2*x-3*I*c*d^3*a^2/x-3/2*I*c^2*d^3*b^2*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))-3/2*I*c^2*d^3*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3*I*c^2*d^3*a*b*ln(c*x)*ln(1+I*c*x)+3*I*c^2*d^3*a*b*ln(c*x)*ln(1-I*c*x)-3/2*I*c^2*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3*c^2*d^3*a^2*ln(c*x)-2*c^2*d^3*b^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+c*d^3*b^2*arctan(c*x)/x*(c^2*x^2+1)^(1/2)-6*c^2*d^3*a*b*arctan(c*x)*ln(c*x)-I*c^3*d^3*b^2*arctan(c*x)^2*x-3*I*c*d^3*b^2*arctan(c*x)^2/x-3*I*c^2*d^3*a*b*dilog(1+I*c*x)+3*I*c^2*d^3*a*b*dilog(1-I*c*x)+6*I*c^2*d^3*a*b*ln(c*x)-2*I*c^2*d^3*b^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*c^2*d^3*b^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*I*c^2*d^3*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+6*I*c^2*d^3*b^2*arctan(c*x)*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*I*c^2*d^3*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*I*c^2*d^3*b^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*c^2*d^3*a*b*ln(c^2*x^2+1)-3/2*I*c^2*d^3*b^2*arctan(c*x)^2*Pi+3/2*I*c^2*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*c^2*d^3*b^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*c^2*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*c^2*d^3*b^2*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))","C"
91,1,1814,391,8.401000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^4,x)","\frac{3 c^{2} d^{3} a^{2}}{x}-\frac{d^{3} b^{2} \arctan \left(c x \right)^{2}}{3 x^{3}}+\frac{6 c^{2} d^{3} a b \arctan \left(c x \right)}{x}-\frac{c^{3} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{c^{3} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{c^{3} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}-\frac{c^{3} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-2 i c^{3} d^{3} a b \arctan \left(c x \right) \ln \left(c x \right)-\frac{3 i c \,d^{3} a b \arctan \left(c x \right)}{x^{2}}+\frac{8 b^{2} c^{3} d^{3} \arctan \left(c x \right)}{3}-\frac{d^{3} a^{2}}{3 x^{3}}+c^{3} d^{3} a b \ln \left(c x \right) \ln \left(i c x +1\right)-c^{3} d^{3} a b \ln \left(c x \right) \ln \left(-i c x +1\right)+i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)+\frac{c^{3} d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}-\frac{c^{3} d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{c^{3} d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}-\frac{3 i c^{2} d^{3} a b}{x}-\frac{3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2}}{2 x^{2}}-\frac{3 i c^{2} d^{3} b^{2} \arctan \left(c x \right)}{x}-i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{i c^{3} d^{3} b^{2} \sqrt{c^{2} x^{2}+1}}{3 \left(i c x -\sqrt{c^{2} x^{2}+1}+1\right)}-i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)-3 i c^{3} d^{3} a b \arctan \left(c x \right)+\frac{c^{3} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}+\frac{i c^{3} d^{3} b^{2} \sqrt{c^{2} x^{2}+1}}{3 i c x +3 \sqrt{c^{2} x^{2}+1}+3}-2 i c^{3} d^{3} b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 i c^{3} d^{3} b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{20 i c^{3} d^{3} b^{2} \dilog \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{3}-c^{3} d^{3} a b \dilog \left(-i c x +1\right)-2 c^{3} d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+c^{3} d^{3} a b \dilog \left(i c x +1\right)-2 c^{3} d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{20 c^{3} d^{3} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{3}+3 i c^{3} d^{3} b^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+3 i c^{3} d^{3} b^{2} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}-1\right)-\frac{3 i c \,d^{3} a^{2}}{2 x^{2}}+\frac{11 i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2}}{6}-i c^{3} d^{3} a^{2} \ln \left(c x \right)+c^{3} d^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)+\frac{i c^{3} d^{3} b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}-\frac{20 i c^{3} d^{3} b^{2} \dilog \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{3}+\frac{c^{3} d^{3} b^{2} \pi  \arctan \left(c x \right)^{2}}{2}+\frac{3 c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2}}{x}-\frac{c \,d^{3} b^{2} \arctan \left(c x \right)}{3 x^{2}}-\frac{20 c^{3} d^{3} a b \ln \left(c x \right)}{3}+\frac{10 c^{3} d^{3} a b \ln \left(c^{2} x^{2}+1\right)}{3}-\frac{c \,d^{3} a b}{3 x^{2}}-\frac{2 d^{3} a b \arctan \left(c x \right)}{3 x^{3}}"," ",0,"3*c^2*d^3*a^2/x-1/3*d^3*b^2*arctan(c*x)^2/x^3+6*c^2*d^3*a*b*arctan(c*x)/x+c^3*d^3*a*b*ln(c*x)*ln(1+I*c*x)-c^3*d^3*a*b*ln(c*x)*ln(1-I*c*x)+I*c^3*d^3*b^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+1/2*c^3*d^3*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-1/2*c^3*d^3*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*c^3*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3*I*c^2*d^3*a*b/x-3/2*I*c*d^3*b^2*arctan(c*x)^2/x^2-3*I*c^2*d^3*b^2*arctan(c*x)/x-I*c^3*d^3*b^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-I*c^3*d^3*b^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/3*I*c^3*d^3*b^2/(I*c*x-(c^2*x^2+1)^(1/2)+1)*(c^2*x^2+1)^(1/2)-I*c^3*d^3*b^2*arctan(c*x)^2*ln(c*x)+8/3*b^2*c^3*d^3*arctan(c*x)-1/3*d^3*a^2/x^3-1/2*c^3*d^3*b^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*c^3*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*c^3*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*c^3*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-2*I*c^3*d^3*a*b*arctan(c*x)*ln(c*x)-3*I*c*d^3*a*b*arctan(c*x)/x^2+1/3*I*c^3*d^3*b^2/(I*c*x+(c^2*x^2+1)^(1/2)+1)*(c^2*x^2+1)^(1/2)-3*I*c^3*d^3*a*b*arctan(c*x)+1/2*c^3*d^3*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+1/2*I*c^3*d^3*b^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-20/3*I*c^3*d^3*b^2*dilog((1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*c^3*d^3*b^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I*c^3*d^3*b^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I*c^3*d^3*b^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)-2*I*c^3*d^3*b^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+20/3*I*c^3*d^3*b^2*dilog(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*I*c*d^3*a^2/x^2+11/6*I*c^3*d^3*b^2*arctan(c*x)^2-I*c^3*d^3*a^2*ln(c*x)-c^3*d^3*a*b*dilog(1-I*c*x)-20/3*c^3*d^3*b^2*arctan(c*x)*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*c^3*d^3*b^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*c^3*d^3*b^2*Pi*arctan(c*x)^2+3*c^2*d^3*b^2*arctan(c*x)^2/x-1/3*c*d^3*b^2*arctan(c*x)/x^2-20/3*c^3*d^3*a*b*ln(c*x)+10/3*c^3*d^3*a*b*ln(c^2*x^2+1)+c^3*d^3*a*b*dilog(1+I*c*x)-1/3*c*d^3*a*b/x^2-2/3*d^3*a*b*arctan(c*x)/x^3-2*c^3*d^3*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+c^3*d^3*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))","C"
92,1,757,271,0.122000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^5,x)","-\frac{d^{3} a^{2}}{4 x^{4}}-\frac{2 i c \,d^{3} a b \arctan \left(c x \right)}{x^{3}}+\frac{2 i c^{3} d^{3} a b \arctan \left(c x \right)}{x}-\frac{b^{2} c^{2} d^{3}}{12 x^{2}}-\frac{i c^{2} d^{3} a b}{x^{2}}+\frac{11 b^{2} c^{4} d^{3} \ln \left(c^{2} x^{2}+1\right)}{6}+c^{4} d^{3} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)-c^{4} d^{3} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)-\frac{i b^{2} c^{3} d^{3}}{x}-i b^{2} c^{4} d^{3} \arctan \left(c x \right)-c^{4} d^{3} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)+c^{4} d^{3} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)-\frac{i c \,d^{3} a^{2}}{x^{3}}+\frac{i c^{3} d^{3} a^{2}}{x}+2 c^{4} d^{3} b^{2} \ln \left(c x \right) \ln \left(i c x +1\right)-2 c^{4} d^{3} b^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)+\frac{7 c^{3} d^{3} a b}{2 x}-\frac{c \,d^{3} a b}{6 x^{3}}+\frac{7 c^{3} d^{3} b^{2} \arctan \left(c x \right)}{2 x}-\frac{d^{3} a b \arctan \left(c x \right)}{2 x^{4}}+\frac{3 c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2}}{2 x^{2}}+\frac{7 c^{4} d^{3} a b \arctan \left(c x \right)}{2}-\frac{i c \,d^{3} b^{2} \arctan \left(c x \right)^{2}}{x^{3}}-\frac{i c^{2} d^{3} b^{2} \arctan \left(c x \right)}{x^{2}}+2 i c^{4} d^{3} a b \ln \left(c^{2} x^{2}+1\right)-4 i c^{4} d^{3} a b \ln \left(c x \right)-4 i c^{4} d^{3} b^{2} \arctan \left(c x \right) \ln \left(c x \right)+\frac{i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2}}{x}+2 i c^{4} d^{3} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)-\frac{c \,d^{3} b^{2} \arctan \left(c x \right)}{6 x^{3}}+\frac{3 c^{2} d^{3} a b \arctan \left(c x \right)}{x^{2}}-\frac{c^{4} d^{3} b^{2} \ln \left(c x +i\right)^{2}}{2}+2 c^{4} d^{3} b^{2} \dilog \left(i c x +1\right)-2 c^{4} d^{3} b^{2} \dilog \left(-i c x +1\right)+c^{4} d^{3} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)-c^{4} d^{3} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)+\frac{c^{4} d^{3} b^{2} \ln \left(c x -i\right)^{2}}{2}-\frac{11 c^{4} d^{3} b^{2} \ln \left(c x \right)}{3}+\frac{7 c^{4} d^{3} b^{2} \arctan \left(c x \right)^{2}}{4}+\frac{3 c^{2} d^{3} a^{2}}{2 x^{2}}-\frac{d^{3} b^{2} \arctan \left(c x \right)^{2}}{4 x^{4}}"," ",0,"-I*b^2*c^3*d^3/x-I*b^2*c^4*d^3*arctan(c*x)-1/4*d^3*a^2/x^4-2*I*c*d^3*a*b*arctan(c*x)/x^3+2*I*c^3*d^3*a*b*arctan(c*x)/x-1/12*b^2*c^2*d^3/x^2+11/6*b^2*c^4*d^3*ln(c^2*x^2+1)-c^4*d^3*b^2*ln(c*x-I)*ln(c^2*x^2+1)+c^4*d^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+7/2*c^3*d^3*a*b/x-1/6*c*d^3*a*b/x^3+7/2*c^3*d^3*b^2*arctan(c*x)/x-1/2*d^3*a*b*arctan(c*x)/x^4-I*c*d^3*a^2/x^3+3/2*c^2*d^3*b^2*arctan(c*x)^2/x^2+I*c^3*d^3*a^2/x+7/2*c^4*d^3*a*b*arctan(c*x)+2*c^4*d^3*b^2*ln(c*x)*ln(1+I*c*x)-2*c^4*d^3*b^2*ln(c*x)*ln(1-I*c*x)+c^4*d^3*b^2*ln(I+c*x)*ln(c^2*x^2+1)-c^4*d^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-1/6*c*d^3*b^2*arctan(c*x)/x^3+I*c^3*d^3*b^2*arctan(c*x)^2/x+3*c^2*d^3*a*b*arctan(c*x)/x^2+2*I*c^4*d^3*b^2*arctan(c*x)*ln(c^2*x^2+1)-4*I*c^4*d^3*b^2*arctan(c*x)*ln(c*x)+2*I*c^4*d^3*a*b*ln(c^2*x^2+1)-4*I*c^4*d^3*a*b*ln(c*x)-I*c*d^3*b^2*arctan(c*x)^2/x^3-I*c^2*d^3*b^2*arctan(c*x)/x^2-I*c^2*d^3*a*b/x^2-1/2*c^4*d^3*b^2*ln(I+c*x)^2+1/2*c^4*d^3*b^2*ln(c*x-I)^2-11/3*c^4*d^3*b^2*ln(c*x)+7/4*c^4*d^3*b^2*arctan(c*x)^2+3/2*c^2*d^3*a^2/x^2-1/4*d^3*b^2*arctan(c*x)^2/x^4+2*c^4*d^3*b^2*dilog(1+I*c*x)-2*c^4*d^3*b^2*dilog(1-I*c*x)+c^4*d^3*b^2*dilog(-1/2*I*(I+c*x))-c^4*d^3*b^2*dilog(1/2*I*(c*x-I))","B"
93,1,816,337,0.117000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^6,x)","-\frac{d^{3} a^{2}}{5 x^{5}}-\frac{3 i c^{5} d^{3} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{5}+\frac{3 i c^{5} d^{3} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{5}+\frac{6 i c^{5} d^{3} b^{2} \ln \left(c x \right) \ln \left(i c x +1\right)}{5}-\frac{6 i c^{5} d^{3} b^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)}{5}+\frac{3 i c^{5} d^{3} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{5}+\frac{i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2}}{2 x^{2}}-\frac{3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2}}{4 x^{4}}-\frac{i c^{2} d^{3} b^{2} \arctan \left(c x \right)}{2 x^{3}}+\frac{5 i c^{4} d^{3} b^{2} \arctan \left(c x \right)}{2 x}+\frac{5 i c^{5} d^{3} a b \arctan \left(c x \right)}{2}-\frac{i c^{2} d^{3} a b}{2 x^{3}}+\frac{5 i c^{4} d^{3} a b}{2 x}-\frac{3 i c^{5} d^{3} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{5}+\frac{6 i c^{5} d^{3} b^{2} \dilog \left(i c x +1\right)}{5}-\frac{6 i c^{5} d^{3} b^{2} \dilog \left(-i c x +1\right)}{5}-\frac{3 i c^{5} d^{3} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{5}-\frac{c \,d^{3} b^{2} \arctan \left(c x \right)}{10 x^{4}}+\frac{6 c^{3} d^{3} b^{2} \arctan \left(c x \right)}{5 x^{2}}+\frac{c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2}}{x^{3}}+\frac{12 c^{5} d^{3} b^{2} \arctan \left(c x \right) \ln \left(c x \right)}{5}-\frac{6 c^{5} d^{3} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{5}-\frac{2 d^{3} a b \arctan \left(c x \right)}{5 x^{5}}-\frac{c \,d^{3} a b}{10 x^{4}}+\frac{12 c^{5} d^{3} a b \ln \left(c x \right)}{5}-\frac{6 c^{5} d^{3} a b \ln \left(c^{2} x^{2}+1\right)}{5}+\frac{6 c^{3} d^{3} a b}{5 x^{2}}+\frac{2 c^{2} d^{3} a b \arctan \left(c x \right)}{x^{3}}+\frac{i c^{3} d^{3} a b \arctan \left(c x \right)}{x^{2}}-\frac{3 i c \,d^{3} a b \arctan \left(c x \right)}{2 x^{4}}-\frac{d^{3} b^{2} \arctan \left(c x \right)^{2}}{5 x^{5}}+\frac{c^{2} d^{3} a^{2}}{x^{3}}+\frac{3 i c^{5} d^{3} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{5}-\frac{3 i c \,d^{3} a^{2}}{4 x^{4}}+\frac{i c^{3} d^{3} a^{2}}{2 x^{2}}-\frac{3 i c^{5} d^{3} b^{2} \ln \left(c x +i\right)^{2}}{10}+\frac{3 i c^{5} d^{3} b^{2} \ln \left(c x -i\right)^{2}}{10}-3 i c^{5} d^{3} b^{2} \ln \left(c x \right)-\frac{i b^{2} c^{3} d^{3}}{4 x^{2}}+\frac{3 i b^{2} c^{5} d^{3} \ln \left(c^{2} x^{2}+1\right)}{2}+\frac{5 i c^{5} d^{3} b^{2} \arctan \left(c x \right)^{2}}{4}-\frac{b^{2} c^{2} d^{3}}{30 x^{3}}+\frac{13 b^{2} c^{4} d^{3}}{10 x}+\frac{13 b^{2} c^{5} d^{3} \arctan \left(c x \right)}{10}"," ",0,"-1/5*d^3*a^2/x^5-1/10*c*d^3*b^2*arctan(c*x)/x^4+6/5*c^3*d^3*b^2*arctan(c*x)/x^2+c^2*d^3*b^2*arctan(c*x)^2/x^3+12/5*c^5*d^3*b^2*arctan(c*x)*ln(c*x)-6/5*c^5*d^3*b^2*arctan(c*x)*ln(c^2*x^2+1)-2/5*d^3*a*b*arctan(c*x)/x^5-1/10*c*d^3*a*b/x^4+12/5*c^5*d^3*a*b*ln(c*x)-6/5*c^5*d^3*a*b*ln(c^2*x^2+1)+6/5*c^3*d^3*a*b/x^2-6/5*I*c^5*d^3*b^2*ln(c*x)*ln(1-I*c*x)+3/5*I*c^5*d^3*b^2*ln(I+c*x)*ln(c^2*x^2+1)+1/2*I*c^3*d^3*b^2*arctan(c*x)^2/x^2-3/4*I*c*d^3*b^2*arctan(c*x)^2/x^4-1/2*I*c^2*d^3*b^2*arctan(c*x)/x^3+5/2*I*c^4*d^3*b^2*arctan(c*x)/x+5/2*I*c^5*d^3*a*b*arctan(c*x)-1/2*I*c^2*d^3*a*b/x^3+5/2*I*c^4*d^3*a*b/x-3/5*I*c^5*d^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-3/5*I*c^5*d^3*b^2*ln(c*x-I)*ln(c^2*x^2+1)+3/5*I*c^5*d^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+2*c^2*d^3*a*b*arctan(c*x)/x^3+6/5*I*c^5*d^3*b^2*ln(c*x)*ln(1+I*c*x)-3/4*I*c*d^3*a^2/x^4+1/2*I*c^3*d^3*a^2/x^2+6/5*I*c^5*d^3*b^2*dilog(1+I*c*x)-6/5*I*c^5*d^3*b^2*dilog(1-I*c*x)-3/10*I*c^5*d^3*b^2*ln(I+c*x)^2-3/5*I*c^5*d^3*b^2*dilog(1/2*I*(c*x-I))+3/10*I*c^5*d^3*b^2*ln(c*x-I)^2+3/5*I*c^5*d^3*b^2*dilog(-1/2*I*(I+c*x))-3*I*c^5*d^3*b^2*ln(c*x)-1/4*I*b^2*c^3*d^3/x^2+I*c^3*d^3*a*b*arctan(c*x)/x^2-3/2*I*c*d^3*a*b*arctan(c*x)/x^4-1/5*d^3*b^2*arctan(c*x)^2/x^5+c^2*d^3*a^2/x^3+3/2*I*b^2*c^5*d^3*ln(c^2*x^2+1)+5/4*I*c^5*d^3*b^2*arctan(c*x)^2-1/30*b^2*c^2*d^3/x^3+13/10*b^2*c^4*d^3/x+13/10*b^2*c^5*d^3*arctan(c*x)","B"
94,1,853,451,0.125000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^7,x)","-\frac{d^{3} a^{2}}{6 x^{6}}+\frac{14 i c^{4} d^{3} a b}{15 x^{2}}+\frac{28 i c^{6} d^{3} a b \ln \left(c x \right)}{15}-\frac{14 i c^{6} d^{3} a b \ln \left(c^{2} x^{2}+1\right)}{15}-\frac{14 i c^{6} d^{3} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{15}+\frac{28 i c^{6} d^{3} b^{2} \arctan \left(c x \right) \ln \left(c x \right)}{15}-\frac{3 i c^{2} d^{3} a b}{10 x^{4}}+\frac{14 i c^{4} d^{3} b^{2} \arctan \left(c x \right)}{15 x^{2}}+\frac{i c^{3} d^{3} b^{2} \arctan \left(c x \right)^{2}}{3 x^{3}}-\frac{3 i c \,d^{3} b^{2} \arctan \left(c x \right)^{2}}{5 x^{5}}-\frac{3 i c^{2} d^{3} b^{2} \arctan \left(c x \right)}{10 x^{4}}+\frac{3 c^{2} d^{3} b^{2} \arctan \left(c x \right)^{2}}{4 x^{4}}+\frac{11 c^{3} d^{3} b^{2} \arctan \left(c x \right)}{18 x^{3}}-\frac{11 c^{5} d^{3} b^{2} \arctan \left(c x \right)}{6 x}-\frac{c \,d^{3} b^{2} \arctan \left(c x \right)}{15 x^{5}}-\frac{c \,d^{3} a b}{15 x^{5}}-\frac{d^{3} a b \arctan \left(c x \right)}{3 x^{6}}-\frac{11 c^{5} d^{3} a b}{6 x}+\frac{11 c^{3} d^{3} a b}{18 x^{3}}-\frac{6 i c \,d^{3} a b \arctan \left(c x \right)}{5 x^{5}}+\frac{2 i c^{3} d^{3} a b \arctan \left(c x \right)}{3 x^{3}}-\frac{113 b^{2} c^{6} d^{3} \ln \left(c^{2} x^{2}+1\right)}{90}+\frac{14 c^{6} d^{3} b^{2} \dilog \left(-i c x +1\right)}{15}-\frac{7 c^{6} d^{3} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{15}+\frac{7 c^{6} d^{3} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{15}+\frac{7 c^{6} d^{3} b^{2} \ln \left(c x +i\right)^{2}}{30}-\frac{7 c^{6} d^{3} b^{2} \ln \left(c x -i\right)^{2}}{30}-\frac{14 c^{6} d^{3} b^{2} \dilog \left(i c x +1\right)}{15}+\frac{i c^{3} d^{3} a^{2}}{3 x^{3}}-\frac{3 i c \,d^{3} a^{2}}{5 x^{5}}+\frac{7 c^{6} d^{3} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{15}-\frac{7 c^{6} d^{3} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{15}-\frac{14 c^{6} d^{3} b^{2} \ln \left(c x \right) \ln \left(i c x +1\right)}{15}+\frac{14 c^{6} d^{3} b^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)}{15}-\frac{7 c^{6} d^{3} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{15}+\frac{7 c^{6} d^{3} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{15}-\frac{i b^{2} c^{3} d^{3}}{10 x^{3}}+\frac{37 i b^{2} c^{5} d^{3}}{30 x}+\frac{37 i b^{2} c^{6} d^{3} \arctan \left(c x \right)}{30}+\frac{113 c^{6} d^{3} b^{2} \ln \left(c x \right)}{45}-\frac{11 c^{6} d^{3} b^{2} \arctan \left(c x \right)^{2}}{12}+\frac{3 c^{2} d^{3} a^{2}}{4 x^{4}}-\frac{d^{3} b^{2} \arctan \left(c x \right)^{2}}{6 x^{6}}-\frac{11 c^{6} d^{3} a b \arctan \left(c x \right)}{6}+\frac{3 c^{2} d^{3} a b \arctan \left(c x \right)}{2 x^{4}}-\frac{b^{2} c^{2} d^{3}}{60 x^{4}}+\frac{61 b^{2} c^{4} d^{3}}{180 x^{2}}"," ",0,"-1/6*d^3*a^2/x^6+1/3*I*c^3*d^3*a^2/x^3-3/5*I*c*d^3*a^2/x^5+3/4*c^2*d^3*b^2*arctan(c*x)^2/x^4+11/18*c^3*d^3*b^2*arctan(c*x)/x^3-11/6*c^5*d^3*b^2*arctan(c*x)/x-1/15*c*d^3*b^2*arctan(c*x)/x^5+7/15*c^6*d^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-1/15*c*d^3*a*b/x^5-1/3*d^3*a*b*arctan(c*x)/x^6-7/15*c^6*d^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-14/15*c^6*d^3*b^2*ln(c*x)*ln(1+I*c*x)+14/15*c^6*d^3*b^2*ln(c*x)*ln(1-I*c*x)-7/15*c^6*d^3*b^2*ln(I+c*x)*ln(c^2*x^2+1)-11/6*c^5*d^3*a*b/x+11/18*c^3*d^3*a*b/x^3+7/15*c^6*d^3*b^2*ln(c*x-I)*ln(c^2*x^2+1)-1/10*I*b^2*c^3*d^3/x^3+37/30*I*b^2*c^5*d^3/x+37/30*I*b^2*c^6*d^3*arctan(c*x)-6/5*I*c*d^3*a*b*arctan(c*x)/x^5+2/3*I*c^3*d^3*a*b*arctan(c*x)/x^3-113/90*b^2*c^6*d^3*ln(c^2*x^2+1)+7/30*c^6*d^3*b^2*ln(I+c*x)^2-7/30*c^6*d^3*b^2*ln(c*x-I)^2+113/45*c^6*d^3*b^2*ln(c*x)-11/12*c^6*d^3*b^2*arctan(c*x)^2+3/4*c^2*d^3*a^2/x^4-1/6*d^3*b^2*arctan(c*x)^2/x^6-14/15*c^6*d^3*b^2*dilog(1+I*c*x)+14/15*c^6*d^3*b^2*dilog(1-I*c*x)-7/15*c^6*d^3*b^2*dilog(-1/2*I*(I+c*x))+7/15*c^6*d^3*b^2*dilog(1/2*I*(c*x-I))-11/6*c^6*d^3*a*b*arctan(c*x)+3/2*c^2*d^3*a*b*arctan(c*x)/x^4-3/10*I*c^2*d^3*a*b/x^4+14/15*I*c^4*d^3*b^2*arctan(c*x)/x^2+1/3*I*c^3*d^3*b^2*arctan(c*x)^2/x^3-3/5*I*c*d^3*b^2*arctan(c*x)^2/x^5-3/10*I*c^2*d^3*b^2*arctan(c*x)/x^4-14/15*I*c^6*d^3*b^2*arctan(c*x)*ln(c^2*x^2+1)+28/15*I*c^6*d^3*b^2*arctan(c*x)*ln(c*x)+14/15*I*c^4*d^3*a*b/x^2+28/15*I*c^6*d^3*a*b*ln(c*x)-14/15*I*c^6*d^3*a*b*ln(c^2*x^2+1)-1/60*b^2*c^2*d^3/x^4+61/180*b^2*c^4*d^3/x^2","A"
95,1,1331,324,7.939000," ","int(x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x),x)","-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c^{4} d}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{4} d}-\frac{2 i a b \arctan \left(c x \right) x^{3}}{3 c d}+\frac{2 i a b \arctan \left(c x \right) x}{c^{3} d}+\frac{a b \arctan \left(c x \right) x^{2}}{c^{2} d}-\frac{a b x}{c^{3} d}-\frac{b^{2} x \arctan \left(c x \right)}{c^{3} d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c^{4} d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c^{4} d}+\frac{8 i b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{4} d}+\frac{b^{2}}{3 c^{4} d}+\frac{8 i b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{4} d}+\frac{i b^{2} \arctan \left(c x \right)^{2} x}{c^{3} d}+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2}}{c^{4} d}-\frac{2 a b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{4} d}-\frac{i b^{2} \arctan \left(c x \right)^{2} x^{3}}{3 c d}+\frac{i b^{2} \arctan \left(c x \right) x^{2}}{3 c^{2} d}+\frac{i a b \,x^{2}}{3 c^{2} d}-\frac{11 i a b \ln \left(c^{2} x^{2}+1\right)}{12 c^{4} d}-\frac{i a b \ln \left(c x -i\right)^{2}}{2 c^{4} d}-\frac{5 i a b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{24 c^{4} d}-\frac{i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{4} d}+\frac{i a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{4} d}-\frac{i b^{2} x}{3 c^{3} d}+\frac{4 i b^{2} \arctan \left(c x \right)}{3 c^{4} d}-\frac{i a^{2} \arctan \left(c x \right)}{c^{4} d}-\frac{i a^{2} x^{3}}{3 c d}-\frac{5 a b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{6 c^{4} d}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{4} d}-\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(c x -i\right)}{c^{4} d}+\frac{i a^{2} x}{c^{3} d}-\frac{2 i b^{2} \arctan \left(c x \right)^{3}}{3 c^{4} d}+\frac{4 i a b}{3 c^{4} d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c^{4} d}-\frac{5 a b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{12 c^{4} d}+\frac{5 a b \arctan \left(\frac{c x}{2}\right)}{12 c^{4} d}+\frac{11 a b \arctan \left(c x \right)}{6 c^{4} d}+\frac{b^{2} \arctan \left(c x \right)^{2} x^{2}}{2 c^{2} d}+\frac{a^{2} x^{2}}{2 c^{2} d}+\frac{11 b^{2} \arctan \left(c x \right)^{2}}{6 c^{4} d}-\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{4} d}-\frac{b^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{4} d}+\frac{b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{4} d}+\frac{8 b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{4} d}+\frac{8 b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{4} d}+\frac{i a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{4} d}"," ",0,"8/3*I/c^4*b^2/d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+8/3*I/c^4*b^2/d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^4*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+I/c^3*b^2/d*arctan(c*x)^2*x+1/c^2*a*b/d*arctan(c*x)*x^2+I/c^4*b^2/d*Pi*arctan(c*x)^2+I/c^4*a*b/d*dilog(-1/2*I*(I+c*x))-2/c^4*a*b/d*arctan(c*x)*ln(c*x-I)-1/3*I/c*b^2/d*arctan(c*x)^2*x^3+1/3*I/c^2*b^2/d*arctan(c*x)*x^2+1/3*I/c^2*a*b/d*x^2-11/12*I/c^4*a*b/d*ln(c^2*x^2+1)-1/2*I/c^4*a*b/d*ln(c*x-I)^2-5/24*I/c^4*a*b/d*ln(c^4*x^4+10*c^2*x^2+9)-1/3*I*b^2*x/c^3/d-1/2*I/c^4*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I/c^4*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-a*b*x/c^3/d-b^2*x*arctan(c*x)/c^3/d+1/3/c^4*b^2/d-1/2*I/c^4*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+I/c^4*a*b/d*ln(c*x-I)*ln(-1/2*I*(I+c*x))+4/3*I/c^4*b^2/d*arctan(c*x)-I/c^4*a^2/d*arctan(c*x)-1/3*I/c*a^2/d*x^3-5/12/c^4*a*b/d*arctan(1/6*c^3*x^3+7/6*c*x)+5/12/c^4*a*b/d*arctan(1/2*c*x)-5/6/c^4*a*b/d*arctan(1/2*c*x-1/2*I)+11/6/c^4*a*b/d*arctan(c*x)+1/c^4*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-1/c^4*b^2/d*arctan(c*x)^2*ln(c*x-I)+1/2/c^2*b^2/d*arctan(c*x)^2*x^2+I/c^3*a^2/d*x-2/3*I/c^4*b^2/d*arctan(c*x)^3+1/2/c^2*a^2/d*x^2+11/6/c^4*b^2/d*arctan(c*x)^2+1/2/c^4*b^2/d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+8/3/c^4*b^2/d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c^4*b^2/d*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+8/3/c^4*b^2/d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2/c^4*a^2/d*ln(c^2*x^2+1)+4/3*I/c^4*a*b/d-1/2*I/c^4*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-I/c^4*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-2/3*I/c*a*b/d*arctan(c*x)*x^3+2*I/c^3*a*b/d*arctan(c*x)*x","C"
96,1,1212,256,4.065000," ","int(x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x),x)","-\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c^{3} d}+\frac{b^{2} \arctan \left(c x \right)^{2} x}{c^{2} d}+\frac{b^{2} \pi  \arctan \left(c x \right)^{2}}{c^{3} d}-\frac{a b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{8 c^{3} d}-\frac{3 a b \ln \left(c^{2} x^{2}+1\right)}{4 c^{3} d}-\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c^{3} d}+\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c^{3} d}-\frac{i a b \arctan \left(c x \right) x^{2}}{c d}+\frac{2 i a b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{3} d}+\frac{i a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{3} d}-\frac{i a^{2} x^{2}}{2 c d}+\frac{i b^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{3} d}-\frac{a b \ln \left(c x -i\right)^{2}}{2 c^{3} d}+\frac{2 b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{2 b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}-\frac{3 i b^{2} \arctan \left(c x \right)^{2}}{2 c^{3} d}-\frac{2 i b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{3} d}-\frac{2 i b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}-\frac{b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{3} d}-\frac{i b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{3} d}+\frac{i a b x}{c^{2} d}+\frac{i b^{2} x \arctan \left(c x \right)}{c^{2} d}-\frac{b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c^{3} d}+\frac{i b^{2} \arctan \left(c x \right)^{2} \ln \left(c x -i\right)}{c^{3} d}+\frac{a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{3} d}-\frac{b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{3} d}-\frac{i b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{3} d}-\frac{i b^{2} \arctan \left(c x \right)^{2} x^{2}}{2 c d}-\frac{i a b \arctan \left(\frac{c x}{2}\right)}{4 c^{3} d}+\frac{i a b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{4 c^{3} d}+\frac{i a b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{2 c^{3} d}-\frac{3 i a b \arctan \left(c x \right)}{2 c^{3} d}+\frac{2 a b \arctan \left(c x \right) x}{c^{2} d}+\frac{a b}{c^{3} d}+\frac{a^{2} x}{c^{2} d}-\frac{a^{2} \arctan \left(c x \right)}{c^{3} d}+\frac{b^{2} \arctan \left(c x \right)}{c^{3} d}-\frac{2 b^{2} \arctan \left(c x \right)^{3}}{3 c^{3} d}"," ",0,"-2*I/c^3*b^2/d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I/c^3*a^2/d*ln(c^2*x^2+1)-1/2/c^3*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*I/c*a^2/d*x^2+1/c^2*b^2/d*arctan(c*x)^2*x+1/c^3*b^2/d*Pi*arctan(c*x)^2+I/c^3*b^2/d*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/c^3*a*b/d*dilog(-1/2*I*(I+c*x))-1/2/c^3*a*b/d*ln(c*x-I)^2-1/8/c^3*a*b/d*ln(c^4*x^4+10*c^2*x^2+9)-3/4/c^3*a*b/d*ln(c^2*x^2+1)+2/c^3*b^2/d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I*a*b*x/c^2/d+I*b^2*x*arctan(c*x)/c^2/d-2*I/c^3*b^2/d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2/c^3*b^2/d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c^3*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-3/2*I/c^3*b^2/d*arctan(c*x)^2-1/2*I/c^3*b^2/d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-1/2/c^3*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2/c^3*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-I/c*a*b/d*arctan(c*x)*x^2+2*I/c^3*a*b/d*arctan(c*x)*ln(c*x-I)-1/2/c^3*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+I/c^3*b^2/d*arctan(c*x)^2*ln(c*x-I)+1/c^3*a*b/d*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/c^3*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+2/c^2*a*b/d*arctan(c*x)*x-I/c^3*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-1/2*I/c*b^2/d*arctan(c*x)^2*x^2-1/4*I/c^3*a*b/d*arctan(1/2*c*x)+1/4*I/c^3*a*b/d*arctan(1/6*c^3*x^3+7/6*c*x)+1/2*I/c^3*a*b/d*arctan(1/2*c*x-1/2*I)-3/2*I/c^3*a*b/d*arctan(c*x)+1/c^3*a*b/d+1/c^2*a^2/d*x-1/c^3*a^2/d*arctan(c*x)+1/c^3*b^2/d*arctan(c*x)-2/3/c^3*b^2/d*arctan(c*x)^3","C"
97,1,4589,182,0.911000," ","int(x*(a+b*arctan(c*x))^2/(d+I*c*d*x),x)","\text{output too large to display}"," ",0,"-1/c^2*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))+1/c^2*b^2/d*ln(c*x-I)*arctan(c*x)^2-1/2/c^2*a*b/d*arctan(1/4*c*x)+1/c^2*a*b/d*arctan(1/2*c*x-1/2*I)-1/2/c^2*a*b/d*arctan(1/12*c^3*x^3+13/12*c*x)+I/c^2*a^2/d*arctan(c*x)-I/c*a^2/d*x+2/3*I/c^2*b^2/d*arctan(c*x)^3-1/c^2*b^2/d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2/c^2*b^2/d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-1/c^2*b^2/d*arctan(c*x)^2-1/2/c^2*b^2/d*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-1/c^2*b^2/d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2/c^2*a^2/d*ln(c^2*x^2+1)+1/2/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*I/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/4*I/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-1/2*I/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/2/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I/c*a*b/d*arctan(c*x)*x-I/c^2*a*b/d*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/4*I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+1/2*I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2*I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-1/2*I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/2/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I/c^2*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+2/c^2*a*b/d*ln(c*x-I)*arctan(c*x)-I/c^2*b^2/d*arctan(c*x)^2*Pi-I/c^2*b^2/d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^2*b^2/d*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-I/c^2*b^2/d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c*b^2/d*arctan(c*x)^2*x-1/2*I/c^2*b^2/d*Pi*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-I/c^2*a*b/d*dilog(-1/2*I*(I+c*x))+1/2*I/c^2*a*b/d*ln(c*x-I)^2+1/4*I/c^2*a*b/d*ln(c^8*x^8+12*c^6*x^6+30*c^4*x^4+28*c^2*x^2+9)-1/c^2*b^2/d*Pi*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I/c^2*b^2/d*Pi*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I/c^2*b^2/d*Pi*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/c^2*b^2/d*Pi*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/c^2*b^2/d*Pi*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*I/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/4*I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+1/2/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/2/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/2*I/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/4*I/c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+1/2*I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I/c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))","C"
98,1,1062,91,0.553000," ","int((a+b*arctan(c*x))^2/(d+I*c*d*x),x)","\frac{i b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c d}+\frac{a^{2} \arctan \left(c x \right)}{c d}-\frac{2 i a b \ln \left(i c x +1\right) \arctan \left(c x \right)}{c d}-\frac{i b^{2} \ln \left(i c x +1\right) \arctan \left(c x \right)^{2}}{c d}-\frac{b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c d}-\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c d}-\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c d}-\frac{b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{2} \pi  \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c d}-\frac{i a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c d}+\frac{2 b^{2} \arctan \left(c x \right)^{3}}{3 c d}+\frac{i b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c d}+\frac{a b \ln \left(\frac{1}{2}-\frac{i c x}{2}\right) \ln \left(\frac{i c x}{2}+\frac{1}{2}\right)}{c d}-\frac{a b \ln \left(\frac{1}{2}-\frac{i c x}{2}\right) \ln \left(i c x +1\right)}{c d}+\frac{a b \dilog \left(\frac{i c x}{2}+\frac{1}{2}\right)}{c d}+\frac{a b \ln \left(i c x +1\right)^{2}}{2 c d}"," ",0,"I/c*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))+1/c*a^2/d*arctan(c*x)-2*I/c*a*b/d*ln(1+I*c*x)*arctan(c*x)-I/c*b^2/d*ln(1+I*c*x)*arctan(c*x)^2-1/2/c*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-1/2/c*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2/c*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2/c*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+1/2/c*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2/c*b^2/d*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-1/2/c*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2/c*b^2/d*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2/c*b^2/d*Pi*arctan(c*x)^2+1/c*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-1/2*I/c*a^2/d*ln(c^2*x^2+1)+2/3/c*b^2/d*arctan(c*x)^3+1/2*I/c*b^2/d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+1/c*a*b/d*ln(1/2-1/2*I*c*x)*ln(1/2*I*c*x+1/2)-1/c*a*b/d*ln(1/2-1/2*I*c*x)*ln(1+I*c*x)+1/c*a*b/d*dilog(1/2*I*c*x+1/2)+1/2/c*a*b/d*ln(1+I*c*x)^2","C"
99,1,1741,82,0.500000," ","int((a+b*arctan(c*x))^2/x/(d+I*c*d*x),x)","\frac{2 b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{2 b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}-\frac{i a b \ln \left(c x \right) \ln \left(-i c x +1\right)}{d}+\frac{i a b \ln \left(c x \right) \ln \left(i c x +1\right)}{d}-\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3}}{2 d}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2}}{2 d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 d}+\frac{a^{2} \ln \left(c x \right)}{d}-\frac{2 i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{2 i b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{i a b \dilog \left(i c x +1\right)}{d}+\frac{i a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{d}-\frac{i a b \dilog \left(-i c x +1\right)}{d}+\frac{3 i b^{2} \pi  \arctan \left(c x \right)^{2}}{2 d}-\frac{2 a b \ln \left(c x -i\right) \arctan \left(c x \right)}{d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}-\frac{i a b \ln \left(c x -i\right)^{2}}{2 d}-\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{d}-\frac{2 i b^{2} \arctan \left(c x \right)^{3}}{3 d}-\frac{i a^{2} \arctan \left(c x \right)}{d}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{d}-\frac{b^{2} \ln \left(c x -i\right) \arctan \left(c x \right)^{2}}{d}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{2 a b \arctan \left(c x \right) \ln \left(c x \right)}{d}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)}{d}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d}+\frac{i a b \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right)}{d}-\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 d}"," ",0,"a^2/d*ln(c*x)+2*b^2/d*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2/d*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*I*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2-b^2/d*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)-2/3*I*b^2/d*arctan(c*x)^3-I*a^2/d*arctan(c*x)+b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-b^2/d*ln(c*x-I)*arctan(c*x)^2-2*I*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*b^2/d*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I*b^2/d*Pi*arctan(c*x)^2-2*a*b/d*ln(c*x-I)*arctan(c*x)+2*a*b/d*arctan(c*x)*ln(c*x)+I*a*b/d*dilog(1+I*c*x)+I*a*b/d*dilog(-1/2*I*(I+c*x))-I*a*b/d*dilog(1-I*c*x)-1/2*I*a*b/d*ln(c*x-I)^2-1/2*I*b^2/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-I*a*b/d*ln(c*x)*ln(1-I*c*x)+I*a*b/d*ln(c*x)*ln(1+I*c*x)-1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3-I*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2*I*b^2/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+I*a*b/d*ln(-1/2*I*(I+c*x))*ln(c*x-I)-1/2*I*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+b^2/d*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2/d*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2/d*arctan(c*x)^2*ln(c*x)-1/2*a^2/d*ln(c^2*x^2+1)+1/2*I*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*I*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2","C"
100,1,9235,175,1.289000," ","int((a+b*arctan(c*x))^2/x^2/(d+I*c*d*x),x)","\text{output too large to display}"," ",0,"result too large to display","C"
101,1,2221,257,7.153000," ","int((a+b*arctan(c*x))^2/x^3/(d+I*c*d*x),x)","-\frac{2 c^{2} a b \arctan \left(c x \right) \ln \left(c x \right)}{d}-\frac{a^{2}}{2 d \,x^{2}}+\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}-\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}-\frac{i c^{2} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2 d}-\frac{2 c^{2} b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{2 c^{2} b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{2 c^{2} b^{2} \dilog \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{2 c^{2} b^{2} \dilog \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{c^{2} b^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{c^{2} b^{2} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}-1\right)}{d}-\frac{i c^{2} b^{2} \arctan \left(c x \right)}{d}+\frac{2 i c^{2} b^{2} \arctan \left(c x \right)^{3}}{3 d}-\frac{b^{2} \arctan \left(c x \right)^{2}}{2 d \,x^{2}}-\frac{c^{2} a^{2} \ln \left(c x \right)}{d}-\frac{3 c^{2} b^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{c^{2} a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d}+\frac{i c^{2} a^{2} \arctan \left(c x \right)}{d}-\frac{c^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{c^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{c^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{d}-\frac{c^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{d}+\frac{c^{2} b^{2} \ln \left(c x -i\right) \arctan \left(c x \right)^{2}}{d}+\frac{i c \,a^{2}}{d x}-\frac{i c^{2} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2 d}+\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 d}+\frac{2 c^{2} a b \ln \left(c x -i\right) \arctan \left(c x \right)}{d}+\frac{i c \,b^{2} \arctan \left(c x \right)^{2}}{d x}+\frac{i c^{2} a b \ln \left(c^{2} x^{2}+1\right)}{d}+\frac{i c^{2} a b \ln \left(c x -i\right)^{2}}{2 d}-\frac{2 i c^{2} a b \ln \left(c x \right)}{d}-\frac{a b \arctan \left(c x \right)}{d \,x^{2}}-\frac{c \,b^{2} \arctan \left(c x \right)}{d x}-\frac{c^{2} a b \arctan \left(c x \right)}{d}-\frac{c^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)}{d}+\frac{i c^{2} a b \ln \left(c x \right) \ln \left(-i c x +1\right)}{d}+\frac{i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{d}-\frac{i c^{2} a b \ln \left(c x \right) \ln \left(i c x +1\right)}{d}-\frac{i c^{2} a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{d}-\frac{i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d}-\frac{i c^{2} b^{2} \arctan \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3}}{2 d}+\frac{i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 d}+\frac{2 i c a b \arctan \left(c x \right)}{d x}-\frac{2 i c^{2} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{3 i c^{2} b^{2} \arctan \left(c x \right)^{2} \pi}{2 d}+\frac{i c^{2} a b \dilog \left(-i c x +1\right)}{d}-\frac{i c^{2} a b \dilog \left(i c x +1\right)}{d}+\frac{2 i c^{2} b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{2 i c^{2} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{i c^{2} a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{d}-\frac{c a b}{d x}"," ",0,"2*c^2*a*b/d*ln(c*x-I)*arctan(c*x)-2*c^2*a*b/d*arctan(c*x)*ln(c*x)+I*c*b^2/d*arctan(c*x)^2/x+I*c^2*a*b/d*ln(c^2*x^2+1)+I*c^2*a*b/d*dilog(1-I*c*x)+1/2*I*c^2*a*b/d*ln(c*x-I)^2-2*I*c^2*a*b/d*ln(c*x)-I*c^2*a*b/d*dilog(1+I*c*x)-2*I*c^2*b^2/d*arctan(c*x)*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*I*c^2*b^2/d*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*I*c^2*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*I*c^2*b^2/d*arctan(c*x)^2*Pi-I*c^2*a*b/d*dilog(-1/2*I*(I+c*x))-1/2*a^2/d/x^2-1/2*b^2/d*arctan(c*x)^2/x^2-c^2*a^2/d*ln(c*x)-2*c^2*b^2/d*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*c^2*b^2/d*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*c^2*b^2/d*dilog(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*c^2*b^2/d*dilog((1+I*c*x)/(c^2*x^2+1)^(1/2))+c^2*b^2/d*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+c^2*b^2/d*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)-3/2*c^2*b^2/d*arctan(c*x)^2+1/2*c^2*a^2/d*ln(c^2*x^2+1)-a*b/d*arctan(c*x)/x^2-c*b^2/d*arctan(c*x)/x+I*c^2*a^2/d*arctan(c*x)-c^2*a*b/d*arctan(c*x)-c^2*b^2/d*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-c^2*b^2/d*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-c^2*b^2/d*arctan(c*x)^2*ln(c*x)+c^2*b^2/d*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)-c^2*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))+c^2*b^2/d*ln(c*x-I)*arctan(c*x)^2+I*c*a^2/d/x-I*c^2*b^2/d*arctan(c*x)+2/3*I*c^2*b^2/d*arctan(c*x)^3+1/2*I*c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*c^2*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*c^2*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*c^2*b^2/d*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))-1/2*I*c^2*b^2/d*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+1/2*I*c^2*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-I*c^2*a*b/d*ln(c*x)*ln(1+I*c*x)-I*c^2*a*b/d*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*I*c^2*b^2/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-1/2*I*c^2*b^2/d*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3+1/2*I*c^2*b^2/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+2*I*c*a*b/d*arctan(c*x)/x+I*c^2*a*b/d*ln(c*x)*ln(1-I*c*x)+I*c^2*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-c*a*b/d/x","C"
102,1,2380,332,9.979000," ","int((a+b*arctan(c*x))^2/x^4/(d+I*c*d*x),x)","-\frac{c^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{c^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{c^{2} b^{2} \arctan \left(c x \right)^{2}}{d x}-\frac{c^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 d}+\frac{c^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 d}+\frac{c^{2} a^{2}}{d x}-\frac{b^{2} \arctan \left(c x \right)^{2}}{3 d \,x^{3}}+\frac{2 c^{3} b^{2} \arctan \left(c x \right)^{3}}{3 d}+\frac{c^{3} a^{2} \arctan \left(c x \right)}{d}-\frac{4 b^{2} c^{3} \arctan \left(c x \right)}{3 d}-\frac{3 c^{3} b^{2} \pi  \arctan \left(c x \right)^{2}}{2 d}+\frac{i c a b \arctan \left(c x \right)}{d \,x^{2}}+\frac{c^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{c^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{c^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}-\frac{c^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 d}-\frac{2 i c^{3} a b \arctan \left(c x \right) \ln \left(c x -i\right)}{d}+\frac{2 i c^{3} a b \arctan \left(c x \right) \ln \left(c x \right)}{d}+\frac{2 c^{2} a b \arctan \left(c x \right)}{d x}-\frac{a^{2}}{3 d \,x^{3}}-\frac{c \,b^{2} \arctan \left(c x \right)}{3 d \,x^{2}}-\frac{2 a b \arctan \left(c x \right)}{3 d \,x^{3}}-\frac{8 c^{3} a b \ln \left(c x \right)}{3 d}-\frac{c a b}{3 d \,x^{2}}+\frac{4 c^{3} a b \ln \left(c^{2} x^{2}+1\right)}{3 d}-\frac{i c^{3} b^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{11 i c^{3} b^{2} \arctan \left(c x \right)^{2}}{6 d}+\frac{c^{3} a b \ln \left(c x -i\right)^{2}}{2 d}+\frac{2 c^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{2 c^{3} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{c^{3} a b \dilog \left(-i c x +1\right)}{d}+\frac{8 i c^{3} b^{2} \dilog \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{3 d}+\frac{2 i c^{3} b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{2 i c^{3} b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{8 i c^{3} b^{2} \dilog \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{3 d}-\frac{c^{3} a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{d}-\frac{c^{3} a b \dilog \left(i c x +1\right)}{d}+\frac{i c^{2} a b}{d x}+\frac{i c^{2} b^{2} \arctan \left(c x \right)}{d x}-\frac{c^{3} a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{d}-\frac{c^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d}+\frac{i c^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{d}+\frac{c^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d}+\frac{i c^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{i c^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{c^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d}+\frac{i c^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)}{d}+\frac{c^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{d}+\frac{c^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 d}-\frac{c^{3} a b \ln \left(c x \right) \ln \left(i c x +1\right)}{d}+\frac{c^{3} a b \ln \left(c x \right) \ln \left(-i c x +1\right)}{d}+\frac{i c^{3} a b \arctan \left(c x \right)}{d}+\frac{i c \,b^{2} \arctan \left(c x \right)^{2}}{2 d \,x^{2}}-\frac{i c^{3} b^{2} \sqrt{c^{2} x^{2}+1}}{3 d \left(i c x -\sqrt{c^{2} x^{2}+1}+1\right)}-\frac{i c^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{d}+\frac{i c^{3} b^{2} \sqrt{c^{2} x^{2}+1}}{3 d \left(i c x +\sqrt{c^{2} x^{2}+1}+1\right)}-\frac{i c^{3} b^{2} \arctan \left(c x \right)^{2} \ln \left(c x -i\right)}{d}+\frac{i c^{3} a^{2} \ln \left(c x \right)}{d}-\frac{8 c^{3} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{3 d}-\frac{i c^{3} a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d}-\frac{i c^{3} b^{2} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}-1\right)}{d}+\frac{i c \,a^{2}}{2 d \,x^{2}}"," ",0,"I*c*a*b/d*arctan(c*x)/x^2+1/2*c^3*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*c^3*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+2*c^3*b^2/d*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+c^2*b^2/d*arctan(c*x)^2/x+1/2*c^3*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*c^3*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*c^3*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-2*I*c^3*a*b/d*arctan(c*x)*ln(c*x-I)+2*I*c^3*a*b/d*arctan(c*x)*ln(c*x)+1/2*c^3*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+c^2*a^2/d/x-1/3*b^2/d*arctan(c*x)^2/x^3+2/3*c^3*b^2/d*arctan(c*x)^3+c^3*a^2/d*arctan(c*x)-4/3*b^2*c^3*arctan(c*x)/d-3/2*c^3*b^2/d*Pi*arctan(c*x)^2+I*c^3*a^2/d*ln(c*x)+2*c^3*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-8/3*c^3*b^2/d*arctan(c*x)*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+I*c^2*a*b/d/x+2*c^2*a*b/d*arctan(c*x)/x+I*c^2*b^2/d*arctan(c*x)/x-c^3*a*b/d*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*c^3*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+I*c^3*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))+1/2*c^3*b^2/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+I*c^3*b^2/d*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+I*c^3*b^2/d*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*c^3*b^2/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+I*c^3*b^2/d*arctan(c*x)^2*ln(c*x)+c^3*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*c^3*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-c^3*a*b/d*ln(c*x)*ln(1+I*c*x)+c^3*a*b/d*ln(c*x)*ln(1-I*c*x)+I*c^3*a*b/d*arctan(c*x)+1/2*I*c*b^2/d*arctan(c*x)^2/x^2-1/3*I*c^3*b^2/d/(I*c*x-(c^2*x^2+1)^(1/2)+1)*(c^2*x^2+1)^(1/2)-I*c^3*b^2/d*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+1/3*I*c^3*b^2/d/(I*c*x+(c^2*x^2+1)^(1/2)+1)*(c^2*x^2+1)^(1/2)-I*c^3*b^2/d*arctan(c*x)^2*ln(c*x-I)-1/3*a^2/d/x^3-1/3*c*b^2/d*arctan(c*x)/x^2-2/3*a*b/d*arctan(c*x)/x^3+c^3*a*b/d*dilog(1-I*c*x)-8/3*c^3*a*b/d*ln(c*x)+8/3*I*c^3*b^2/d*dilog(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*I*c^3*b^2/d*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*I*c^3*b^2/d*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*I*c^3*a^2/d*ln(c^2*x^2+1)-I*c^3*b^2/d*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)+1/2*I*c*a^2/d/x^2-I*c^3*b^2/d*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-8/3*I*c^3*b^2/d*dilog((1+I*c*x)/(c^2*x^2+1)^(1/2))+11/6*I*c^3*b^2/d*arctan(c*x)^2-1/3*c*a*b/d/x^2+4/3*c^3*a*b/d*ln(c^2*x^2+1)-c^3*a*b/d*dilog(-1/2*I*(I+c*x))+1/2*c^3*a*b/d*ln(c*x-I)^2-c^3*a*b/d*dilog(1+I*c*x)-1/2*c^3*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*c^3*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2","C"
103,1,1498,400,7.904000," ","int(x^4*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x)","-\frac{2 b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{c^{5} d^{2}}-\frac{b^{2} x}{3 c^{4} d^{2}}-\frac{4 i b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{5} d^{2}}-\frac{i a b}{c^{5} d^{2} \left(c x -i\right)}+\frac{2 i a b x}{d^{2} c^{4}}+\frac{2 i b^{2} x \arctan \left(c x \right)}{d^{2} c^{4}}-\frac{b^{2} \arctan \left(c x \right) x}{2 c^{4} d^{2} \left(c x -i\right)}-\frac{2 b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{c^{5} d^{2}}-\frac{4 b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{5} d^{2}}+\frac{4 a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{5} d^{2}}+\frac{2 a b \arctan \left(c x \right)}{c^{5} d^{2} \left(c x -i\right)}-\frac{i b^{2} \arctan \left(c x \right)^{2} x^{2}}{c^{3} d^{2}}+\frac{2 i b^{2} x}{c^{4} d^{2} \left(8 c x -8 i\right)}+\frac{11 i a b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{12 c^{5} d^{2}}-\frac{29 i a b \arctan \left(c x \right)}{6 c^{5} d^{2}}+\frac{11 i a b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{6 c^{5} d^{2}}-\frac{11 i a b \arctan \left(\frac{c x}{2}\right)}{12 c^{5} d^{2}}+\frac{4 i b^{2} \arctan \left(c x \right)^{2} \ln \left(c x -i\right)}{c^{5} d^{2}}-\frac{i b^{2} \arctan \left(c x \right)}{2 c^{5} d^{2} \left(c x -i\right)}+\frac{b^{2} \arctan \left(c x \right) x^{2}}{3 c^{3} d^{2}}+\frac{3 b^{2} \arctan \left(c x \right)^{2} x}{c^{4} d^{2}}+\frac{4 b^{2} \pi  \arctan \left(c x \right)^{2}}{c^{5} d^{2}}+\frac{a b \,x^{2}}{3 c^{3} d^{2}}+\frac{7 b^{2} \arctan \left(c x \right)}{3 c^{5} d^{2}}-\frac{29 i b^{2} \arctan \left(c x \right)^{2}}{6 c^{5} d^{2}}+\frac{2 i b^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{5} d^{2}}+\frac{2 i a^{2} \ln \left(c^{2} x^{2}+1\right)}{c^{5} d^{2}}-\frac{i a^{2} x^{2}}{c^{3} d^{2}}-\frac{2 a b \ln \left(c x -i\right)^{2}}{c^{5} d^{2}}-\frac{4 b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{5} d^{2}}-\frac{2 i b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{5} d^{2}}-\frac{20 i b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{5} d^{2}}-\frac{20 i b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{5} d^{2}}+\frac{4 a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{5} d^{2}}+\frac{b^{2} \arctan \left(c x \right)^{2}}{c^{5} d^{2} \left(c x -i\right)}+\frac{20 b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{5} d^{2}}+\frac{20 b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{5} d^{2}}+\frac{6 a b \arctan \left(c x \right) x}{c^{4} d^{2}}+\frac{7 a b}{3 c^{5} d^{2}}-\frac{a^{2} x^{3}}{3 c^{2} d^{2}}+\frac{3 a^{2} x}{c^{4} d^{2}}-\frac{8 b^{2} \arctan \left(c x \right)^{3}}{3 c^{5} d^{2}}-\frac{4 a^{2} \arctan \left(c x \right)}{c^{5} d^{2}}-\frac{i b^{2}}{3 c^{5} d^{2}}-\frac{2 b^{2}}{c^{5} d^{2} \left(8 c x -8 i\right)}+\frac{a^{2}}{c^{5} d^{2} \left(c x -i\right)}+\frac{2 b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{5} d^{2}}-\frac{2 b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{5} d^{2}}+\frac{8 i a b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{5} d^{2}}-\frac{2 i a b \arctan \left(c x \right) x^{2}}{c^{3} d^{2}}-\frac{11 a b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{24 c^{5} d^{2}}-\frac{29 a b \ln \left(c^{2} x^{2}+1\right)}{12 c^{5} d^{2}}-\frac{b^{2} \arctan \left(c x \right)^{2} x^{3}}{3 c^{2} d^{2}}-\frac{2 a b \arctan \left(c x \right) x^{3}}{3 c^{2} d^{2}}"," ",0,"2/c^5*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-2/c^5*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/3*b^2*x/c^4/d^2-29/6*I/c^5*b^2/d^2*arctan(c*x)^2-2*I/c^5*b^2/d^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-20/3*I/c^5*b^2/d^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-20/3*I/c^5*b^2/d^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*I/c^5*b^2/d^2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+2*I/c^5*a^2/d^2*ln(c^2*x^2+1)-I/c^3*a^2/d^2*x^2+1/3/c^3*b^2/d^2*arctan(c*x)*x^2+3/c^4*b^2/d^2*arctan(c*x)^2*x+4/c^5*b^2/d^2*Pi*arctan(c*x)^2-2/c^5*a*b/d^2*ln(c*x-I)^2+4/c^5*a*b/d^2*dilog(-1/2*I*(I+c*x))+1/3/c^3*a*b/d^2*x^2+7/3*b^2*arctan(c*x)/c^5/d^2+6/c^4*a*b/d^2*arctan(c*x)*x-1/2/c^4*b^2/d^2*arctan(c*x)/(c*x-I)*x-2/c^5*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-4/c^5*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+4/c^5*a*b/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+2/c^5*a*b/d^2*arctan(c*x)/(c*x-I)-I/c^3*b^2/d^2*arctan(c*x)^2*x^2+2*I/c^4*b^2/d^2/(8*c*x-8*I)*x+11/12*I/c^5*a*b/d^2*arctan(1/6*c^3*x^3+7/6*c*x)-29/6*I/c^5*a*b/d^2*arctan(c*x)+11/6*I/c^5*a*b/d^2*arctan(1/2*c*x-1/2*I)-11/12*I/c^5*a*b/d^2*arctan(1/2*c*x)+4*I/c^5*b^2/d^2*arctan(c*x)^2*ln(c*x-I)-1/2*I/c^5*b^2/d^2*arctan(c*x)/(c*x-I)-4*I/c^5*b^2/d^2*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-I/c^5*a*b/d^2/(c*x-I)+7/3/c^5*a*b/d^2-1/3*I/c^5*b^2/d^2-1/3/c^2*a^2/d^2*x^3+3/c^4*a^2/d^2*x-2/c^5*b^2/d^2/(8*c*x-8*I)-8/3/c^5*b^2/d^2*arctan(c*x)^3-4/c^5*a^2/d^2*arctan(c*x)+1/c^5*a^2/d^2/(c*x-I)-2/c^5*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+8*I/c^5*a*b/d^2*arctan(c*x)*ln(c*x-I)-2*I/c^3*a*b/d^2*arctan(c*x)*x^2+2*I*a*b*x/d^2/c^4+2*I*b^2*x*arctan(c*x)/d^2/c^4-11/24/c^5*a*b/d^2*ln(c^4*x^4+10*c^2*x^2+9)-29/12/c^5*a*b/d^2*ln(c^2*x^2+1)+1/c^5*b^2/d^2*arctan(c*x)^2/(c*x-I)+20/3/c^5*b^2/d^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+20/3/c^5*b^2/d^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-4/c^5*b^2/d^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-1/3/c^2*b^2/d^2*arctan(c*x)^2*x^3-2/3/c^2*a*b/d^2*arctan(c*x)*x^3","C"
104,1,1395,340,5.345000," ","int(x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x)","\frac{a b x}{c^{3} d^{2}}+\frac{b^{2} x \arctan \left(c x \right)}{c^{3} d^{2}}-\frac{a b \arctan \left(c x \right) x^{2}}{c^{2} d^{2}}-\frac{a^{2} x^{2}}{2 c^{2} d^{2}}-\frac{3 b^{2} \arctan \left(c x \right)^{2}}{c^{4} d^{2}}+\frac{3 a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{4} d^{2}}+\frac{3 i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c^{4} d^{2}}-\frac{4 i a b \arctan \left(c x \right) x}{c^{3} d^{2}}-\frac{2 i a b \arctan \left(c x \right)}{c^{4} d^{2} \left(c x -i\right)}-\frac{3 i a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{4} d^{2}}+\frac{3 i b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c^{4} d^{2}}+\frac{3 i b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{4} d^{2}}+\frac{i b^{2} \arctan \left(c x \right) x}{c^{3} d^{2} \left(2 c x -2 i\right)}-\frac{a b \arctan \left(\frac{c x}{2}\right)}{2 c^{4} d^{2}}-\frac{3 a b \arctan \left(c x \right)}{c^{4} d^{2}}-\frac{b^{2} \arctan \left(c x \right)^{2} x^{2}}{2 c^{2} d^{2}}+\frac{a b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{2 c^{4} d^{2}}+\frac{a b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{c^{4} d^{2}}+\frac{b^{2} x}{4 c^{3} d^{2} \left(c x -i\right)}-\frac{a b}{c^{4} d^{2} \left(c x -i\right)}-\frac{b^{2} \arctan \left(c x \right)}{c^{4} d^{2} \left(2 c x -2 i\right)}+\frac{3 b^{2} \ln \left(c x -i\right) \arctan \left(c x \right)^{2}}{c^{4} d^{2}}-\frac{3 b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{4} d^{2}}+\frac{3 i a^{2} \arctan \left(c x \right)}{c^{4} d^{2}}-\frac{i a^{2}}{c^{4} d^{2} \left(c x -i\right)}-\frac{2 i a^{2} x}{c^{3} d^{2}}-\frac{i b^{2} \arctan \left(c x \right)}{c^{4} d^{2}}+\frac{i b^{2}}{4 c^{4} d^{2} \left(c x -i\right)}+\frac{2 i b^{2} \arctan \left(c x \right)^{3}}{c^{4} d^{2}}-\frac{i a b}{c^{4} d^{2}}+\frac{3 i b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c^{4} d^{2}}-\frac{3 i b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2}}{2 c^{4} d^{2}}+\frac{3 i a b \ln \left(c^{2} x^{2}+1\right)}{2 c^{4} d^{2}}+\frac{i a b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{4 c^{4} d^{2}}-\frac{4 i b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{4} d^{2}}-\frac{4 i b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{4} d^{2}}+\frac{b^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{4} d^{2}}-\frac{4 b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{4} d^{2}}-\frac{4 b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{4} d^{2}}-\frac{3 b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{4} d^{2}}-\frac{i b^{2} \arctan \left(c x \right)^{2}}{c^{4} d^{2} \left(c x -i\right)}+\frac{6 a b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{4} d^{2}}-\frac{2 i b^{2} \arctan \left(c x \right)^{2} x}{c^{3} d^{2}}-\frac{3 i b^{2} \pi  \arctan \left(c x \right)^{2}}{c^{4} d^{2}}+\frac{3 i a b \ln \left(c x -i\right)^{2}}{2 c^{4} d^{2}}+\frac{3 i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{4} d^{2}}-\frac{3 i a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{4} d^{2}}"," ",0,"3/2*I/c^4*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+a*b*x/c^3/d^2+b^2*x*arctan(c*x)/c^3/d^2+3/2*I/c^4*a*b/d^2*ln(c^2*x^2+1)+1/4*I/c^4*a*b/d^2*ln(c^4*x^4+10*c^2*x^2+9)-4*I/c^4*b^2/d^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-4*I/c^4*b^2/d^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I/c^4*b^2/d^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-I/c^4*b^2/d^2*arctan(c*x)^2/(c*x-I)-1/c^2*a*b/d^2*arctan(c*x)*x^2+6/c^4*a*b/d^2*arctan(c*x)*ln(c*x-I)-2*I/c^3*b^2/d^2*arctan(c*x)^2*x-3*I/c^4*b^2/d^2*Pi*arctan(c*x)^2+3/2*I/c^4*a*b/d^2*ln(c*x-I)^2-3*I/c^4*a*b/d^2*dilog(-1/2*I*(I+c*x))-1/2/c^2*a^2/d^2*x^2-3/c^4*b^2/d^2*arctan(c*x)^2-4/c^4*b^2/d^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-4/c^4*b^2/d^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/c^4*b^2/d^2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-3/2/c^4*b^2/d^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+3/2/c^4*a^2/d^2*ln(c^2*x^2+1)+3/2*I/c^4*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-4*I/c^3*a*b/d^2*arctan(c*x)*x-2*I/c^4*a*b/d^2*arctan(c*x)/(c*x-I)-3*I/c^4*a*b/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+3/2*I/c^4*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+3*I/c^4*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2/c^4*a*b/d^2*arctan(1/2*c*x)+1/c^4*a*b/d^2*arctan(1/2*c*x-1/2*I)+1/4/c^3*b^2/d^2/(c*x-I)*x-1/c^4*a*b/d^2/(c*x-I)-3/c^4*a*b/d^2*arctan(c*x)-1/2/c^2*b^2/d^2*arctan(c*x)^2*x^2-1/c^4*b^2/d^2*arctan(c*x)/(2*c*x-2*I)+3/c^4*b^2/d^2*ln(c*x-I)*arctan(c*x)^2-3/c^4*b^2/d^2*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))+1/2/c^4*a*b/d^2*arctan(1/6*c^3*x^3+7/6*c*x)+3*I/c^4*a^2/d^2*arctan(c*x)-I/c^4*a^2/d^2/(c*x-I)-2*I/c^3*a^2/d^2*x-I/c^4*b^2/d^2*arctan(c*x)+1/4*I/c^4*b^2/d^2/(c*x-I)+2*I/c^4*b^2/d^2*arctan(c*x)^3+I/c^3*b^2/d^2*arctan(c*x)/(2*c*x-2*I)*x-I/c^4*a*b/d^2-3/2*I/c^4*b^2/d^2*arctan(c*x)^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2","C"
105,1,4774,273,0.884000," ","int(x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x)","\text{output too large to display}"," ",0,"-2*I/c^3*b^2/d^2*arctan(c*x)^2*ln(c*x-I)+1/2*I/c^3*b^2/d^2*arctan(c*x)/(c*x-I)+2*I/c^3*b^2/d^2*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-1/4*I/c^3*a*b/d^2*arctan(1/6*c^3*x^3+7/6*c*x)+1/4*I/c^3*a*b/d^2*arctan(1/2*c*x)-1/2*I/c^3*a*b/d^2*arctan(1/2*c*x-1/2*I)+3/2*I/c^3*a*b/d^2*arctan(c*x)+1/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+2/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-2/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-1/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+I/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-I/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-2*I/c^3*b^2/d^2*Pi*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+2*I/c^3*b^2/d^2*Pi*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*I/c^3*b^2/d^2*Pi*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-4*I/c^3*a*b/d^2*arctan(c*x)*ln(c*x-I)-2/c^3*b^2/d^2*Pi*arctan(c*x)^2+1/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-1/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+1/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c^2*a^2/d^2*x+2/c^3*a^2/d^2*arctan(c*x)-1/c^3*a^2/d^2/(c*x-I)+2/c^3*b^2/d^2/(8*c*x-8*I)+1/8/c^3*a*b/d^2*ln(c^4*x^4+10*c^2*x^2+9)+3/4/c^3*a*b/d^2*ln(c^2*x^2+1)+I/c^3*b^2/d^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+1/c^3*a*b/d^2*ln(c*x-I)^2-2/c^3*a*b/d^2*dilog(-1/2*I*(I+c*x))+4/3/c^3*b^2/d^2*arctan(c*x)^3+2/c^3*b^2/d^2*Pi*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2/c^3*b^2/d^2*Pi*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c^3*b^2/d^2*Pi*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-1/c^2*b^2/d^2*arctan(c*x)^2*x-3/2/c^3*b^2/d^2*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/c^3*b^2/d^2*arctan(c*x)^2/(c*x-I)-1/2/c^3*b^2/d^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2/c^3*b^2/d^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2/c^3*b^2/d^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+3/4*I/c^3*b^2/d^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+1/2*I/c^3*b^2/d^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^3*a^2/d^2*ln(c^2*x^2+1)+3/2*I/c^3*b^2/d^2*arctan(c*x)^2+1/2*I/c^3*b^2/d^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-2/c^3*a*b/d^2*arctan(c*x)/(c*x-I)-2/c^3*a*b/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-2/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+I/c^3*a*b/d^2/(c*x-I)-2/c^2*a*b/d^2*arctan(c*x)*x+1/2/c^2*b^2/d^2*arctan(c*x)/(c*x-I)*x-2*I/c^2*b^2/d^2/(8*c*x-8*I)*x-1/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-2*I/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*I/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-I/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I/c^3*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+I/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-I/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^3*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))","C"
106,1,1059,198,0.405000," ","int(x*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x)","\frac{a b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{2 c^{2} d^{2}}+\frac{2 b^{2} \arctan \left(c x \right)}{c^{2} d^{2} \left(4 c x -4 i\right)}-\frac{b^{2} \ln \left(c x -i\right) \arctan \left(c x \right)^{2}}{c^{2} d^{2}}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{2} d^{2}}-\frac{2 i b^{2} \arctan \left(c x \right)^{3}}{3 c^{2} d^{2}}-\frac{i b^{2}}{4 c^{2} d^{2} \left(c x -i\right)}-\frac{i a^{2} \arctan \left(c x \right)}{c^{2} d^{2}}+\frac{i a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{2} d^{2}}-\frac{i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{2} d^{2}}-\frac{i b^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \pi  \arctan \left(c x \right)^{2}}{2 c^{2} d^{2}}-\frac{i a b \ln \left(c^{2} x^{2}+1\right)}{4 c^{2} d^{2}}-\frac{i a b \ln \left(c x -i\right)^{2}}{2 c^{2} d^{2}}+\frac{i b^{2} \arctan \left(c x \right)^{2}}{c^{2} d^{2} \left(c x -i\right)}-\frac{2 a b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{2} d^{2}}+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2}}{c^{2} d^{2}}+\frac{i a b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{8 c^{2} d^{2}}+\frac{b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{2} d^{2}}+\frac{b^{2} \arctan \left(c x \right)^{2}}{2 c^{2} d^{2}}-\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{2} d^{2}}-\frac{2 i b^{2} \arctan \left(c x \right) x}{c \,d^{2} \left(4 c x -4 i\right)}+\frac{2 i a b \arctan \left(c x \right)}{c^{2} d^{2} \left(c x -i\right)}-\frac{i b^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \pi  \arctan \left(c x \right)^{2}}{2 c^{2} d^{2}}+\frac{i a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{2} d^{2}}-\frac{i b^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \pi  \arctan \left(c x \right)^{2}}{c^{2} d^{2}}+\frac{a b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{4 c^{2} d^{2}}+\frac{a b \arctan \left(c x \right)}{2 c^{2} d^{2}}-\frac{a b \arctan \left(\frac{c x}{2}\right)}{4 c^{2} d^{2}}+\frac{i a^{2}}{c^{2} d^{2} \left(c x -i\right)}-\frac{b^{2} x}{4 c \,d^{2} \left(c x -i\right)}+\frac{a b}{c^{2} d^{2} \left(c x -i\right)}-\frac{i b^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \pi  \arctan \left(c x \right)^{2}}{2 c^{2} d^{2}}+\frac{i b^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \pi  \arctan \left(c x \right)^{2}}{2 c^{2} d^{2}}"," ",0,"-1/2*I/c^2*b^2/d^2*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*Pi*arctan(c*x)^2-1/4*I/c^2*a*b/d^2*ln(c^2*x^2+1)-1/2*I/c^2*a*b/d^2*ln(c*x-I)^2+I/c^2*b^2/d^2*arctan(c*x)^2/(c*x-I)-2/c^2*a*b/d^2*arctan(c*x)*ln(c*x-I)+I/c^2*b^2/d^2*Pi*arctan(c*x)^2+I/c^2*a*b/d^2*dilog(-1/2*I*(I+c*x))-I/c^2*b^2/d^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+1/8*I/c^2*a*b/d^2*ln(c^4*x^4+10*c^2*x^2+9)+I/c^2*a^2/d^2/(c*x-I)+1/2/c^2*b^2/d^2*arctan(c*x)^2+1/2/c^2*b^2/d^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-1/2/c^2*a^2/d^2*ln(c^2*x^2+1)-I/c^2*b^2/d^2*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*arctan(c*x)^2-2*I/c*b^2/d^2*arctan(c*x)/(4*c*x-4*I)*x+2*I/c^2*a*b/d^2*arctan(c*x)/(c*x-I)-1/2*I/c^2*b^2/d^2*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*Pi*arctan(c*x)^2+1/4/c^2*a*b/d^2*arctan(1/6*c^3*x^3+7/6*c*x)-1/4/c*b^2/d^2/(c*x-I)*x+1/c^2*a*b/d^2/(c*x-I)+1/2/c^2*a*b/d^2*arctan(c*x)-1/4/c^2*a*b/d^2*arctan(1/2*c*x)+1/2/c^2*a*b/d^2*arctan(1/2*c*x-1/2*I)+2/c^2*b^2/d^2*arctan(c*x)/(4*c*x-4*I)-1/c^2*b^2/d^2*ln(c*x-I)*arctan(c*x)^2+1/c^2*b^2/d^2*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-2/3*I/c^2*b^2/d^2*arctan(c*x)^3-1/4*I/c^2*b^2/d^2/(c*x-I)-I/c^2*a^2/d^2*arctan(c*x)+I/c^2*a*b/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*I/c^2*b^2/d^2*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*arctan(c*x)^2+1/2*I/c^2*b^2/d^2*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*Pi*arctan(c*x)^2","C"
107,1,344,110,0.081000," ","int((a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x)","\frac{i a^{2}}{c \,d^{2} \left(i c x +1\right)}+\frac{i b^{2} \arctan \left(c x \right)^{2}}{c \,d^{2} \left(i c x +1\right)}+\frac{b^{2} \arctan \left(c x \right) \ln \left(c x +i\right)}{2 c \,d^{2}}-\frac{b^{2} \arctan \left(c x \right) \ln \left(c x -i\right)}{2 c \,d^{2}}-\frac{i b^{2} \arctan \left(c x \right)}{c \,d^{2} \left(c x -i\right)}+\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{4 c \,d^{2}}-\frac{i b^{2} \ln \left(c x -i\right)^{2}}{8 c \,d^{2}}-\frac{b^{2} \arctan \left(c x \right)}{2 c \,d^{2}}-\frac{b^{2}}{2 c \,d^{2} \left(c x -i\right)}-\frac{i b^{2} \ln \left(c x +i\right)^{2}}{8 c \,d^{2}}+\frac{i b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(c x +i\right)}{4 c \,d^{2}}-\frac{i b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{4 c \,d^{2}}+\frac{2 i a b \arctan \left(c x \right)}{c \,d^{2} \left(i c x +1\right)}-\frac{i a b \arctan \left(c x \right)}{c \,d^{2}}-\frac{i a b}{c \,d^{2} \left(c x -i\right)}"," ",0,"I/c*a^2/d^2/(1+I*c*x)+I/c*b^2/d^2/(1+I*c*x)*arctan(c*x)^2+1/2/c*b^2/d^2*arctan(c*x)*ln(I+c*x)-1/2/c*b^2/d^2*arctan(c*x)*ln(c*x-I)-I/c*b^2/d^2*arctan(c*x)/(c*x-I)+1/4*I/c*b^2/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/8*I/c*b^2/d^2*ln(c*x-I)^2-1/2*b^2*arctan(c*x)/c/d^2-1/2/c*b^2/d^2/(c*x-I)-1/8*I/c*b^2/d^2*ln(I+c*x)^2+1/4*I/c*b^2/d^2*ln(-1/2*I*(-c*x+I))*ln(I+c*x)-1/4*I/c*b^2/d^2*ln(-1/2*I*(-c*x+I))*ln(-1/2*I*(I+c*x))+2*I/c*a*b/d^2/(1+I*c*x)*arctan(c*x)-I/c*a*b/d^2*arctan(c*x)-I/c*a*b/d^2/(c*x-I)","B"
108,1,1921,202,0.544000," ","int((a+b*arctan(c*x))^2/x/(d+I*c*d*x)^2,x)","-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{2 b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{2 b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{b^{2} \arctan \left(c x \right)^{2}}{2 d^{2}}-\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d^{2}}+\frac{a^{2} \ln \left(c x \right)}{d^{2}}-\frac{i b^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \pi  \arctan \left(c x \right)^{2}}{d^{2}}+\frac{i a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{d^{2}}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{2 a b \arctan \left(c x \right) \ln \left(c x \right)}{d^{2}}+\frac{2 i b^{2} \arctan \left(c x \right) c x}{d^{2} \left(4 c x -4 i\right)}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{b^{2} c x}{4 d^{2} \left(c x -i\right)}+\frac{i a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{d^{2}}+\frac{i a b \dilog \left(i c x +1\right)}{d^{2}}-\frac{i a b \dilog \left(-i c x +1\right)}{d^{2}}-\frac{2 i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{i a b \ln \left(c x -i\right)^{2}}{2 d^{2}}-\frac{i b^{2} \arctan \left(c x \right)^{2}}{d^{2} \left(c x -i\right)}-\frac{2 a b \arctan \left(c x \right) \ln \left(c x -i\right)}{d^{2}}-\frac{2 i b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{3 i b^{2} \pi  \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{i b^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \pi  \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 d^{2}}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{2}}-\frac{i b^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \pi  \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)}{d^{2}}-\frac{a b \arctan \left(c x \right)}{d^{2}}-\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{d^{2}}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{a b}{d^{2} \left(c x -i\right)}-\frac{2 b^{2} \arctan \left(c x \right)}{d^{2} \left(4 c x -4 i\right)}-\frac{2 i b^{2} \arctan \left(c x \right)^{3}}{3 d^{2}}-\frac{i a^{2} \arctan \left(c x \right)}{d^{2}}-\frac{b^{2} \ln \left(c x -i\right) \arctan \left(c x \right)^{2}}{d^{2}}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{i b^{2}}{4 d^{2} \left(c x -i\right)}-\frac{i a^{2}}{d^{2} \left(c x -i\right)}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{i a b \ln \left(c x \right) \ln \left(i c x +1\right)}{d^{2}}-\frac{2 i a b \arctan \left(c x \right)}{d^{2} \left(c x -i\right)}-\frac{i a b \ln \left(c x \right) \ln \left(-i c x +1\right)}{d^{2}}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{2}}-\frac{i b^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \pi  \arctan \left(c x \right)^{2}}{2 d^{2}}-\frac{i b^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \pi  \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 d^{2}}"," ",0,"1/2*I*b^2/d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+I*a*b/d^2*ln(c*x)*ln(1+I*c*x)-2*I*a*b/d^2*arctan(c*x)/(c*x-I)-I*a*b/d^2*ln(c*x)*ln(1-I*c*x)-1/2*I*b^2/d^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2/d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*b^2/d^2*arctan(c*x)^2-1/2*a^2/d^2*ln(c^2*x^2+1)+a^2/d^2*ln(c*x)+2*b^2/d^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2/d^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*I*b^2/d^2*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*Pi*arctan(c*x)^2-I*b^2/d^2*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*arctan(c*x)^2+I*a*b/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/2*I*b^2/d^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-1/2*I*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+2*a*b/d^2*arctan(c*x)*ln(c*x)+1/4*b^2/d^2/(c*x-I)*c*x+2*I*b^2/d^2*arctan(c*x)/(4*c*x-4*I)*c*x-1/2*I*a*b/d^2*ln(c*x-I)^2+I*a*b/d^2*dilog(-1/2*I*(I+c*x))-I*b^2/d^2*arctan(c*x)^2/(c*x-I)-2*a*b/d^2*arctan(c*x)*ln(c*x-I)+I*a*b/d^2*dilog(1+I*c*x)-I*a*b/d^2*dilog(1-I*c*x)-2*I*b^2/d^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*b^2/d^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I*b^2/d^2*Pi*arctan(c*x)^2-1/2*I*b^2/d^2*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*arctan(c*x)^2+1/2*I*b^2/d^2*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*Pi*arctan(c*x)^2-1/2*I*b^2/d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+b^2/d^2*arctan(c*x)^2*ln(c*x)-b^2/d^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+b^2/d^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2/d^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-a*b/d^2/(c*x-I)-a*b/d^2*arctan(c*x)-2*b^2/d^2*arctan(c*x)/(4*c*x-4*I)-2/3*I*b^2/d^2*arctan(c*x)^3-I*a^2/d^2*arctan(c*x)-b^2/d^2*ln(c*x-I)*arctan(c*x)^2+b^2/d^2*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))+1/2*I*b^2/d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+1/4*I*b^2/d^2/(c*x-I)-I*a^2/d^2/(c*x-I)-1/2*I*b^2/d^2*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*Pi*arctan(c*x)^2+1/2*I*b^2/d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2","C"
109,1,9420,285,1.530000," ","int((a+b*arctan(c*x))^2/x^2/(d+I*c*d*x)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
110,1,2378,378,7.142000," ","int((a+b*arctan(c*x))^2/x^3/(d+I*c*d*x)^2,x)","-\frac{3 i c^{2} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2}}{2 d^{2}}+\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{2}}-\frac{a b \arctan \left(c x \right)}{d^{2} x^{2}}+\frac{3 i c^{2} a b \dilog \left(-i c x +1\right)}{d^{2}}-\frac{3 i c^{2} a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{d^{2}}-\frac{3 i c^{2} a b \dilog \left(i c x +1\right)}{d^{2}}+\frac{6 i c^{2} b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{6 i c^{2} b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{3 c^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)}{d^{2}}-\frac{3 i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d^{2}}-\frac{3 i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{3 i c^{2} a b \ln \left(c x \right) \ln \left(-i c x +1\right)}{d^{2}}+\frac{3 i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{4 i c a b \arctan \left(c x \right)}{d^{2} x}+\frac{i c^{2} b^{2} \arctan \left(c x \right)^{2}}{d^{2} \left(c x -i\right)}+\frac{6 c^{2} a b \arctan \left(c x \right) \ln \left(c x -i\right)}{d^{2}}+\frac{3 i c^{2} a b \ln \left(c x -i\right)^{2}}{2 d^{2}}+\frac{2 i c \,b^{2} \arctan \left(c x \right)^{2}}{d^{2} x}-\frac{4 i c^{2} a b \ln \left(c x \right)}{d^{2}}-\frac{4 i c^{2} b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{2 i c^{2} a b \ln \left(c^{2} x^{2}+1\right)}{d^{2}}-\frac{9 i c^{2} b^{2} \pi  \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{4 c^{2} b^{2} \dilog \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{4 c^{2} b^{2} \dilog \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{c^{2} b^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{i c^{3} b^{2} \arctan \left(c x \right) x}{d^{2} \left(2 c x -2 i\right)}+\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 d^{2}}-\frac{3 i c^{2} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2 d^{2}}-\frac{3 i c^{2} b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2 d^{2}}+\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{2}}+\frac{c \,b^{2} \arctan \left(c x \right) \sqrt{c^{2} x^{2}+1}}{d^{2} x}-\frac{6 c^{2} a b \arctan \left(c x \right) \ln \left(c x \right)}{d^{2}}-\frac{3 c^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{c^{2} b^{2} \arctan \left(c x \right)}{d^{2} \left(2 c x -2 i\right)}+\frac{3 c^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{d^{2}}-\frac{3 c^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{3 c^{2} b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{c^{3} b^{2} x}{4 d^{2} \left(c x -i\right)}+\frac{i c^{2} a^{2}}{d^{2} \left(c x -i\right)}+\frac{c^{2} a b}{d^{2} \left(c x -i\right)}+\frac{3 c^{2} b^{2} \ln \left(c x -i\right) \arctan \left(c x \right)^{2}}{d^{2}}+\frac{2 i c \,a^{2}}{d^{2} x}-\frac{i c^{2} b^{2}}{4 d^{2} \left(c x -i\right)}+\frac{2 i c^{2} b^{2} \arctan \left(c x \right)^{3}}{d^{2}}+\frac{3 i c^{2} a^{2} \arctan \left(c x \right)}{d^{2}}-\frac{c a b}{d^{2} x}+\frac{c^{2} b^{2} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}-1\right)}{d^{2}}-\frac{6 c^{2} b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{6 c^{2} b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{3 i c^{2} a b \ln \left(c x \right) \ln \left(i c x +1\right)}{d^{2}}+\frac{2 i c^{2} a b \arctan \left(c x \right)}{d^{2} \left(c x -i\right)}-\frac{3 i c^{2} a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{d^{2}}-\frac{b^{2} \arctan \left(c x \right)^{2}}{2 d^{2} x^{2}}-\frac{2 c^{2} b^{2} \arctan \left(c x \right)^{2}}{d^{2}}-\frac{3 c^{2} a^{2} \ln \left(c x \right)}{d^{2}}+\frac{3 c^{2} a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d^{2}}-\frac{a^{2}}{2 d^{2} x^{2}}+\frac{3 i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{d^{2}}+\frac{3 i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 d^{2}}"," ",0,"c^2*b^2/d^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)+3*I*c^2*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*c^2*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3/2*I*c^2*b^2/d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3/2*I*c^2*b^2/d^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+3*I*c^2*a*b/d^2*ln(c*x)*ln(1-I*c*x)-3*I*c^2*a*b/d^2*ln(c*x)*ln(1+I*c*x)+2*I*c^2*a*b/d^2*arctan(c*x)/(c*x-I)-3*I*c^2*a*b/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-a*b/d^2*arctan(c*x)/x^2-3*c^2*b^2/d^2*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))+c^2*b^2/d^2*arctan(c*x)/(2*c*x-2*I)-3*c^2*b^2/d^2*arctan(c*x)^2*ln(c*x)+3*c^2*b^2/d^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)-3*c^2*b^2/d^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*c^2*b^2/d^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/4*c^3*b^2/d^2/(c*x-I)*x+I*c^2*a^2/d^2/(c*x-I)+c^2*a*b/d^2/(c*x-I)+3*c^2*b^2/d^2*ln(c*x-I)*arctan(c*x)^2+2*I*c*a^2/d^2/x-1/4*I*c^2*b^2/d^2/(c*x-I)+2*I*c^2*b^2/d^2*arctan(c*x)^3+3*I*c^2*a^2/d^2*arctan(c*x)+3/2*I*c^2*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-3/2*I*c^2*b^2/d^2*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+c*b^2/d^2*arctan(c*x)/x*(c^2*x^2+1)^(1/2)+I*c^2*b^2/d^2*arctan(c*x)^2/(c*x-I)-6*c^2*a*b/d^2*arctan(c*x)*ln(c*x)+6*c^2*a*b/d^2*arctan(c*x)*ln(c*x-I)+3*I*c^2*a*b/d^2*dilog(1-I*c*x)+3/2*I*c^2*a*b/d^2*ln(c*x-I)^2+2*I*c*b^2/d^2*arctan(c*x)^2/x-4*I*c^2*a*b/d^2*ln(c*x)-3*I*c^2*a*b/d^2*dilog(-1/2*I*(I+c*x))-3*I*c^2*a*b/d^2*dilog(1+I*c*x)+6*I*c^2*b^2/d^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*I*c^2*b^2/d^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-4*I*c^2*b^2/d^2*arctan(c*x)*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*I*c^2*a*b/d^2*ln(c^2*x^2+1)-9/2*I*c^2*b^2/d^2*Pi*arctan(c*x)^2-c*a*b/d^2/x+3/2*I*c^2*b^2/d^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+4*I*c*a*b/d^2*arctan(c*x)/x-I*c^3*b^2/d^2*arctan(c*x)/(2*c*x-2*I)*x-1/2*b^2/d^2*arctan(c*x)^2/x^2-2*c^2*b^2/d^2*arctan(c*x)^2-6*c^2*b^2/d^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*c^2*b^2/d^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*c^2*a^2/d^2*ln(c*x)+3/2*c^2*a^2/d^2*ln(c^2*x^2+1)+c^2*b^2/d^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+4*c^2*b^2/d^2*dilog((1+I*c*x)/(c^2*x^2+1)^(1/2))-4*c^2*b^2/d^2*dilog(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*I*c^2*b^2/d^2*arctan(c*x)^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2+3/2*I*c^2*b^2/d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*c^2*b^2/d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*c^2*b^2/d^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*c^2*b^2/d^2*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+3/2*I*c^2*b^2/d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*a^2/d^2/x^2","C"
111,1,1618,422,5.834000," ","int(x^4*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x)","\frac{7 b^{2}}{c^{5} d^{3} \left(8 c x -8 i\right)}-\frac{4 a^{2}}{c^{5} d^{3} \left(c x -i\right)}-\frac{6 a b \arctan \left(c x \right) x}{c^{4} d^{3}}-\frac{i a b x}{c^{4} d^{3}}-\frac{i b^{2} x \arctan \left(c x \right)}{c^{4} d^{3}}+\frac{3 b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{c^{5} d^{3}}-\frac{8 a b \arctan \left(c x \right)}{c^{5} d^{3} \left(c x -i\right)}-\frac{6 a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{5} d^{3}}+\frac{6 b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{5} d^{3}}+\frac{b^{2} \arctan \left(c x \right) x^{2}}{16 c^{3} d^{3} \left(c x -i\right)^{2}}+\frac{7 b^{2} \arctan \left(c x \right) x}{4 c^{4} d^{3} \left(c x -i\right)}-\frac{5 i a b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{16 c^{5} d^{3}}+\frac{43 i a b \arctan \left(c x \right)}{8 c^{5} d^{3}}-\frac{5 i a b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{8 c^{5} d^{3}}-\frac{b^{2} \arctan \left(c x \right)}{c^{5} d^{3}}+\frac{i b^{2} \arctan \left(c x \right)^{2} x^{2}}{2 c^{3} d^{3}}-\frac{i b^{2} x^{2}}{64 c^{3} d^{3} \left(c x -i\right)^{2}}-\frac{7 i b^{2} x}{c^{4} d^{3} \left(8 c x -8 i\right)}+\frac{7 i b^{2} \arctan \left(c x \right)}{4 c^{5} d^{3} \left(c x -i\right)}+\frac{6 i b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{5} d^{3}}-\frac{6 i b^{2} \arctan \left(c x \right)^{2} \ln \left(c x -i\right)}{c^{5} d^{3}}-\frac{i b^{2} \arctan \left(c x \right)^{2}}{2 c^{5} d^{3} \left(c x -i\right)^{2}}+\frac{5 i a b \arctan \left(\frac{c x}{2}\right)}{16 c^{5} d^{3}}+\frac{15 i a b}{4 c^{5} d^{3} \left(c x -i\right)}-\frac{3 a^{2} x}{c^{4} d^{3}}+\frac{4 b^{2} \arctan \left(c x \right)^{3}}{c^{5} d^{3}}+\frac{6 a^{2} \arctan \left(c x \right)}{c^{5} d^{3}}+\frac{3 b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{c^{5} d^{3}}-\frac{a b}{c^{5} d^{3}}+\frac{6 b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{5} d^{3}}+\frac{3 a b \ln \left(c x -i\right)^{2}}{c^{5} d^{3}}+\frac{b^{2} x}{32 c^{4} d^{3} \left(c x -i\right)^{2}}+\frac{i b^{2}}{64 c^{5} d^{3} \left(c x -i\right)^{2}}+\frac{43 i b^{2} \arctan \left(c x \right)^{2}}{8 c^{5} d^{3}}-\frac{3 i a^{2} \ln \left(c^{2} x^{2}+1\right)}{c^{5} d^{3}}-\frac{i a^{2}}{2 c^{5} d^{3} \left(c x -i\right)^{2}}-\frac{i b^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{5} d^{3}}+\frac{i a^{2} x^{2}}{2 c^{3} d^{3}}-\frac{b^{2} \arctan \left(c x \right)}{16 c^{5} d^{3} \left(c x -i\right)^{2}}-\frac{6 b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{5} d^{3}}-\frac{4 b^{2} \arctan \left(c x \right)^{2}}{c^{5} d^{3} \left(c x -i\right)}-\frac{6 b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{5} d^{3}}-\frac{a b}{4 c^{5} d^{3} \left(c x -i\right)^{2}}-\frac{6 a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{5} d^{3}}+\frac{6 i b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{5} d^{3}}+\frac{6 i b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{5} d^{3}}+\frac{3 i b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{5} d^{3}}+\frac{i a b \arctan \left(c x \right) x^{2}}{c^{3} d^{3}}+\frac{3 b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{5} d^{3}}-\frac{3 b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{5} d^{3}}+\frac{i b^{2} \arctan \left(c x \right) x}{8 c^{4} d^{3} \left(c x -i\right)^{2}}-\frac{i a b \arctan \left(c x \right)}{c^{5} d^{3} \left(c x -i\right)^{2}}-\frac{12 i a b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{5} d^{3}}-\frac{6 b^{2} \pi  \arctan \left(c x \right)^{2}}{c^{5} d^{3}}-\frac{3 b^{2} \arctan \left(c x \right)^{2} x}{c^{4} d^{3}}+\frac{5 a b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{32 c^{5} d^{3}}+\frac{43 a b \ln \left(c^{2} x^{2}+1\right)}{16 c^{5} d^{3}}"," ",0,"-I*a*b*x/c^4/d^3-I*b^2*x*arctan(c*x)/c^4/d^3+3/c^5*b^2/d^3*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-8/c^5*a*b/d^3*arctan(c*x)/(c*x-I)-6/c^5*a*b/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))+6/c^5*b^2/d^3*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/16/c^3*b^2/d^3*arctan(c*x)/(c*x-I)^2*x^2+7/4/c^4*b^2/d^3*arctan(c*x)/(c*x-I)*x-6/c^4*a*b/d^3*arctan(c*x)*x-5/16*I/c^5*a*b/d^3*arctan(1/6*c^3*x^3+7/6*c*x)+43/8*I/c^5*a*b/d^3*arctan(c*x)-5/8*I/c^5*a*b/d^3*arctan(1/2*c*x-1/2*I)+1/2*I/c^3*b^2/d^3*arctan(c*x)^2*x^2-1/64*I/c^3*b^2/d^3/(c*x-I)^2*x^2-7*I/c^4*b^2/d^3/(8*c*x-8*I)*x+7/4*I/c^5*b^2/d^3*arctan(c*x)/(c*x-I)+6*I/c^5*b^2/d^3*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-6*I/c^5*b^2/d^3*arctan(c*x)^2*ln(c*x-I)-1/2*I/c^5*b^2/d^3*arctan(c*x)^2/(c*x-I)^2+5/16*I/c^5*a*b/d^3*arctan(1/2*c*x)+15/4*I/c^5*a*b/d^3/(c*x-I)-b^2*arctan(c*x)/c^5/d^3-3/c^4*a^2/d^3*x+7/c^5*b^2/d^3/(8*c*x-8*I)+4/c^5*b^2/d^3*arctan(c*x)^3+6/c^5*a^2/d^3*arctan(c*x)-4/c^5*a^2/d^3/(c*x-I)+I/c^3*a*b/d^3*arctan(c*x)*x^2+3/c^5*b^2/d^3*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/c^5*b^2/d^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/8*I/c^4*b^2/d^3*arctan(c*x)/(c*x-I)^2*x-I/c^5*a*b/d^3*arctan(c*x)/(c*x-I)^2-12*I/c^5*a*b/d^3*arctan(c*x)*ln(c*x-I)+3/c^5*b^2/d^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/c^5*a*b/d^3+3/c^5*a*b/d^3*ln(c*x-I)^2-6/c^5*a*b/d^3*dilog(-1/2*I*(I+c*x))-6/c^5*b^2/d^3*Pi*arctan(c*x)^2+1/32/c^4*b^2/d^3/(c*x-I)^2*x-3/c^4*b^2/d^3*arctan(c*x)^2*x+1/64*I/c^5*b^2/d^3/(c*x-I)^2+43/8*I/c^5*b^2/d^3*arctan(c*x)^2-3*I/c^5*a^2/d^3*ln(c^2*x^2+1)-1/2*I/c^5*a^2/d^3/(c*x-I)^2-I/c^5*b^2/d^3*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+6*I/c^5*b^2/d^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*I/c^5*b^2/d^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I/c^5*b^2/d^3*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+1/2*I/c^3*a^2/d^3*x^2-1/16/c^5*b^2/d^3*arctan(c*x)/(c*x-I)^2-6/c^5*b^2/d^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+6/c^5*b^2/d^3*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-4/c^5*b^2/d^3*arctan(c*x)^2/(c*x-I)-6/c^5*b^2/d^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+5/32/c^5*a*b/d^3*ln(c^4*x^4+10*c^2*x^2+9)-1/4/c^5*a*b/d^3/(c*x-I)^2+43/16/c^5*a*b/d^3*ln(c^2*x^2+1)","C"
112,1,5012,349,0.934000," ","int(x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
113,1,1276,273,0.470000," ","int(x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x)","\frac{4 a b \arctan \left(c x \right)}{c^{3} d^{3} \left(c x -i\right)}+\frac{a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{3} d^{3}}+\frac{i b^{2} \arctan \left(c x \right)^{2} \ln \left(c x -i\right)}{c^{3} d^{3}}-\frac{b^{2} \arctan \left(c x \right) x^{2}}{16 c \,d^{3} \left(c x -i\right)^{2}}-\frac{3 b^{2} \arctan \left(c x \right) x}{4 c^{2} d^{3} \left(c x -i\right)}-\frac{b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c^{3} d^{3}}-\frac{b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{3} d^{3}}+\frac{3 i b^{2} x}{c^{2} d^{3} \left(8 c x -8 i\right)}-\frac{i b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{3} d^{3}}-\frac{3 i b^{2} \arctan \left(c x \right)}{4 c^{3} d^{3} \left(c x -i\right)}+\frac{i b^{2} \arctan \left(c x \right)^{2}}{2 c^{3} d^{3} \left(c x -i\right)^{2}}-\frac{7 i a b \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{16 c^{3} d^{3}}+\frac{7 i a b \arctan \left(\frac{c x}{2}\right)}{16 c^{3} d^{3}}-\frac{7 i a b \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{8 c^{3} d^{3}}-\frac{7 i a b}{4 c^{3} d^{3} \left(c x -i\right)}-\frac{7 i a b \arctan \left(c x \right)}{8 c^{3} d^{3}}+\frac{i b^{2} x^{2}}{64 c \,d^{3} \left(c x -i\right)^{2}}+\frac{i a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{3} d^{3}}-\frac{i b^{2}}{64 c^{3} d^{3} \left(c x -i\right)^{2}}-\frac{b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{3} d^{3}}+\frac{a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c^{3} d^{3}}-\frac{i b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{3} d^{3}}-\frac{2 b^{2} \arctan \left(c x \right)^{3}}{3 c^{3} d^{3}}-\frac{a^{2} \arctan \left(c x \right)}{c^{3} d^{3}}-\frac{3 b^{2}}{c^{3} d^{3} \left(8 c x -8 i\right)}+\frac{2 a^{2}}{c^{3} d^{3} \left(c x -i\right)}-\frac{7 a b \ln \left(c^{2} x^{2}+1\right)}{16 c^{3} d^{3}}+\frac{b^{2} \pi  \arctan \left(c x \right)^{2}}{c^{3} d^{3}}+\frac{7 a b \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{32 c^{3} d^{3}}+\frac{i a b \arctan \left(c x \right)}{c^{3} d^{3} \left(c x -i\right)^{2}}-\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c^{3} d^{3}}+\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c^{3} d^{3}}-\frac{i b^{2} \arctan \left(c x \right) x}{8 c^{2} d^{3} \left(c x -i\right)^{2}}+\frac{2 i a b \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{3} d^{3}}-\frac{b^{2} x}{32 c^{2} d^{3} \left(c x -i\right)^{2}}+\frac{2 b^{2} \arctan \left(c x \right)^{2}}{c^{3} d^{3} \left(c x -i\right)}-\frac{a b \ln \left(c x -i\right)^{2}}{2 c^{3} d^{3}}+\frac{b^{2} \arctan \left(c x \right)}{16 c^{3} d^{3} \left(c x -i\right)^{2}}+\frac{a b}{4 c^{3} d^{3} \left(c x -i\right)^{2}}-\frac{7 i b^{2} \arctan \left(c x \right)^{2}}{8 c^{3} d^{3}}+\frac{i a^{2}}{2 c^{3} d^{3} \left(c x -i\right)^{2}}-\frac{b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c^{3} d^{3}}"," ",0,"-3/4*I/c^3*b^2/d^3*arctan(c*x)/(c*x-I)+1/2*I/c^3*b^2/d^3*arctan(c*x)^2/(c*x-I)^2-7/16*I/c^3*a*b/d^3*arctan(1/6*c^3*x^3+7/6*c*x)+7/16*I/c^3*a*b/d^3*arctan(1/2*c*x)-7/8*I/c^3*a*b/d^3*arctan(1/2*c*x-1/2*I)-7/4*I/c^3*a*b/d^3/(c*x-I)-7/8*I/c^3*a*b/d^3*arctan(c*x)+1/64*I/c*b^2/d^3/(c*x-I)^2*x^2-1/32/c^2*b^2/d^3/(c*x-I)^2*x-3/c^3*b^2/d^3/(8*c*x-8*I)-2/3/c^3*b^2/d^3*arctan(c*x)^3-1/c^3*a^2/d^3*arctan(c*x)+2/c^3*a^2/d^3/(c*x-I)-1/c^3*b^2/d^3*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+2/c^3*b^2/d^3*arctan(c*x)^2/(c*x-I)-7/16/c^3*a*b/d^3*ln(c^2*x^2+1)-1/2/c^3*a*b/d^3*ln(c*x-I)^2+1/c^3*a*b/d^3*dilog(-1/2*I*(I+c*x))+1/16/c^3*b^2/d^3*arctan(c*x)/(c*x-I)^2+1/c^3*b^2/d^3*Pi*arctan(c*x)^2+7/32/c^3*a*b/d^3*ln(c^4*x^4+10*c^2*x^2+9)+1/4/c^3*a*b/d^3/(c*x-I)^2-7/8*I/c^3*b^2/d^3*arctan(c*x)^2+1/2*I/c^3*a^2/d^3/(c*x-I)^2+1/2*I/c^3*a^2/d^3*ln(c^2*x^2+1)-1/64*I/c^3*b^2/d^3/(c*x-I)^2-1/2*I/c^3*b^2/d^3*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+I/c^3*a*b/d^3*arctan(c*x)/(c*x-I)^2-1/2/c^3*b^2/d^3*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2/c^3*b^2/d^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/8*I/c^2*b^2/d^3*arctan(c*x)/(c*x-I)^2*x+2*I/c^3*a*b/d^3*arctan(c*x)*ln(c*x-I)+4/c^3*a*b/d^3*arctan(c*x)/(c*x-I)+1/c^3*a*b/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))+I/c^3*b^2/d^3*arctan(c*x)^2*ln(c*x-I)-1/16/c*b^2/d^3*arctan(c*x)/(c*x-I)^2*x^2-3/4/c^2*b^2/d^3*arctan(c*x)/(c*x-I)*x-1/2/c^3*b^2/d^3*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-1/c^3*b^2/d^3*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3*I/c^2*b^2/d^3/(8*c*x-8*I)*x-I/c^3*b^2/d^3*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-1/2/c^3*b^2/d^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2","C"
114,1,464,156,0.095000," ","int(x*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x)","-\frac{i a^{2}}{c^{2} d^{3} \left(c x -i\right)}+\frac{a^{2}}{2 c^{2} d^{3} \left(c x -i\right)^{2}}-\frac{i b^{2} \arctan \left(c x \right)^{2}}{c^{2} d^{3} \left(c x -i\right)}+\frac{b^{2} \arctan \left(c x \right)^{2}}{2 c^{2} d^{3} \left(c x -i\right)^{2}}-\frac{3 i b^{2} \arctan \left(c x \right) \ln \left(c x +i\right)}{8 c^{2} d^{3}}+\frac{3 i b^{2} \arctan \left(c x \right) \ln \left(c x -i\right)}{8 c^{2} d^{3}}-\frac{i b^{2} \arctan \left(c x \right)}{4 c^{2} d^{3} \left(c x -i\right)^{2}}-\frac{3 b^{2} \arctan \left(c x \right)}{4 c^{2} d^{3} \left(c x -i\right)}-\frac{i a b}{4 c^{2} d^{3} \left(c x -i\right)^{2}}+\frac{5 i b^{2}}{16 c^{2} d^{3} \left(c x -i\right)}-\frac{b^{2}}{16 c^{2} d^{3} \left(c x -i\right)^{2}}-\frac{3 b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{16 c^{2} d^{3}}+\frac{3 b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(c x +i\right)}{16 c^{2} d^{3}}-\frac{3 b^{2} \ln \left(c x +i\right)^{2}}{32 c^{2} d^{3}}+\frac{3 b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{16 c^{2} d^{3}}-\frac{3 b^{2} \ln \left(c x -i\right)^{2}}{32 c^{2} d^{3}}+\frac{5 i b^{2} \arctan \left(c x \right)}{16 c^{2} d^{3}}+\frac{a b \arctan \left(c x \right)}{c^{2} d^{3} \left(c x -i\right)^{2}}-\frac{3 a b \arctan \left(c x \right)}{4 c^{2} d^{3}}-\frac{2 i a b \arctan \left(c x \right)}{c^{2} d^{3} \left(c x -i\right)}-\frac{3 a b}{4 c^{2} d^{3} \left(c x -i\right)}"," ",0,"-I/c^2*a^2/d^3/(c*x-I)+1/2/c^2*a^2/d^3/(c*x-I)^2-I/c^2*b^2/d^3*arctan(c*x)^2/(c*x-I)+1/2/c^2*b^2/d^3*arctan(c*x)^2/(c*x-I)^2-3/8*I/c^2*b^2/d^3*arctan(c*x)*ln(I+c*x)+3/8*I/c^2*b^2/d^3*arctan(c*x)*ln(c*x-I)-1/4*I/c^2*b^2/d^3*arctan(c*x)/(c*x-I)^2-3/4/c^2*b^2/d^3*arctan(c*x)/(c*x-I)-1/4*I/c^2*a*b/d^3/(c*x-I)^2+5/16*I/c^2*b^2/d^3/(c*x-I)-1/16/c^2*b^2/d^3/(c*x-I)^2-3/16/c^2*b^2/d^3*ln(-1/2*I*(-c*x+I))*ln(-1/2*I*(I+c*x))+3/16/c^2*b^2/d^3*ln(-1/2*I*(-c*x+I))*ln(I+c*x)-3/32/c^2*b^2/d^3*ln(I+c*x)^2+3/16/c^2*b^2/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))-3/32/c^2*b^2/d^3*ln(c*x-I)^2+5/16*I*b^2*arctan(c*x)/c^2/d^3+1/c^2*a*b/d^3*arctan(c*x)/(c*x-I)^2-3/4/c^2*a*b/d^3*arctan(c*x)-2*I/c^2*a*b/d^3*arctan(c*x)/(c*x-I)-3/4/c^2*a*b/d^3/(c*x-I)","B"
115,1,405,157,0.073000," ","int((a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x)","-\frac{i b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{16 c \,d^{3}}+\frac{i a^{2}}{2 c \,d^{3} \left(i c x +1\right)^{2}}+\frac{b^{2} \arctan \left(c x \right) \ln \left(c x +i\right)}{8 c \,d^{3}}-\frac{b^{2} \arctan \left(c x \right) \ln \left(c x -i\right)}{8 c \,d^{3}}-\frac{b^{2} \arctan \left(c x \right)}{4 c \,d^{3} \left(c x -i\right)^{2}}-\frac{i a b}{4 c \,d^{3} \left(c x -i\right)}+\frac{i b^{2}}{16 c \,d^{3} \left(c x -i\right)^{2}}+\frac{i b^{2} \arctan \left(c x \right)^{2}}{2 c \,d^{3} \left(i c x +1\right)^{2}}-\frac{i b^{2} \ln \left(c x -i\right)^{2}}{32 c \,d^{3}}-\frac{3 b^{2} \arctan \left(c x \right)}{16 c \,d^{3}}-\frac{3 b^{2}}{16 c \,d^{3} \left(c x -i\right)}-\frac{i b^{2} \arctan \left(c x \right)}{4 c \,d^{3} \left(c x -i\right)}+\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{16 c \,d^{3}}-\frac{i b^{2} \ln \left(c x +i\right)^{2}}{32 c \,d^{3}}+\frac{i b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(c x +i\right)}{16 c \,d^{3}}+\frac{i a b \arctan \left(c x \right)}{c \,d^{3} \left(i c x +1\right)^{2}}-\frac{a b}{4 c \,d^{3} \left(c x -i\right)^{2}}-\frac{i a b \arctan \left(c x \right)}{4 c \,d^{3}}"," ",0,"-1/16*I/c*b^2/d^3*ln(-1/2*I*(-c*x+I))*ln(-1/2*I*(I+c*x))+1/2*I/c*a^2/d^3/(1+I*c*x)^2+1/8/c*b^2/d^3*arctan(c*x)*ln(I+c*x)-1/8/c*b^2/d^3*arctan(c*x)*ln(c*x-I)-1/4/c*b^2/d^3*arctan(c*x)/(c*x-I)^2-1/4*I/c*a*b/d^3/(c*x-I)+1/16*I/c*b^2/d^3/(c*x-I)^2+1/2*I/c*b^2/d^3/(1+I*c*x)^2*arctan(c*x)^2-1/32*I/c*b^2/d^3*ln(c*x-I)^2-3/16*b^2*arctan(c*x)/c/d^3-3/16/c*b^2/d^3/(c*x-I)-1/4*I/c*b^2/d^3*arctan(c*x)/(c*x-I)+1/16*I/c*b^2/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/32*I/c*b^2/d^3*ln(I+c*x)^2+1/16*I/c*b^2/d^3*ln(-1/2*I*(-c*x+I))*ln(I+c*x)+I/c*a*b/d^3/(1+I*c*x)^2*arctan(c*x)-1/4/c*a*b/d^3/(c*x-I)^2-1/4*I/c*a*b/d^3*arctan(c*x)","B"
116,1,2151,268,0.598000," ","int((a+b*arctan(c*x))^2/x/(d+I*c*d*x)^3,x)","-\frac{i a b \dilog \left(-i c x \right)}{d^{3}}-\frac{2 i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{3}}-\frac{2 i b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{3}}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)}{d^{3}}-\frac{5 a b \arctan \left(c x \right)}{4 d^{3}}-\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{d^{3}}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{3}}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{3}}+\frac{3 i b^{2}}{8 d^{3} \left(c x -i\right)}-\frac{2 i b^{2} \arctan \left(c x \right)^{3}}{3 d^{3}}-\frac{i a^{2}}{d^{3} \left(c x -i\right)}-\frac{i a^{2} \arctan \left(c x \right)}{d^{3}}-\frac{5 a b}{4 d^{3} \left(c x -i\right)}-\frac{3 b^{2} \arctan \left(c x \right)}{d^{3} \left(4 c x -4 i\right)}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{b^{2} \arctan \left(c x \right)^{2}}{2 d^{3} \left(c x -i\right)^{2}}-\frac{b^{2} \ln \left(c x -i\right) \arctan \left(c x \right)^{2}}{d^{3}}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d^{3}}-\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2}}{d^{3}}+\frac{i a b \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{d^{3}}-\frac{i a b \ln \left(c x \right) \ln \left(-i \left(c x +i\right)\right)}{d^{3}}-\frac{i a b \ln \left(-i c x \right) \ln \left(-i \left(-c x +i\right)\right)}{d^{3}}+\frac{b^{2} \arctan \left(c x \right) c x}{8 d^{3} \left(c x -i\right)^{2}}-\frac{i b^{2} c x}{32 d^{3} \left(c x -i\right)^{2}}+\frac{i a b \ln \left(c x \right) \ln \left(-i \left(-c x +i\right)\right)}{d^{3}}-\frac{2 i a b \arctan \left(c x \right)}{d^{3} \left(c x -i\right)}-\frac{i b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2}}{2 d^{3}}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 d^{3}}+\frac{2 a b \arctan \left(c x \right) \ln \left(c x \right)}{d^{3}}-\frac{b^{2} c^{2} x^{2}}{64 d^{3} \left(c x -i\right)^{2}}+\frac{i a b \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{d^{3}}-\frac{i a b \dilog \left(-i \left(c x +i\right)\right)}{d^{3}}+\frac{i b^{2} \arctan \left(c x \right)}{16 d^{3} \left(c x -i\right)^{2}}-\frac{2 a b \arctan \left(c x \right) \ln \left(c x -i\right)}{d^{3}}-\frac{a b \arctan \left(c x \right)}{d^{3} \left(c x -i\right)^{2}}-\frac{i b^{2} \arctan \left(c x \right)^{2}}{d^{3} \left(c x -i\right)}+\frac{i a b}{4 d^{3} \left(c x -i\right)^{2}}+\frac{3 b^{2} c x}{8 d^{3} \left(c x -i\right)}-\frac{i a b \ln \left(c x -i\right)^{2}}{2 d^{3}}+\frac{3 i b^{2} \arctan \left(c x \right)^{2} \pi}{2 d^{3}}+\frac{2 b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{3}}+\frac{2 b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{3}}+\frac{b^{2}}{64 d^{3} \left(c x -i\right)^{2}}-\frac{a^{2}}{2 d^{3} \left(c x -i\right)^{2}}-\frac{i b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)}{2 d^{3}}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 d^{3}}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{3}}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 d^{3}}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 d^{3}}+\frac{i b^{2} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2}}{2 d^{3}}-\frac{i b^{2} \arctan \left(c x \right) c^{2} x^{2}}{16 d^{3} \left(c x -i\right)^{2}}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{3}}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{3}}+\frac{3 i b^{2} \arctan \left(c x \right) c x}{d^{3} \left(4 c x -4 i\right)}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 d^{3}}-\frac{5 b^{2} \arctan \left(c x \right)^{2}}{8 d^{3}}-\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d^{3}}+\frac{a^{2} \ln \left(c x \right)}{d^{3}}"," ",0,"-b^2/d^3*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+b^2/d^3*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2/d^3*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2/d^3*arctan(c*x)^2*ln(c*x)+3/8*I*b^2/d^3/(c*x-I)-2/3*I*b^2/d^3*arctan(c*x)^3-I*a^2/d^3/(c*x-I)-I*a^2/d^3*arctan(c*x)-5/4*a*b/d^3*arctan(c*x)-5/4*a*b/d^3/(c*x-I)-3*b^2/d^3*arctan(c*x)/(4*c*x-4*I)+b^2/d^3*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-1/2*I*b^2/d^3*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2/d^3*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-1/2*I*b^2/d^3*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2*I*b^2/d^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-I*b^2/d^3*Pi*arctan(c*x)^2*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2+I*a*b/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))-I*a*b/d^3*ln(c*x)*ln(-I*(I+c*x))-I*a*b/d^3*ln(-I*c*x)*ln(-I*(-c*x+I))+1/8*b^2/d^3*arctan(c*x)/(c*x-I)^2*c*x-1/32*I*b^2/d^3/(c*x-I)^2*c*x+I*a*b/d^3*ln(c*x)*ln(-I*(-c*x+I))-2*I*a*b/d^3*arctan(c*x)/(c*x-I)-1/2*b^2/d^3*arctan(c*x)^2/(c*x-I)^2-b^2/d^3*ln(c*x-I)*arctan(c*x)^2+1/2*I*b^2/d^3*arctan(c*x)^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2-1/64*b^2/d^3/(c*x-I)^2*c^2*x^2+2*b^2/d^3*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2/d^3*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/16*I*b^2/d^3*arctan(c*x)/(c*x-I)^2-2*a*b/d^3*arctan(c*x)*ln(c*x-I)-a*b/d^3*arctan(c*x)/(c*x-I)^2-I*b^2/d^3*arctan(c*x)^2/(c*x-I)+1/4*I*a*b/d^3/(c*x-I)^2+3/8*b^2/d^3/(c*x-I)*c*x+I*a*b/d^3*dilog(-1/2*I*(I+c*x))-I*a*b/d^3*dilog(-I*(I+c*x))-I*a*b/d^3*dilog(-I*c*x)-1/2*I*a*b/d^3*ln(c*x-I)^2-2*I*b^2/d^3*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*b^2/d^3*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I*b^2/d^3*arctan(c*x)^2*Pi+2*a*b/d^3*arctan(c*x)*ln(c*x)-1/16*I*b^2/d^3*arctan(c*x)/(c*x-I)^2*c^2*x^2-1/2*I*b^2/d^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2/d^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3*I*b^2/d^3*arctan(c*x)/(4*c*x-4*I)*c*x-1/2*I*b^2/d^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2/d^3*arctan(c*x)^2*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2+1/2*I*b^2/d^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*I*b^2/d^3*arctan(c*x)^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+1/2*I*b^2/d^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+1/64*b^2/d^3/(c*x-I)^2-5/8*b^2/d^3*arctan(c*x)^2-1/2*a^2/d^3*ln(c^2*x^2+1)-1/2*a^2/d^3/(c*x-I)^2+a^2/d^3*ln(c*x)","C"
117,1,9659,355,1.625000," ","int((a+b*arctan(c*x))^2/x^2/(d+I*c*d*x)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
118,1,404,177,0.087000," ","int((a+b*arctan(c*x))^2/(1+I*c*x)^4,x)","-\frac{i b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{48 c}-\frac{i b^{2} \ln \left(c x +i\right)^{2}}{96 c}+\frac{b^{2} \arctan \left(c x \right) \ln \left(c x +i\right)}{24 c}-\frac{b^{2} \arctan \left(c x \right) \ln \left(c x -i\right)}{24 c}-\frac{b^{2} \arctan \left(c x \right)}{12 c \left(c x -i\right)^{2}}+\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{48 c}+\frac{i b^{2} \arctan \left(c x \right)}{9 c \left(c x -i\right)^{3}}-\frac{11 b^{2} \arctan \left(c x \right)}{144 c}+\frac{b^{2}}{54 c \left(c x -i\right)^{3}}-\frac{11 b^{2}}{144 c \left(c x -i\right)}-\frac{i b^{2} \arctan \left(c x \right)}{12 c \left(c x -i\right)}+\frac{i a b}{9 c \left(c x -i\right)^{3}}+\frac{2 i a b \arctan \left(c x \right)}{3 c \left(i c x +1\right)^{3}}-\frac{i a b \arctan \left(c x \right)}{12 c}+\frac{5 i b^{2}}{144 c \left(c x -i\right)^{2}}+\frac{i b^{2} \arctan \left(c x \right)^{2}}{3 c \left(i c x +1\right)^{3}}-\frac{i b^{2} \ln \left(c x -i\right)^{2}}{96 c}+\frac{i a^{2}}{3 c \left(i c x +1\right)^{3}}-\frac{a b}{12 c \left(c x -i\right)^{2}}+\frac{i b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(c x +i\right)}{48 c}-\frac{i a b}{12 c \left(c x -i\right)}"," ",0,"-1/48*I/c*b^2*ln(-1/2*I*(-c*x+I))*ln(-1/2*I*(I+c*x))-1/96*I/c*b^2*ln(I+c*x)^2+1/24/c*b^2*arctan(c*x)*ln(I+c*x)-1/24/c*b^2*arctan(c*x)*ln(c*x-I)-1/12/c*b^2*arctan(c*x)/(c*x-I)^2+1/48*I/c*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/9*I/c*b^2*arctan(c*x)/(c*x-I)^3-11/144*b^2*arctan(c*x)/c+1/54/c*b^2/(c*x-I)^3-11/144/c*b^2/(c*x-I)-1/12*I/c*b^2*arctan(c*x)/(c*x-I)+1/9*I/c*a*b/(c*x-I)^3+2/3*I/c*a*b/(1+I*c*x)^3*arctan(c*x)-1/12*I/c*a*b*arctan(c*x)+5/144*I/c*b^2/(c*x-I)^2+1/3*I/c*b^2/(1+I*c*x)^3*arctan(c*x)^2-1/96*I/c*b^2*ln(c*x-I)^2+1/3*I/c*a^2/(1+I*c*x)^3-1/12/c*a*b/(c*x-I)^2+1/48*I/c*b^2*ln(-1/2*I*(-c*x+I))*ln(I+c*x)-1/12*I/c*a*b/(c*x-I)","B"
119,1,183,70,0.529000," ","int(arctan(a*x)^2/(c*x-I*a*c*x^2),x)","\frac{\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{2 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}"," ",0,"1/c*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I/c*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2/c*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I/c*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+2/c*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))","B"
120,1,2004,350,12.778000," ","int((d+I*c*d*x)^3*(a+b*arctan(c*x))^3,x)","-\frac{3 i d^{3} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \arctan \left(c x \right)^{2}}{2 c}+\frac{3 i d^{3} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(c x \right)^{2}}{2 c}-\frac{3 i d^{3} b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)^{2} \arctan \left(c x \right)^{2}}{c}+\frac{3 i d^{3} b^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right) \arctan \left(c x \right)^{2}}{2 c}-3 a \,b^{2} d^{3} x -3 b^{3} d^{3} x \arctan \left(c x \right)+x \,a^{3} d^{3}-\frac{3 i d^{3} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(c x \right)^{2}}{2 c}+\frac{3 c \,d^{3} a^{2} b \,x^{2}}{2}-\frac{3 d^{3} a^{2} b \ln \left(c^{2} x^{2}+1\right)}{c}+\frac{3 d^{3} a \,b^{2} \arctan \left(c x \right)}{c}-\frac{3 d^{3} b^{3} \arctan \left(c x \right)^{2} \ln \left(c^{2} x^{2}+1\right)}{c}+\frac{3 c \,d^{3} b^{3} \arctan \left(c x \right)^{2} x^{2}}{2}-c^{2} d^{3} b^{3} \arctan \left(c x \right)^{3} x^{3}+\frac{6 d^{3} b^{3} \ln \left(2\right) \arctan \left(c x \right)^{2}}{c}+3 d^{3} a \,b^{2} \arctan \left(c x \right)^{2} x +3 d^{3} a^{2} b \arctan \left(c x \right) x -3 c^{2} d^{3} a \,b^{2} \arctan \left(c x \right)^{2} x^{3}+3 c \,d^{3} a \,b^{2} \arctan \left(c x \right) x^{2}-3 c^{2} d^{3} a^{2} b \arctan \left(c x \right) x^{3}-\frac{6 d^{3} a \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{c}-\frac{11 i d^{3} b^{3} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c}-\frac{11 i d^{3} b^{3} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c}+\frac{3 i d^{3} a \,b^{2} \ln \left(c x -i\right)^{2}}{2 c}+\frac{21 i d^{3} a^{2} b \arctan \left(c x \right)}{4 c}+\frac{i c^{2} d^{3} a^{2} b \,x^{3}}{4}-\frac{i c \,d^{3} b^{3} \arctan \left(c x \right) x^{2}}{4}-\frac{i c^{3} d^{3} b^{3} \arctan \left(c x \right)^{3} x^{4}}{4}+\frac{3 i c \,d^{3} b^{3} \arctan \left(c x \right)^{3} x^{2}}{2}+\frac{i c^{2} d^{3} b^{3} \arctan \left(c x \right)^{2} x^{3}}{4}-\frac{3 i d^{3} a \,b^{2} \ln \left(c x +i\right)^{2}}{2 c}+\frac{11 i d^{3} a \,b^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c}+\frac{21 i d^{3} a \,b^{2} \arctan \left(c x \right)^{2}}{4 c}-\frac{i c \,d^{3} a \,b^{2} x^{2}}{4}-\frac{21 i d^{3} a \,b^{2} \arctan \left(c x \right) x}{2}-\frac{6 i d^{3} b^{3} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c}-\frac{3 i d^{3} a \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{c}+\frac{3 i d^{3} a \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c}+\frac{6 d^{3} b^{3} \arctan \left(c x \right)^{2} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{c}+\frac{11 i d^{3} b^{3} \arctan \left(c x \right)}{4 c}-\frac{i c^{3} x^{4} a^{3} d^{3}}{4}+\frac{3 i c \,x^{2} a^{3} d^{3}}{2}-\frac{i d^{3} b^{3} \arctan \left(c x \right)^{3}}{4 c}-\frac{21 i d^{3} b^{3} \arctan \left(c x \right)^{2} x}{4}-\frac{21 i d^{3} a^{2} b x}{4}-c^{2} x^{3} a^{3} d^{3}+d^{3} b^{3} \arctan \left(c x \right)^{3} x -\frac{4 d^{3} b^{3} \arctan \left(c x \right)^{2}}{c}+\frac{i b^{3} d^{3} x}{4}-\frac{i d^{3} a^{3}}{4 c}-\frac{3 d^{3} b^{3} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c}-\frac{11 d^{3} b^{3} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c}-\frac{11 d^{3} b^{3} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c}+\frac{3 d^{3} b^{3} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c}+\frac{9 i c \,d^{3} a \,b^{2} \arctan \left(c x \right)^{2} x^{2}}{2}+\frac{i c^{2} d^{3} a \,b^{2} \arctan \left(c x \right) x^{3}}{2}-\frac{3 i c^{3} d^{3} a \,b^{2} \arctan \left(c x \right)^{2} x^{4}}{4}-\frac{3 i d^{3} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 c}-\frac{3 i d^{3} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(c x \right)^{2}}{2 c}+\frac{3 i d^{3} a \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{c}+\frac{3 i d^{3} a \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c}-\frac{3 i d^{3} a \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{c}-\frac{3 i d^{3} a \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{c}+\frac{3 i d^{3} b^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(c x \right)^{2}}{2 c}-\frac{3 i c^{3} d^{3} a^{2} b \arctan \left(c x \right) x^{4}}{4}+\frac{9 i c \,d^{3} a^{2} b \arctan \left(c x \right) x^{2}}{2}-\frac{d^{3} b^{3}}{4 c}+\frac{3 i d^{3} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)^{2} \arctan \left(c x \right)^{2}}{c}+\frac{3 i d^{3} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(c x \right)^{2}}{2 c}"," ",0,"-3*a*b^2*d^3*x-3*b^3*d^3*x*arctan(c*x)+x*a^3*d^3-3/2*I/c*d^3*b^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2+1/4*I*b^3*d^3*x+3/2*c*d^3*a^2*b*x^2-3/c*d^3*a^2*b*ln(c^2*x^2+1)+3/c*d^3*a*b^2*arctan(c*x)-3/c*d^3*b^3*arctan(c*x)^2*ln(c^2*x^2+1)+6/c*d^3*b^3*arctan(c*x)^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*c*d^3*b^3*arctan(c*x)^2*x^2-c^2*d^3*b^3*arctan(c*x)^3*x^3+6/c*d^3*b^3*ln(2)*arctan(c*x)^2+3*d^3*a*b^2*arctan(c*x)^2*x+3*d^3*a^2*b*arctan(c*x)*x+11/4*I/c*d^3*b^3*arctan(c*x)-1/4*I*c^3*x^4*a^3*d^3+3/2*I*c*x^2*a^3*d^3-1/4*I/c*d^3*b^3*arctan(c*x)^3-21/4*I*d^3*b^3*arctan(c*x)^2*x-21/4*I*d^3*a^2*b*x-3*c^2*d^3*a*b^2*arctan(c*x)^2*x^3+3*c*d^3*a*b^2*arctan(c*x)*x^2-3*c^2*d^3*a^2*b*arctan(c*x)*x^3-6/c*d^3*a*b^2*arctan(c*x)*ln(c^2*x^2+1)-6*I/c*d^3*b^3*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-11*I/c*d^3*b^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-11*I/c*d^3*b^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I/c*d^3*a*b^2*ln(c*x-I)^2-3*I/c*d^3*a*b^2*dilog(1/2*I*(c*x-I))+21/4*I/c*d^3*a^2*b*arctan(c*x)+1/4*I*c^2*d^3*a^2*b*x^3-1/4*I*c*d^3*b^3*arctan(c*x)*x^2-1/4*I*c^3*d^3*b^3*arctan(c*x)^3*x^4+3/2*I*c*d^3*b^3*arctan(c*x)^3*x^2+1/4*I*c^2*d^3*b^3*arctan(c*x)^2*x^3-3/2*I/c*d^3*a*b^2*ln(I+c*x)^2+3*I/c*d^3*a*b^2*dilog(-1/2*I*(I+c*x))+11/2*I/c*d^3*a*b^2*ln(c^2*x^2+1)+21/4*I/c*d^3*a*b^2*arctan(c*x)^2-1/4*I*c*d^3*a*b^2*x^2-21/2*I*d^3*a*b^2*arctan(c*x)*x-1/4*I/c*d^3*a^3-c^2*x^3*a^3*d^3+d^3*b^3*arctan(c*x)^3*x-11/c*d^3*b^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/c*d^3*b^3*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-4/c*d^3*b^3*arctan(c*x)^2-11/c*d^3*b^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/c*d^3*b^3*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+9/2*I*c*d^3*a*b^2*arctan(c*x)^2*x^2+1/2*I*c^2*d^3*a*b^2*arctan(c*x)*x^3-3/4*I*c^3*d^3*a*b^2*arctan(c*x)^2*x^4-3/2*I/c*d^3*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*arctan(c*x)^2-3/2*I/c*d^3*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+3*I/c*d^3*a*b^2*ln(I+c*x)*ln(c^2*x^2+1)+3*I/c*d^3*a*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-3*I/c*d^3*a*b^2*ln(c*x-I)*ln(c^2*x^2+1)-3*I/c*d^3*a*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+3/2*I/c*d^3*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2-3/4*I*c^3*d^3*a^2*b*arctan(c*x)*x^4+9/2*I*c*d^3*a^2*b*arctan(c*x)*x^2-1/4/c*d^3*b^3+3*I/c*d^3*b^3*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*arctan(c*x)^2+3/2*I/c*d^3*b^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2-3/2*I/c*d^3*b^3*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^2+3/2*I/c*d^3*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2-3*I/c*d^3*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+3/2*I/c*d^3*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2","C"
121,1,1815,280,6.232000," ","int((d+I*c*d*x)^2*(a+b*arctan(c*x))^3,x)","-\frac{5 d^{2} b^{3} \arctan \left(c x \right)^{2}}{2 c}-\frac{c^{2} x^{3} a^{3} d^{2}}{3}-\frac{i d^{2} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)^{3} \arctan \left(c x \right)^{2}}{c}-\frac{i d^{2} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(c x \right)^{2}}{c}-a \,b^{2} d^{2} x -b^{3} d^{2} x \arctan \left(c x \right)-\frac{4 a \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d^{2}}{c}-\frac{2 b^{3} \arctan \left(c x \right)^{2} \ln \left(c^{2} x^{2}+1\right) d^{2}}{c}+\frac{4 b^{3} d^{2} \ln \left(2\right) \arctan \left(c x \right)^{2}}{c}-\frac{2 a^{2} b \ln \left(c^{2} x^{2}+1\right) d^{2}}{c}+3 a \,b^{2} \arctan \left(c x \right)^{2} x \,d^{2}+3 a^{2} b \arctan \left(c x \right) x \,d^{2}-c^{2} d^{2} a^{2} b \arctan \left(c x \right) x^{3}+c \,d^{2} a \,b^{2} \arctan \left(c x \right) x^{2}-c^{2} d^{2} a \,b^{2} \arctan \left(c x \right)^{2} x^{3}-\frac{i d^{2} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(c x \right)^{2}}{c}+\frac{c \,d^{2} a^{2} b \,x^{2}}{2}+\frac{d^{2} a \,b^{2} \arctan \left(c x \right)}{c}+\frac{c \,d^{2} b^{3} \arctan \left(c x \right)^{2} x^{2}}{2}-\frac{c^{2} d^{2} b^{3} \arctan \left(c x \right)^{3} x^{3}}{3}+b^{3} \arctan \left(c x \right)^{3} x \,d^{2}+\frac{4 b^{3} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right) \arctan \left(c x \right)^{2} d^{2}}{c}-\frac{i d^{2} b^{3} \arctan \left(c x \right)^{3}}{3 c}-3 i d^{2} b^{3} \arctan \left(c x \right)^{2} x -3 i d^{2} a^{2} b x +\frac{i d^{2} b^{3} \arctan \left(c x \right)}{c}+i c \,x^{2} a^{3} d^{2}+\frac{i d^{2} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(c x \right)^{2}}{c}+\frac{i d^{2} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(c x \right)^{2}}{c}+\frac{i d^{2} b^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right) \arctan \left(c x \right)^{2}}{c}-\frac{2 i d^{2} b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)^{2} \arctan \left(c x \right)^{2}}{c}+\frac{2 i d^{2} b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)^{2} \arctan \left(c x \right)^{2}}{c}-\frac{i d^{2} b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \arctan \left(c x \right)^{2}}{c}-\frac{2 i d^{2} a \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{c}+\frac{2 i d^{2} a \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{c}-\frac{4 i d^{2} b^{3} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c}+i c \,d^{2} b^{3} \arctan \left(c x \right)^{3} x^{2}+\frac{i d^{2} a \,b^{2} \ln \left(c x -i\right)^{2}}{c}-6 i d^{2} a \,b^{2} \arctan \left(c x \right) x +\frac{3 i d^{2} a^{2} b \arctan \left(c x \right)}{c}+\frac{3 i d^{2} a \,b^{2} \arctan \left(c x \right)^{2}}{c}-\frac{i d^{2} a \,b^{2} \ln \left(c x +i\right)^{2}}{c}+\frac{3 i d^{2} a \,b^{2} \ln \left(c^{2} x^{2}+1\right)}{c}-\frac{6 i d^{2} b^{3} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c}-\frac{6 i d^{2} b^{3} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c}+\frac{i d^{2} b^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(c x \right)^{2}}{c}+\frac{2 i d^{2} a \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{c}+3 i c \,d^{2} a^{2} b \arctan \left(c x \right) x^{2}+3 i c \,d^{2} a \,b^{2} \arctan \left(c x \right)^{2} x^{2}-\frac{2 i d^{2} a \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{c}-\frac{2 i d^{2} a \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{c}+\frac{2 i d^{2} a \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{c}+a^{3} x \,d^{2}-\frac{6 d^{2} b^{3} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c}+\frac{2 b^{3} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) d^{2}}{c}-\frac{i d^{2} a^{3}}{3 c}-\frac{d^{2} b^{3} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c}-\frac{6 d^{2} b^{3} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c}"," ",0,"-5/2/c*d^2*b^3*arctan(c*x)^2-6/c*d^2*b^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/3*I/c*d^2*a^3-1/3*c^2*x^3*a^3*d^2-1/c*d^2*b^3*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-6/c*d^2*b^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-a*b^2*d^2*x-b^3*d^2*x*arctan(c*x)-4/c*a*b^2*arctan(c*x)*ln(c^2*x^2+1)*d^2-2/c*b^3*arctan(c*x)^2*ln(c^2*x^2+1)*d^2+4/c*b^3*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))*arctan(c*x)^2*d^2+4/c*b^3*d^2*ln(2)*arctan(c*x)^2-2/c*a^2*b*ln(c^2*x^2+1)*d^2+3*a*b^2*arctan(c*x)^2*x*d^2+3*a^2*b*arctan(c*x)*x*d^2-c^2*d^2*a^2*b*arctan(c*x)*x^3+I*c*d^2*b^3*arctan(c*x)^3*x^2+I/c*d^2*a*b^2*ln(c*x-I)^2-6*I*d^2*a*b^2*arctan(c*x)*x+3*I/c*d^2*a^2*b*arctan(c*x)+3*I/c*d^2*a*b^2*arctan(c*x)^2-I/c*d^2*a*b^2*ln(I+c*x)^2+3*I/c*d^2*a*b^2*ln(c^2*x^2+1)-2*I/c*d^2*a*b^2*dilog(1/2*I*(c*x-I))+2*I/c*d^2*a*b^2*dilog(-1/2*I*(I+c*x))-6*I/c*d^2*b^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*I/c*d^2*b^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-4*I/c*d^2*b^3*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+c*d^2*a*b^2*arctan(c*x)*x^2-c^2*d^2*a*b^2*arctan(c*x)^2*x^3-I/c*d^2*b^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2-1/3*I/c*d^2*b^3*arctan(c*x)^3-3*I*d^2*b^3*arctan(c*x)^2*x-3*I*d^2*a^2*b*x+1/2*c*d^2*a^2*b*x^2+I/c*d^2*b^3*arctan(c*x)+1/c*d^2*a*b^2*arctan(c*x)+1/2*c*d^2*b^3*arctan(c*x)^2*x^2-1/3*c^2*d^2*b^3*arctan(c*x)^3*x^3+I*c*x^2*a^3*d^2+b^3*arctan(c*x)^3*x*d^2+2/c*b^3*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))*d^2+I/c*d^2*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+2*I/c*d^2*a*b^2*ln(I+c*x)*ln(c^2*x^2+1)+3*I*c*d^2*a^2*b*arctan(c*x)*x^2+3*I*c*d^2*a*b^2*arctan(c*x)^2*x^2-2*I/c*d^2*a*b^2*ln(c*x-I)*ln(c^2*x^2+1)-2*I/c*d^2*a*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+2*I/c*d^2*a*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-I/c*d^2*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*arctan(c*x)^2-I/c*d^2*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+I/c*d^2*b^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+I/c*d^2*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+I/c*d^2*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2-2*I/c*d^2*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+2*I/c*d^2*b^3*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*arctan(c*x)^2-I/c*d^2*b^3*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^2+a^3*x*d^2","C"
122,1,7451,200,2.542000," ","int((d+I*c*d*x)*(a+b*arctan(c*x))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
123,1,2044,127,0.503000," ","int((a+b*arctan(c*x))^3/(d+I*c*d*x),x)","\frac{3 a^{2} b \dilog \left(\frac{i c x}{2}+\frac{1}{2}\right)}{2 c d}+\frac{3 b^{3} \arctan \left(c x \right)^{2} \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c d}+\frac{3 a^{2} b \ln \left(i c x +1\right)^{2}}{4 c d}-\frac{i a^{3} \ln \left(c^{2} x^{2}+1\right)}{2 c d}+\frac{2 a \,b^{2} \arctan \left(c x \right)^{3}}{c d}+\frac{b^{3} \pi  \arctan \left(c x \right)^{3}}{2 c d}-\frac{3 i a \,b^{2} \ln \left(i c x +1\right) \arctan \left(c x \right)^{2}}{c d}+\frac{3 i a \,b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c d}-\frac{3 i a^{2} b \ln \left(i c x +1\right) \arctan \left(c x \right)}{c d}+\frac{3 a \,b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c d}-\frac{3 a \,b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \arctan \left(c x \right)^{3}}{2 c d}+\frac{b^{3} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{3}}{2 c d}-\frac{b^{3} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{3}}{2 c d}-\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{3}}{2 c d}-\frac{3 a \,b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c d}+\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c d}-\frac{3 b^{3} \polylog \left(4, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{4 c d}+\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{3}}{2 c d}-\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{3}}{2 c d}-\frac{3 a^{2} b \ln \left(\frac{1}{2}-\frac{i c x}{2}\right) \ln \left(i c x +1\right)}{2 c d}+\frac{3 a^{2} b \ln \left(\frac{1}{2}-\frac{i c x}{2}\right) \ln \left(\frac{i c x}{2}+\frac{1}{2}\right)}{2 c d}+\frac{3 a \,b^{2} \pi  \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{3} \arctan \left(c x \right)^{4}}{2 c d}+\frac{a^{3} \arctan \left(c x \right)}{c d}+\frac{3 i b^{3} \arctan \left(c x \right) \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c d}+\frac{3 i a \,b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c d}+\frac{3 a \,b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c d}-\frac{i b^{3} \ln \left(i c x +1\right) \arctan \left(c x \right)^{3}}{c d}+\frac{i b^{3} \arctan \left(c x \right)^{3} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c d}-\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{3}}{2 c d}-\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}+\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}+\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{3} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \arctan \left(c x \right)^{3}}{2 c d}-\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c d}"," ",0,"-3/2/c*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2/c*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2/c*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^3-3/2/c*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+2/c*a*b^2/d*arctan(c*x)^3+3/2/c*a^2*b/d*dilog(1/2*I*c*x+1/2)+3/2/c*b^3/d*arctan(c*x)^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+3/4/c*a^2*b/d*ln(1+I*c*x)^2+1/2/c*b^3/d*Pi*arctan(c*x)^3-1/2*I/c*a^3/d*ln(c^2*x^2+1)+1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3-1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^3-1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^3-3/2/c*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3*I/c*a*b^2/d*ln(1+I*c*x)*arctan(c*x)^2+3*I/c*a*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-3*I/c*a^2*b/d*ln(1+I*c*x)*arctan(c*x)+3/2/c*a*b^2/d*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3/2/c*a*b^2/d*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn((1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^3+3/2/c*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+1/2/c*b^3/d*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^3-1/2/c*b^3/d*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3-3/2/c*a^2*b/d*ln(1/2-1/2*I*c*x)*ln(1+I*c*x)+3/2/c*a^2*b/d*ln(1/2-1/2*I*c*x)*ln(1/2*I*c*x+1/2)+3/2/c*a*b^2/d*Pi*arctan(c*x)^2-I/c*b^3/d*ln(1+I*c*x)*arctan(c*x)^3+3/2*I/c*b^3/d*arctan(c*x)*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+3/2*I/c*a*b^2/d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+3/c*a*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+I/c*b^3/d*arctan(c*x)^3*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^3-3/4/c*b^3/d*polylog(4,-(1+I*c*x)^2/(c^2*x^2+1))+1/2/c*b^3/d*arctan(c*x)^4+1/c*a^3/d*arctan(c*x)","C"
124,1,551,161,0.889000," ","int((a+b*arctan(c*x))^3/(d+I*c*d*x)^2,x)","\frac{3 i b^{3}}{4 c \,d^{2} \left(c x -i\right)}-\frac{3 i a^{2} b \arctan \left(c x \right)}{2 c \,d^{2}}-\frac{b^{3} \arctan \left(c x \right)^{3}}{2 c \,d^{2} \left(c x -i\right)}+\frac{i b^{3} \arctan \left(c x \right)^{3}}{c \,d^{2} \left(i c x +1\right)}-\frac{3 b^{3} \arctan \left(c x \right)^{2} x}{4 d^{2} \left(c x -i\right)}+\frac{3 i a \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{4 c \,d^{2}}-\frac{3 b^{3} \arctan \left(c x \right)}{4 c \,d^{2} \left(c x -i\right)}+\frac{i a^{3}}{c \,d^{2} \left(i c x +1\right)}+\frac{3 i a^{2} b \arctan \left(c x \right)}{c \,d^{2} \left(i c x +1\right)}+\frac{3 i b^{3} \arctan \left(c x \right) x}{4 d^{2} \left(c x -i\right)}+\frac{3 a \,b^{2} \arctan \left(c x \right) \ln \left(c x +i\right)}{2 c \,d^{2}}-\frac{3 a \,b^{2} \arctan \left(c x \right) \ln \left(c x -i\right)}{2 c \,d^{2}}-\frac{3 i b^{3} \arctan \left(c x \right)^{2}}{4 c \,d^{2} \left(c x -i\right)}-\frac{3 i a \,b^{2} \arctan \left(c x \right)}{c \,d^{2} \left(c x -i\right)}-\frac{3 i a \,b^{2} \ln \left(c x +i\right)^{2}}{8 c \,d^{2}}-\frac{3 a \,b^{2} \arctan \left(c x \right)}{2 c \,d^{2}}-\frac{3 a \,b^{2}}{2 c \,d^{2} \left(c x -i\right)}-\frac{3 i a^{2} b}{2 c \,d^{2} \left(c x -i\right)}-\frac{3 i a \,b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{4 c \,d^{2}}-\frac{i b^{3} \arctan \left(c x \right)^{3} x}{2 d^{2} \left(c x -i\right)}+\frac{3 i a \,b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(c x +i\right)}{4 c \,d^{2}}+\frac{3 i a \,b^{2} \arctan \left(c x \right)^{2}}{c \,d^{2} \left(i c x +1\right)}-\frac{3 i a \,b^{2} \ln \left(c x -i\right)^{2}}{8 c \,d^{2}}"," ",0,"3/4*I/c*b^3/d^2/(c*x-I)-3/2*I/c*a^2*b/d^2*arctan(c*x)-1/2/c*b^3/d^2/(c*x-I)*arctan(c*x)^3+I/c*b^3/d^2/(1+I*c*x)*arctan(c*x)^3-3/4*b^3/d^2/(c*x-I)*arctan(c*x)^2*x+3/4*I/c*a*b^2/d^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-3/4/c*b^3/d^2/(c*x-I)*arctan(c*x)+I/c*a^3/d^2/(1+I*c*x)+3*I/c*a^2*b/d^2/(1+I*c*x)*arctan(c*x)+3/4*I*b^3/d^2/(c*x-I)*arctan(c*x)*x+3/2/c*a*b^2/d^2*arctan(c*x)*ln(I+c*x)-3/2/c*a*b^2/d^2*arctan(c*x)*ln(c*x-I)-3/4*I/c*b^3/d^2/(c*x-I)*arctan(c*x)^2-3*I/c*a*b^2/d^2*arctan(c*x)/(c*x-I)-3/8*I/c*a*b^2/d^2*ln(I+c*x)^2-3/2/c*a*b^2/d^2*arctan(c*x)-3/2/c*a*b^2/d^2/(c*x-I)-3/2*I/c*a^2*b/d^2/(c*x-I)-3/4*I/c*a*b^2/d^2*ln(-1/2*I*(-c*x+I))*ln(-1/2*I*(I+c*x))-1/2*I*b^3/d^2/(c*x-I)*arctan(c*x)^3*x+3/4*I/c*a*b^2/d^2*ln(-1/2*I*(-c*x+I))*ln(I+c*x)+3*I/c*a*b^2/d^2/(1+I*c*x)*arctan(c*x)^2-3/8*I/c*a*b^2/d^2*ln(c*x-I)^2","B"
125,1,711,238,1.024000," ","int((a+b*arctan(c*x))^3/(d+I*c*d*x)^3,x)","\frac{3 i a \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{16 c \,d^{3}}+\frac{3 i a^{2} b \arctan \left(c x \right)}{2 c \,d^{3} \left(i c x +1\right)^{2}}-\frac{3 i a \,b^{2} \ln \left(c x -i\right)^{2}}{32 c \,d^{3}}-\frac{3 i a^{2} b \arctan \left(c x \right)}{8 c \,d^{3}}+\frac{3 i b^{3} \arctan \left(c x \right)^{2} x}{16 d^{3} \left(c x -i\right)^{2}}-\frac{9 c \,b^{3} \arctan \left(c x \right)^{2} x^{2}}{32 d^{3} \left(c x -i\right)^{2}}+\frac{3 a \,b^{2} \arctan \left(c x \right) \ln \left(c x +i\right)}{8 c \,d^{3}}-\frac{3 i a^{2} b}{8 c \,d^{3} \left(c x -i\right)}+\frac{3 i a \,b^{2} \arctan \left(c x \right)^{2}}{2 c \,d^{3} \left(i c x +1\right)^{2}}-\frac{3 i a \,b^{2} \arctan \left(c x \right)}{4 c \,d^{3} \left(c x -i\right)}-\frac{i c \,b^{3} \arctan \left(c x \right)^{3} x^{2}}{8 d^{3} \left(c x -i\right)^{2}}+\frac{21 i c \,b^{3} x^{2} \arctan \left(c x \right)}{64 d^{3} \left(c x -i\right)^{2}}-\frac{3 i a \,b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{16 c \,d^{3}}+\frac{3 i a \,b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(c x +i\right)}{16 c \,d^{3}}+\frac{3 b^{3}}{8 c \,d^{3} \left(c x -i\right)^{2}}-\frac{3 a \,b^{2} \arctan \left(c x \right) \ln \left(c x -i\right)}{8 c \,d^{3}}-\frac{3 a \,b^{2} \arctan \left(c x \right)}{4 c \,d^{3} \left(c x -i\right)^{2}}+\frac{i b^{3} \arctan \left(c x \right)^{3}}{2 c \,d^{3} \left(i c x +1\right)^{2}}+\frac{i b^{3} \arctan \left(c x \right)^{3}}{8 c \,d^{3} \left(c x -i\right)^{2}}+\frac{27 i b^{3} \arctan \left(c x \right)}{64 c \,d^{3} \left(c x -i\right)^{2}}+\frac{3 i a \,b^{2}}{16 c \,d^{3} \left(c x -i\right)^{2}}-\frac{15 b^{3} \arctan \left(c x \right)^{2}}{32 c \,d^{3} \left(c x -i\right)^{2}}-\frac{9 a \,b^{2}}{16 c \,d^{3} \left(c x -i\right)}-\frac{b^{3} \arctan \left(c x \right)^{3} x}{4 d^{3} \left(c x -i\right)^{2}}+\frac{3 b^{3} \arctan \left(c x \right) x}{32 d^{3} \left(c x -i\right)^{2}}+\frac{i a^{3}}{2 c \,d^{3} \left(i c x +1\right)^{2}}+\frac{21 i b^{3} x}{64 d^{3} \left(c x -i\right)^{2}}-\frac{3 a^{2} b}{8 c \,d^{3} \left(c x -i\right)^{2}}-\frac{9 a \,b^{2} \arctan \left(c x \right)}{16 c \,d^{3}}-\frac{3 i a \,b^{2} \ln \left(c x +i\right)^{2}}{32 c \,d^{3}}"," ",0,"3/2*I/c*a*b^2/d^3/(1+I*c*x)^2*arctan(c*x)^2-3/4*I/c*a*b^2/d^3*arctan(c*x)/(c*x-I)-1/8*I*c*b^3/d^3/(c*x-I)^2*arctan(c*x)^3*x^2+21/64*I*c*b^3/d^3/(c*x-I)^2*x^2*arctan(c*x)-3/16*I/c*a*b^2/d^3*ln(-1/2*I*(-c*x+I))*ln(-1/2*I*(I+c*x))+3/16*I/c*a*b^2/d^3*ln(-1/2*I*(-c*x+I))*ln(I+c*x)+3/16*I/c*a*b^2/d^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))+3/2*I/c*a^2*b/d^3/(1+I*c*x)^2*arctan(c*x)-3/8/c*a*b^2/d^3*arctan(c*x)*ln(c*x-I)-3/4/c*a*b^2/d^3/(c*x-I)^2*arctan(c*x)+1/2*I/c*b^3/d^3/(1+I*c*x)^2*arctan(c*x)^3+1/8*I/c*b^3/d^3/(c*x-I)^2*arctan(c*x)^3+27/64*I/c*b^3/d^3/(c*x-I)^2*arctan(c*x)+3/16*I/c*a*b^2/d^3/(c*x-I)^2-3/32*I/c*a*b^2/d^3*ln(c*x-I)^2-3/8*I/c*a^2*b/d^3*arctan(c*x)+3/16*I*b^3/d^3/(c*x-I)^2*arctan(c*x)^2*x-9/32*c*b^3/d^3/(c*x-I)^2*arctan(c*x)^2*x^2+3/8/c*a*b^2/d^3*arctan(c*x)*ln(I+c*x)-3/8*I/c*a^2*b/d^3/(c*x-I)-3/32*I/c*a*b^2/d^3*ln(I+c*x)^2-9/16/c*a*b^2/d^3*arctan(c*x)-15/32/c*b^3/d^3/(c*x-I)^2*arctan(c*x)^2-9/16/c*a*b^2/d^3/(c*x-I)-1/4*b^3/d^3/(c*x-I)^2*arctan(c*x)^3*x+3/32*b^3/d^3/(c*x-I)^2*arctan(c*x)*x+1/2*I/c*a^3/d^3/(1+I*c*x)^2+21/64*I*b^3/d^3/(c*x-I)^2*x+3/8/c*b^3/d^3/(c*x-I)^2-3/8/c*a^2*b/d^3/(c*x-I)^2","B"
126,1,881,316,1.093000," ","int((a+b*arctan(c*x))^3/(d+I*c*d*x)^4,x)","\frac{139 b^{3} \arctan \left(c x \right)}{576 c \,d^{4} \left(c x -i\right)^{3}}-\frac{41 i b^{3}}{216 c \,d^{4} \left(c x -i\right)^{3}}+\frac{i a^{3}}{3 c \,d^{4} \left(i c x +1\right)^{3}}-\frac{11 a \,b^{2}}{48 c \,d^{4} \left(c x -i\right)}+\frac{a \,b^{2}}{18 c \,d^{4} \left(c x -i\right)^{3}}-\frac{c \,b^{3} \arctan \left(c x \right)^{3} x^{2}}{8 d^{4} \left(c x -i\right)^{3}}-\frac{11 a \,b^{2} \arctan \left(c x \right)}{48 c \,d^{4}}-\frac{i a^{2} b \arctan \left(c x \right)}{8 c \,d^{4}}-\frac{i a^{2} b}{8 c \,d^{4} \left(c x -i\right)}+\frac{85 i c^{2} b^{3} \arctan \left(c x \right) x^{3}}{576 d^{4} \left(c x -i\right)^{3}}+\frac{i a^{2} b \arctan \left(c x \right)}{c \,d^{4} \left(i c x +1\right)^{3}}+\frac{i a \,b^{2} \arctan \left(c x \right)^{2}}{c \,d^{4} \left(i c x +1\right)^{3}}+\frac{41 c \,b^{3} x^{2} \arctan \left(c x \right)}{192 d^{4} \left(c x -i\right)^{3}}+\frac{i b^{3} \arctan \left(c x \right)^{3}}{3 c \,d^{4} \left(i c x +1\right)^{3}}-\frac{11 c^{2} b^{3} \arctan \left(c x \right)^{2} x^{3}}{96 d^{4} \left(c x -i\right)^{3}}+\frac{21 b^{3} x}{64 d^{4} \left(c x -i\right)^{3}}+\frac{23 i b^{3} \arctan \left(c x \right) x}{192 d^{4} \left(c x -i\right)^{3}}+\frac{i b^{3} \arctan \left(c x \right)^{3} x}{8 d^{4} \left(c x -i\right)^{3}}-\frac{a \,b^{2} \arctan \left(c x \right)}{4 c \,d^{4} \left(c x -i\right)^{2}}+\frac{a \,b^{2} \arctan \left(c x \right) \ln \left(c x +i\right)}{8 c \,d^{4}}-\frac{a \,b^{2} \arctan \left(c x \right) \ln \left(c x -i\right)}{8 c \,d^{4}}-\frac{i a \,b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{16 c \,d^{4}}+\frac{i a \,b^{2} \ln \left(-\frac{i \left(-c x +i\right)}{2}\right) \ln \left(c x +i\right)}{16 c \,d^{4}}+\frac{i a \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{16 c \,d^{4}}+\frac{i a \,b^{2} \arctan \left(c x \right)}{3 c \,d^{4} \left(c x -i\right)^{3}}-\frac{i a \,b^{2} \arctan \left(c x \right)}{4 c \,d^{4} \left(c x -i\right)}-\frac{i c^{2} b^{3} \arctan \left(c x \right)^{3} x^{3}}{24 d^{4} \left(c x -i\right)^{3}}+\frac{7 i c \,b^{3} \arctan \left(c x \right)^{2} x^{2}}{32 d^{4} \left(c x -i\right)^{3}}-\frac{i a \,b^{2} \ln \left(c x +i\right)^{2}}{32 c \,d^{4}}-\frac{i a \,b^{2} \ln \left(c x -i\right)^{2}}{32 c \,d^{4}}+\frac{5 i a \,b^{2}}{48 c \,d^{4} \left(c x -i\right)^{2}}+\frac{i a^{2} b}{6 c \,d^{4} \left(c x -i\right)^{3}}+\frac{29 i b^{3} \arctan \left(c x \right)^{2}}{96 c \,d^{4} \left(c x -i\right)^{3}}-\frac{b^{3} \arctan \left(c x \right)^{2} x}{32 d^{4} \left(c x -i\right)^{3}}-\frac{a^{2} b}{8 c \,d^{4} \left(c x -i\right)^{2}}+\frac{b^{3} \arctan \left(c x \right)^{3}}{24 c \,d^{4} \left(c x -i\right)^{3}}+\frac{85 i c \,b^{3} x^{2}}{576 d^{4} \left(c x -i\right)^{3}}"," ",0,"41/192*c*b^3/d^4/(c*x-I)^3*x^2*arctan(c*x)+85/576*I*c*b^3/d^4/(c*x-I)^3*x^2-1/8*I/c*a^2*b/d^4*arctan(c*x)+1/3*I/c*b^3/d^4/(1+I*c*x)^3*arctan(c*x)^3+29/96*I/c*b^3/d^4/(c*x-I)^3*arctan(c*x)^2-1/8*c*b^3/d^4/(c*x-I)^3*arctan(c*x)^3*x^2-11/96*c^2*b^3/d^4/(c*x-I)^3*arctan(c*x)^2*x^3+1/6*I/c*a^2*b/d^4/(c*x-I)^3-1/8*I/c*a^2*b/d^4/(c*x-I)-1/32*I/c*a*b^2/d^4*ln(I+c*x)^2-1/32*I/c*a*b^2/d^4*ln(c*x-I)^2+5/48*I/c*a*b^2/d^4/(c*x-I)^2+23/192*I*b^3/d^4/(c*x-I)^3*arctan(c*x)*x+1/8*I*b^3/d^4/(c*x-I)^3*arctan(c*x)^3*x-1/32*b^3/d^4/(c*x-I)^3*arctan(c*x)^2*x-11/48/c*a*b^2/d^4*arctan(c*x)-1/8/c*a^2*b/d^4/(c*x-I)^2+1/24/c*b^3/d^4/(c*x-I)^3*arctan(c*x)^3+139/576/c*b^3/d^4/(c*x-I)^3*arctan(c*x)-41/216*I/c*b^3/d^4/(c*x-I)^3+1/3*I/c*a^3/d^4/(1+I*c*x)^3-11/48/c*a*b^2/d^4/(c*x-I)-1/4/c*a*b^2/d^4*arctan(c*x)/(c*x-I)^2+1/8/c*a*b^2/d^4*arctan(c*x)*ln(I+c*x)-1/8/c*a*b^2/d^4*arctan(c*x)*ln(c*x-I)-1/16*I/c*a*b^2/d^4*ln(-1/2*I*(-c*x+I))*ln(-1/2*I*(I+c*x))+1/16*I/c*a*b^2/d^4*ln(-1/2*I*(-c*x+I))*ln(I+c*x)+1/16*I/c*a*b^2/d^4*ln(c*x-I)*ln(-1/2*I*(I+c*x))+1/3*I/c*a*b^2/d^4*arctan(c*x)/(c*x-I)^3-1/4*I/c*a*b^2/d^4*arctan(c*x)/(c*x-I)-1/24*I*c^2*b^3/d^4/(c*x-I)^3*arctan(c*x)^3*x^3+7/32*I*c*b^3/d^4/(c*x-I)^3*arctan(c*x)^2*x^2+85/576*I*c^2*b^3/d^4/(c*x-I)^3*arctan(c*x)*x^3+I/c*a^2*b/d^4/(1+I*c*x)^3*arctan(c*x)+I/c*a*b^2/d^4/(1+I*c*x)^3*arctan(c*x)^2+1/18/c*a*b^2/d^4/(c*x-I)^3+21/64*b^3/d^4/(c*x-I)^3*x","B"
127,1,1725,376,12.328000," ","int(x^2*(a+b*arctan(c*x))^3/(d+I*c*d*x),x)","\frac{b^{3} \arctan \left(c x \right)^{3} x}{c^{2} d}+\frac{3 a \,b^{2} \pi  \arctan \left(c x \right)^{2}}{c^{3} d}+\frac{3 b \,a^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{3} d}+\frac{6 a \,b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{6 a \,b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{3 i b \,a^{2} x}{2 c^{2} d}-\frac{9 i b \,a^{2} \arctan \left(c x \right)}{4 c^{3} d}-\frac{i b^{3} \arctan \left(c x \right)^{3} x^{2}}{2 c d}+\frac{3 i b^{3} \arctan \left(c x \right)^{2} x}{2 c^{2} d}+\frac{3 i a \,b^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{3} d}+\frac{3 i b \,a^{2} \arctan \left(\frac{1}{6} c^{3} x^{3}+\frac{7}{6} c x \right)}{8 c^{3} d}-\frac{3 i b \,a^{2} \arctan \left(\frac{c x}{2}\right)}{8 c^{3} d}-\frac{i b^{3} \arctan \left(c x \right)^{3} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{3} d}+\frac{3 i b^{3} \arctan \left(c x \right) \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{3} d}+\frac{3 i b \,a^{2} \arctan \left(\frac{c x}{2}-\frac{i}{2}\right)}{4 c^{3} d}-\frac{9 i a \,b^{2} \arctan \left(c x \right)^{2}}{2 c^{3} d}-\frac{3 a \,b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{3} d}-\frac{3 i a \,b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{3} d}-\frac{6 i a \,b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}-\frac{6 i a \,b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{3 a \,b^{2} \arctan \left(c x \right)^{2} x}{c^{2} d}+\frac{3 b \,a^{2} \arctan \left(c x \right) x}{c^{2} d}-\frac{3 i b^{3} \arctan \left(c x \right) \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{3} d}-\frac{3 i b^{3} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{3} d}+\frac{3 b \,a^{2}}{2 c^{3} d}+\frac{a^{3} x}{c^{2} d}+\frac{3 b^{3} \arctan \left(c x \right)^{2}}{2 c^{3} d}-\frac{a^{3} \arctan \left(c x \right)}{c^{3} d}-\frac{b^{3} \arctan \left(c x \right)^{4}}{2 c^{3} d}-\frac{2 a \,b^{2} \arctan \left(c x \right)^{3}}{c^{3} d}+\frac{3 a \,b^{2} \arctan \left(c x \right)}{c^{3} d}-\frac{3 b \,a^{2} \ln \left(c^{4} x^{4}+10 c^{2} x^{2}+9\right)}{16 c^{3} d}-\frac{9 b \,a^{2} \ln \left(c^{2} x^{2}+1\right)}{8 c^{3} d}-\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c^{3} d}-\frac{3 i b^{3} \arctan \left(c x \right)^{3}}{2 c^{3} d}+\frac{3 b^{3} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{3} d}-\frac{3 b \,a^{2} \ln \left(c x -i\right)^{2}}{4 c^{3} d}-\frac{3 b^{3} \arctan \left(c x \right)^{2} \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{3} d}+\frac{3 b \,a^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{3} d}-\frac{3 a \,b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c^{3} d}-\frac{3 a \,b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{c^{3} d}+\frac{3 i b \,a^{2} \arctan \left(c x \right) \ln \left(c x -i\right)}{c^{3} d}-\frac{3 i a \,b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{3} d}+\frac{3 i a \,b^{2} \arctan \left(c x \right)^{2} \ln \left(c x -i\right)}{c^{3} d}-\frac{3 i b \,a^{2} \arctan \left(c x \right) x^{2}}{2 c d}-\frac{3 i a \,b^{2} \arctan \left(c x \right)^{2} x^{2}}{2 c d}+\frac{3 i a \,b^{2} \arctan \left(c x \right) x}{c^{2} d}-\frac{i a^{3} x^{2}}{2 c d}+\frac{i a^{3} \ln \left(c^{2} x^{2}+1\right)}{2 c^{3} d}+\frac{3 b^{3} \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{3} d}+\frac{3 b^{3} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{3} d}+\frac{3 b^{3} \polylog \left(4, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{4 c^{3} d}+\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c^{3} d}-\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c^{3} d}"," ",0,"1/c^2*b^3/d*arctan(c*x)^3*x-1/2*I/c*a^3/d*x^2+3/2/c^3*b*a^2/d*ln(c*x-I)*ln(-1/2*I*(I+c*x))-3/c^3*a*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+6/c^3*a*b^2/d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+6/c^3*a*b^2/d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I/c^2*b*a^2/d*x-9/4*I/c^3*b*a^2/d*arctan(c*x)-1/2*I/c*b^3/d*arctan(c*x)^3*x^2+3/2*I/c^2*b^3/d*arctan(c*x)^2*x-3/2*I/c^3*a*b^2/d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-6*I/c^3*a*b^2/d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*I/c^3*a*b^2/d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I/c^3*a*b^2/d*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+3/8*I/c^3*b*a^2/d*arctan(1/6*c^3*x^3+7/6*c*x)-3/8*I/c^3*b*a^2/d*arctan(1/2*c*x)-I/c^3*b^3/d*arctan(c*x)^3*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-3/2*I/c^3*b^3/d*arctan(c*x)*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+3*I/c^3*b^3/d*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-3*I/c^3*b^3/d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+3/4*I/c^3*b*a^2/d*arctan(1/2*c*x-1/2*I)-9/2*I/c^3*a*b^2/d*arctan(c*x)^2+3/c^3*a*b^2/d*Pi*arctan(c*x)^2+3/c^2*a*b^2/d*arctan(c*x)^2*x+3/c^2*b*a^2/d*arctan(c*x)*x+1/2*I/c^3*a^3/d*ln(c^2*x^2+1)-3/2*I/c^3*b^3/d*arctan(c*x)^3+3/2/c^3*b*a^2/d+1/c^2*a^3/d*x+3/2/c^3*b^3/d*arctan(c*x)^2+3/2/c^3*b^3/d*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+3/2/c^3*b^3/d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-1/c^3*a^3/d*arctan(c*x)+3/4/c^3*b^3/d*polylog(4,-(1+I*c*x)^2/(c^2*x^2+1))-1/2/c^3*b^3/d*arctan(c*x)^4-2/c^3*a*b^2/d*arctan(c*x)^3+3/c^3*b^3/d*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-3/2/c^3*b^3/d*arctan(c*x)^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+3/c^3*a*b^2/d*arctan(c*x)+3/2/c^3*b*a^2/d*dilog(-1/2*I*(I+c*x))-3/4/c^3*b*a^2/d*ln(c*x-I)^2-3/16/c^3*b*a^2/d*ln(c^4*x^4+10*c^2*x^2+9)-9/8/c^3*b*a^2/d*ln(c^2*x^2+1)-3/2/c^3*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-3/2/c^3*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3/c^3*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3*I/c^3*b*a^2/d*arctan(c*x)*ln(c*x-I)-3*I/c^3*a*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))+3*I/c^3*a*b^2/d*arctan(c*x)^2*ln(c*x-I)-3/2*I/c*b*a^2/d*arctan(c*x)*x^2-3/2*I/c*a*b^2/d*arctan(c*x)^2*x^2+3*I/c^2*a*b^2/d*arctan(c*x)*x+3/2/c^3*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2/c^3*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2","C"
128,1,5478,257,0.984000," ","int(x*(a+b*arctan(c*x))^3/(d+I*c*d*x),x)","\text{output too large to display}"," ",0,"result too large to display","C"
129,1,2044,127,0.315000," ","int((a+b*arctan(c*x))^3/(d+I*c*d*x),x)","\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{3} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \arctan \left(c x \right)^{3}}{2 c d}+\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}-\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c d}+\frac{3 a^{2} b \dilog \left(\frac{i c x}{2}+\frac{1}{2}\right)}{2 c d}+\frac{3 b^{3} \arctan \left(c x \right)^{2} \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c d}-\frac{3 b^{3} \polylog \left(4, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{4 c d}+\frac{a^{3} \arctan \left(c x \right)}{c d}+\frac{3 a^{2} b \ln \left(i c x +1\right)^{2}}{4 c d}-\frac{i a^{3} \ln \left(c^{2} x^{2}+1\right)}{2 c d}+\frac{2 a \,b^{2} \arctan \left(c x \right)^{3}}{c d}+\frac{b^{3} \pi  \arctan \left(c x \right)^{3}}{2 c d}-\frac{3 i a^{2} b \ln \left(i c x +1\right) \arctan \left(c x \right)}{c d}-\frac{b^{3} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{3}}{2 c d}-\frac{3 i a \,b^{2} \ln \left(i c x +1\right) \arctan \left(c x \right)^{2}}{c d}+\frac{3 i a \,b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c d}+\frac{3 a \,b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c d}-\frac{3 a \,b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \arctan \left(c x \right)^{3}}{2 c d}+\frac{b^{3} \pi  \,\mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{3}}{2 c d}-\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{3}}{2 c d}-\frac{3 a \,b^{2} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{2}}{2 c d}+\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right) \arctan \left(c x \right)^{2}}{2 c d}+\frac{3 a \,b^{2} \pi  \arctan \left(c x \right)^{2}}{2 c d}+\frac{b^{3} \arctan \left(c x \right)^{4}}{2 c d}+\frac{3 i a \,b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c d}-\frac{i b^{3} \ln \left(i c x +1\right) \arctan \left(c x \right)^{3}}{c d}+\frac{i b^{3} \arctan \left(c x \right)^{3} \ln \left(\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c d}-\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{3}}{2 c d}+\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{3} \arctan \left(c x \right)^{3}}{2 c d}-\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{3}}{2 c d}-\frac{3 a^{2} b \ln \left(\frac{1}{2}-\frac{i c x}{2}\right) \ln \left(i c x +1\right)}{2 c d}+\frac{3 a^{2} b \ln \left(\frac{1}{2}-\frac{i c x}{2}\right) \ln \left(\frac{i c x}{2}+\frac{1}{2}\right)}{2 c d}+\frac{3 i b^{3} \arctan \left(c x \right) \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c d}+\frac{3 a \,b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c d}-\frac{3 a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}\right)^{2} \arctan \left(c x \right)^{2}}{2 c d}"," ",0,"3/2/c*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2/c*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+3/2/c*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^3-3/2/c*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-I/c*b^3/d*ln(1+I*c*x)*arctan(c*x)^3+3/2*I/c*b^3/d*arctan(c*x)*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+3/2*I/c*a*b^2/d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+3/c*a*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+3/2/c*a^2*b/d*dilog(1/2*I*c*x+1/2)+3/4/c*a^2*b/d*ln(1+I*c*x)^2+3/2/c*b^3/d*arctan(c*x)^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-1/2*I/c*a^3/d*ln(c^2*x^2+1)+3/2/c*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-3/4/c*b^3/d*polylog(4,-(1+I*c*x)^2/(c^2*x^2+1))+1/c*a^3/d*arctan(c*x)+2/c*a*b^2/d*arctan(c*x)^3+1/2/c*b^3/d*Pi*arctan(c*x)^3+1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3-1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^3-3*I/c*a*b^2/d*ln(1+I*c*x)*arctan(c*x)^2+3*I/c*a*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-3*I/c*a^2*b/d*ln(1+I*c*x)*arctan(c*x)-1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^3-3/2/c*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn((1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^3+3/2/c*a*b^2/d*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3/2/c*a*b^2/d*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2/c*a*b^2/d*Pi*arctan(c*x)^2+1/2/c*b^3/d*arctan(c*x)^4+I/c*b^3/d*arctan(c*x)^3*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-1/2/c*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^3+1/2/c*b^3/d*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^3-1/2/c*b^3/d*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3-3/2/c*a^2*b/d*ln(1/2-1/2*I*c*x)*ln(1+I*c*x)+3/2/c*a^2*b/d*ln(1/2-1/2*I*c*x)*ln(1/2*I*c*x+1/2)","C"
130,1,3393,116,0.465000," ","int((a+b*arctan(c*x))^3/x/(d+I*c*d*x),x)","\text{output too large to display}"," ",0,"3/2*I*a*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-3/2*I*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*I*b^3/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3-1/2*I*b^3/d*Pi*arctan(c*x)^3*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2-1/2*I*b^3/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3-1/2*I*b^3/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3+3/2*I*a*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3/2*I*a*b^2/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*a*b^2/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3/2*I*a*b^2/d*Pi*arctan(c*x)^2*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3-3*I*a*b^2/d*Pi*arctan(c*x)^2*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2+1/2*I*b^3/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3+1/2*I*b^3/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^3-b^3/d*ln(c*x-I)*arctan(c*x)^3+b^3/d*arctan(c*x)^3*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))+6*a*b^2/d*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*a*b^2/d*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^3/d*arctan(c*x)^3*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^3/d*arctan(c*x)^3*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-b^3/d*arctan(c*x)^3*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+6*b^3/d*arctan(c*x)*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^3/d*arctan(c*x)^3*ln(c*x)+6*b^3/d*arctan(c*x)*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*I*b^3/d*arctan(c*x)^4+6*I*b^3/d*polylog(4,(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*I*b^3/d*polylog(4,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-I*a^3/d*arctan(c*x)-I*b^3/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3-1/2*I*b^3/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3+3/2*I*b*a^2/d*ln(c*x)*ln(1+I*c*x)-3/2*I*b*a^2/d*ln(c*x)*ln(1-I*c*x)+3/2*I*b*a^2/d*ln(c*x-I)*ln(-1/2*I*(I+c*x))-6*I*a*b^2/d*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*I*a*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+9/2*I*a*b^2/d*Pi*arctan(c*x)^2-3*I*b^3/d*arctan(c*x)^2*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*I*b^3/d*arctan(c*x)^2*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I*b^3/d*Pi*arctan(c*x)^3-3*b*a^2/d*ln(c*x-I)*arctan(c*x)+3*a*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))-3*a*b^2/d*ln(c*x-I)*arctan(c*x)^2+3*b*a^2/d*arctan(c*x)*ln(c*x)+3/2*I*b*a^2/d*dilog(1+I*c*x)-3/2*I*b*a^2/d*dilog(1-I*c*x)+3/2*I*b*a^2/d*dilog(-1/2*I*(I+c*x))-3/4*I*b*a^2/d*ln(c*x-I)^2+3*a*b^2/d*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*a*b^2/d*arctan(c*x)^2*ln(c*x)-3*a*b^2/d*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+3*a*b^2/d*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*a*b^2/d*arctan(c*x)^3-1/2*a^3/d*ln(c^2*x^2+1)+a^3/d*ln(c*x)-3/2*I*a*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*a*b^2/d*Pi*arctan(c*x)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2-3/2*I*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*a*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*a*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+1/2*I*b^3/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^3-1/2*I*b^3/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^3+1/2*I*b^3/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^3+1/2*I*b^3/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^3-1/2*I*b^3/d*Pi*arctan(c*x)^3*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3","C"
131,1,11233,244,1.321000," ","int((a+b*arctan(c*x))^3/x^2/(d+I*c*d*x),x)","\text{output too large to display}"," ",0,"result too large to display","C"
132,1,3058,380,21.296000," ","int((a+b*arctan(c*x))^3/x^3/(d+I*c*d*x),x)","\text{output too large to display}"," ",0,"3*I*c^2*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*c^2*a*b^2/d*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3+3/2*I*c^2*a*b^2/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*c^2*a*b^2/d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+3/2*I*c^2*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3/2*I*c^2*a^2*b/d*dilog(1+I*c*x)+3/2*I*c^2*a^2*b/d*dilog(1-I*c*x)-3/2*I*c^2*a^2*b/d*dilog(-1/2*I*(I+c*x))+3/4*I*c^2*a^2*b/d*ln(c*x-I)^2-3*I*c^2*a*b^2/d*arctan(c*x)+2*I*c^2*a*b^2/d*arctan(c*x)^3-3*c^2*a*b^2/d*arctan(c*x)^2*ln(c*x)+3*c^2*a*b^2/d*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)-3*c^2*a*b^2/d*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*c^2*a^2*b/d*arctan(c*x)*ln(c*x)+3/2*I*c^2*a*b^2/d*Pi*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*c^2*a*b^2/d*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+3/2*I*c^2*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*c^2*a*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*c^2*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*c^2*a*b^2/d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-6*I*c^2*b^3/d*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*I*c^2*b^3/d*arctan(c*x)^2-3/2*c*a^2*b/d/x-1/2*a^3/d/x^2-3/2*I*c^2*a*b^2/d*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+3/2*I*c^2*a*b^2/d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn((1+I*c*x)^2/(c^2*x^2+1))*csgn((1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+6*c^2*a*b^2/d*dilog((1+I*c*x)/(c^2*x^2+1)^(1/2))-6*c^2*a*b^2/d*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*c^2*a*b^2/d*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*c^2*a^2*b/d*arctan(c*x)+I*c^2*a^3/d*arctan(c*x)+I*c*a^3/d/x-3/2*c*b^3/d*arctan(c*x)^2/x-3/2*a^2*b/d*arctan(c*x)/x^2-3/2*a*b^2/d*arctan(c*x)^2/x^2-3*I*c^2*b^3/d*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I*c^2*b^3/d*arctan(c*x)^4-3*I*c^2*b^3/d*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*I*c^2*b^3/d*polylog(4,(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*I*c^2*b^3/d*polylog(4,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*I*c^2*b^3/d*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*c^2*b^3/d*arctan(c*x)^3+1/2*c^2*a^3/d*ln(c^2*x^2+1)-c^2*a^3/d*ln(c*x)-1/2*b^3/d*arctan(c*x)^3/x^2+3*c^2*a^2*b/d*arctan(c*x)*ln(c*x-I)-3*c^2*a*b^2/d*arctan(c*x)^2*ln(2*I*(1+I*c*x)^2/(c^2*x^2+1))+3*c^2*a*b^2/d*ln(c*x-I)*arctan(c*x)^2-3*c^2*a*b^2/d*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*c*a*b^2/d*arctan(c*x)/x+I*c*b^3/d*arctan(c*x)^3/x-3*I*c^2*b^3/d*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*I*c^2*b^3/d*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I*c^2*b^3/d*arctan(c*x)^2*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I*c^2*b^3/d*arctan(c*x)^2*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-3*I*c^2*a^2*b/d*ln(c*x)+3/2*I*c^2*a^2*b/d*ln(c^2*x^2+1)-6*c^2*b^3/d*arctan(c*x)*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*c^2*b^3/d*arctan(c*x)*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*c^2*b^3/d*arctan(c*x)*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*c^2*b^3/d*arctan(c*x)*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*c^2*b^3/d*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-c^2*b^3/d*arctan(c*x)^3*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-c^2*b^3/d*arctan(c*x)^3*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*c^2*b^3/d*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*c^2*a*b^2/d*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)-6*c^2*a*b^2/d*dilog(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-9/2*c^2*a*b^2/d*arctan(c*x)^2+3*c^2*a*b^2/d*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*I*c*a^2*b/d*arctan(c*x)/x+3*I*c*a*b^2/d*arctan(c*x)^2/x-9/2*I*c^2*a*b^2/d*arctan(c*x)^2*Pi+6*I*c^2*a*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*I*c^2*a*b^2/d*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*I*c^2*a^2*b/d*ln(c*x)*ln(1+I*c*x)+3/2*I*c^2*a^2*b/d*ln(c*x)*ln(1-I*c*x)-3/2*I*c^2*a^2*b/d*ln(-1/2*I*(I+c*x))*ln(c*x-I)-6*I*c^2*a*b^2/d*arctan(c*x)*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))","C"
133,0,0,23,1.473000," ","int(1/(d+I*c*d*x)/(a+b*arctan(c*x)),x)","\int \frac{1}{\left(i c d x +d \right) \left(a +b \arctan \left(c x \right)\right)}\, dx"," ",0,"int(1/(d+I*c*d*x)/(a+b*arctan(c*x)),x)","F"
134,1,394,271,0.065000," ","int(x^3*(a+b*arctan(c*x))/(e*x+d),x)","\frac{a \,x^{3}}{3 e}-\frac{a \,x^{2} d}{2 e^{2}}+\frac{a \,d^{2} x}{e^{3}}-\frac{a \,d^{3} \ln \left(c e x +d c \right)}{e^{4}}+\frac{b \arctan \left(c x \right) x^{3}}{3 e}-\frac{b \arctan \left(c x \right) x^{2} d}{2 e^{2}}+\frac{b \,d^{2} x \arctan \left(c x \right)}{e^{3}}-\frac{b \arctan \left(c x \right) d^{3} \ln \left(c e x +d c \right)}{e^{4}}-\frac{b \ln \left(c^{2} d^{2}-2 \left(c e x +d c \right) c d +\left(c e x +d c \right)^{2}+e^{2}\right) d^{2}}{2 c \,e^{3}}-\frac{b d \arctan \left(c x \right)}{2 c^{2} e^{2}}+\frac{b \ln \left(c^{2} d^{2}-2 \left(c e x +d c \right) c d +\left(c e x +d c \right)^{2}+e^{2}\right)}{6 c^{3} e}+\frac{b d x}{2 c \,e^{2}}+\frac{2 b \,d^{2}}{3 c \,e^{3}}-\frac{b \,x^{2}}{6 c e}-\frac{i b \,d^{3} \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e^{4}}-\frac{i b \,d^{3} \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e^{4}}+\frac{i b \,d^{3} \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e^{4}}+\frac{i b \,d^{3} \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e^{4}}"," ",0,"1/3*a/e*x^3-1/2*a/e^2*x^2*d+a*d^2*x/e^3-a*d^3/e^4*ln(c*e*x+c*d)+1/3*b*arctan(c*x)/e*x^3-1/2*b*arctan(c*x)/e^2*x^2*d+b*d^2*x*arctan(c*x)/e^3-b*arctan(c*x)*d^3/e^4*ln(c*e*x+c*d)-1/2/c*b/e^3*ln(c^2*d^2-2*(c*e*x+c*d)*c*d+(c*e*x+c*d)^2+e^2)*d^2-1/2*b*d*arctan(c*x)/c^2/e^2+1/6/c^3*b/e*ln(c^2*d^2-2*(c*e*x+c*d)*c*d+(c*e*x+c*d)^2+e^2)+1/2*b*d*x/c/e^2+2/3/c*b*d^2/e^3-1/6*b*x^2/c/e-1/2*I*b/e^4*d^3*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))+1/2*I*b/e^4*d^3*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))-1/2*I*b/e^4*d^3*dilog((I*e-c*e*x)/(d*c+I*e))+1/2*I*b/e^4*d^3*dilog((I*e+c*e*x)/(I*e-d*c))","A"
135,1,305,217,0.076000," ","int(x^2*(a+b*arctan(c*x))/(e*x+d),x)","\frac{a \,x^{2}}{2 e}-\frac{a d x}{e^{2}}+\frac{a \,d^{2} \ln \left(c e x +d c \right)}{e^{3}}+\frac{b \arctan \left(c x \right) x^{2}}{2 e}-\frac{b d x \arctan \left(c x \right)}{e^{2}}+\frac{b \arctan \left(c x \right) d^{2} \ln \left(c e x +d c \right)}{e^{3}}+\frac{i b \,d^{2} \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e^{3}}-\frac{i b \,d^{2} \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e^{3}}+\frac{i b \,d^{2} \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e^{3}}-\frac{i b \,d^{2} \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e^{3}}+\frac{b d \ln \left(c^{2} d^{2}-2 \left(c e x +d c \right) c d +\left(c e x +d c \right)^{2}+e^{2}\right)}{2 c \,e^{2}}+\frac{b \arctan \left(c x \right)}{2 c^{2} e}-\frac{b x}{2 c e}-\frac{b d}{2 c \,e^{2}}"," ",0,"1/2*a/e*x^2-a*d*x/e^2+a*d^2/e^3*ln(c*e*x+c*d)+1/2*b*arctan(c*x)*x^2/e-b*d*x*arctan(c*x)/e^2+b*arctan(c*x)*d^2/e^3*ln(c*e*x+c*d)+1/2*I*b/e^3*d^2*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))-1/2*I*b/e^3*d^2*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))+1/2*I*b/e^3*d^2*dilog((I*e-c*e*x)/(d*c+I*e))-1/2*I*b/e^3*d^2*dilog((I*e+c*e*x)/(I*e-d*c))+1/2/c*b/e^2*d*ln(c^2*d^2-2*(c*e*x+c*d)*c*d+(c*e*x+c*d)^2+e^2)+1/2*b*arctan(c*x)/c^2/e-1/2*b*x/c/e-1/2/c*b*d/e^2","A"
136,1,235,165,0.052000," ","int(x*(a+b*arctan(c*x))/(e*x+d),x)","\frac{a x}{e}-\frac{a d \ln \left(c e x +d c \right)}{e^{2}}+\frac{b x \arctan \left(c x \right)}{e}-\frac{b \arctan \left(c x \right) d \ln \left(c e x +d c \right)}{e^{2}}-\frac{b \ln \left(c^{2} d^{2}-2 \left(c e x +d c \right) c d +\left(c e x +d c \right)^{2}+e^{2}\right)}{2 c e}-\frac{i b d \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e^{2}}+\frac{i b d \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e^{2}}-\frac{i b d \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e^{2}}+\frac{i b d \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e^{2}}"," ",0,"a*x/e-a*d/e^2*ln(c*e*x+c*d)+b*x*arctan(c*x)/e-b*arctan(c*x)*d/e^2*ln(c*e*x+c*d)-1/2/c*b/e*ln(c^2*d^2-2*(c*e*x+c*d)*c*d+(c*e*x+c*d)^2+e^2)-1/2*I*b/e^2*d*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))+1/2*I*b/e^2*d*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))-1/2*I*b/e^2*d*dilog((I*e-c*e*x)/(d*c+I*e))+1/2*I*b/e^2*d*dilog((I*e+c*e*x)/(I*e-d*c))","A"
137,1,168,126,0.059000," ","int((a+b*arctan(c*x))/(e*x+d),x)","\frac{a \ln \left(c e x +d c \right)}{e}+\frac{b \ln \left(c e x +d c \right) \arctan \left(c x \right)}{e}+\frac{i b \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e}-\frac{i b \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e}+\frac{i b \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{2 e}-\frac{i b \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{2 e}"," ",0,"a*ln(c*e*x+c*d)/e+b*ln(c*e*x+c*d)/e*arctan(c*x)+1/2*I*b*ln(c*e*x+c*d)/e*ln((I*e-c*e*x)/(d*c+I*e))-1/2*I*b*ln(c*e*x+c*d)/e*ln((I*e+c*e*x)/(I*e-d*c))+1/2*I*b/e*dilog((I*e-c*e*x)/(d*c+I*e))-1/2*I*b/e*dilog((I*e+c*e*x)/(I*e-d*c))","A"
138,1,260,161,0.061000," ","int((a+b*arctan(c*x))/x/(e*x+d),x)","\frac{a \ln \left(c x \right)}{d}-\frac{a \ln \left(c e x +d c \right)}{d}+\frac{b \arctan \left(c x \right) \ln \left(c x \right)}{d}-\frac{b \arctan \left(c x \right) \ln \left(c e x +d c \right)}{d}+\frac{i b \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d}-\frac{i b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d}+\frac{i b \dilog \left(i c x +1\right)}{2 d}-\frac{i b \dilog \left(-i c x +1\right)}{2 d}-\frac{i b \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{2 d}+\frac{i b \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{2 d}-\frac{i b \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{2 d}+\frac{i b \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{2 d}"," ",0,"a/d*ln(c*x)-a/d*ln(c*e*x+c*d)+b*arctan(c*x)/d*ln(c*x)-b*arctan(c*x)/d*ln(c*e*x+c*d)+1/2*I*b/d*ln(c*x)*ln(1+I*c*x)-1/2*I*b/d*ln(c*x)*ln(1-I*c*x)+1/2*I*b/d*dilog(1+I*c*x)-1/2*I*b/d*dilog(1-I*c*x)-1/2*I*b/d*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))+1/2*I*b/d*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))-1/2*I*b/d*dilog((I*e-c*e*x)/(d*c+I*e))+1/2*I*b/d*dilog((I*e+c*e*x)/(I*e-d*c))","A"
139,1,321,212,0.064000," ","int((a+b*arctan(c*x))/x^2/(e*x+d),x)","-\frac{a}{d x}-\frac{a e \ln \left(c x \right)}{d^{2}}+\frac{a e \ln \left(c e x +d c \right)}{d^{2}}-\frac{b \arctan \left(c x \right)}{d x}-\frac{b \arctan \left(c x \right) e \ln \left(c x \right)}{d^{2}}+\frac{b \arctan \left(c x \right) e \ln \left(c e x +d c \right)}{d^{2}}+\frac{i b e \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{2 d^{2}}+\frac{i b e \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d^{2}}-\frac{i b e \dilog \left(i c x +1\right)}{2 d^{2}}-\frac{i b e \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{2 d^{2}}+\frac{c b \ln \left(c x \right)}{d}-\frac{b c \ln \left(c^{2} x^{2}+1\right)}{2 d}+\frac{i b e \dilog \left(-i c x +1\right)}{2 d^{2}}-\frac{i b e \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d^{2}}-\frac{i b e \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{2 d^{2}}+\frac{i b e \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{2 d^{2}}"," ",0,"-a/d/x-a/d^2*e*ln(c*x)+a/d^2*e*ln(c*e*x+c*d)-b*arctan(c*x)/d/x-b*arctan(c*x)/d^2*e*ln(c*x)+b*arctan(c*x)/d^2*e*ln(c*e*x+c*d)+1/2*I*b/d^2*e*dilog(1-I*c*x)+1/2*I*b/d^2*e*ln(c*x)*ln(1-I*c*x)+1/2*I*b/d^2*e*dilog((I*e-c*e*x)/(d*c+I*e))-1/2*I*b/d^2*e*dilog((I*e+c*e*x)/(I*e-d*c))+c*b/d*ln(c*x)-1/2*b*c*ln(c^2*x^2+1)/d-1/2*I*b/d^2*e*dilog(1+I*c*x)-1/2*I*b/d^2*e*ln(c*x)*ln(1+I*c*x)-1/2*I*b/d^2*e*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))+1/2*I*b/d^2*e*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))","A"
140,1,393,268,0.080000," ","int((a+b*arctan(c*x))/x^3/(e*x+d),x)","-\frac{a}{2 d \,x^{2}}+\frac{a \,e^{2} \ln \left(c x \right)}{d^{3}}+\frac{a e}{d^{2} x}-\frac{a \,e^{2} \ln \left(c e x +d c \right)}{d^{3}}-\frac{b \arctan \left(c x \right)}{2 d \,x^{2}}+\frac{b \arctan \left(c x \right) e^{2} \ln \left(c x \right)}{d^{3}}+\frac{b \arctan \left(c x \right) e}{d^{2} x}-\frac{b \arctan \left(c x \right) e^{2} \ln \left(c e x +d c \right)}{d^{3}}-\frac{c b e \ln \left(c x \right)}{d^{2}}-\frac{b c}{2 d x}+\frac{b c e \ln \left(c^{2} x^{2}+1\right)}{2 d^{2}}-\frac{b \,c^{2} \arctan \left(c x \right)}{2 d}+\frac{i b \,e^{2} \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{2 d^{3}}-\frac{i b \,e^{2} \dilog \left(-i c x +1\right)}{2 d^{3}}-\frac{i b \,e^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d^{3}}+\frac{i b \,e^{2} \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{2 d^{3}}+\frac{i b \,e^{2} \dilog \left(i c x +1\right)}{2 d^{3}}+\frac{i b \,e^{2} \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d^{3}}-\frac{i b \,e^{2} \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{2 d^{3}}-\frac{i b \,e^{2} \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{2 d^{3}}"," ",0,"-1/2*a/d/x^2+a/d^3*e^2*ln(c*x)+a/d^2*e/x-a/d^3*e^2*ln(c*e*x+c*d)-1/2*b*arctan(c*x)/d/x^2+b*arctan(c*x)/d^3*e^2*ln(c*x)+b*arctan(c*x)/d^2*e/x-b*arctan(c*x)/d^3*e^2*ln(c*e*x+c*d)-c*b/d^2*e*ln(c*x)-1/2*b*c/d/x+1/2*b*c*e*ln(c^2*x^2+1)/d^2-1/2*b*c^2*arctan(c*x)/d-1/2*I*b/d^3*e^2*dilog((I*e-c*e*x)/(d*c+I*e))-1/2*I*b/d^3*e^2*dilog(1-I*c*x)+1/2*I*b/d^3*e^2*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))-1/2*I*b/d^3*e^2*ln(c*x)*ln(1-I*c*x)+1/2*I*b/d^3*e^2*dilog(1+I*c*x)+1/2*I*b/d^3*e^2*ln(c*x)*ln(1+I*c*x)-1/2*I*b/d^3*e^2*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))+1/2*I*b/d^3*e^2*dilog((I*e+c*e*x)/(I*e-d*c))","A"
141,1,2136,555,50.034000," ","int(x^3*(a+b*arctan(c*x))^2/(e*x+d),x)","-\frac{i b^{2} d^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 e^{4}}-\frac{a b \arctan \left(c x \right) d \,x^{2}}{e^{2}}+\frac{2 a b \arctan \left(c x \right) x \,d^{2}}{e^{3}}-\frac{2 a b \arctan \left(c x \right) d^{3} \ln \left(c e x +d c \right)}{e^{4}}-\frac{a b \ln \left(c^{2} d^{2}-2 \left(c e x +d c \right) c d +\left(c e x +d c \right)^{2}+e^{2}\right) d^{2}}{c \,e^{3}}-\frac{a b \arctan \left(c x \right) d}{c^{2} e^{2}}-\frac{i b^{2} d \arctan \left(c x \right)}{c^{2} e^{2}}-\frac{i b^{2} d^{2} \arctan \left(c x \right)^{2}}{c \,e^{3}}+\frac{2 b^{2} d^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c \,e^{3}}+\frac{2 b^{2} d^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c \,e^{3}}-\frac{i a b \,d^{3} \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{e^{4}}+\frac{a^{2} x \,d^{2}}{e^{3}}-\frac{a^{2} d^{3} \ln \left(c e x +d c \right)}{e^{4}}+\frac{b^{2} \arctan \left(c x \right)^{2} x^{3}}{3 e}-\frac{a^{2} x^{2} d}{2 e^{2}}+\frac{b^{2} d^{3} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 e^{4}}+\frac{i b^{2}}{3 c^{3} e}+\frac{4 a b \,d^{2}}{3 c \,e^{3}}+\frac{i b^{2} d^{3} \pi  \,\mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 e^{4}}+\frac{i b^{2} d^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 e^{4}}+\frac{i c \,b^{2} d^{4} \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e^{4} \left(d c -i e \right)}-\frac{a b \,x^{2}}{3 c e}+\frac{a b \ln \left(c^{2} d^{2}-2 \left(c e x +d c \right) c d +\left(c e x +d c \right)^{2}+e^{2}\right)}{3 c^{3} e}-\frac{b^{2} d \arctan \left(c x \right)^{2}}{2 c^{2} e^{2}}-\frac{b^{2} \arctan \left(c x \right) x^{2}}{3 c e}-\frac{b^{2} \arctan \left(c x \right)^{2} d^{3} \ln \left(c e x +d c \right)}{e^{4}}-\frac{b^{2} \arctan \left(c x \right)^{2} x^{2} d}{2 e^{2}}+\frac{b^{2} \arctan \left(c x \right)^{2} x \,d^{2}}{e^{3}}+\frac{2 a b \arctan \left(c x \right) x^{3}}{3 e}+\frac{i b^{2} \arctan \left(c x \right)^{2}}{3 c^{3} e}+\frac{2 i b^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{3} e}+\frac{2 i b^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{3} e}-\frac{i b^{2} d^{3} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{e^{4}}-\frac{2 i b^{2} d^{2} \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c \,e^{3}}-\frac{2 i b^{2} d^{2} \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c \,e^{3}}+\frac{i a b \,d^{3} \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{e^{4}}-\frac{c \,b^{2} d^{4} \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 e^{4} \left(d c -i e \right)}+\frac{b^{2} d^{3} \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e^{3} \left(d c -i e \right)}+\frac{i b^{2} d^{3} \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 e^{3} \left(d c -i e \right)}-\frac{i a b \,d^{3} \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{e^{4}}+\frac{b^{2} d \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{2} e^{2}}-\frac{2 b^{2} \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{3} e}-\frac{2 b^{2} \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{3 c^{3} e}+\frac{b^{2} d^{3} \arctan \left(c x \right)^{2} \ln \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{e^{4}}+\frac{a^{2} x^{3}}{3 e}+\frac{i b^{2} d^{3} \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e^{3} \left(d c -i e \right)}+\frac{i a b \,d^{3} \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{e^{4}}-\frac{c \,b^{2} d^{4} \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e^{4} \left(d c -i e \right)}-\frac{i b^{2} d^{3} \pi  \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 e^{4}}+\frac{a b d x}{c \,e^{2}}+\frac{b^{2} d x \arctan \left(c x \right)}{c \,e^{2}}+\frac{b^{2} x}{3 c^{2} e}-\frac{b^{2} \arctan \left(c x \right)}{3 c^{3} e}"," ",0,"-1/2*I*b^2/e^4*d^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-I*b^2*d^3/e^4*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-2*I/c*b^2/e^3*d^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^2*b^2*d*arctan(c*x)/e^2-2*I/c*b^2/e^3*d^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c*b^2/e^3*d^2*arctan(c*x)^2+I*a*b/e^4*d^3*dilog((I*e+c*e*x)/(I*e-d*c))-a*b*arctan(c*x)/e^2*d*x^2+2*a*b*arctan(c*x)*x*d^2/e^3-2*a*b*arctan(c*x)*d^3/e^4*ln(c*e*x+c*d)+2/c*b^2/e^3*d^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+2/c*b^2/e^3*d^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c*a*b/e^3*ln(c^2*d^2-2*(c*e*x+c*d)*c*d+(c*e*x+c*d)^2+e^2)*d^2-1/c^2*a*b/e^2*arctan(c*x)*d-1/2*c*b^2*d^4/e^4/(d*c-I*e)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+b^2*d^3/e^3/(d*c-I*e)*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+1/2*I*b^2*d^3/e^3/(d*c-I*e)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))-I*a*b/e^4*d^3*dilog((I*e-c*e*x)/(d*c+I*e))+a^2/e^3*x*d^2-a^2*d^3/e^4*ln(c*e*x+c*d)+1/2*b^2*d^3/e^4*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+1/3*b^2*arctan(c*x)^2/e*x^3-1/2*a^2/e^2*x^2*d+I*c*b^2*d^4/e^4/(d*c-I*e)*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+1/2*I*b^2/e^4*d^3*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2/e^4*d^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+4/3/c*a*b*d^2/e^3+1/3*I/c^3*b^2/e-1/3/c*a*b*x^2/e+1/c^2*b^2/e^2*d*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-2/3/c^3*b^2/e*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-2/3/c^3*b^2/e*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/3/c^3*a*b/e*ln(c^2*d^2-2*(c*e*x+c*d)*c*d+(c*e*x+c*d)^2+e^2)-1/2/c^2*b^2/e^2*d*arctan(c*x)^2-1/3/c*b^2*arctan(c*x)/e*x^2+b^2*d^3/e^4*arctan(c*x)^2*ln(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)-b^2*arctan(c*x)^2*d^3/e^4*ln(c*e*x+c*d)-1/2*b^2*arctan(c*x)^2/e^2*x^2*d+b^2*arctan(c*x)^2/e^3*x*d^2+2/3*a*b*arctan(c*x)/e*x^3+2/3*I/c^3*b^2/e*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/3*I/c^3*b^2/e*arctan(c*x)^2+2/3*I/c^3*b^2/e*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/3*a^2/e*x^3+I*b^2*d^3/e^3/(d*c-I*e)*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+I*a*b/e^4*d^3*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))-c*b^2*d^4/e^4/(d*c-I*e)*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))-1/2*I*b^2/e^4*d^3*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-I*a*b/e^4*d^3*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))+a*b*d*x/c/e^2+b^2*d*x*arctan(c*x)/c/e^2+1/3*b^2*x/c^2/e-1/3*b^2*arctan(c*x)/c^3/e","C"
142,1,1784,405,40.436000," ","int(x^2*(a+b*arctan(c*x))^2/(e*x+d),x)","\frac{2 a b \arctan \left(c x \right) d^{2} \ln \left(c e x +d c \right)}{e^{3}}-\frac{2 a b \arctan \left(c x \right) d x}{e^{2}}+\frac{a b d \ln \left(c^{2} d^{2}-2 \left(c e x +d c \right) c d +\left(c e x +d c \right)^{2}+e^{2}\right)}{c \,e^{2}}+\frac{c \,b^{2} d^{3} \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e^{3} \left(d c -i e \right)}+\frac{i a b \,d^{2} \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{e^{3}}-\frac{i b^{2} d^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e^{2} \left(d c -i e \right)}+\frac{i b^{2} d^{2} \pi  \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 e^{3}}-\frac{i a b \,d^{2} \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{e^{3}}-\frac{a b x}{c e}-\frac{b^{2} x \arctan \left(c x \right)}{c e}+\frac{b^{2} \arctan \left(c x \right)^{2}}{2 c^{2} e}+\frac{b^{2} \arctan \left(c x \right)^{2} x^{2}}{2 e}+\frac{a^{2} d^{2} \ln \left(c e x +d c \right)}{e^{3}}+\frac{a^{2} x^{2}}{2 e}-\frac{b^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{2} e}-\frac{b^{2} d^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 e^{3}}+\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 e^{3}}+\frac{i b^{2} d \arctan \left(c x \right)^{2}}{c \,e^{2}}-\frac{2 b^{2} d \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c \,e^{2}}-\frac{2 b^{2} d \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c \,e^{2}}+\frac{i b^{2} d^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{e^{3}}-\frac{b^{2} d^{2} \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e^{2} \left(d c -i e \right)}+\frac{c \,b^{2} d^{3} \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 e^{3} \left(d c -i e \right)}-\frac{i b^{2} d^{2} \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 e^{2} \left(d c -i e \right)}-\frac{i a b \,d^{2} \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{e^{3}}+\frac{2 i b^{2} d \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c \,e^{2}}+\frac{i b^{2} \arctan \left(c x \right)}{c^{2} e}-\frac{b^{2} d^{2} \arctan \left(c x \right)^{2} \ln \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{e^{3}}+\frac{a b \arctan \left(c x \right) x^{2}}{e}-\frac{b^{2} \arctan \left(c x \right)^{2} d x}{e^{2}}+\frac{a b \arctan \left(c x \right)}{c^{2} e}-\frac{a b d}{c \,e^{2}}+\frac{b^{2} \arctan \left(c x \right)^{2} d^{2} \ln \left(c e x +d c \right)}{e^{3}}-\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 e^{3}}-\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2 e^{3}}-\frac{i c \,b^{2} d^{3} \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e^{3} \left(d c -i e \right)}+\frac{2 i b^{2} d \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c \,e^{2}}+\frac{i a b \,d^{2} \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{e^{3}}-\frac{a^{2} d x}{e^{2}}"," ",0,"I*b^2*d^2/e^3*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-b^2*d^2/e^2/(d*c-I*e)*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+2*a*b*arctan(c*x)*d^2/e^3*ln(c*e*x+c*d)-2*a*b*arctan(c*x)*d/e^2*x+1/2*c*b^2*d^3/e^3/(d*c-I*e)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+I/c*b^2/e^2*d*arctan(c*x)^2-2/c*b^2/e^2*d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-2/c*b^2/e^2*d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/c*a*b/e^2*d*ln(c^2*d^2-2*(c*e*x+c*d)*c*d+(c*e*x+c*d)^2+e^2)-1/2*I*b^2*d^2/e^2/(d*c-I*e)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))-I*a*b/e^3*d^2*dilog((I*e+c*e*x)/(I*e-d*c))+2*I/c*b^2/e^2*d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-a*b*x/c/e-b^2*x*arctan(c*x)/c/e-1/c^2*b^2/e*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/2/c^2*b^2*arctan(c*x)^2/e+1/2*b^2*arctan(c*x)^2*x^2/e-1/2*b^2*d^2/e^3*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+a^2*d^2/e^3*ln(c*e*x+c*d)+c*b^2*d^3/e^3/(d*c-I*e)*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+I*a*b/e^3*d^2*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))-I*b^2*d^2/e^2/(d*c-I*e)*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+1/2*a^2*x^2/e+1/2*I*b^2/e^3*d^2*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-I*a*b/e^3*d^2*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))-I*c*b^2*d^3/e^3/(d*c-I*e)*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))-1/2*I*b^2/e^3*d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2/e^3*d^2*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2/e^3*d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+2*I/c*b^2/e^2*d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I*a*b/e^3*d^2*dilog((I*e-c*e*x)/(d*c+I*e))+a*b*arctan(c*x)*x^2/e-b^2*arctan(c*x)^2*d/e^2*x+1/c^2*a*b/e*arctan(c*x)+I/c^2*b^2*arctan(c*x)/e-1/c*a*b*d/e^2+b^2*arctan(c*x)^2*d^2/e^3*ln(c*e*x+c*d)-b^2*d^2/e^3*arctan(c*x)^2*ln(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)-a^2*d/e^2*x","C"
143,1,16024,304,15.750000," ","int(x*(a+b*arctan(c*x))^2/(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","C"
144,1,1297,208,0.240000," ","int((a+b*arctan(c*x))^2/(e*x+d),x)","\frac{a^{2} \ln \left(c e x +d c \right)}{e}+\frac{b^{2} \ln \left(c e x +d c \right) \arctan \left(c x \right)^{2}}{e}-\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{e}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2 e}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 e}-\frac{i a b \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{e}-\frac{i a b \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{e}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2 e}-\frac{b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 e}+\frac{c \,b^{2} d \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e \left(d c -i e \right)}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \arctan \left(c x \right)^{2}}{2 e}+\frac{c \,b^{2} d \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 e \left(d c -i e \right)}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{i d c +e}+\frac{i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{e}+\frac{b^{2} \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 i d c +2 e}+\frac{2 a b \ln \left(c e x +d c \right) \arctan \left(c x \right)}{e}-\frac{i b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{i d c +e}+\frac{i a b \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{e}+\frac{i a b \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{e}-\frac{i c \,b^{2} d \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{e \left(d c -i e \right)}"," ",0,"a^2*ln(c*e*x+c*d)/e+b^2*ln(c*e*x+c*d)/e*arctan(c*x)^2-b^2/e*arctan(c*x)^2*ln(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)+1/2*I*b^2/e*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2*I*b^2/e*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-I*a*b*ln(c*e*x+c*d)/e*ln((I*e+c*e*x)/(I*e-d*c))+I*b^2/e*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+I*a*b/e*dilog((I*e-c*e*x)/(d*c+I*e))-1/2*b^2/e*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+c*b^2/e*d/(d*c-I*e)*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))-1/2*I*b^2/e*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+1/2*c*b^2/e*d/(d*c-I*e)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+b^2*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)-I*b^2*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)+1/2*b^2*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/(e+I*d*c)+2*a*b*ln(c*e*x+c*d)/e*arctan(c*x)-1/2*I*b^2/e*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*arctan(c*x)^2-I*a*b/e*dilog((I*e+c*e*x)/(I*e-d*c))+I*a*b*ln(c*e*x+c*d)/e*ln((I*e-c*e*x)/(d*c+I*e))-I*c*b^2/e*d/(d*c-I*e)*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))","C"
145,1,2363,343,0.714000," ","int((a+b*arctan(c*x))^2/x/(e*x+d),x)","-\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2}}{2 d}+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2 d}+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2}}{2 d}+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2}}{2 d}-\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2}}{2 d}+\frac{i b^{2} e \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{d \left(i d c +e \right)}-\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2}}{2 d}+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2 d}-\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)\right) \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2 d}+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2}}{2 d}-\frac{2 i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{2 i b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{b^{2} e \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 d \left(i d c +e \right)}+\frac{i a b \dilog \left(i c x +1\right)}{d}+\frac{i a b \dilog \left(\frac{c e x +i e}{-d c +i e}\right)}{d}-\frac{i a b \dilog \left(-i c x +1\right)}{d}-\frac{i a b \dilog \left(\frac{-c e x +i e}{d c +i e}\right)}{d}+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3}}{2 d}-\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3}}{2 d}+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3}}{2 d}-\frac{i b^{2} \pi  \arctan \left(c x \right)^{2} \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2}}{2 d}+\frac{i a b \ln \left(c x \right) \ln \left(i c x +1\right)}{d}+\frac{i a b \ln \left(c e x +d c \right) \ln \left(\frac{c e x +i e}{-d c +i e}\right)}{d}-\frac{i a b \ln \left(c x \right) \ln \left(-i c x +1\right)}{d}-\frac{i a b \ln \left(c e x +d c \right) \ln \left(\frac{-c e x +i e}{d c +i e}\right)}{d}-\frac{b^{2} e \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{d \left(i d c +e \right)}+\frac{i b^{2} c \arctan \left(c x \right) \polylog \left(2, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{d c -i e}+\frac{2 a b \arctan \left(c x \right) \ln \left(c x \right)}{d}-\frac{2 a b \arctan \left(c x \right) \ln \left(c e x +d c \right)}{d}-\frac{b^{2} c \polylog \left(3, \frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{2 \left(d c -i e \right)}-\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{d}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(-\frac{i \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}+\frac{c d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i e +d c \right)}{d}+\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(c x \right)}{d}-\frac{b^{2} \arctan \left(c x \right)^{2} \ln \left(c e x +d c \right)}{d}-\frac{a^{2} \ln \left(c e x +d c \right)}{d}+\frac{a^{2} \ln \left(c x \right)}{d}-\frac{b^{2} c \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(-d c +i e \right) \left(i c x +1\right)^{2}}{\left(d c +i e \right) \left(c^{2} x^{2}+1\right)}\right)}{d c -i e}+\frac{2 b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{2 b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}"," ",0,"I*b^2*c/(d*c-I*e)*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3-1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3+1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3-1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2+I*a*b/d*ln(c*x)*ln(1+I*c*x)+I*a*b/d*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))-I*a*b/d*ln(c*x)*ln(1-I*c*x)-I*a*b/d*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))-b^2*e*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/d/(e+I*d*c)-b^2*c/(d*c-I*e)*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))-2*I*b^2/d*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*b^2/d*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I*b^2/d*Pi*arctan(c*x)^2+1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))-1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2-1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))-1/2*b^2*e*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/d/(e+I*d*c)+1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))+I*b^2*e*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/d/(e+I*d*c)+1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2+1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2-1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2-1/2*I*b^2/d*Pi*arctan(c*x)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2+2*a*b*arctan(c*x)/d*ln(c*x)-2*a*b*arctan(c*x)/d*ln(c*e*x+c*d)+I*a*b/d*dilog(1+I*c*x)+I*a*b/d*dilog((I*e+c*e*x)/(I*e-d*c))-I*a*b/d*dilog(1-I*c*x)-I*a*b/d*dilog((I*e-c*e*x)/(d*c+I*e))-1/2*b^2*c/(d*c-I*e)*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))+b^2*arctan(c*x)^2/d*ln(c*x)-b^2*arctan(c*x)^2/d*ln(c*e*x+c*d)-b^2*arctan(c*x)^2/d*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+b^2/d*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2/d*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2*arctan(c*x)^2/d*ln(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)+2*b^2/d*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2/d*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))-a^2/d*ln(c*e*x+c*d)+a^2/d*ln(c*x)","C"
146,1,40579,443,24.031000," ","int((a+b*arctan(c*x))^2/x^2/(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","C"
147,1,2861,555,65.501000," ","int((a+b*arctan(c*x))^2/x^3/(e*x+d),x)","\text{output too large to display}"," ",0,"-1/2*a^2/d/x^2+1/2*I*b^2/d^3*e^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-c*b^2*e^2*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/d^2/(e+I*d*c)+I*a*b*e^2/d^3*ln(c*x)*ln(1+I*c*x)+I*b^2*e^3*arctan(c*x)*polylog(2,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/d^3/(e+I*d*c)+I*a*b/d^3*e^2*ln(c*e*x+c*d)*ln((I*e+c*e*x)/(I*e-d*c))-1/2*I*c*b^2*e^2*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/d^2/(e+I*d*c)-2*c*b^2/d^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))*arctan(c*x)*e-2*c*a*b/d^2*e*ln(c*x)+c*a*b/d^2*e*ln(c^2*x^2+1)+I*c*b^2/d^2*e*arctan(c*x)^2-I*a*b/d^3*e^2*dilog((I*e-c*e*x)/(d*c+I*e))+1/2*I*b^2/d^3*e^2*Pi*arctan(c*x)^2-I*a*b*e^2/d^3*dilog(1-I*c*x)-2*I*b^2/d^3*e^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*b^2/d^3*e^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*c*b^2*dilog((1+I*c*x)/(c^2*x^2+1)^(1/2))/d^2*e+2*I*c*b^2/d^2*dilog(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))*e-b^2*e^3*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/d^3/(e+I*d*c)+I*a*b/d^3*e^2*dilog((I*e+c*e*x)/(I*e-d*c))+I*a*b*e^2/d^3*dilog(1+I*c*x)+2*a*b*arctan(c*x)/d^2*e/x+2*a*b*arctan(c*x)/d^3*e^2*ln(c*x)-2*a*b*arctan(c*x)/d^3*e^2*ln(c*e*x+c*d)-1/2*I*b^2/d^3*e^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2/d^3*e^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2/d^3*e^2*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2/d^3*e^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-I*c*b^2*e^2*arctan(c*x)^2*ln(1-(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/d^2/(e+I*d*c)-1/2*I*b^2/d^3*e^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2/d^3*e^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*I*b^2/d^3*e^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c))*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+1/2*I*b^2/d^3*e^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-c*a*b/d/x-c^2*a*b/d*arctan(c*x)-c*b^2*arctan(c*x)/x/d+b^2*arctan(c*x)^2/d^3*e^2*ln(c*x)-b^2*arctan(c*x)^2/d^3*e^2*ln(c*e*x+c*d)+b^2/d^3*e^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2*arctan(c*x)^2/d^2*e/x+b^2*e^2/d^3*arctan(c*x)^2*ln(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)-b^2/d^3*e^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)-a*b*arctan(c*x)/d/x^2+b^2/d^3*e^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*b^2*e^3*polylog(3,(I*e-d*c)/(d*c+I*e)*(1+I*c*x)^2/(c^2*x^2+1))/d^3/(e+I*d*c)-I*c^2*b^2*arctan(c*x)/d-1/2*c^2*b^2/d*arctan(c*x)^2+c^2*b^2/d*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)+c^2*b^2/d*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2/d^3*e^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2/d^3*e^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+a^2/d^3*e^2*ln(c*x)-a^2/d^3*e^2*ln(c*e*x+c*d)-1/2*b^2*arctan(c*x)^2/d/x^2+a^2/d^2*e/x-1/2*I*b^2/d^3*e^2*Pi*csgn(I*(-I*(1+I*c*x)^2/(c^2*x^2+1)*e+c*d*(1+I*c*x)^2/(c^2*x^2+1)+I*e+d*c)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-1/2*I*b^2/d^3*e^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2/d^3*e^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-I*a*b/d^3*e^2*ln(c*e*x+c*d)*ln((I*e-c*e*x)/(d*c+I*e))-I*a*b*e^2/d^3*ln(c*x)*ln(1-I*c*x)","C"
148,0,0,20,0.737000," ","int(1/(e*x+d)/(a+b*arctan(c*x)),x)","\int \frac{1}{\left(e x +d \right) \left(a +b \arctan \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x+d)/(a+b*arctan(c*x)),x)","F"
149,1,58,57,0.025000," ","int(x^3*(a^2*c*x^2+c)*arctan(a*x),x)","\frac{c x}{12 a^{3}}-\frac{c \,x^{3}}{36 a}-\frac{a c \,x^{5}}{30}-\frac{c \arctan \left(a x \right)}{12 a^{4}}+\frac{c \,x^{4} \arctan \left(a x \right)}{4}+\frac{a^{2} c \,x^{6} \arctan \left(a x \right)}{6}"," ",0,"1/12*c*x/a^3-1/36*c*x^3/a-1/30*a*c*x^5-1/12*c*arctan(a*x)/a^4+1/4*c*x^4*arctan(a*x)+1/6*a^2*c*x^6*arctan(a*x)","A"
150,1,57,56,0.026000," ","int(x^2*(a^2*c*x^2+c)*arctan(a*x),x)","-\frac{c \,x^{2}}{15 a}-\frac{a c \,x^{4}}{20}+\frac{c \,x^{3} \arctan \left(a x \right)}{3}+\frac{a^{2} c \,x^{5} \arctan \left(a x \right)}{5}+\frac{c \ln \left(a^{2} x^{2}+1\right)}{15 a^{3}}"," ",0,"-1/15*c*x^2/a-1/20*a*c*x^4+1/3*c*x^3*arctan(a*x)+1/5*a^2*c*x^5*arctan(a*x)+1/15*c*ln(a^2*x^2+1)/a^3","A"
151,1,49,36,0.024000," ","int(x*(a^2*c*x^2+c)*arctan(a*x),x)","\frac{a^{2} c \arctan \left(a x \right) x^{4}}{4}+\frac{c \arctan \left(a x \right) x^{2}}{2}-\frac{a c \,x^{3}}{12}-\frac{c x}{4 a}+\frac{c \arctan \left(a x \right)}{4 a^{2}}"," ",0,"1/4*a^2*c*arctan(a*x)*x^4+1/2*c*arctan(a*x)*x^2-1/12*a*c*x^3-1/4*c*x/a+1/4/a^2*c*arctan(a*x)","A"
152,1,45,44,0.025000," ","int((a^2*c*x^2+c)*arctan(a*x),x)","-\frac{a \,x^{2} c}{6}+c x \arctan \left(a x \right)+\frac{a^{2} c \,x^{3} \arctan \left(a x \right)}{3}-\frac{c \ln \left(a^{2} x^{2}+1\right)}{3 a}"," ",0,"-1/6*a*x^2*c+c*x*arctan(a*x)+1/3*a^2*c*x^3*arctan(a*x)-1/3*c*ln(a^2*x^2+1)/a","A"
153,1,93,48,0.047000," ","int((a^2*c*x^2+c)*arctan(a*x)/x,x)","\frac{a^{2} c \,x^{2} \arctan \left(a x \right)}{2}+c \arctan \left(a x \right) \ln \left(a x \right)+\frac{i \ln \left(a x \right) \ln \left(i a x +1\right) c}{2}-\frac{i \ln \left(a x \right) \ln \left(-i a x +1\right) c}{2}-\frac{i \dilog \left(-i a x +1\right) c}{2}+\frac{i \dilog \left(i a x +1\right) c}{2}-\frac{a c x}{2}+\frac{c \arctan \left(a x \right)}{2}"," ",0,"1/2*a^2*c*x^2*arctan(a*x)+c*arctan(a*x)*ln(a*x)+1/2*I*ln(a*x)*ln(1+I*a*x)*c-1/2*I*ln(a*x)*ln(1-I*a*x)*c-1/2*I*dilog(1-I*a*x)*c+1/2*I*dilog(1+I*a*x)*c-1/2*a*c*x+1/2*c*arctan(a*x)","A"
154,1,43,40,0.032000," ","int((a^2*c*x^2+c)*arctan(a*x)/x^2,x)","a^{2} c x \arctan \left(a x \right)-\frac{c \arctan \left(a x \right)}{x}-a c \ln \left(a^{2} x^{2}+1\right)+a c \ln \left(a x \right)"," ",0,"a^2*c*x*arctan(a*x)-c*arctan(a*x)/x-a*c*ln(a^2*x^2+1)+a*c*ln(a*x)","A"
155,1,110,56,0.052000," ","int((a^2*c*x^2+c)*arctan(a*x)/x^3,x)","a^{2} c \arctan \left(a x \right) \ln \left(a x \right)-\frac{c \arctan \left(a x \right)}{2 x^{2}}-\frac{a c}{2 x}-\frac{a^{2} c \arctan \left(a x \right)}{2}+\frac{i a^{2} c \ln \left(a x \right) \ln \left(i a x +1\right)}{2}-\frac{i a^{2} c \ln \left(a x \right) \ln \left(-i a x +1\right)}{2}+\frac{i a^{2} c \dilog \left(i a x +1\right)}{2}-\frac{i a^{2} c \dilog \left(-i a x +1\right)}{2}"," ",0,"a^2*c*arctan(a*x)*ln(a*x)-1/2*c*arctan(a*x)/x^2-1/2*a*c/x-1/2*a^2*c*arctan(a*x)+1/2*I*a^2*c*ln(a*x)*ln(1+I*a*x)-1/2*I*a^2*c*ln(a*x)*ln(1-I*a*x)+1/2*I*a^2*c*dilog(1+I*a*x)-1/2*I*a^2*c*dilog(1-I*a*x)","A"
156,1,58,55,0.036000," ","int((a^2*c*x^2+c)*arctan(a*x)/x^4,x)","-\frac{c \arctan \left(a x \right)}{3 x^{3}}-\frac{a^{2} c \arctan \left(a x \right)}{x}-\frac{a c}{6 x^{2}}+\frac{2 a^{3} c \ln \left(a x \right)}{3}-\frac{a^{3} c \ln \left(a^{2} x^{2}+1\right)}{3}"," ",0,"-1/3*c*arctan(a*x)/x^3-a^2*c*arctan(a*x)/x-1/6*a*c/x^2+2/3*a^3*c*ln(a*x)-1/3*a^3*c*ln(a^2*x^2+1)","A"
157,1,96,95,0.035000," ","int(x^3*(a^2*c*x^2+c)^2*arctan(a*x),x)","\frac{c^{2} x}{24 a^{3}}-\frac{c^{2} x^{3}}{72 a}-\frac{a \,c^{2} x^{5}}{24}-\frac{a^{3} c^{2} x^{7}}{56}-\frac{c^{2} \arctan \left(a x \right)}{24 a^{4}}+\frac{c^{2} x^{4} \arctan \left(a x \right)}{4}+\frac{a^{2} c^{2} x^{6} \arctan \left(a x \right)}{3}+\frac{a^{4} c^{2} x^{8} \arctan \left(a x \right)}{8}"," ",0,"1/24*c^2*x/a^3-1/72*c^2*x^3/a-1/24*a*c^2*x^5-1/56*a^3*c^2*x^7-1/24*c^2*arctan(a*x)/a^4+1/4*c^2*x^4*arctan(a*x)+1/3*a^2*c^2*x^6*arctan(a*x)+1/8*a^4*c^2*x^8*arctan(a*x)","A"
158,1,93,92,0.026000," ","int(x^2*(a^2*c*x^2+c)^2*arctan(a*x),x)","-\frac{4 c^{2} x^{2}}{105 a}-\frac{9 a \,c^{2} x^{4}}{140}-\frac{a^{3} c^{2} x^{6}}{42}+\frac{c^{2} x^{3} \arctan \left(a x \right)}{3}+\frac{2 a^{2} c^{2} x^{5} \arctan \left(a x \right)}{5}+\frac{a^{4} c^{2} x^{7} \arctan \left(a x \right)}{7}+\frac{4 c^{2} \ln \left(a^{2} x^{2}+1\right)}{105 a^{3}}"," ",0,"-4/105*c^2*x^2/a-9/140*a*c^2*x^4-1/42*a^3*c^2*x^6+1/3*c^2*x^3*arctan(a*x)+2/5*a^2*c^2*x^5*arctan(a*x)+1/7*a^4*c^2*x^7*arctan(a*x)+4/105*c^2*ln(a^2*x^2+1)/a^3","A"
159,1,85,53,0.026000," ","int(x*(a^2*c*x^2+c)^2*arctan(a*x),x)","\frac{a^{4} c^{2} \arctan \left(a x \right) x^{6}}{6}+\frac{a^{2} c^{2} \arctan \left(a x \right) x^{4}}{2}+\frac{c^{2} \arctan \left(a x \right) x^{2}}{2}-\frac{a^{3} c^{2} x^{5}}{30}-\frac{a \,c^{2} x^{3}}{9}-\frac{c^{2} x}{6 a}+\frac{c^{2} \arctan \left(a x \right)}{6 a^{2}}"," ",0,"1/6*a^4*c^2*arctan(a*x)*x^6+1/2*a^2*c^2*arctan(a*x)*x^4+1/2*c^2*arctan(a*x)*x^2-1/30*a^3*c^2*x^5-1/9*a*c^2*x^3-1/6*c^2*x/a+1/6/a^2*c^2*arctan(a*x)","A"
160,1,79,105,0.032000," ","int((a^2*c*x^2+c)^2*arctan(a*x),x)","\frac{a^{4} c^{2} \arctan \left(a x \right) x^{5}}{5}+\frac{2 a^{2} c^{2} \arctan \left(a x \right) x^{3}}{3}+c^{2} x \arctan \left(a x \right)-\frac{a^{3} c^{2} x^{4}}{20}-\frac{7 c^{2} x^{2} a}{30}-\frac{4 c^{2} \ln \left(a^{2} x^{2}+1\right)}{15 a}"," ",0,"1/5*a^4*c^2*arctan(a*x)*x^5+2/3*a^2*c^2*arctan(a*x)*x^3+c^2*x*arctan(a*x)-1/20*a^3*c^2*x^4-7/30*c^2*x^2*a-4/15*c^2*ln(a^2*x^2+1)/a","A"
161,1,134,83,0.051000," ","int((a^2*c*x^2+c)^2*arctan(a*x)/x,x)","\frac{a^{4} c^{2} x^{4} \arctan \left(a x \right)}{4}+a^{2} c^{2} x^{2} \arctan \left(a x \right)+c^{2} \arctan \left(a x \right) \ln \left(a x \right)-\frac{a^{3} c^{2} x^{3}}{12}-\frac{3 a \,c^{2} x}{4}+\frac{3 c^{2} \arctan \left(a x \right)}{4}+\frac{i c^{2} \ln \left(a x \right) \ln \left(i a x +1\right)}{2}-\frac{i c^{2} \ln \left(a x \right) \ln \left(-i a x +1\right)}{2}+\frac{i c^{2} \dilog \left(i a x +1\right)}{2}-\frac{i c^{2} \dilog \left(-i a x +1\right)}{2}"," ",0,"1/4*a^4*c^2*x^4*arctan(a*x)+a^2*c^2*x^2*arctan(a*x)+c^2*arctan(a*x)*ln(a*x)-1/12*a^3*c^2*x^3-3/4*a*c^2*x+3/4*c^2*arctan(a*x)+1/2*I*c^2*ln(a*x)*ln(1+I*a*x)-1/2*I*c^2*ln(a*x)*ln(1-I*a*x)+1/2*I*c^2*dilog(1+I*a*x)-1/2*I*c^2*dilog(1-I*a*x)","A"
162,1,78,75,0.030000," ","int((a^2*c*x^2+c)^2*arctan(a*x)/x^2,x)","\frac{a^{4} c^{2} x^{3} \arctan \left(a x \right)}{3}+2 a^{2} c^{2} x \arctan \left(a x \right)-\frac{c^{2} \arctan \left(a x \right)}{x}-\frac{a^{3} c^{2} x^{2}}{6}+a \,c^{2} \ln \left(a x \right)-\frac{4 a \,c^{2} \ln \left(a^{2} x^{2}+1\right)}{3}"," ",0,"1/3*a^4*c^2*x^3*arctan(a*x)+2*a^2*c^2*x*arctan(a*x)-c^2*arctan(a*x)/x-1/6*a^3*c^2*x^2+a*c^2*ln(a*x)-4/3*a*c^2*ln(a^2*x^2+1)","A"
163,1,139,78,0.060000," ","int((a^2*c*x^2+c)^2*arctan(a*x)/x^3,x)","\frac{a^{4} c^{2} x^{2} \arctan \left(a x \right)}{2}+2 a^{2} c^{2} \arctan \left(a x \right) \ln \left(a x \right)-\frac{c^{2} \arctan \left(a x \right)}{2 x^{2}}-\frac{a^{3} c^{2} x}{2}-\frac{a \,c^{2}}{2 x}+i a^{2} c^{2} \ln \left(a x \right) \ln \left(i a x +1\right)-i a^{2} c^{2} \ln \left(a x \right) \ln \left(-i a x +1\right)+i a^{2} c^{2} \dilog \left(i a x +1\right)-i a^{2} c^{2} \dilog \left(-i a x +1\right)"," ",0,"1/2*a^4*c^2*x^2*arctan(a*x)+2*a^2*c^2*arctan(a*x)*ln(a*x)-1/2*c^2*arctan(a*x)/x^2-1/2*a^3*c^2*x-1/2*a*c^2/x+I*a^2*c^2*ln(a*x)*ln(1+I*a*x)-I*a^2*c^2*ln(a*x)*ln(1-I*a*x)+I*a^2*c^2*dilog(1+I*a*x)-I*a^2*c^2*dilog(1-I*a*x)","A"
164,1,80,77,0.038000," ","int((a^2*c*x^2+c)^2*arctan(a*x)/x^4,x)","a^{4} c^{2} x \arctan \left(a x \right)-\frac{c^{2} \arctan \left(a x \right)}{3 x^{3}}-\frac{2 a^{2} c^{2} \arctan \left(a x \right)}{x}-\frac{a \,c^{2}}{6 x^{2}}+\frac{5 a^{3} c^{2} \ln \left(a x \right)}{3}-\frac{4 a^{3} c^{2} \ln \left(a^{2} x^{2}+1\right)}{3}"," ",0,"a^4*c^2*x*arctan(a*x)-1/3*c^2*arctan(a*x)/x^3-2*a^2*c^2*arctan(a*x)/x-1/6*a*c^2/x^2+5/3*a^3*c^2*ln(a*x)-4/3*a^3*c^2*ln(a^2*x^2+1)","A"
165,1,122,121,0.024000," ","int(x^3*(a^2*c*x^2+c)^3*arctan(a*x),x)","\frac{c^{3} x}{40 a^{3}}-\frac{c^{3} x^{3}}{120 a}-\frac{9 a \,c^{3} x^{5}}{200}-\frac{11 a^{3} c^{3} x^{7}}{280}-\frac{a^{5} c^{3} x^{9}}{90}-\frac{c^{3} \arctan \left(a x \right)}{40 a^{4}}+\frac{c^{3} x^{4} \arctan \left(a x \right)}{4}+\frac{a^{2} c^{3} x^{6} \arctan \left(a x \right)}{2}+\frac{3 a^{4} c^{3} x^{8} \arctan \left(a x \right)}{8}+\frac{a^{6} c^{3} x^{10} \arctan \left(a x \right)}{10}"," ",0,"1/40*c^3*x/a^3-1/120*c^3*x^3/a-9/200*a*c^3*x^5-11/280*a^3*c^3*x^7-1/90*a^5*c^3*x^9-1/40*c^3*arctan(a*x)/a^4+1/4*c^3*x^4*arctan(a*x)+1/2*a^2*c^3*x^6*arctan(a*x)+3/8*a^4*c^3*x^8*arctan(a*x)+1/10*a^6*c^3*x^10*arctan(a*x)","A"
166,1,119,118,0.030000," ","int(x^2*(a^2*c*x^2+c)^3*arctan(a*x),x)","-\frac{8 c^{3} x^{2}}{315 a}-\frac{89 a \,c^{3} x^{4}}{1260}-\frac{10 a^{3} c^{3} x^{6}}{189}-\frac{a^{5} c^{3} x^{8}}{72}+\frac{c^{3} x^{3} \arctan \left(a x \right)}{3}+\frac{3 a^{2} c^{3} x^{5} \arctan \left(a x \right)}{5}+\frac{3 a^{4} c^{3} x^{7} \arctan \left(a x \right)}{7}+\frac{a^{6} c^{3} x^{9} \arctan \left(a x \right)}{9}+\frac{8 c^{3} \ln \left(a^{2} x^{2}+1\right)}{315 a^{3}}"," ",0,"-8/315*c^3*x^2/a-89/1260*a*c^3*x^4-10/189*a^3*c^3*x^6-1/72*a^5*c^3*x^8+1/3*c^3*x^3*arctan(a*x)+3/5*a^2*c^3*x^5*arctan(a*x)+3/7*a^4*c^3*x^7*arctan(a*x)+1/9*a^6*c^3*x^9*arctan(a*x)+8/315*c^3*ln(a^2*x^2+1)/a^3","A"
167,1,111,64,0.034000," ","int(x*(a^2*c*x^2+c)^3*arctan(a*x),x)","\frac{a^{6} c^{3} \arctan \left(a x \right) x^{8}}{8}+\frac{a^{4} c^{3} \arctan \left(a x \right) x^{6}}{2}+\frac{3 a^{2} c^{3} \arctan \left(a x \right) x^{4}}{4}+\frac{c^{3} \arctan \left(a x \right) x^{2}}{2}-\frac{a^{5} c^{3} x^{7}}{56}-\frac{3 a^{3} c^{3} x^{5}}{40}-\frac{a \,c^{3} x^{3}}{8}-\frac{c^{3} x}{8 a}+\frac{c^{3} \arctan \left(a x \right)}{8 a^{2}}"," ",0,"1/8*a^6*c^3*arctan(a*x)*x^8+1/2*a^4*c^3*arctan(a*x)*x^6+3/4*a^2*c^3*arctan(a*x)*x^4+1/2*c^3*arctan(a*x)*x^2-1/56*a^5*c^3*x^7-3/40*a^3*c^3*x^5-1/8*a*c^3*x^3-1/8*c^3*x/a+1/8/a^2*c^3*arctan(a*x)","A"
168,1,104,145,0.025000," ","int((a^2*c*x^2+c)^3*arctan(a*x),x)","\frac{a^{6} c^{3} \arctan \left(a x \right) x^{7}}{7}+\frac{3 a^{4} c^{3} \arctan \left(a x \right) x^{5}}{5}+a^{2} c^{3} \arctan \left(a x \right) x^{3}+c^{3} x \arctan \left(a x \right)-\frac{a^{5} c^{3} x^{6}}{42}-\frac{4 a^{3} c^{3} x^{4}}{35}-\frac{19 a \,c^{3} x^{2}}{70}-\frac{8 c^{3} \ln \left(a^{2} x^{2}+1\right)}{35 a}"," ",0,"1/7*a^6*c^3*arctan(a*x)*x^7+3/5*a^4*c^3*arctan(a*x)*x^5+a^2*c^3*arctan(a*x)*x^3+c^3*x*arctan(a*x)-1/42*a^5*c^3*x^6-4/35*a^3*c^3*x^4-19/70*a*c^3*x^2-8/35*c^3*ln(a^2*x^2+1)/a","A"
169,1,161,110,0.046000," ","int((a^2*c*x^2+c)^3*arctan(a*x)/x,x)","\frac{a^{6} c^{3} x^{6} \arctan \left(a x \right)}{6}+\frac{3 a^{4} c^{3} x^{4} \arctan \left(a x \right)}{4}+\frac{3 a^{2} c^{3} x^{2} \arctan \left(a x \right)}{2}+c^{3} \arctan \left(a x \right) \ln \left(a x \right)-\frac{a^{5} c^{3} x^{5}}{30}-\frac{7 a^{3} c^{3} x^{3}}{36}-\frac{11 a \,c^{3} x}{12}+\frac{11 c^{3} \arctan \left(a x \right)}{12}+\frac{i c^{3} \ln \left(a x \right) \ln \left(i a x +1\right)}{2}-\frac{i c^{3} \ln \left(a x \right) \ln \left(-i a x +1\right)}{2}+\frac{i c^{3} \dilog \left(i a x +1\right)}{2}-\frac{i c^{3} \dilog \left(-i a x +1\right)}{2}"," ",0,"1/6*a^6*c^3*x^6*arctan(a*x)+3/4*a^4*c^3*x^4*arctan(a*x)+3/2*a^2*c^3*x^2*arctan(a*x)+c^3*arctan(a*x)*ln(a*x)-1/30*a^5*c^3*x^5-7/36*a^3*c^3*x^3-11/12*a*c^3*x+11/12*c^3*arctan(a*x)+1/2*I*c^3*ln(a*x)*ln(1+I*a*x)-1/2*I*c^3*ln(a*x)*ln(1-I*a*x)+1/2*I*c^3*dilog(1+I*a*x)-1/2*I*c^3*dilog(1-I*a*x)","A"
170,1,103,100,0.033000," ","int((a^2*c*x^2+c)^3*arctan(a*x)/x^2,x)","\frac{a^{6} c^{3} x^{5} \arctan \left(a x \right)}{5}+a^{4} c^{3} x^{3} \arctan \left(a x \right)+3 a^{2} c^{3} x \arctan \left(a x \right)-\frac{c^{3} \arctan \left(a x \right)}{x}-\frac{a^{5} c^{3} x^{4}}{20}-\frac{2 a^{3} c^{3} x^{2}}{5}+a \,c^{3} \ln \left(a x \right)-\frac{8 a \,c^{3} \ln \left(a^{2} x^{2}+1\right)}{5}"," ",0,"1/5*a^6*c^3*x^5*arctan(a*x)+a^4*c^3*x^3*arctan(a*x)+3*a^2*c^3*x*arctan(a*x)-c^3*arctan(a*x)/x-1/20*a^5*c^3*x^4-2/5*a^3*c^3*x^2+a*c^3*ln(a*x)-8/5*a*c^3*ln(a^2*x^2+1)","A"
171,1,177,116,0.050000," ","int((a^2*c*x^2+c)^3*arctan(a*x)/x^3,x)","\frac{a^{6} c^{3} x^{4} \arctan \left(a x \right)}{4}+\frac{3 a^{4} c^{3} x^{2} \arctan \left(a x \right)}{2}+3 a^{2} c^{3} \arctan \left(a x \right) \ln \left(a x \right)-\frac{c^{3} \arctan \left(a x \right)}{2 x^{2}}-\frac{a^{5} c^{3} x^{3}}{12}-\frac{5 a^{3} c^{3} x}{4}-\frac{a \,c^{3}}{2 x}+\frac{3 a^{2} c^{3} \arctan \left(a x \right)}{4}+\frac{3 i a^{2} c^{3} \ln \left(a x \right) \ln \left(i a x +1\right)}{2}-\frac{3 i a^{2} c^{3} \ln \left(a x \right) \ln \left(-i a x +1\right)}{2}+\frac{3 i a^{2} c^{3} \dilog \left(i a x +1\right)}{2}-\frac{3 i a^{2} c^{3} \dilog \left(-i a x +1\right)}{2}"," ",0,"1/4*a^6*c^3*x^4*arctan(a*x)+3/2*a^4*c^3*x^2*arctan(a*x)+3*a^2*c^3*arctan(a*x)*ln(a*x)-1/2*c^3*arctan(a*x)/x^2-1/12*a^5*c^3*x^3-5/4*a^3*c^3*x-1/2*a*c^3/x+3/4*a^2*c^3*arctan(a*x)+3/2*I*a^2*c^3*ln(a*x)*ln(1+I*a*x)-3/2*I*a^2*c^3*ln(a*x)*ln(1-I*a*x)+3/2*I*a^2*c^3*dilog(1+I*a*x)-3/2*I*a^2*c^3*dilog(1-I*a*x)","A"
172,1,107,104,0.035000," ","int((a^2*c*x^2+c)^3*arctan(a*x)/x^4,x)","\frac{a^{6} c^{3} x^{3} \arctan \left(a x \right)}{3}+3 a^{4} c^{3} x \arctan \left(a x \right)-\frac{c^{3} \arctan \left(a x \right)}{3 x^{3}}-\frac{3 a^{2} c^{3} \arctan \left(a x \right)}{x}-\frac{a^{5} c^{3} x^{2}}{6}-\frac{a \,c^{3}}{6 x^{2}}+\frac{8 a^{3} c^{3} \ln \left(a x \right)}{3}-\frac{8 a^{3} c^{3} \ln \left(a^{2} x^{2}+1\right)}{3}"," ",0,"1/3*a^6*c^3*x^3*arctan(a*x)+3*a^4*c^3*x*arctan(a*x)-1/3*c^3*arctan(a*x)/x^3-3*a^2*c^3*arctan(a*x)/x-1/6*a^5*c^3*x^2-1/6*a*c^3/x^2+8/3*a^3*c^3*ln(a*x)-8/3*a^3*c^3*ln(a^2*x^2+1)","A"
173,1,73,72,0.042000," ","int(x^4*arctan(a*x)/(a^2*c*x^2+c),x)","-\frac{x^{2}}{6 a^{3} c}-\frac{x \arctan \left(a x \right)}{a^{4} c}+\frac{x^{3} \arctan \left(a x \right)}{3 a^{2} c}+\frac{\arctan \left(a x \right)^{2}}{2 a^{5} c}+\frac{2 \ln \left(a^{2} x^{2}+1\right)}{3 a^{5} c}"," ",0,"-1/6*x^2/a^3/c-x*arctan(a*x)/a^4/c+1/3*x^3*arctan(a*x)/a^2/c+1/2*arctan(a*x)^2/a^5/c+2/3*ln(a^2*x^2+1)/a^5/c","A"
174,1,238,99,0.118000," ","int(x^3*arctan(a*x)/(a^2*c*x^2+c),x)","\frac{x^{2} \arctan \left(a x \right)}{2 a^{2} c}-\frac{\arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{2 a^{4} c}-\frac{x}{2 a^{3} c}+\frac{\arctan \left(a x \right)}{2 a^{4} c}-\frac{i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{4 a^{4} c}+\frac{i \ln \left(a x -i\right)^{2}}{8 a^{4} c}+\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 a^{4} c}+\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 a^{4} c}+\frac{i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{4 a^{4} c}-\frac{i \ln \left(a x +i\right)^{2}}{8 a^{4} c}-\frac{i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{4 a^{4} c}-\frac{i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{4 a^{4} c}"," ",0,"1/2*x^2*arctan(a*x)/a^2/c-1/2/a^4/c*arctan(a*x)*ln(a^2*x^2+1)-1/2*x/a^3/c+1/2*arctan(a*x)/a^4/c-1/4*I/a^4/c*ln(a*x-I)*ln(a^2*x^2+1)+1/8*I/a^4/c*ln(a*x-I)^2+1/4*I/a^4/c*dilog(-1/2*I*(I+a*x))+1/4*I/a^4/c*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/4*I/a^4/c*ln(I+a*x)*ln(a^2*x^2+1)-1/8*I/a^4/c*ln(I+a*x)^2-1/4*I/a^4/c*dilog(1/2*I*(a*x-I))-1/4*I/a^4/c*ln(I+a*x)*ln(1/2*I*(a*x-I))","B"
175,1,46,45,0.033000," ","int(x^2*arctan(a*x)/(a^2*c*x^2+c),x)","\frac{x \arctan \left(a x \right)}{a^{2} c}-\frac{\arctan \left(a x \right)^{2}}{2 a^{3} c}-\frac{\ln \left(a^{2} x^{2}+1\right)}{2 a^{3} c}"," ",0,"x*arctan(a*x)/a^2/c-1/2*arctan(a*x)^2/a^3/c-1/2*ln(a^2*x^2+1)/a^3/c","A"
176,1,202,64,0.090000," ","int(x*arctan(a*x)/(a^2*c*x^2+c),x)","\frac{\arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{2 a^{2} c}+\frac{i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{4 a^{2} c}-\frac{i \ln \left(a x -i\right)^{2}}{8 a^{2} c}-\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 a^{2} c}-\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 a^{2} c}-\frac{i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{4 a^{2} c}+\frac{i \ln \left(a x +i\right)^{2}}{8 a^{2} c}+\frac{i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{4 a^{2} c}+\frac{i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{4 a^{2} c}"," ",0,"1/2/a^2/c*arctan(a*x)*ln(a^2*x^2+1)+1/4*I/a^2/c*ln(a*x-I)*ln(a^2*x^2+1)-1/8*I/a^2/c*ln(a*x-I)^2-1/4*I/a^2/c*dilog(-1/2*I*(I+a*x))-1/4*I/a^2/c*ln(a*x-I)*ln(-1/2*I*(I+a*x))-1/4*I/a^2/c*ln(I+a*x)*ln(a^2*x^2+1)+1/8*I/a^2/c*ln(I+a*x)^2+1/4*I/a^2/c*dilog(1/2*I*(a*x-I))+1/4*I/a^2/c*ln(I+a*x)*ln(1/2*I*(a*x-I))","B"
177,1,15,14,0.031000," ","int(arctan(a*x)/(a^2*c*x^2+c),x)","\frac{\arctan \left(a x \right)^{2}}{2 a c}"," ",0,"1/2*arctan(a*x)^2/a/c","A"
178,1,251,56,0.112000," ","int(arctan(a*x)/x/(a^2*c*x^2+c),x)","\frac{\arctan \left(a x \right) \ln \left(a x \right)}{c}-\frac{\arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{2 c}+\frac{i \ln \left(a x \right) \ln \left(i a x +1\right)}{2 c}-\frac{i \ln \left(a x \right) \ln \left(-i a x +1\right)}{2 c}+\frac{i \dilog \left(i a x +1\right)}{2 c}-\frac{i \dilog \left(-i a x +1\right)}{2 c}-\frac{i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{4 c}+\frac{i \ln \left(a x -i\right)^{2}}{8 c}+\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 c}+\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 c}+\frac{i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{4 c}-\frac{i \ln \left(a x +i\right)^{2}}{8 c}-\frac{i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{4 c}-\frac{i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{4 c}"," ",0,"1/c*arctan(a*x)*ln(a*x)-1/2/c*arctan(a*x)*ln(a^2*x^2+1)+1/2*I/c*ln(a*x)*ln(1+I*a*x)-1/2*I/c*ln(a*x)*ln(1-I*a*x)+1/2*I/c*dilog(1+I*a*x)-1/2*I/c*dilog(1-I*a*x)-1/4*I/c*ln(a*x-I)*ln(a^2*x^2+1)+1/8*I/c*ln(a*x-I)^2+1/4*I/c*dilog(-1/2*I*(I+a*x))+1/4*I/c*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/4*I/c*ln(I+a*x)*ln(a^2*x^2+1)-1/8*I/c*ln(I+a*x)^2-1/4*I/c*dilog(1/2*I*(a*x-I))-1/4*I/c*ln(I+a*x)*ln(1/2*I*(a*x-I))","B"
179,1,51,48,0.043000," ","int(arctan(a*x)/x^2/(a^2*c*x^2+c),x)","-\frac{\arctan \left(a x \right)}{c x}-\frac{a \arctan \left(a x \right)^{2}}{2 c}+\frac{a \ln \left(a x \right)}{c}-\frac{a \ln \left(a^{2} x^{2}+1\right)}{2 c}"," ",0,"-arctan(a*x)/c/x-1/2*a*arctan(a*x)^2/c+a/c*ln(a*x)-1/2*a*ln(a^2*x^2+1)/c","A"
180,1,327,99,0.105000," ","int(arctan(a*x)/x^3/(a^2*c*x^2+c),x)","-\frac{\arctan \left(a x \right)}{2 c \,x^{2}}-\frac{a^{2} \arctan \left(a x \right) \ln \left(a x \right)}{c}+\frac{a^{2} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{2 c}-\frac{i a^{2} \ln \left(a x \right) \ln \left(i a x +1\right)}{2 c}+\frac{i a^{2} \dilog \left(-i a x +1\right)}{2 c}-\frac{i a^{2} \dilog \left(i a x +1\right)}{2 c}+\frac{i a^{2} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{4 c}-\frac{i a^{2} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 c}+\frac{i a^{2} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{4 c}+\frac{i a^{2} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{4 c}-\frac{i a^{2} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{4 c}-\frac{a}{2 c x}-\frac{a^{2} \arctan \left(a x \right)}{2 c}-\frac{i a^{2} \ln \left(a x -i\right)^{2}}{8 c}+\frac{i a^{2} \ln \left(a x \right) \ln \left(-i a x +1\right)}{2 c}-\frac{i a^{2} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 c}+\frac{i a^{2} \ln \left(a x +i\right)^{2}}{8 c}"," ",0,"-1/2*arctan(a*x)/c/x^2-a^2/c*arctan(a*x)*ln(a*x)+1/2*a^2/c*arctan(a*x)*ln(a^2*x^2+1)-1/2*I*a^2/c*ln(a*x)*ln(1+I*a*x)-1/2*I*a^2/c*dilog(1+I*a*x)+1/2*I*a^2/c*dilog(1-I*a*x)+1/4*I*a^2/c*ln(a*x-I)*ln(a^2*x^2+1)-1/4*I*a^2/c*dilog(-1/2*I*(I+a*x))+1/4*I*a^2/c*ln(I+a*x)*ln(1/2*I*(a*x-I))-1/4*I*a^2/c*ln(I+a*x)*ln(a^2*x^2+1)+1/4*I*a^2/c*dilog(1/2*I*(a*x-I))-1/2*a/c/x-1/2*a^2*arctan(a*x)/c-1/8*I*a^2/c*ln(a*x-I)^2+1/2*I*a^2/c*ln(a*x)*ln(1-I*a*x)-1/4*I*a^2/c*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/8*I*a^2/c*ln(I+a*x)^2","B"
181,1,81,78,0.043000," ","int(arctan(a*x)/x^4/(a^2*c*x^2+c),x)","-\frac{\arctan \left(a x \right)}{3 c \,x^{3}}+\frac{a^{2} \arctan \left(a x \right)}{c x}+\frac{a^{3} \arctan \left(a x \right)^{2}}{2 c}-\frac{a}{6 c \,x^{2}}-\frac{4 a^{3} \ln \left(a x \right)}{3 c}+\frac{2 a^{3} \ln \left(a^{2} x^{2}+1\right)}{3 c}"," ",0,"-1/3*arctan(a*x)/c/x^3+a^2*arctan(a*x)/c/x+1/2*a^3*arctan(a*x)^2/c-1/6*a/c/x^2-4/3*a^3/c*ln(a*x)+2/3*a^3*ln(a^2*x^2+1)/c","A"
182,1,281,143,0.115000," ","int(x^5*arctan(a*x)/(a^2*c*x^2+c)^2,x)","\frac{x^{2} \arctan \left(a x \right)}{2 a^{4} c^{2}}-\frac{\arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{a^{6} c^{2}}-\frac{\arctan \left(a x \right)}{2 a^{6} c^{2} \left(a^{2} x^{2}+1\right)}-\frac{x}{2 a^{5} c^{2}}+\frac{x}{4 a^{5} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{3 \arctan \left(a x \right)}{4 a^{6} c^{2}}-\frac{i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{2 a^{6} c^{2}}+\frac{i \ln \left(a x -i\right)^{2}}{4 a^{6} c^{2}}+\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 a^{6} c^{2}}+\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 a^{6} c^{2}}+\frac{i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{2 a^{6} c^{2}}-\frac{i \ln \left(a x +i\right)^{2}}{4 a^{6} c^{2}}-\frac{i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{2 a^{6} c^{2}}-\frac{i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{2 a^{6} c^{2}}"," ",0,"1/2*x^2*arctan(a*x)/a^4/c^2-1/a^6/c^2*arctan(a*x)*ln(a^2*x^2+1)-1/2*arctan(a*x)/a^6/c^2/(a^2*x^2+1)-1/2*x/a^5/c^2+1/4*x/a^5/c^2/(a^2*x^2+1)+3/4*arctan(a*x)/a^6/c^2-1/2*I/a^6/c^2*ln(a*x-I)*ln(a^2*x^2+1)+1/4*I/a^6/c^2*ln(a*x-I)^2+1/2*I/a^6/c^2*dilog(-1/2*I*(I+a*x))+1/2*I/a^6/c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/2*I/a^6/c^2*ln(I+a*x)*ln(a^2*x^2+1)-1/4*I/a^6/c^2*ln(I+a*x)^2-1/2*I/a^6/c^2*dilog(1/2*I*(a*x-I))-1/2*I/a^6/c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))","A"
183,1,89,88,0.046000," ","int(x^4*arctan(a*x)/(a^2*c*x^2+c)^2,x)","\frac{1}{4 a^{5} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{x \arctan \left(a x \right)}{a^{4} c^{2}}+\frac{x \arctan \left(a x \right)}{2 a^{4} c^{2} \left(a^{2} x^{2}+1\right)}-\frac{3 \arctan \left(a x \right)^{2}}{4 a^{5} c^{2}}-\frac{\ln \left(a^{2} x^{2}+1\right)}{2 a^{5} c^{2}}"," ",0,"1/4/a^5/c^2/(a^2*x^2+1)+x*arctan(a*x)/a^4/c^2+1/2*x*arctan(a*x)/a^4/c^2/(a^2*x^2+1)-3/4*arctan(a*x)^2/a^5/c^2-1/2*ln(a^2*x^2+1)/a^5/c^2","A"
184,1,257,119,0.098000," ","int(x^3*arctan(a*x)/(a^2*c*x^2+c)^2,x)","\frac{\arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{2 a^{4} c^{2}}+\frac{\arctan \left(a x \right)}{2 a^{4} c^{2} \left(a^{2} x^{2}+1\right)}-\frac{x}{4 a^{3} c^{2} \left(a^{2} x^{2}+1\right)}-\frac{\arctan \left(a x \right)}{4 a^{4} c^{2}}+\frac{i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{4 a^{4} c^{2}}-\frac{i \ln \left(a x -i\right)^{2}}{8 a^{4} c^{2}}-\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 a^{4} c^{2}}-\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 a^{4} c^{2}}-\frac{i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{4 a^{4} c^{2}}+\frac{i \ln \left(a x +i\right)^{2}}{8 a^{4} c^{2}}+\frac{i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{4 a^{4} c^{2}}+\frac{i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{4 a^{4} c^{2}}"," ",0,"1/2/a^4/c^2*arctan(a*x)*ln(a^2*x^2+1)+1/2*arctan(a*x)/a^4/c^2/(a^2*x^2+1)-1/4*x/a^3/c^2/(a^2*x^2+1)-1/4*arctan(a*x)/a^4/c^2+1/4*I/a^4/c^2*ln(a*x-I)*ln(a^2*x^2+1)-1/8*I/a^4/c^2*ln(a*x-I)^2-1/4*I/a^4/c^2*dilog(-1/2*I*(I+a*x))-1/4*I/a^4/c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))-1/4*I/a^4/c^2*ln(I+a*x)*ln(a^2*x^2+1)+1/8*I/a^4/c^2*ln(I+a*x)^2+1/4*I/a^4/c^2*dilog(1/2*I*(a*x-I))+1/4*I/a^4/c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))","B"
185,1,59,58,0.040000," ","int(x^2*arctan(a*x)/(a^2*c*x^2+c)^2,x)","-\frac{1}{4 a^{3} c^{2} \left(a^{2} x^{2}+1\right)}-\frac{x \arctan \left(a x \right)}{2 a^{2} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{2}}{4 a^{3} c^{2}}"," ",0,"-1/4/a^3/c^2/(a^2*x^2+1)-1/2*x*arctan(a*x)/a^2/c^2/(a^2*x^2+1)+1/4*arctan(a*x)^2/a^3/c^2","A"
186,1,57,56,0.028000," ","int(x*arctan(a*x)/(a^2*c*x^2+c)^2,x)","\frac{x}{4 a \,c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)}{4 a^{2} c^{2}}-\frac{\arctan \left(a x \right)}{2 a^{2} c^{2} \left(a^{2} x^{2}+1\right)}"," ",0,"1/4*x/a/c^2/(a^2*x^2+1)+1/4*arctan(a*x)/a^2/c^2-1/2*arctan(a*x)/a^2/c^2/(a^2*x^2+1)","A"
187,1,56,55,0.037000," ","int(arctan(a*x)/(a^2*c*x^2+c)^2,x)","\frac{1}{4 a \,c^{2} \left(a^{2} x^{2}+1\right)}+\frac{x \arctan \left(a x \right)}{2 c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{2}}{4 a \,c^{2}}"," ",0,"1/4/a/c^2/(a^2*x^2+1)+1/2*x*arctan(a*x)/c^2/(a^2*x^2+1)+1/4*arctan(a*x)^2/a/c^2","A"
188,1,298,103,0.124000," ","int(arctan(a*x)/x/(a^2*c*x^2+c)^2,x)","\frac{\arctan \left(a x \right) \ln \left(a x \right)}{c^{2}}-\frac{\arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{2 c^{2}}+\frac{\arctan \left(a x \right)}{2 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{a x}{4 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{\arctan \left(a x \right)}{4 c^{2}}-\frac{i \dilog \left(-i a x +1\right)}{2 c^{2}}-\frac{i \ln \left(a x +i\right)^{2}}{8 c^{2}}+\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 c^{2}}+\frac{i \ln \left(a x \right) \ln \left(i a x +1\right)}{2 c^{2}}+\frac{i \dilog \left(i a x +1\right)}{2 c^{2}}+\frac{i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{4 c^{2}}-\frac{i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{4 c^{2}}-\frac{i \ln \left(a x \right) \ln \left(-i a x +1\right)}{2 c^{2}}+\frac{i \ln \left(a x -i\right)^{2}}{8 c^{2}}-\frac{i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{4 c^{2}}-\frac{i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{4 c^{2}}+\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 c^{2}}"," ",0,"1/c^2*arctan(a*x)*ln(a*x)-1/2/c^2*arctan(a*x)*ln(a^2*x^2+1)+1/2*arctan(a*x)/c^2/(a^2*x^2+1)-1/4*a*x/c^2/(a^2*x^2+1)-1/4*arctan(a*x)/c^2-1/4*I/c^2*dilog(1/2*I*(a*x-I))-1/8*I/c^2*ln(I+a*x)^2+1/4*I/c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/2*I/c^2*ln(a*x)*ln(1+I*a*x)+1/4*I/c^2*ln(I+a*x)*ln(a^2*x^2+1)-1/2*I/c^2*dilog(1-I*a*x)+1/4*I/c^2*dilog(-1/2*I*(I+a*x))-1/2*I/c^2*ln(a*x)*ln(1-I*a*x)+1/8*I/c^2*ln(a*x-I)^2-1/4*I/c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))-1/4*I/c^2*ln(a*x-I)*ln(a^2*x^2+1)+1/2*I/c^2*dilog(1+I*a*x)","B"
189,1,92,89,0.049000," ","int(arctan(a*x)/x^2/(a^2*c*x^2+c)^2,x)","-\frac{\arctan \left(a x \right)}{c^{2} x}-\frac{a^{2} x \arctan \left(a x \right)}{2 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{3 a \arctan \left(a x \right)^{2}}{4 c^{2}}+\frac{a \ln \left(a x \right)}{c^{2}}-\frac{a \ln \left(a^{2} x^{2}+1\right)}{2 c^{2}}-\frac{a}{4 c^{2} \left(a^{2} x^{2}+1\right)}"," ",0,"-arctan(a*x)/c^2/x-1/2*a^2*x*arctan(a*x)/c^2/(a^2*x^2+1)-3/4*a*arctan(a*x)^2/c^2+a/c^2*ln(a*x)-1/2*a*ln(a^2*x^2+1)/c^2-1/4*a/c^2/(a^2*x^2+1)","A"
190,1,369,142,0.111000," ","int(arctan(a*x)/x^3/(a^2*c*x^2+c)^2,x)","-\frac{\arctan \left(a x \right)}{2 c^{2} x^{2}}-\frac{2 a^{2} \arctan \left(a x \right) \ln \left(a x \right)}{c^{2}}+\frac{a^{2} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{c^{2}}-\frac{a^{2} \arctan \left(a x \right)}{2 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{i a^{2} \dilog \left(i a x +1\right)}{c^{2}}-\frac{i a^{2} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{2 c^{2}}-\frac{i a^{2} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 c^{2}}-\frac{i a^{2} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 c^{2}}+\frac{i a^{2} \ln \left(a x +i\right)^{2}}{4 c^{2}}-\frac{i a^{2} \ln \left(a x -i\right)^{2}}{4 c^{2}}-\frac{i a^{2} \ln \left(a x \right) \ln \left(i a x +1\right)}{c^{2}}+\frac{i a^{2} \dilog \left(-i a x +1\right)}{c^{2}}+\frac{i a^{2} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{2 c^{2}}+\frac{i a^{2} \ln \left(a x \right) \ln \left(-i a x +1\right)}{c^{2}}+\frac{i a^{2} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{2 c^{2}}+\frac{i a^{2} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{2 c^{2}}-\frac{a}{2 c^{2} x}+\frac{a^{3} x}{4 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{a^{2} \arctan \left(a x \right)}{4 c^{2}}"," ",0,"-1/2*arctan(a*x)/c^2/x^2-2*a^2/c^2*arctan(a*x)*ln(a*x)+a^2/c^2*arctan(a*x)*ln(a^2*x^2+1)-1/2*a^2*arctan(a*x)/c^2/(a^2*x^2+1)+I*a^2/c^2*dilog(1-I*a*x)-1/2*I*a^2/c^2*ln(I+a*x)*ln(a^2*x^2+1)-1/2*I*a^2/c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/4*I*a^2/c^2*ln(I+a*x)^2-1/4*I*a^2/c^2*ln(a*x-I)^2-I*a^2/c^2*ln(a*x)*ln(1+I*a*x)+1/2*I*a^2/c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))+I*a^2/c^2*ln(a*x)*ln(1-I*a*x)+1/2*I*a^2/c^2*ln(a*x-I)*ln(a^2*x^2+1)+1/2*I*a^2/c^2*dilog(1/2*I*(a*x-I))-I*a^2/c^2*dilog(1+I*a*x)-1/2*I*a^2/c^2*dilog(-1/2*I*(I+a*x))-1/2*a/c^2/x+1/4*a^3*x/c^2/(a^2*x^2+1)-1/4*a^2*arctan(a*x)/c^2","B"
191,1,125,122,0.054000," ","int(arctan(a*x)/x^4/(a^2*c*x^2+c)^2,x)","-\frac{\arctan \left(a x \right)}{3 c^{2} x^{3}}+\frac{2 a^{2} \arctan \left(a x \right)}{c^{2} x}+\frac{a^{4} x \arctan \left(a x \right)}{2 c^{2} \left(a^{2} x^{2}+1\right)}+\frac{5 a^{3} \arctan \left(a x \right)^{2}}{4 c^{2}}-\frac{a}{6 c^{2} x^{2}}-\frac{7 a^{3} \ln \left(a x \right)}{3 c^{2}}+\frac{7 a^{3} \ln \left(a^{2} x^{2}+1\right)}{6 c^{2}}+\frac{a^{3}}{4 c^{2} \left(a^{2} x^{2}+1\right)}"," ",0,"-1/3*arctan(a*x)/c^2/x^3+2*a^2*arctan(a*x)/c^2/x+1/2*a^4*x*arctan(a*x)/c^2/(a^2*x^2+1)+5/4*a^3*arctan(a*x)^2/c^2-1/6*a/c^2/x^2-7/3*a^3/c^2*ln(a*x)+7/6*a^3*ln(a^2*x^2+1)/c^2+1/4*a^3/c^2/(a^2*x^2+1)","A"
192,1,102,78,0.044000," ","int(x^3*arctan(a*x)/(a^2*c*x^2+c)^3,x)","\frac{\arctan \left(a x \right)}{4 a^{4} c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{\arctan \left(a x \right)}{2 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{5 x^{3}}{32 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 x}{32 a^{3} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{5 \arctan \left(a x \right)}{32 a^{4} c^{3}}"," ",0,"1/4/a^4/c^3*arctan(a*x)/(a^2*x^2+1)^2-1/2*arctan(a*x)/a^4/c^3/(a^2*x^2+1)+5/32*x^3/a/c^3/(a^2*x^2+1)^2+3/32/a^3/c^3/(a^2*x^2+1)^2*x+5/32*arctan(a*x)/a^4/c^3","A"
193,1,101,101,0.046000," ","int(x^2*arctan(a*x)/(a^2*c*x^2+c)^3,x)","\frac{\arctan \left(a x \right) x^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{x \arctan \left(a x \right)}{8 a^{2} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{\arctan \left(a x \right)^{2}}{16 a^{3} c^{3}}-\frac{1}{16 a^{3} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{1}{16 a^{3} c^{3} \left(a^{2} x^{2}+1\right)}"," ",0,"1/8/c^3*arctan(a*x)/(a^2*x^2+1)^2*x^3-1/8*x*arctan(a*x)/a^2/c^3/(a^2*x^2+1)^2+1/16*arctan(a*x)^2/a^3/c^3-1/16/a^3/c^3/(a^2*x^2+1)^2+1/16/a^3/c^3/(a^2*x^2+1)","A"
194,1,77,76,0.029000," ","int(x*arctan(a*x)/(a^2*c*x^2+c)^3,x)","\frac{x}{16 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 x}{32 a \,c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 \arctan \left(a x \right)}{32 a^{2} c^{3}}-\frac{\arctan \left(a x \right)}{4 a^{2} c^{3} \left(a^{2} x^{2}+1\right)^{2}}"," ",0,"1/16*x/a/c^3/(a^2*x^2+1)^2+3/32*x/a/c^3/(a^2*x^2+1)+3/32*arctan(a*x)/a^2/c^3-1/4*arctan(a*x)/a^2/c^3/(a^2*x^2+1)^2","A"
195,1,96,95,0.042000," ","int(arctan(a*x)/(a^2*c*x^2+c)^3,x)","\frac{1}{16 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3}{16 a \,c^{3} \left(a^{2} x^{2}+1\right)}+\frac{x \arctan \left(a x \right)}{4 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 x \arctan \left(a x \right)}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 \arctan \left(a x \right)^{2}}{16 a \,c^{3}}"," ",0,"1/16/a/c^3/(a^2*x^2+1)^2+3/16/a/c^3/(a^2*x^2+1)+1/4*x*arctan(a*x)/c^3/(a^2*x^2+1)^2+3/8*x*arctan(a*x)/c^3/(a^2*x^2+1)+3/16*arctan(a*x)^2/a/c^3","A"
196,1,340,141,0.107000," ","int(arctan(a*x)/x/(a^2*c*x^2+c)^3,x)","\frac{\arctan \left(a x \right) \ln \left(a x \right)}{c^{3}}-\frac{\arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{2 c^{3}}+\frac{\arctan \left(a x \right)}{4 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{\arctan \left(a x \right)}{2 c^{3} \left(a^{2} x^{2}+1\right)}-\frac{11 x^{3} a^{3}}{32 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{13 a x}{32 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{11 \arctan \left(a x \right)}{32 c^{3}}+\frac{i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{4 c^{3}}-\frac{i \dilog \left(-i a x +1\right)}{2 c^{3}}-\frac{i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{4 c^{3}}+\frac{i \ln \left(a x -i\right)^{2}}{8 c^{3}}-\frac{i \ln \left(a x \right) \ln \left(-i a x +1\right)}{2 c^{3}}+\frac{i \dilog \left(i a x +1\right)}{2 c^{3}}-\frac{i \ln \left(a x +i\right)^{2}}{8 c^{3}}+\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 c^{3}}-\frac{i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{4 c^{3}}+\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 c^{3}}+\frac{i \ln \left(a x \right) \ln \left(i a x +1\right)}{2 c^{3}}-\frac{i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{4 c^{3}}"," ",0,"1/c^3*arctan(a*x)*ln(a*x)-1/2/c^3*arctan(a*x)*ln(a^2*x^2+1)+1/4*arctan(a*x)/c^3/(a^2*x^2+1)^2+1/2*arctan(a*x)/c^3/(a^2*x^2+1)-11/32/c^3/(a^2*x^2+1)^2*x^3*a^3-13/32*a*x/c^3/(a^2*x^2+1)^2-11/32*arctan(a*x)/c^3+1/4*I/c^3*ln(I+a*x)*ln(a^2*x^2+1)-1/2*I/c^3*dilog(1-I*a*x)-1/4*I/c^3*ln(a*x-I)*ln(a^2*x^2+1)+1/8*I/c^3*ln(a*x-I)^2-1/2*I/c^3*ln(a*x)*ln(1-I*a*x)-1/8*I/c^3*ln(I+a*x)^2+1/4*I/c^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/4*I/c^3*dilog(-1/2*I*(I+a*x))+1/2*I/c^3*ln(a*x)*ln(1+I*a*x)-1/4*I/c^3*dilog(1/2*I*(a*x-I))-1/4*I/c^3*ln(I+a*x)*ln(1/2*I*(a*x-I))+1/2*I/c^3*dilog(1+I*a*x)","B"
197,1,135,130,0.052000," ","int(arctan(a*x)/x^2/(a^2*c*x^2+c)^3,x)","-\frac{\arctan \left(a x \right)}{c^{3} x}-\frac{7 \arctan \left(a x \right) a^{4} x^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{9 a^{2} x \arctan \left(a x \right)}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{15 a \arctan \left(a x \right)^{2}}{16 c^{3}}+\frac{a \ln \left(a x \right)}{c^{3}}-\frac{a \ln \left(a^{2} x^{2}+1\right)}{2 c^{3}}-\frac{a}{16 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{7 a}{16 c^{3} \left(a^{2} x^{2}+1\right)}"," ",0,"-arctan(a*x)/c^3/x-7/8/c^3*arctan(a*x)/(a^2*x^2+1)^2*a^4*x^3-9/8*a^2*x*arctan(a*x)/c^3/(a^2*x^2+1)^2-15/16*a*arctan(a*x)^2/c^3+a/c^3*ln(a*x)-1/2*a*ln(a^2*x^2+1)/c^3-1/16*a/c^3/(a^2*x^2+1)^2-7/16*a/c^3/(a^2*x^2+1)","A"
198,1,415,185,0.128000," ","int(arctan(a*x)/x^3/(a^2*c*x^2+c)^3,x)","-\frac{\arctan \left(a x \right)}{2 c^{3} x^{2}}-\frac{3 a^{2} \arctan \left(a x \right) \ln \left(a x \right)}{c^{3}}+\frac{3 a^{2} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{2 c^{3}}-\frac{a^{2} \arctan \left(a x \right)}{4 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{a^{2} \arctan \left(a x \right)}{c^{3} \left(a^{2} x^{2}+1\right)}-\frac{3 i a^{2} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 c^{3}}-\frac{3 i a^{2} \ln \left(a x \right) \ln \left(i a x +1\right)}{2 c^{3}}+\frac{3 i a^{2} \dilog \left(-i a x +1\right)}{2 c^{3}}-\frac{3 i a^{2} \dilog \left(i a x +1\right)}{2 c^{3}}+\frac{3 i a^{2} \ln \left(a x +i\right)^{2}}{8 c^{3}}+\frac{3 i a^{2} \ln \left(a x \right) \ln \left(-i a x +1\right)}{2 c^{3}}+\frac{3 i a^{2} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{4 c^{3}}+\frac{3 i a^{2} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{4 c^{3}}-\frac{3 i a^{2} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{4 c^{3}}-\frac{3 i a^{2} \ln \left(a x -i\right)^{2}}{8 c^{3}}+\frac{3 i a^{2} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{4 c^{3}}-\frac{3 i a^{2} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 c^{3}}-\frac{a}{2 c^{3} x}+\frac{19 a^{5} x^{3}}{32 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{21 a^{3} x}{32 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 a^{2} \arctan \left(a x \right)}{32 c^{3}}"," ",0,"-1/2*arctan(a*x)/c^3/x^2-3*a^2/c^3*arctan(a*x)*ln(a*x)+3/2*a^2/c^3*arctan(a*x)*ln(a^2*x^2+1)-1/4*a^2*arctan(a*x)/c^3/(a^2*x^2+1)^2-a^2*arctan(a*x)/c^3/(a^2*x^2+1)+3/2*I*a^2/c^3*dilog(1-I*a*x)+3/4*I*a^2/c^3*dilog(1/2*I*(a*x-I))-3/2*I*a^2/c^3*ln(a*x)*ln(1+I*a*x)-3/2*I*a^2/c^3*dilog(1+I*a*x)+3/8*I*a^2/c^3*ln(I+a*x)^2+3/2*I*a^2/c^3*ln(a*x)*ln(1-I*a*x)+3/4*I*a^2/c^3*ln(a*x-I)*ln(a^2*x^2+1)+3/4*I*a^2/c^3*ln(I+a*x)*ln(1/2*I*(a*x-I))-3/4*I*a^2/c^3*ln(I+a*x)*ln(a^2*x^2+1)-3/8*I*a^2/c^3*ln(a*x-I)^2-3/4*I*a^2/c^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))-3/4*I*a^2/c^3*dilog(-1/2*I*(I+a*x))-1/2*a/c^3/x+19/32*a^5/c^3/(a^2*x^2+1)^2*x^3+21/32*a^3*x/c^3/(a^2*x^2+1)^2+3/32*a^2*arctan(a*x)/c^3","B"
199,1,170,165,0.056000," ","int(arctan(a*x)/x^4/(a^2*c*x^2+c)^3,x)","-\frac{\arctan \left(a x \right)}{3 c^{3} x^{3}}+\frac{3 a^{2} \arctan \left(a x \right)}{c^{3} x}+\frac{11 a^{6} \arctan \left(a x \right) x^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{13 a^{4} x \arctan \left(a x \right)}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{35 a^{3} \arctan \left(a x \right)^{2}}{16 c^{3}}-\frac{a}{6 c^{3} x^{2}}-\frac{10 a^{3} \ln \left(a x \right)}{3 c^{3}}+\frac{5 a^{3} \ln \left(a^{2} x^{2}+1\right)}{3 c^{3}}+\frac{a^{3}}{16 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{11 a^{3}}{16 c^{3} \left(a^{2} x^{2}+1\right)}"," ",0,"-1/3*arctan(a*x)/c^3/x^3+3*a^2*arctan(a*x)/c^3/x+11/8*a^6/c^3*arctan(a*x)/(a^2*x^2+1)^2*x^3+13/8*a^4*x*arctan(a*x)/c^3/(a^2*x^2+1)^2+35/16*a^3*arctan(a*x)^2/c^3-1/6*a/c^3/x^2-10/3*a^3/c^3*ln(a*x)+5/3*a^3*ln(a^2*x^2+1)/c^3+1/16*a^3/c^3/(a^2*x^2+1)^2+11/16*a^3/c^3/(a^2*x^2+1)","A"
200,1,176,132,2.716000," ","int(x^3*arctan(a*x)*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(24 \arctan \left(a x \right) x^{4} a^{4}-6 a^{3} x^{3}+8 \arctan \left(a x \right) x^{2} a^{2}+5 a x -16 \arctan \left(a x \right)\right)}{120 a^{4}}+\frac{11 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}+i\right)}{120 a^{4} \sqrt{a^{2} x^{2}+1}}-\frac{11 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-i\right)}{120 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/120/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*(24*arctan(a*x)*x^4*a^4-6*a^3*x^3+8*arctan(a*x)*x^2*a^2+5*a*x-16*arctan(a*x))+11/120/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)+I)/(a^2*x^2+1)^(1/2)-11/120/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-I)/(a^2*x^2+1)^(1/2)","C"
201,1,199,241,1.304000," ","int(x^2*arctan(a*x)*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(6 \arctan \left(a x \right) x^{3} a^{3}-2 a^{2} x^{2}+3 \arctan \left(a x \right) x a +1\right)}{24 a^{3}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{8 a^{3} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/24/a^3*(c*(a*x-I)*(I+a*x))^(1/2)*(6*arctan(a*x)*x^3*a^3-2*a^2*x^2+3*arctan(a*x)*x*a+1)+1/8*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^3/(a^2*x^2+1)^(1/2)","A"
202,1,156,70,0.930000," ","int(x*arctan(a*x)*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 \arctan \left(a x \right) x^{2} a^{2}-a x +2 \arctan \left(a x \right)\right)}{6 a^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}+i\right)}{6 a^{2} \sqrt{a^{2} x^{2}+1}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-i\right)}{6 a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/6/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(2*arctan(a*x)*x^2*a^2-a*x+2*arctan(a*x))-1/6/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)+I)/(a^2*x^2+1)^(1/2)+1/6/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-I)/(a^2*x^2+1)^(1/2)","C"
203,1,178,197,0.585000," ","int(arctan(a*x)*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right) x a -1\right)}{2 a}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 a \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2/a*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)*x*a-1)-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a/(a^2*x^2+1)^(1/2)","A"
204,1,151,189,0.703000," ","int(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x,x)","\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 i \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+i \dilog \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+i \dilog \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{\sqrt{a^{2} x^{2}+1}}"," ",0,"(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)+(c*(a*x-I)*(I+a*x))^(1/2)*(2*I*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))+I*dilog(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*dilog((1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
205,1,221,199,0.747000," ","int(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x^2,x)","-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)}{x}+\frac{i a \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+i \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-i \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)+\dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{\sqrt{a^{2} x^{2}+1}}"," ",0,"-(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)/x+I*a*(c*(a*x-I)*(I+a*x))^(1/2)*(I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)+dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
206,1,169,196,1.056000," ","int(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x^3,x)","-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +\arctan \left(a x \right)\right)}{2 x^{2}}+\frac{i a^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(a*x+arctan(a*x))/x^2+1/2*I*a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(I*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
207,1,153,68,1.221000," ","int(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x^4,x)","-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 \arctan \left(a x \right) x^{2} a^{2}+a x +2 \arctan \left(a x \right)\right)}{6 x^{3}}+\frac{a^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)}{6 \sqrt{a^{2} x^{2}+1}}-\frac{a^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{6 \sqrt{a^{2} x^{2}+1}}"," ",0,"-1/6*(c*(a*x-I)*(I+a*x))^(1/2)*(2*arctan(a*x)*x^2*a^2+a*x+2*arctan(a*x))/x^3+1/6*a^3*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)/(a^2*x^2+1)^(1/2)-1/6*a^3*(c*(a*x-I)*(I+a*x))^(1/2)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)","C"
208,1,199,181,2.558000," ","int(x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(240 \arctan \left(a x \right) x^{6} a^{6}-40 x^{5} a^{5}+384 \arctan \left(a x \right) x^{4} a^{4}-46 a^{3} x^{3}+48 \arctan \left(a x \right) x^{2} a^{2}+45 a x -96 \arctan \left(a x \right)\right)}{1680 a^{4}}+\frac{17 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}+i\right)}{560 a^{4} \sqrt{a^{2} x^{2}+1}}-\frac{17 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-i\right)}{560 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/1680*c/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*(240*arctan(a*x)*x^6*a^6-40*x^5*a^5+384*arctan(a*x)*x^4*a^4-46*a^3*x^3+48*arctan(a*x)*x^2*a^2+45*a*x-96*arctan(a*x))+17/560*c/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)+I)/(a^2*x^2+1)^(1/2)-17/560*c/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-I)/(a^2*x^2+1)^(1/2)","C"
209,1,221,292,1.321000," ","int(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(120 \arctan \left(a x \right) x^{5} a^{5}-24 a^{4} x^{4}+210 \arctan \left(a x \right) x^{3} a^{3}-38 a^{2} x^{2}+45 \arctan \left(a x \right) x a +31\right)}{720 a^{3}}+\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{16 a^{3} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/720*c/a^3*(c*(a*x-I)*(I+a*x))^(1/2)*(120*arctan(a*x)*x^5*a^5-24*a^4*x^4+210*arctan(a*x)*x^3*a^3-38*a^2*x^2+45*arctan(a*x)*x*a+31)+1/16*c*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^3/(a^2*x^2+1)^(1/2)","A"
210,1,179,89,0.886000," ","int(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(8 \arctan \left(a x \right) x^{4} a^{4}-2 a^{3} x^{3}+16 \arctan \left(a x \right) x^{2} a^{2}-5 a x +8 \arctan \left(a x \right)\right)}{40 a^{2}}+\frac{3 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-i\right)}{40 a^{2} \sqrt{a^{2} x^{2}+1}}-\frac{3 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}+i\right)}{40 a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/40*c/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(8*arctan(a*x)*x^4*a^4-2*a^3*x^3+16*arctan(a*x)*x^2*a^2-5*a*x+8*arctan(a*x))+3/40*c/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-I)/(a^2*x^2+1)^(1/2)-3/40*c/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)+I)/(a^2*x^2+1)^(1/2)","C"
211,1,201,241,0.563000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x),x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(6 \arctan \left(a x \right) x^{3} a^{3}-2 a^{2} x^{2}+15 \arctan \left(a x \right) x a -11\right)}{24 a}-\frac{3 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{8 a \sqrt{a^{2} x^{2}+1}}"," ",0,"1/24*c/a*(c*(a*x-I)*(I+a*x))^(1/2)*(6*arctan(a*x)*x^3*a^3-2*a^2*x^2+15*arctan(a*x)*x*a-11)-3/8*c*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a/(a^2*x^2+1)^(1/2)","A"
212,1,174,231,0.676000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 \arctan \left(a x \right) x^{2} a^{2}-a x +8 \arctan \left(a x \right)\right)}{6}+\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(7 i \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 i \dilog \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 i \dilog \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{3 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/6*c*(c*(a*x-I)*(I+a*x))^(1/2)*(2*arctan(a*x)*x^2*a^2-a*x+8*arctan(a*x))+1/3*c*(c*(a*x-I)*(I+a*x))^(1/2)*(7*I*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))+3*I*dilog(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*I*dilog((1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
213,1,240,245,0.705000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^2,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right) x^{2} a^{2}-a x -2 \arctan \left(a x \right)\right)}{2 x}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(3 \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)+3 i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) a c}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2*c*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)*x^2*a^2-a*x-2*arctan(a*x))/x-1/2*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)*(3*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)+3*I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*a*c","A"
214,1,180,252,1.006000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^3,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 \arctan \left(a x \right) x^{2} a^{2}-a x -\arctan \left(a x \right)\right)}{2 x^{2}}+\frac{a^{2} c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(4 i \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 i \dilog \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 i \dilog \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2*c*(c*(a*x-I)*(I+a*x))^(1/2)*(2*arctan(a*x)*x^2*a^2-a*x-arctan(a*x))/x^2+1/2*a^2*c*(c*(a*x-I)*(I+a*x))^(1/2)*(4*I*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))+3*I*dilog(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*I*dilog((1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
215,1,245,257,1.340000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^4,x)","-\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(8 \arctan \left(a x \right) x^{2} a^{2}+a x +2 \arctan \left(a x \right)\right)}{6 x^{3}}+\frac{i a^{3} c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(6 i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+7 i \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-7 i \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)-6 \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{6 \sqrt{a^{2} x^{2}+1}}"," ",0,"-1/6*c*(c*(a*x-I)*(I+a*x))^(1/2)*(8*arctan(a*x)*x^2*a^2+a*x+2*arctan(a*x))/x^3+1/6*I*a^3*c*(c*(a*x-I)*(I+a*x))^(1/2)*(6*I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+7*I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-7*I*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)-6*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
216,1,225,245,2.671000," ","int(x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2688 \arctan \left(a x \right) x^{8} a^{8}-336 x^{7} a^{7}+7296 \arctan \left(a x \right) x^{6} a^{6}-824 x^{5} a^{5}+5760 \arctan \left(a x \right) x^{4} a^{4}-410 a^{3} x^{3}+384 \arctan \left(a x \right) x^{2} a^{2}+423 a x -768 \arctan \left(a x \right)\right)}{24192 a^{4}}-\frac{115 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-i\right)}{8064 a^{4} \sqrt{a^{2} x^{2}+1}}+\frac{115 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}+i\right)}{8064 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/24192*c^2/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*(2688*arctan(a*x)*x^8*a^8-336*x^7*a^7+7296*arctan(a*x)*x^6*a^6-824*x^5*a^5+5760*arctan(a*x)*x^4*a^4-410*a^3*x^3+384*arctan(a*x)*x^2*a^2+423*a*x-768*arctan(a*x))-115/8064*c^2/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-I)/(a^2*x^2+1)^(1/2)+115/8064*c^2/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)+I)/(a^2*x^2+1)^(1/2)","C"
217,1,245,345,1.350000," ","int(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(5040 \arctan \left(a x \right) x^{7} a^{7}-720 a^{6} x^{6}+14280 \arctan \left(a x \right) x^{5} a^{5}-1992 a^{4} x^{4}+12390 \arctan \left(a x \right) x^{3} a^{3}-1474 a^{2} x^{2}+1575 \arctan \left(a x \right) x a +1373\right)}{40320 a^{3}}+\frac{5 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{128 a^{3} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/40320*c^2/a^3*(c*(a*x-I)*(I+a*x))^(1/2)*(5040*arctan(a*x)*x^7*a^7-720*a^6*x^6+14280*arctan(a*x)*x^5*a^5-1992*a^4*x^4+12390*arctan(a*x)*x^3*a^3-1474*a^2*x^2+1575*arctan(a*x)*x*a+1373)+5/128*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^3/(a^2*x^2+1)^(1/2)","A"
218,1,205,110,0.904000," ","int(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(48 \arctan \left(a x \right) x^{6} a^{6}-8 x^{5} a^{5}+144 \arctan \left(a x \right) x^{4} a^{4}-26 a^{3} x^{3}+144 \arctan \left(a x \right) x^{2} a^{2}-33 a x +48 \arctan \left(a x \right)\right)}{336 a^{2}}-\frac{5 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}+i\right)}{112 a^{2} \sqrt{a^{2} x^{2}+1}}+\frac{5 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-i\right)}{112 a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/336*c^2/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(48*arctan(a*x)*x^6*a^6-8*x^5*a^5+144*arctan(a*x)*x^4*a^4-26*a^3*x^3+144*arctan(a*x)*x^2*a^2-33*a*x+48*arctan(a*x))-5/112*c^2/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)+I)/(a^2*x^2+1)^(1/2)+5/112*c^2/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-I)/(a^2*x^2+1)^(1/2)","C"
219,1,225,283,0.607000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x),x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(120 \arctan \left(a x \right) x^{5} a^{5}-24 a^{4} x^{4}+390 \arctan \left(a x \right) x^{3} a^{3}-98 a^{2} x^{2}+495 \arctan \left(a x \right) x a -299\right)}{720 a}-\frac{5 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{16 a \sqrt{a^{2} x^{2}+1}}"," ",0,"1/720*c^2/a*(c*(a*x-I)*(I+a*x))^(1/2)*(120*arctan(a*x)*x^5*a^5-24*a^4*x^4+390*arctan(a*x)*x^3*a^3-98*a^2*x^2+495*arctan(a*x)*x*a-299)-5/16*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a/(a^2*x^2+1)^(1/2)","A"
220,1,198,271,0.737000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(24 \arctan \left(a x \right) x^{4} a^{4}-6 a^{3} x^{3}+88 \arctan \left(a x \right) x^{2} a^{2}-35 a x +184 \arctan \left(a x \right)\right)}{120}+\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(149 i \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+60 i \dilog \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-60 \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+60 i \dilog \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{60 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/120*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(24*arctan(a*x)*x^4*a^4-6*a^3*x^3+88*arctan(a*x)*x^2*a^2-35*a*x+184*arctan(a*x))+1/60*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(149*I*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))+60*I*dilog(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-60*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+60*I*dilog((1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
221,1,265,290,0.786000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^2,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(6 \arctan \left(a x \right) x^{4} a^{4}-2 a^{3} x^{3}+27 \arctan \left(a x \right) x^{2} a^{2}-23 a x -24 \arctan \left(a x \right)\right)}{24 x}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(15 \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-15 \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+8 \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-8 \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)+15 i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-15 i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) a \,c^{2}}{8 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/24*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(6*arctan(a*x)*x^4*a^4-2*a^3*x^3+27*arctan(a*x)*x^2*a^2-23*a*x-24*arctan(a*x))/x-1/8*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)*(15*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-15*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+8*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-8*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)+15*I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-15*I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*a*c^2","A"
222,1,204,302,1.077000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^3,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 \arctan \left(a x \right) x^{4} a^{4}-a^{3} x^{3}+14 \arctan \left(a x \right) x^{2} a^{2}-3 a x -3 \arctan \left(a x \right)\right)}{6 x^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-26 i \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-15 i \dilog \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-15 i \dilog \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+15 \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) c^{2} a^{2}}{6 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/6*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(2*arctan(a*x)*x^4*a^4-a^3*x^3+14*arctan(a*x)*x^2*a^2-3*a*x-3*arctan(a*x))/x^2-1/6*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)*(-26*I*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))-15*I*dilog(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-15*I*dilog((1+I*a*x)/(a^2*x^2+1)^(1/2))+15*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2)))*c^2*a^2","A"
223,1,270,307,1.424000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^4,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(3 \arctan \left(a x \right) x^{4} a^{4}-3 a^{3} x^{3}-14 \arctan \left(a x \right) x^{2} a^{2}-a x -2 \arctan \left(a x \right)\right)}{6 x^{3}}+\frac{i a^{3} c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(15 i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-15 i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+13 i \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-13 i \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)+15 \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-15 \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{6 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/6*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(3*arctan(a*x)*x^4*a^4-3*a^3*x^3-14*arctan(a*x)*x^2*a^2-a*x-2*arctan(a*x))/x^3+1/6*I*a^3*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(15*I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-15*I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+13*I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-13*I*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)+15*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-15*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
224,1,165,100,3.157000," ","int(x^3*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(2 \arctan \left(a x \right) x^{2} a^{2}-a x -4 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 c \,a^{4}}+\frac{5 \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}+i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 \sqrt{a^{2} x^{2}+1}\, a^{4} c}-\frac{5 \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 \sqrt{a^{2} x^{2}+1}\, a^{4} c}"," ",0,"1/6*(2*arctan(a*x)*x^2*a^2-a*x-4*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)/c/a^4+5/6*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^4/c-5/6*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^4/c","C"
225,1,184,203,3.030000," ","int(x^2*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(\arctan \left(a x \right) x a -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 c \,a^{3}}-\frac{i \left(i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, a^{3} c}"," ",0,"1/2*(arctan(a*x)*x*a-1)*(c*(a*x-I)*(I+a*x))^(1/2)/c/a^3-1/2*I*(I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^3/c","A"
226,1,144,51,0.918000," ","int(x*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","\frac{\arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{a^{2} c}-\frac{\ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}+i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{2} c}+\frac{\ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{2} c}"," ",0,"arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/a^2/c-ln((1+I*a*x)/(a^2*x^2+1)^(1/2)+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^2/c+ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^2/c","C"
227,1,150,158,0.593000," ","int(arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","\frac{i \left(i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c a}"," ",0,"I*(I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c/a","A"
228,1,139,145,0.669000," ","int(arctan(a*x)/x/(a^2*c*x^2+c)^(1/2),x)","-\frac{i \left(-i \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+i \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}"," ",0,"-I*(-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c","A"
229,1,139,48,0.585000," ","int(arctan(a*x)/x^2/(a^2*c*x^2+c)^(1/2),x)","-\frac{\arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{c x}+\frac{a \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}-\frac{a \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}"," ",0,"-arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/c/x+a*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c-a*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c","C"
230,1,175,198,1.101000," ","int(arctan(a*x)/x^3/(a^2*c*x^2+c)^(1/2),x)","-\frac{\left(a x +\arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 x^{2} c}+\frac{i a^{2} \left(-i \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+i \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, c}"," ",0,"-1/2*(a*x+arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)/x^2/c+1/2*I*a^2*(-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c","A"
231,1,163,98,3.226000," ","int(arctan(a*x)/x^4/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(4 \arctan \left(a x \right) x^{2} a^{2}-a x -2 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 c \,x^{3}}+\frac{5 a^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 \sqrt{a^{2} x^{2}+1}\, c}-\frac{5 a^{3} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 \sqrt{a^{2} x^{2}+1}\, c}"," ",0,"1/6*(4*arctan(a*x)*x^2*a^2-a*x-2*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)/c/x^3+5/6*a^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c-5/6*a^3*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c","C"
232,1,242,95,3.018000," ","int(x^3*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(i+\arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) a^{4} c^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)-i\right)}{2 \left(a^{2} x^{2}+1\right) a^{4} c^{2}}+\frac{\arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{a^{4} c^{2}}+\frac{\ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{4} c^{2}}-\frac{\ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}+i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{4} c^{2}}"," ",0,"1/2*(I+arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/a^4/c^2-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)-I)/(a^2*x^2+1)/a^4/c^2+arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/a^4/c^2+ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-I)/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a^4/c^2-ln((1+I*a*x)/(a^2*x^2+1)^(1/2)+I)/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a^4/c^2","C"
233,1,247,212,2.998000," ","int(x^2*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x)","-\frac{\left(i+\arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2} a^{3}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)-i\right)}{2 \left(a^{2} x^{2}+1\right) c^{2} a^{3}}+\frac{i \left(i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{2} a^{3}}"," ",0,"-1/2*(I+arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2/a^3-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)-I)/(a^2*x^2+1)/c^2/a^3+I*(I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c^2/a^3","A"
234,1,100,45,0.858000," ","int(x*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x)","-\frac{\left(i+\arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2} a^{2}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)-i\right)}{2 \left(a^{2} x^{2}+1\right) c^{2} a^{2}}"," ",0,"-1/2*(I+arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2/a^2+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)-I)/(a^2*x^2+1)/c^2/a^2","C"
235,1,98,41,0.456000," ","int(arctan(a*x)/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(i+\arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2} a}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)-i\right)}{2 \left(a^{2} x^{2}+1\right) c^{2} a}"," ",0,"1/2*(I+arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2/a+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)-I)/(a^2*x^2+1)/c^2/a","C"
236,1,232,193,0.665000," ","int(arctan(a*x)/x/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(i+\arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)-i\right)}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{i \left(-i \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+i \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{2}}"," ",0,"1/2*(I+arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)-I)/(a^2*x^2+1)/c^2-I*(-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c^2","A"
237,1,231,91,0.592000," ","int(arctan(a*x)/x^2/(a^2*c*x^2+c)^(3/2),x)","-\frac{a \left(i+\arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)-i\right) a}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{x \,c^{2}}-\frac{a \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{2}}+\frac{a \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{2}}"," ",0,"-1/2*a*(I+arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)-I)*a/(a^2*x^2+1)/c^2-arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/x/c^2-a*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2+a*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2","C"
238,1,273,252,1.116000," ","int(arctan(a*x)/x^3/(a^2*c*x^2+c)^(3/2),x)","-\frac{a^{2} \left(i+\arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)-i\right) a^{2}}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\left(a x +\arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 c^{2} x^{2}}+\frac{3 i a^{2} \left(-i \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+i \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, c^{2}}"," ",0,"-1/2*a^2*(I+arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)-I)*a^2/(a^2*x^2+1)/c^2-1/2*(a*x+arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)/c^2/x^2+3/2*I*a^2*(-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2","A"
239,1,259,141,2.924000," ","int(arctan(a*x)/x^4/(a^2*c*x^2+c)^(3/2),x)","\frac{a^{3} \left(i+\arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)-i\right) a^{3}}{2 \left(a^{2} x^{2}+1\right) c^{2}}+\frac{\left(10 \arctan \left(a x \right) x^{2} a^{2}-a x -2 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 x^{3} c^{2}}-\frac{11 a^{3} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 \sqrt{a^{2} x^{2}+1}\, c^{2}}+\frac{11 a^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 \sqrt{a^{2} x^{2}+1}\, c^{2}}"," ",0,"1/2*a^3*(I+arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)-I)*a^3/(a^2*x^2+1)/c^2+1/6*(10*arctan(a*x)*x^2*a^2-a*x-2*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)/x^3/c^2-11/6*a^3*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2+11/6*a^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2","C"
240,1,386,146,5.819000," ","int(x^5*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(i+3 \arctan \left(a x \right)\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{72 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{6}}+\frac{7 \left(i+\arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{6} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{7 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)-i\right)}{8 a^{6} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right) \left(-i+3 \arctan \left(a x \right)\right)}{72 a^{6} c^{3} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{c^{3} a^{6}}-\frac{\ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}+i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{6} c^{3}}+\frac{\ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{6} c^{3}}"," ",0,"1/72*(I+3*arctan(a*x))*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^6+7/8*(I+arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/a^6/c^3/(a^2*x^2+1)-7/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)-I)/a^6/c^3/(a^2*x^2+1)-1/72*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)*(-I+3*arctan(a*x))/a^6/c^3/(a^4*x^4+2*a^2*x^2+1)+arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a^6-ln((1+I*a*x)/(a^2*x^2+1)^(1/2)+I)/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a^6/c^3+ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-I)/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a^6/c^3","C"
241,1,389,259,3.239000," ","int(x^4*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x)","-\frac{\left(i+3 \arctan \left(a x \right)\right) \left(a^{3} x^{3}-3 i x^{2} a^{2}-3 a x +i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{72 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{5}}-\frac{5 \left(i+\arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{5} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{5 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)-i\right)}{8 a^{5} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{\left(-i+3 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a^{3} x^{3}+3 i x^{2} a^{2}-3 a x -i\right)}{72 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{5}}+\frac{i \left(i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{5} c^{3}}"," ",0,"-1/72*(I+3*arctan(a*x))*(a^3*x^3-3*I*x^2*a^2-3*a*x+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^5-5/8*(I+arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/a^5/c^3/(a^2*x^2+1)-5/8*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)-I)/a^5/c^3/(a^2*x^2+1)-1/72*(-I+3*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)*(a^3*x^3+3*I*x^2*a^2-3*a*x-I)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^5+I*(I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^5/c^3","A"
242,1,244,96,3.059000," ","int(x^3*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x)","-\frac{\left(i+3 \arctan \left(a x \right)\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{72 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{4}}-\frac{3 \left(i+\arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)-i\right)}{8 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\left(-i+3 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right)}{72 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{4}}"," ",0,"-1/72*(I+3*arctan(a*x))*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^4-3/8*(I+arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/a^4/c^3/(a^2*x^2+1)+3/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)-I)/a^4/c^3/(a^2*x^2+1)+1/72*(-I+3*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^4","C"
243,1,240,65,2.834000," ","int(x^2*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(i+3 \arctan \left(a x \right)\right) \left(a^{3} x^{3}-3 i x^{2} a^{2}-3 a x +i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{72 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{3}}+\frac{\left(i+\arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{3} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)-i\right)}{8 a^{3} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\left(-i+3 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a^{3} x^{3}+3 i x^{2} a^{2}-3 a x -i\right)}{72 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{3}}"," ",0,"1/72*(I+3*arctan(a*x))*(a^3*x^3-3*I*x^2*a^2-3*a*x+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^3+1/8*(I+arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/a^3/c^3/(a^2*x^2+1)+1/8*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)-I)/a^3/c^3/(a^2*x^2+1)+1/72*(-I+3*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)*(a^3*x^3+3*I*x^2*a^2-3*a*x-I)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^3","C"
244,1,244,67,0.896000," ","int(x*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(i+3 \arctan \left(a x \right)\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{72 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{2}}-\frac{\left(i+\arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{2} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)-i\right)}{8 a^{2} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right) \left(-i+3 \arctan \left(a x \right)\right)}{72 a^{2} c^{3} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right)}"," ",0,"1/72*(I+3*arctan(a*x))*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^2-1/8*(I+arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/a^2/c^3/(a^2*x^2+1)+1/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)-I)/a^2/c^3/(a^2*x^2+1)-1/72*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)*(-I+3*arctan(a*x))/a^2/c^3/(a^4*x^4+2*a^2*x^2+1)","C"
245,1,240,85,0.503000," ","int(arctan(a*x)/(a^2*c*x^2+c)^(5/2),x)","-\frac{\left(i+3 \arctan \left(a x \right)\right) \left(a^{3} x^{3}-3 i x^{2} a^{2}-3 a x +i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{72 \left(a^{2} x^{2}+1\right)^{2} a \,c^{3}}+\frac{3 \left(i+\arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 c^{3} a \left(a^{2} x^{2}+1\right)}+\frac{3 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)-i\right)}{8 c^{3} a \left(a^{2} x^{2}+1\right)}-\frac{\left(-i+3 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a^{3} x^{3}+3 i x^{2} a^{2}-3 a x -i\right)}{72 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) a \,c^{3}}"," ",0,"-1/72*(I+3*arctan(a*x))*(a^3*x^3-3*I*x^2*a^2-3*a*x+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/a/c^3+3/8*(I+arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a/(a^2*x^2+1)+3/8*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)-I)/c^3/a/(a^2*x^2+1)-1/72*(-I+3*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)*(a^3*x^3+3*I*x^2*a^2-3*a*x-I)/(a^4*x^4+2*a^2*x^2+1)/a/c^3","C"
246,1,370,233,0.720000," ","int(arctan(a*x)/x/(a^2*c*x^2+c)^(5/2),x)","-\frac{\left(i+3 \arctan \left(a x \right)\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{72 \left(a^{2} x^{2}+1\right)^{2} c^{3}}+\frac{5 \left(i+\arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 c^{3} \left(a^{2} x^{2}+1\right)}-\frac{5 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)-i\right)}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\left(-i+3 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right)}{72 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3}}-\frac{i \left(-i \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+i \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{3}}"," ",0,"-1/72*(I+3*arctan(a*x))*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3+5/8*(I+arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/(a^2*x^2+1)-5/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)-I)/c^3/(a^2*x^2+1)+1/72*(-I+3*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)/(a^4*x^4+2*a^2*x^2+1)/c^3-I*(-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c^3","A"
247,1,369,134,0.664000," ","int(arctan(a*x)/x^2/(a^2*c*x^2+c)^(5/2),x)","\frac{a \left(i+3 \arctan \left(a x \right)\right) \left(a^{3} x^{3}-3 i x^{2} a^{2}-3 a x +i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{72 \left(a^{2} x^{2}+1\right)^{2} c^{3}}-\frac{7 a \left(i+\arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 c^{3} \left(a^{2} x^{2}+1\right)}-\frac{7 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)-i\right) a}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a^{3} x^{3}+3 i x^{2} a^{2}-3 a x -i\right) \left(-i+3 \arctan \left(a x \right)\right) a}{72 c^{3} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right)}-\frac{\arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{x \,c^{3}}-\frac{a \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{3}}+\frac{a \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{3}}"," ",0,"1/72*a*(I+3*arctan(a*x))*(a^3*x^3-3*I*x^2*a^2-3*a*x+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3-7/8*a*(I+arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/(a^2*x^2+1)-7/8*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)-I)*a/c^3/(a^2*x^2+1)+1/72*(c*(a*x-I)*(I+a*x))^(1/2)*(a^3*x^3+3*I*x^2*a^2-3*a*x-I)*(-I+3*arctan(a*x))*a/c^3/(a^4*x^4+2*a^2*x^2+1)-arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/x/c^3-a*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3+a*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3","C"
248,1,600,262,1.618000," ","int(x^m*(a^2*c*x^2+c)^3*arctan(a*x),x)","\frac{a^{-1-m} c^{3} \left(-\frac{4 x^{m} a^{m} \left(a^{6} m^{3} x^{6}+6 a^{6} m^{2} x^{6}+8 m \,x^{6} a^{6}-a^{4} m^{3} x^{4}-8 a^{4} m^{2} x^{4}-12 m \,x^{4} a^{4}+a^{2} m^{3} x^{2}+10 a^{2} m^{2} x^{2}+24 m \,x^{2} a^{2}-m^{3}-12 m^{2}-44 m -48\right)}{\left(7+m \right) m \left(2+m \right) \left(4+m \right) \left(6+m \right)}+\frac{8 x^{8+m} a^{8+m} \arctan \left(\sqrt{a^{2} x^{2}}\right)}{\left(14+2 m \right) \sqrt{a^{2} x^{2}}}+\frac{2 x^{m} a^{m} \left(-8-m \right) \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{\left(8+m \right) \left(7+m \right)}\right)}{4}+\frac{3 a^{-1-m} c^{3} \left(-\frac{4 x^{m} a^{m} \left(a^{4} m^{2} x^{4}+2 m \,x^{4} a^{4}-a^{2} m^{2} x^{2}-4 m \,x^{2} a^{2}+m^{2}+6 m +8\right)}{\left(5+m \right) m \left(2+m \right) \left(4+m \right)}+\frac{8 x^{6+m} a^{6+m} \arctan \left(\sqrt{a^{2} x^{2}}\right)}{\left(10+2 m \right) \sqrt{a^{2} x^{2}}}+\frac{2 x^{m} a^{m} \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{5+m}\right)}{4}+\frac{3 a^{-1-m} c^{3} \left(-\frac{4 x^{m} a^{m} \left(m \,x^{2} a^{2}-m -2\right)}{\left(3+m \right) m \left(2+m \right)}+\frac{8 x^{4+m} a^{4+m} \arctan \left(\sqrt{a^{2} x^{2}}\right)}{\left(6+2 m \right) \sqrt{a^{2} x^{2}}}+\frac{2 x^{m} a^{m} \left(-4-m \right) \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{\left(4+m \right) \left(3+m \right)}\right)}{4}+\frac{a^{-1-m} c^{3} \left(\frac{4 x^{m} a^{m} \left(-m -2\right)}{\left(2+m \right) \left(1+m \right) m}+\frac{8 x^{2+m} a^{2+m} \arctan \left(\sqrt{a^{2} x^{2}}\right)}{\left(2+2 m \right) \sqrt{a^{2} x^{2}}}+\frac{2 x^{m} a^{m} \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{1+m}\right)}{4}"," ",0,"1/4*a^(-1-m)*c^3*(-4*x^m*a^m*(a^6*m^3*x^6+6*a^6*m^2*x^6+8*a^6*m*x^6-a^4*m^3*x^4-8*a^4*m^2*x^4-12*a^4*m*x^4+a^2*m^3*x^2+10*a^2*m^2*x^2+24*a^2*m*x^2-m^3-12*m^2-44*m-48)/(7+m)/m/(2+m)/(4+m)/(6+m)+8*x^(8+m)*a^(8+m)/(14+2*m)/(a^2*x^2)^(1/2)*arctan((a^2*x^2)^(1/2))+2/(8+m)*x^m*a^m*(-8-m)/(7+m)*LerchPhi(-a^2*x^2,1,1/2*m))+3/4*a^(-1-m)*c^3*(-4*x^m*a^m*(a^4*m^2*x^4+2*a^4*m*x^4-a^2*m^2*x^2-4*a^2*m*x^2+m^2+6*m+8)/(5+m)/m/(2+m)/(4+m)+8*x^(6+m)*a^(6+m)/(10+2*m)/(a^2*x^2)^(1/2)*arctan((a^2*x^2)^(1/2))+2*x^m*a^m/(5+m)*LerchPhi(-a^2*x^2,1,1/2*m))+3/4*a^(-1-m)*c^3*(-4*x^m*a^m*(a^2*m*x^2-m-2)/(3+m)/m/(2+m)+8*x^(4+m)*a^(4+m)/(6+2*m)/(a^2*x^2)^(1/2)*arctan((a^2*x^2)^(1/2))+2/(4+m)*x^m*a^m*(-4-m)/(3+m)*LerchPhi(-a^2*x^2,1,1/2*m))+1/4*a^(-1-m)*c^3*(4/(2+m)*x^m*a^m*(-m-2)/(1+m)/m+8*x^(2+m)*a^(2+m)/(2+2*m)/(a^2*x^2)^(1/2)*arctan((a^2*x^2)^(1/2))+2*x^m*a^m/(1+m)*LerchPhi(-a^2*x^2,1,1/2*m))","C"
249,1,376,195,1.402000," ","int(x^m*(a^2*c*x^2+c)^2*arctan(a*x),x)","\frac{a^{-1-m} c^{2} \left(-\frac{4 x^{m} a^{m} \left(a^{4} m^{2} x^{4}+2 m \,x^{4} a^{4}-a^{2} m^{2} x^{2}-4 m \,x^{2} a^{2}+m^{2}+6 m +8\right)}{\left(5+m \right) m \left(2+m \right) \left(4+m \right)}+\frac{8 x^{6+m} a^{6+m} \arctan \left(\sqrt{a^{2} x^{2}}\right)}{\left(10+2 m \right) \sqrt{a^{2} x^{2}}}+\frac{2 x^{m} a^{m} \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{5+m}\right)}{4}+\frac{a^{-1-m} c^{2} \left(-\frac{4 x^{m} a^{m} \left(m \,x^{2} a^{2}-m -2\right)}{\left(3+m \right) m \left(2+m \right)}+\frac{8 x^{4+m} a^{4+m} \arctan \left(\sqrt{a^{2} x^{2}}\right)}{\left(6+2 m \right) \sqrt{a^{2} x^{2}}}+\frac{2 x^{m} a^{m} \left(-4-m \right) \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{\left(4+m \right) \left(3+m \right)}\right)}{2}+\frac{a^{-1-m} c^{2} \left(\frac{4 x^{m} a^{m} \left(-m -2\right)}{\left(2+m \right) \left(1+m \right) m}+\frac{8 x^{2+m} a^{2+m} \arctan \left(\sqrt{a^{2} x^{2}}\right)}{\left(2+2 m \right) \sqrt{a^{2} x^{2}}}+\frac{2 x^{m} a^{m} \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{1+m}\right)}{4}"," ",0,"1/4*a^(-1-m)*c^2*(-4*x^m*a^m*(a^4*m^2*x^4+2*a^4*m*x^4-a^2*m^2*x^2-4*a^2*m*x^2+m^2+6*m+8)/(5+m)/m/(2+m)/(4+m)+8*x^(6+m)*a^(6+m)/(10+2*m)/(a^2*x^2)^(1/2)*arctan((a^2*x^2)^(1/2))+2*x^m*a^m/(5+m)*LerchPhi(-a^2*x^2,1,1/2*m))+1/2*a^(-1-m)*c^2*(-4*x^m*a^m*(a^2*m*x^2-m-2)/(3+m)/m/(2+m)+8*x^(4+m)*a^(4+m)/(6+2*m)/(a^2*x^2)^(1/2)*arctan((a^2*x^2)^(1/2))+2/(4+m)*x^m*a^m*(-4-m)/(3+m)*LerchPhi(-a^2*x^2,1,1/2*m))+1/4*a^(-1-m)*c^2*(4/(2+m)*x^m*a^m*(-m-2)/(1+m)/m+8*x^(2+m)*a^(2+m)/(2+2*m)/(a^2*x^2)^(1/2)*arctan((a^2*x^2)^(1/2))+2*x^m*a^m/(1+m)*LerchPhi(-a^2*x^2,1,1/2*m))","C"
250,1,222,120,1.169000," ","int(x^m*(a^2*c*x^2+c)*arctan(a*x),x)","\frac{a^{-1-m} c \left(-\frac{4 x^{m} a^{m} \left(m \,x^{2} a^{2}-m -2\right)}{\left(3+m \right) m \left(2+m \right)}+\frac{8 x^{4+m} a^{4+m} \arctan \left(\sqrt{a^{2} x^{2}}\right)}{\left(6+2 m \right) \sqrt{a^{2} x^{2}}}+\frac{2 x^{m} a^{m} \left(-4-m \right) \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{\left(4+m \right) \left(3+m \right)}\right)}{4}+\frac{a^{-1-m} c \left(\frac{4 x^{m} a^{m} \left(-m -2\right)}{\left(2+m \right) \left(1+m \right) m}+\frac{8 x^{2+m} a^{2+m} \arctan \left(\sqrt{a^{2} x^{2}}\right)}{\left(2+2 m \right) \sqrt{a^{2} x^{2}}}+\frac{2 x^{m} a^{m} \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{1+m}\right)}{4}"," ",0,"1/4*a^(-1-m)*c*(-4*x^m*a^m*(a^2*m*x^2-m-2)/(3+m)/m/(2+m)+8*x^(4+m)*a^(4+m)/(6+2*m)/(a^2*x^2)^(1/2)*arctan((a^2*x^2)^(1/2))+2/(4+m)*x^m*a^m*(-4-m)/(3+m)*LerchPhi(-a^2*x^2,1,1/2*m))+1/4*a^(-1-m)*c*(4/(2+m)*x^m*a^m*(-m-2)/(1+m)/m+8*x^(2+m)*a^(2+m)/(2+2*m)/(a^2*x^2)^(1/2)*arctan((a^2*x^2)^(1/2))+2*x^m*a^m/(1+m)*LerchPhi(-a^2*x^2,1,1/2*m))","C"
251,0,0,22,0.651000," ","int(x^m*arctan(a*x)/(a^2*c*x^2+c),x)","\int \frac{x^{m} \arctan \left(a x \right)}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^m*arctan(a*x)/(a^2*c*x^2+c),x)","F"
252,0,0,22,1.451000," ","int(x^m*arctan(a*x)/(a^2*c*x^2+c)^2,x)","\int \frac{x^{m} \arctan \left(a x \right)}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^m*arctan(a*x)/(a^2*c*x^2+c)^2,x)","F"
253,0,0,22,0.936000," ","int(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x)","F"
254,0,0,22,0.892000," ","int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x)","F"
255,0,0,104,0.932000," ","int(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x),x)","\int x^{m} \sqrt{a^{2} c \,x^{2}+c}\, \arctan \left(a x \right)\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x),x)","F"
256,0,0,22,1.356000," ","int(x^m*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m} \arctan \left(a x \right)}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","F"
257,0,0,22,1.594000," ","int(x^m*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{m} \arctan \left(a x \right)}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x)","F"
258,1,107,106,0.041000," ","int(x^3*(a^2*c*x^2+c)*arctan(a*x)^2,x)","-\frac{c \,x^{2}}{180 a^{2}}+\frac{c \,x^{4}}{60}+\frac{c x \arctan \left(a x \right)}{6 a^{3}}-\frac{c \,x^{3} \arctan \left(a x \right)}{18 a}-\frac{a c \,x^{5} \arctan \left(a x \right)}{15}-\frac{c \arctan \left(a x \right)^{2}}{12 a^{4}}+\frac{c \,x^{4} \arctan \left(a x \right)^{2}}{4}+\frac{a^{2} c \,x^{6} \arctan \left(a x \right)^{2}}{6}-\frac{7 c \ln \left(a^{2} x^{2}+1\right)}{90 a^{4}}"," ",0,"-1/180*c*x^2/a^2+1/60*c*x^4+1/6*c*x*arctan(a*x)/a^3-1/18*c*x^3*arctan(a*x)/a-1/15*a*c*x^5*arctan(a*x)-1/12*c*arctan(a*x)^2/a^4+1/4*c*x^4*arctan(a*x)^2+1/6*a^2*c*x^6*arctan(a*x)^2-7/90*c*ln(a^2*x^2+1)/a^4","A"
259,1,258,132,0.124000," ","int(x^2*(a^2*c*x^2+c)*arctan(a*x)^2,x)","\frac{a^{2} c \,x^{5} \arctan \left(a x \right)^{2}}{5}+\frac{c \,x^{3} \arctan \left(a x \right)^{2}}{3}-\frac{a c \,x^{4} \arctan \left(a x \right)}{10}-\frac{2 c \,x^{2} \arctan \left(a x \right)}{15 a}+\frac{2 c \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{15 a^{3}}+\frac{c \,x^{3}}{30}+\frac{c x}{30 a^{2}}-\frac{c \arctan \left(a x \right)}{30 a^{3}}+\frac{i c \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{15 a^{3}}-\frac{i c \ln \left(a x -i\right)^{2}}{30 a^{3}}+\frac{i c \ln \left(a x +i\right)^{2}}{30 a^{3}}-\frac{i c \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{15 a^{3}}-\frac{i c \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{15 a^{3}}+\frac{i c \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{15 a^{3}}+\frac{i c \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{15 a^{3}}-\frac{i c \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{15 a^{3}}"," ",0,"1/5*a^2*c*x^5*arctan(a*x)^2+1/3*c*x^3*arctan(a*x)^2-1/10*a*c*x^4*arctan(a*x)-2/15*c*x^2*arctan(a*x)/a+2/15/a^3*c*arctan(a*x)*ln(a^2*x^2+1)+1/30*c*x^3+1/30*c*x/a^2-1/30*c*arctan(a*x)/a^3+1/15*I/a^3*c*ln(a*x-I)*ln(a^2*x^2+1)-1/15*I/a^3*c*dilog(-1/2*I*(I+a*x))+1/15*I/a^3*c*dilog(1/2*I*(a*x-I))-1/30*I/a^3*c*ln(a*x-I)^2+1/30*I/a^3*c*ln(I+a*x)^2-1/15*I/a^3*c*ln(I+a*x)*ln(a^2*x^2+1)+1/15*I/a^3*c*ln(I+a*x)*ln(1/2*I*(a*x-I))-1/15*I/a^3*c*ln(a*x-I)*ln(-1/2*I*(I+a*x))","A"
260,1,85,86,0.036000," ","int(x*(a^2*c*x^2+c)*arctan(a*x)^2,x)","\frac{a^{2} c \arctan \left(a x \right)^{2} x^{4}}{4}+\frac{c \arctan \left(a x \right)^{2} x^{2}}{2}-\frac{a c \arctan \left(a x \right) x^{3}}{6}-\frac{c x \arctan \left(a x \right)}{2 a}+\frac{c \arctan \left(a x \right)^{2}}{4 a^{2}}+\frac{c \,x^{2}}{12}+\frac{c \ln \left(a^{2} x^{2}+1\right)}{6 a^{2}}"," ",0,"1/4*a^2*c*arctan(a*x)^2*x^4+1/2*c*arctan(a*x)^2*x^2-1/6*a*c*arctan(a*x)*x^3-1/2*c*x*arctan(a*x)/a+1/4/a^2*c*arctan(a*x)^2+1/12*c*x^2+1/6*c*ln(a^2*x^2+1)/a^2","A"
261,1,233,110,0.095000," ","int((a^2*c*x^2+c)*arctan(a*x)^2,x)","\frac{a^{2} c \arctan \left(a x \right)^{2} x^{3}}{3}+c x \arctan \left(a x \right)^{2}-\frac{a c \arctan \left(a x \right) x^{2}}{3}-\frac{2 c \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3 a}+\frac{c x}{3}-\frac{c \arctan \left(a x \right)}{3 a}-\frac{i c \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{3 a}+\frac{i c \ln \left(a x -i\right)^{2}}{6 a}+\frac{i c \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{3 a}+\frac{i c \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{3 a}+\frac{i c \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{3 a}-\frac{i c \ln \left(a x +i\right)^{2}}{6 a}-\frac{i c \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{3 a}-\frac{i c \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{3 a}"," ",0,"1/3*a^2*c*arctan(a*x)^2*x^3+c*x*arctan(a*x)^2-1/3*a*c*arctan(a*x)*x^2-2/3/a*c*arctan(a*x)*ln(a^2*x^2+1)+1/3*c*x-1/3/a*c*arctan(a*x)-1/3*I/a*c*ln(a*x-I)*ln(a^2*x^2+1)+1/6*I/a*c*ln(a*x-I)^2+1/3*I/a*c*dilog(-1/2*I*(I+a*x))+1/3*I/a*c*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/3*I/a*c*ln(I+a*x)*ln(a^2*x^2+1)-1/6*I/a*c*ln(I+a*x)^2-1/3*I/a*c*dilog(1/2*I*(a*x-I))-1/3*I/a*c*ln(I+a*x)*ln(1/2*I*(a*x-I))","B"
262,1,1078,152,3.746000," ","int((a^2*c*x^2+c)*arctan(a*x)^2/x,x)","\frac{a^{2} c \,x^{2} \arctan \left(a x \right)^{2}}{2}+c \arctan \left(a x \right)^{2} \ln \left(a x \right)-c \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)+c \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{i c \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}+2 c \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+c \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{i c \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2}+2 c \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-a c x \arctan \left(a x \right)+\frac{i c \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2}-\frac{c \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-c \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)-\frac{i c \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}-\frac{i c \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}+\frac{i c \pi  \arctan \left(a x \right)^{2}}{2}+\frac{i c \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2}+i c \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)+i c \arctan \left(a x \right)-\frac{i c \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}+\frac{i c \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2}+\frac{c \arctan \left(a x \right)^{2}}{2}-2 i c \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i c \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)"," ",0,"1/2*a^2*c*x^2*arctan(a*x)^2+c*arctan(a*x)^2*ln(a*x)-c*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+c*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/2*I*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+2*c*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+c*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*c*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+2*c*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-a*c*x*arctan(a*x)+1/2*I*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-1/2*c*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-c*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+1/2*I*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-2*I*c*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*c*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/2*I*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-1/2*I*c*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+1/2*I*c*Pi*arctan(a*x)^2+1/2*I*c*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2+I*c*arctan(a*x)+1/2*c*arctan(a*x)^2-1/2*I*c*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+1/2*I*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2","C"
263,1,262,107,0.129000," ","int((a^2*c*x^2+c)*arctan(a*x)^2/x^2,x)","a^{2} c x \arctan \left(a x \right)^{2}-\frac{c \arctan \left(a x \right)^{2}}{x}+2 a c \arctan \left(a x \right) \ln \left(a x \right)-2 a c \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)+i a c \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)-i a c \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)+\frac{i a c \ln \left(a x -i\right)^{2}}{2}+i a c \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)-i a c \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)-i a c \ln \left(a x \right) \ln \left(-i a x +1\right)-i a c \dilog \left(\frac{i \left(a x -i\right)}{2}\right)+i a c \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)-i a c \dilog \left(-i a x +1\right)+i a c \ln \left(a x \right) \ln \left(i a x +1\right)-\frac{i a c \ln \left(a x +i\right)^{2}}{2}+i a c \dilog \left(i a x +1\right)"," ",0,"a^2*c*x*arctan(a*x)^2-c*arctan(a*x)^2/x+2*a*c*arctan(a*x)*ln(a*x)-2*a*c*arctan(a*x)*ln(a^2*x^2+1)+I*a*c*ln(a*x-I)*ln(-1/2*I*(I+a*x))-I*a*c*ln(I+a*x)*ln(1/2*I*(a*x-I))+1/2*I*a*c*ln(a*x-I)^2+I*a*c*ln(I+a*x)*ln(a^2*x^2+1)-I*a*c*ln(a*x-I)*ln(a^2*x^2+1)-I*a*c*ln(a*x)*ln(1-I*a*x)-I*a*c*dilog(1/2*I*(a*x-I))-I*a*c*dilog(1-I*a*x)+I*a*c*ln(a*x)*ln(1+I*a*x)-1/2*I*a*c*ln(I+a*x)^2+I*a*c*dilog(-1/2*I*(I+a*x))+I*a*c*dilog(1+I*a*x)","B"
264,1,1167,179,6.316000," ","int((a^2*c*x^2+c)*arctan(a*x)^2/x^3,x)","2 a^{2} c \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 a^{2} c \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{a^{2} c \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+a^{2} c \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)+a^{2} c \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+a^{2} c \arctan \left(a x \right)^{2} \ln \left(a x \right)-\frac{a c \arctan \left(a x \right)}{x}-\frac{a^{2} c \arctan \left(a x \right)^{2}}{2}-\frac{c \arctan \left(a x \right)^{2}}{2 x^{2}}-\frac{i a^{2} c \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}-\frac{i a^{2} c \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}-\frac{i a^{2} c \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}+\frac{i a^{2} c \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2}-\frac{i a^{2} c \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}+\frac{i a^{2} c \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2}+\frac{i a^{2} c \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2}+i a^{2} c \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)-2 i a^{2} c \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i a^{2} c \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{i a^{2} c \pi  \arctan \left(a x \right)^{2}}{2}-a^{2} c \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)+a^{2} c \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+a^{2} c \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-i a^{2} c \arctan \left(a x \right)+\frac{i a^{2} c \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2}"," ",0,"a^2*c*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)+a^2*c*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*a^2*c*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*a^2*c*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/2*a^2*c*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+a^2*c*arctan(a*x)^2*ln(a*x)-a^2*c*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+a^2*c*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+a^2*c*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*a^2*c*arctan(a*x)-a*c*arctan(a*x)/x-1/2*a^2*c*arctan(a*x)^2-1/2*c*arctan(a*x)^2/x^2-1/2*I*a^2*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-1/2*I*a^2*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-1/2*I*a^2*c*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+1/2*I*a^2*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-1/2*I*a^2*c*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+1/2*I*a^2*c*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2+1/2*I*a^2*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2+I*a^2*c*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+1/2*I*a^2*c*Pi*arctan(a*x)^2-2*I*a^2*c*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*a^2*c*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/2*I*a^2*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2","C"
265,1,323,117,0.109000," ","int((a^2*c*x^2+c)*arctan(a*x)^2/x^4,x)","-\frac{c \arctan \left(a x \right)^{2}}{3 x^{3}}-\frac{a^{2} c \arctan \left(a x \right)^{2}}{x}-\frac{a c \arctan \left(a x \right)}{3 x^{2}}+\frac{4 a^{3} c \arctan \left(a x \right) \ln \left(a x \right)}{3}-\frac{2 a^{3} c \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3}-\frac{a^{2} c}{3 x}-\frac{a^{3} c \arctan \left(a x \right)}{3}+\frac{2 i a^{3} c \ln \left(a x \right) \ln \left(i a x +1\right)}{3}+\frac{2 i a^{3} c \dilog \left(i a x +1\right)}{3}+\frac{i a^{3} c \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{3}+\frac{i a^{3} c \ln \left(a x -i\right)^{2}}{6}-\frac{i a^{3} c \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{3}-\frac{i a^{3} c \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{3}-\frac{2 i a^{3} c \dilog \left(-i a x +1\right)}{3}-\frac{i a^{3} c \ln \left(a x +i\right)^{2}}{6}+\frac{i a^{3} c \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{3}-\frac{i a^{3} c \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{3}+\frac{i a^{3} c \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{3}-\frac{2 i a^{3} c \ln \left(a x \right) \ln \left(-i a x +1\right)}{3}"," ",0,"-1/3*c*arctan(a*x)^2/x^3-a^2*c*arctan(a*x)^2/x-1/3*a*c*arctan(a*x)/x^2+4/3*a^3*c*arctan(a*x)*ln(a*x)-2/3*a^3*c*arctan(a*x)*ln(a^2*x^2+1)-1/3*a^2*c/x-1/3*a^3*c*arctan(a*x)+2/3*I*a^3*c*ln(a*x)*ln(1+I*a*x)+1/3*I*a^3*c*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/6*I*a^3*c*ln(a*x-I)^2-1/3*I*a^3*c*ln(a*x-I)*ln(a^2*x^2+1)-1/3*I*a^3*c*ln(I+a*x)*ln(1/2*I*(a*x-I))-1/6*I*a^3*c*ln(I+a*x)^2+2/3*I*a^3*c*dilog(1+I*a*x)-1/3*I*a^3*c*dilog(1/2*I*(a*x-I))+1/3*I*a^3*c*dilog(-1/2*I*(I+a*x))+1/3*I*a^3*c*ln(I+a*x)*ln(a^2*x^2+1)-2/3*I*a^3*c*dilog(1-I*a*x)-2/3*I*a^3*c*ln(a*x)*ln(1-I*a*x)","B"
266,1,168,167,0.036000," ","int(x^3*(a^2*c*x^2+c)^2*arctan(a*x)^2,x)","-\frac{5 c^{2} x^{2}}{504 a^{2}}+\frac{c^{2} x^{4}}{84}+\frac{a^{2} c^{2} x^{6}}{168}+\frac{c^{2} x \arctan \left(a x \right)}{12 a^{3}}-\frac{c^{2} x^{3} \arctan \left(a x \right)}{36 a}-\frac{a \,c^{2} x^{5} \arctan \left(a x \right)}{12}-\frac{a^{3} c^{2} x^{7} \arctan \left(a x \right)}{28}-\frac{c^{2} \arctan \left(a x \right)^{2}}{24 a^{4}}+\frac{c^{2} x^{4} \arctan \left(a x \right)^{2}}{4}+\frac{a^{2} c^{2} x^{6} \arctan \left(a x \right)^{2}}{3}+\frac{a^{4} c^{2} x^{8} \arctan \left(a x \right)^{2}}{8}-\frac{2 c^{2} \ln \left(a^{2} x^{2}+1\right)}{63 a^{4}}"," ",0,"-5/504*c^2*x^2/a^2+1/84*c^2*x^4+1/168*a^2*c^2*x^6+1/12*c^2*x*arctan(a*x)/a^3-1/36*c^2*x^3*arctan(a*x)/a-1/12*a*c^2*x^5*arctan(a*x)-1/28*a^3*c^2*x^7*arctan(a*x)-1/24*c^2*arctan(a*x)^2/a^4+1/4*c^2*x^4*arctan(a*x)^2+1/3*a^2*c^2*x^6*arctan(a*x)^2+1/8*a^4*c^2*x^8*arctan(a*x)^2-2/63*c^2*ln(a^2*x^2+1)/a^4","A"
267,1,333,195,0.099000," ","int(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^2,x)","\frac{a^{4} c^{2} x^{7} \arctan \left(a x \right)^{2}}{7}+\frac{2 a^{2} c^{2} x^{5} \arctan \left(a x \right)^{2}}{5}+\frac{c^{2} x^{3} \arctan \left(a x \right)^{2}}{3}-\frac{a^{3} c^{2} x^{6} \arctan \left(a x \right)}{21}-\frac{9 a \,c^{2} x^{4} \arctan \left(a x \right)}{70}-\frac{8 c^{2} x^{2} \arctan \left(a x \right)}{105 a}+\frac{8 c^{2} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{105 a^{3}}+\frac{a^{2} c^{2} x^{5}}{105}+\frac{17 c^{2} x^{3}}{630}-\frac{c^{2} x}{210 a^{2}}+\frac{c^{2} \arctan \left(a x \right)}{210 a^{3}}+\frac{4 i c^{2} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{105 a^{3}}+\frac{2 i c^{2} \ln \left(a x +i\right)^{2}}{105 a^{3}}-\frac{4 i c^{2} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{105 a^{3}}+\frac{4 i c^{2} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{105 a^{3}}-\frac{4 i c^{2} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{105 a^{3}}+\frac{4 i c^{2} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{105 a^{3}}-\frac{4 i c^{2} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{105 a^{3}}-\frac{2 i c^{2} \ln \left(a x -i\right)^{2}}{105 a^{3}}"," ",0,"1/7*a^4*c^2*x^7*arctan(a*x)^2+2/5*a^2*c^2*x^5*arctan(a*x)^2+1/3*c^2*x^3*arctan(a*x)^2-1/21*a^3*c^2*x^6*arctan(a*x)-9/70*a*c^2*x^4*arctan(a*x)-8/105*c^2*x^2*arctan(a*x)/a+8/105/a^3*c^2*arctan(a*x)*ln(a^2*x^2+1)+1/105*a^2*c^2*x^5+17/630*c^2*x^3-1/210*c^2*x/a^2+1/210*c^2*arctan(a*x)/a^3+4/105*I/a^3*c^2*ln(a*x-I)*ln(a^2*x^2+1)+2/105*I/a^3*c^2*ln(I+a*x)^2-4/105*I/a^3*c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))-4/105*I/a^3*c^2*dilog(-1/2*I*(I+a*x))+4/105*I/a^3*c^2*dilog(1/2*I*(a*x-I))+4/105*I/a^3*c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))-4/105*I/a^3*c^2*ln(I+a*x)*ln(a^2*x^2+1)-2/105*I/a^3*c^2*ln(a*x-I)^2","A"
268,1,142,139,0.048000," ","int(x*(a^2*c*x^2+c)^2*arctan(a*x)^2,x)","\frac{a^{4} c^{2} \arctan \left(a x \right)^{2} x^{6}}{6}+\frac{a^{2} c^{2} \arctan \left(a x \right)^{2} x^{4}}{2}+\frac{c^{2} \arctan \left(a x \right)^{2} x^{2}}{2}-\frac{a^{3} c^{2} \arctan \left(a x \right) x^{5}}{15}-\frac{2 a \,c^{2} \arctan \left(a x \right) x^{3}}{9}-\frac{c^{2} x \arctan \left(a x \right)}{3 a}+\frac{c^{2} \arctan \left(a x \right)^{2}}{6 a^{2}}+\frac{a^{2} c^{2} x^{4}}{60}+\frac{7 c^{2} x^{2}}{90}+\frac{4 c^{2} \ln \left(a^{2} x^{2}+1\right)}{45 a^{2}}"," ",0,"1/6*a^4*c^2*arctan(a*x)^2*x^6+1/2*a^2*c^2*arctan(a*x)^2*x^4+1/2*c^2*arctan(a*x)^2*x^2-1/15*a^3*c^2*arctan(a*x)*x^5-2/9*a*c^2*arctan(a*x)*x^3-1/3*c^2*x*arctan(a*x)/a+1/6/a^2*c^2*arctan(a*x)^2+1/60*a^2*c^2*x^4+7/90*c^2*x^2+4/45*c^2*ln(a^2*x^2+1)/a^2","A"
269,1,304,181,0.098000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^2,x)","\frac{a^{4} c^{2} \arctan \left(a x \right)^{2} x^{5}}{5}+\frac{2 a^{2} c^{2} \arctan \left(a x \right)^{2} x^{3}}{3}+c^{2} x \arctan \left(a x \right)^{2}-\frac{a^{3} c^{2} \arctan \left(a x \right) x^{4}}{10}-\frac{7 a \,c^{2} \arctan \left(a x \right) x^{2}}{15}-\frac{8 c^{2} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{15 a}+\frac{a^{2} c^{2} x^{3}}{30}+\frac{11 c^{2} x}{30}-\frac{11 c^{2} \arctan \left(a x \right)}{30 a}-\frac{2 i c^{2} \ln \left(a x +i\right)^{2}}{15 a}+\frac{2 i c^{2} \ln \left(a x -i\right)^{2}}{15 a}+\frac{4 i c^{2} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{15 a}-\frac{4 i c^{2} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{15 a}+\frac{4 i c^{2} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{15 a}-\frac{4 i c^{2} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{15 a}-\frac{4 i c^{2} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{15 a}+\frac{4 i c^{2} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{15 a}"," ",0,"1/5*a^4*c^2*arctan(a*x)^2*x^5+2/3*a^2*c^2*arctan(a*x)^2*x^3+c^2*x*arctan(a*x)^2-1/10*a^3*c^2*arctan(a*x)*x^4-7/15*a*c^2*arctan(a*x)*x^2-8/15/a*c^2*arctan(a*x)*ln(a^2*x^2+1)+1/30*a^2*c^2*x^3+11/30*c^2*x-11/30/a*c^2*arctan(a*x)+4/15*I/a*c^2*dilog(-1/2*I*(I+a*x))-2/15*I/a*c^2*ln(I+a*x)^2+2/15*I/a*c^2*ln(a*x-I)^2-4/15*I/a*c^2*dilog(1/2*I*(a*x-I))+4/15*I/a*c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))-4/15*I/a*c^2*ln(a*x-I)*ln(a^2*x^2+1)-4/15*I/a*c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))+4/15*I/a*c^2*ln(I+a*x)*ln(a^2*x^2+1)","A"
270,1,1173,212,6.293000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^2/x,x)","\frac{a^{2} c^{2} x^{2}}{12}+a^{2} c^{2} x^{2} \arctan \left(a x \right)^{2}+\frac{i c^{2} \arctan \left(a x \right)^{2} \pi}{2}+i c^{2} \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)-2 i c^{2} \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i c^{2} \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+c^{2} \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+c^{2} \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{4 i c^{2} \arctan \left(a x \right)}{3}-c^{2} \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)+\frac{i c^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2}+\frac{3 c^{2} \arctan \left(a x \right)^{2}}{4}+2 c^{2} \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 c^{2} \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{c^{2} \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-\frac{4 c^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{3}-\frac{i c^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2}-\frac{i c^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2}-\frac{i c^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2}+\frac{i c^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2}+\frac{c^{2}}{12}-\frac{i c^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2}+\frac{i c^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2}+\frac{i c^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2}-\frac{3 a \,c^{2} x \arctan \left(a x \right)}{2}-\frac{a^{3} c^{2} x^{3} \arctan \left(a x \right)}{6}+\frac{a^{4} c^{2} x^{4} \arctan \left(a x \right)^{2}}{4}+c^{2} \arctan \left(a x \right)^{2} \ln \left(a x \right)"," ",0,"-1/2*I*c^2*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/12*a^2*c^2*x^2+a^2*c^2*x^2*arctan(a*x)^2+I*c^2*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+1/2*I*c^2*arctan(a*x)^2*Pi-2*I*c^2*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*c^2*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/2*I*c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-1/2*I*c^2*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-1/2*I*c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/2*I*c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+3/4*c^2*arctan(a*x)^2+2*c^2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*c^2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/2*c^2*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-4/3*c^2*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+1/2*I*c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+1/12*c^2-3/2*a*c^2*x*arctan(a*x)-1/6*a^3*c^2*x^3*arctan(a*x)+1/4*a^4*c^2*x^4*arctan(a*x)^2+c^2*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+c^2*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+4/3*I*c^2*arctan(a*x)+c^2*arctan(a*x)^2*ln(a*x)-c^2*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+1/2*I*c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3+1/2*I*c^2*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3","C"
271,1,346,184,0.118000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^2/x^2,x)","\frac{a^{4} c^{2} x^{3} \arctan \left(a x \right)^{2}}{3}+2 a^{2} c^{2} x \arctan \left(a x \right)^{2}-\frac{c^{2} \arctan \left(a x \right)^{2}}{x}-\frac{a^{3} c^{2} x^{2} \arctan \left(a x \right)}{3}+2 a \,c^{2} \arctan \left(a x \right) \ln \left(a x \right)-\frac{8 a \,c^{2} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3}+\frac{a^{2} c^{2} x}{3}-\frac{a \,c^{2} \arctan \left(a x \right)}{3}+\frac{4 i a \,c^{2} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{3}-i a \,c^{2} \dilog \left(-i a x +1\right)-\frac{2 i a \,c^{2} \ln \left(a x +i\right)^{2}}{3}+\frac{2 i a \,c^{2} \ln \left(a x -i\right)^{2}}{3}+\frac{4 i a \,c^{2} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{3}-\frac{4 i a \,c^{2} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{3}+\frac{4 i a \,c^{2} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{3}+i a \,c^{2} \dilog \left(i a x +1\right)-\frac{4 i a \,c^{2} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{3}+i a \,c^{2} \ln \left(a x \right) \ln \left(i a x +1\right)-\frac{4 i a \,c^{2} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{3}-i a \,c^{2} \ln \left(a x \right) \ln \left(-i a x +1\right)"," ",0,"1/3*a^4*c^2*x^3*arctan(a*x)^2+2*a^2*c^2*x*arctan(a*x)^2-c^2*arctan(a*x)^2/x-1/3*a^3*c^2*x^2*arctan(a*x)+2*a*c^2*arctan(a*x)*ln(a*x)-8/3*a*c^2*arctan(a*x)*ln(a^2*x^2+1)+1/3*a^2*c^2*x-1/3*a*c^2*arctan(a*x)+4/3*I*a*c^2*ln(I+a*x)*ln(a^2*x^2+1)-2/3*I*a*c^2*ln(I+a*x)^2+4/3*I*a*c^2*dilog(-1/2*I*(I+a*x))+2/3*I*a*c^2*ln(a*x-I)^2-4/3*I*a*c^2*dilog(1/2*I*(a*x-I))-I*a*c^2*dilog(1-I*a*x)+4/3*I*a*c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))+I*a*c^2*dilog(1+I*a*x)-4/3*I*a*c^2*ln(a*x-I)*ln(a^2*x^2+1)+I*a*c^2*ln(a*x)*ln(1+I*a*x)-4/3*I*a*c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))-I*a*c^2*ln(a*x)*ln(1-I*a*x)","A"
272,1,1255,196,5.533000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^2/x^3,x)","\frac{a^{4} c^{2} x^{2} \arctan \left(a x \right)^{2}}{2}-\frac{a \,c^{2} \arctan \left(a x \right)}{x}-a^{3} c^{2} x \arctan \left(a x \right)-\frac{c^{2} \arctan \left(a x \right)^{2}}{2 x^{2}}+i a^{2} c^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)+i a^{2} c^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}+i a^{2} c^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}-i a^{2} c^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}+i a^{2} c^{2} \arctan \left(a x \right)^{2} \pi +2 i a^{2} c^{2} \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)-4 i a^{2} c^{2} \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-4 i a^{2} c^{2} \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+a^{2} c^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-a^{2} c^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)+a^{2} c^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)-a^{2} c^{2} \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)+4 a^{2} c^{2} \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+4 a^{2} c^{2} \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 a^{2} c^{2} \arctan \left(a x \right)^{2} \ln \left(a x \right)-2 a^{2} c^{2} \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)+2 a^{2} c^{2} \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 a^{2} c^{2} \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+i a^{2} c^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)-i a^{2} c^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}-i a^{2} c^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}-i a^{2} c^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}"," ",0,"1/2*a^4*c^2*x^2*arctan(a*x)^2-a*c^2*arctan(a*x)/x-a^3*c^2*x*arctan(a*x)-1/2*c^2*arctan(a*x)^2/x^2+I*a^2*c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+I*a^2*c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3+I*a^2*c^2*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-I*a^2*c^2*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+a^2*c^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-a^2*c^2*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-a^2*c^2*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+a^2*c^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)+4*a^2*c^2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*a^2*c^2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*a^2*c^2*arctan(a*x)^2*Pi+2*I*a^2*c^2*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-4*I*a^2*c^2*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*I*a^2*c^2*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*a^2*c^2*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+2*a^2*c^2*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*a^2*c^2*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*a^2*c^2*arctan(a*x)^2*ln(a*x)+I*a^2*c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))-I*a^2*c^2*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-I*a^2*c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-I*a^2*c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2","C"
273,1,375,195,0.082000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^2/x^4,x)","a^{4} c^{2} x \arctan \left(a x \right)^{2}-\frac{c^{2} \arctan \left(a x \right)^{2}}{3 x^{3}}-\frac{2 a^{2} c^{2} \arctan \left(a x \right)^{2}}{x}-\frac{a \,c^{2} \arctan \left(a x \right)}{3 x^{2}}+\frac{10 a^{3} c^{2} \arctan \left(a x \right) \ln \left(a x \right)}{3}-\frac{8 a^{3} c^{2} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3}-\frac{a^{2} c^{2}}{3 x}-\frac{a^{3} c^{2} \arctan \left(a x \right)}{3}-\frac{2 i a^{3} c^{2} \ln \left(a x +i\right)^{2}}{3}+\frac{4 i a^{3} c^{2} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{3}-\frac{4 i a^{3} c^{2} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{3}+\frac{2 i a^{3} c^{2} \ln \left(a x -i\right)^{2}}{3}+\frac{5 i a^{3} c^{2} \ln \left(a x \right) \ln \left(i a x +1\right)}{3}-\frac{4 i a^{3} c^{2} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{3}-\frac{5 i a^{3} c^{2} \dilog \left(-i a x +1\right)}{3}-\frac{4 i a^{3} c^{2} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{3}+\frac{4 i a^{3} c^{2} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{3}-\frac{5 i a^{3} c^{2} \ln \left(a x \right) \ln \left(-i a x +1\right)}{3}+\frac{5 i a^{3} c^{2} \dilog \left(i a x +1\right)}{3}+\frac{4 i a^{3} c^{2} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{3}"," ",0,"a^4*c^2*x*arctan(a*x)^2-1/3*c^2*arctan(a*x)^2/x^3-2*a^2*c^2*arctan(a*x)^2/x-1/3*a*c^2*arctan(a*x)/x^2+10/3*a^3*c^2*arctan(a*x)*ln(a*x)-8/3*a^3*c^2*arctan(a*x)*ln(a^2*x^2+1)-1/3*a^2*c^2/x-1/3*a^3*c^2*arctan(a*x)+5/3*I*a^3*c^2*dilog(1+I*a*x)-2/3*I*a^3*c^2*ln(I+a*x)^2+4/3*I*a^3*c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))+4/3*I*a^3*c^2*dilog(-1/2*I*(I+a*x))+2/3*I*a^3*c^2*ln(a*x-I)^2+5/3*I*a^3*c^2*ln(a*x)*ln(1+I*a*x)-4/3*I*a^3*c^2*ln(a*x-I)*ln(a^2*x^2+1)-4/3*I*a^3*c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))+4/3*I*a^3*c^2*ln(I+a*x)*ln(a^2*x^2+1)-5/3*I*a^3*c^2*dilog(1-I*a*x)-5/3*I*a^3*c^2*ln(a*x)*ln(1-I*a*x)-4/3*I*a^3*c^2*dilog(1/2*I*(a*x-I))","A"
274,1,211,210,0.036000," ","int(x^3*(a^2*c*x^2+c)^3*arctan(a*x)^2,x)","-\frac{107 c^{3} x^{2}}{12600 a^{2}}+\frac{53 c^{3} x^{4}}{6300}+\frac{71 a^{2} c^{3} x^{6}}{7560}+\frac{a^{4} c^{3} x^{8}}{360}+\frac{c^{3} x \arctan \left(a x \right)}{20 a^{3}}-\frac{c^{3} x^{3} \arctan \left(a x \right)}{60 a}-\frac{9 a \,c^{3} x^{5} \arctan \left(a x \right)}{100}-\frac{11 a^{3} c^{3} x^{7} \arctan \left(a x \right)}{140}-\frac{a^{5} c^{3} x^{9} \arctan \left(a x \right)}{45}-\frac{c^{3} \arctan \left(a x \right)^{2}}{40 a^{4}}+\frac{c^{3} x^{4} \arctan \left(a x \right)^{2}}{4}+\frac{a^{2} c^{3} x^{6} \arctan \left(a x \right)^{2}}{2}+\frac{3 a^{4} c^{3} x^{8} \arctan \left(a x \right)^{2}}{8}+\frac{a^{6} c^{3} x^{10} \arctan \left(a x \right)^{2}}{10}-\frac{26 c^{3} \ln \left(a^{2} x^{2}+1\right)}{1575 a^{4}}"," ",0,"-107/12600*c^3*x^2/a^2+53/6300*c^3*x^4+71/7560*a^2*c^3*x^6+1/360*a^4*c^3*x^8+1/20*c^3*x*arctan(a*x)/a^3-1/60*c^3*x^3*arctan(a*x)/a-9/100*a*c^3*x^5*arctan(a*x)-11/140*a^3*c^3*x^7*arctan(a*x)-1/45*a^5*c^3*x^9*arctan(a*x)-1/40*c^3*arctan(a*x)^2/a^4+1/4*c^3*x^4*arctan(a*x)^2+1/2*a^2*c^3*x^6*arctan(a*x)^2+3/8*a^4*c^3*x^8*arctan(a*x)^2+1/10*a^6*c^3*x^10*arctan(a*x)^2-26/1575*c^3*ln(a^2*x^2+1)/a^4","A"
275,1,376,238,0.099000," ","int(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^2,x)","\frac{a^{6} c^{3} x^{9} \arctan \left(a x \right)^{2}}{9}+\frac{3 a^{4} c^{3} x^{7} \arctan \left(a x \right)^{2}}{7}+\frac{3 a^{2} c^{3} x^{5} \arctan \left(a x \right)^{2}}{5}+\frac{c^{3} x^{3} \arctan \left(a x \right)^{2}}{3}-\frac{a^{5} c^{3} x^{8} \arctan \left(a x \right)}{36}-\frac{20 a^{3} c^{3} x^{6} \arctan \left(a x \right)}{189}-\frac{89 a \,c^{3} x^{4} \arctan \left(a x \right)}{630}-\frac{16 c^{3} x^{2} \arctan \left(a x \right)}{315 a}+\frac{16 c^{3} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{315 a^{3}}+\frac{a^{4} c^{3} x^{7}}{252}+\frac{59 a^{2} c^{3} x^{5}}{3780}+\frac{239 c^{3} x^{3}}{11340}-\frac{47 c^{3} x}{3780 a^{2}}+\frac{47 c^{3} \arctan \left(a x \right)}{3780 a^{3}}-\frac{8 i c^{3} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{315 a^{3}}-\frac{4 i c^{3} \ln \left(a x -i\right)^{2}}{315 a^{3}}+\frac{8 i c^{3} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{315 a^{3}}-\frac{8 i c^{3} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{315 a^{3}}+\frac{4 i c^{3} \ln \left(a x +i\right)^{2}}{315 a^{3}}-\frac{8 i c^{3} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{315 a^{3}}+\frac{8 i c^{3} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{315 a^{3}}+\frac{8 i c^{3} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{315 a^{3}}"," ",0,"1/9*a^6*c^3*x^9*arctan(a*x)^2+3/7*a^4*c^3*x^7*arctan(a*x)^2+3/5*a^2*c^3*x^5*arctan(a*x)^2+1/3*c^3*x^3*arctan(a*x)^2-1/36*a^5*c^3*x^8*arctan(a*x)-20/189*a^3*c^3*x^6*arctan(a*x)-89/630*a*c^3*x^4*arctan(a*x)-16/315*c^3*x^2*arctan(a*x)/a+16/315/a^3*c^3*arctan(a*x)*ln(a^2*x^2+1)+1/252*a^4*c^3*x^7+59/3780*a^2*c^3*x^5+239/11340*c^3*x^3-47/3780*c^3*x/a^2+47/3780*c^3*arctan(a*x)/a^3-8/315*I/a^3*c^3*ln(I+a*x)*ln(a^2*x^2+1)+8/315*I/a^3*c^3*dilog(1/2*I*(a*x-I))-4/315*I/a^3*c^3*ln(a*x-I)^2+8/315*I/a^3*c^3*ln(a*x-I)*ln(a^2*x^2+1)-8/315*I/a^3*c^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))+4/315*I/a^3*c^3*ln(I+a*x)^2-8/315*I/a^3*c^3*dilog(-1/2*I*(I+a*x))+8/315*I/a^3*c^3*ln(I+a*x)*ln(1/2*I*(a*x-I))","A"
276,1,185,182,0.037000," ","int(x*(a^2*c*x^2+c)^3*arctan(a*x)^2,x)","\frac{a^{6} c^{3} \arctan \left(a x \right)^{2} x^{8}}{8}+\frac{a^{4} c^{3} \arctan \left(a x \right)^{2} x^{6}}{2}+\frac{3 a^{2} c^{3} \arctan \left(a x \right)^{2} x^{4}}{4}+\frac{c^{3} \arctan \left(a x \right)^{2} x^{2}}{2}-\frac{a^{5} c^{3} \arctan \left(a x \right) x^{7}}{28}-\frac{3 a^{3} c^{3} \arctan \left(a x \right) x^{5}}{20}-\frac{a \,c^{3} \arctan \left(a x \right) x^{3}}{4}-\frac{c^{3} x \arctan \left(a x \right)}{4 a}+\frac{c^{3} \arctan \left(a x \right)^{2}}{8 a^{2}}+\frac{a^{4} c^{3} x^{6}}{168}+\frac{a^{2} x^{4} c^{3}}{35}+\frac{19 x^{2} c^{3}}{280}+\frac{2 c^{3} \ln \left(a^{2} x^{2}+1\right)}{35 a^{2}}"," ",0,"1/8*a^6*c^3*arctan(a*x)^2*x^8+1/2*a^4*c^3*arctan(a*x)^2*x^6+3/4*a^2*c^3*arctan(a*x)^2*x^4+1/2*c^3*arctan(a*x)^2*x^2-1/28*a^5*c^3*arctan(a*x)*x^7-3/20*a^3*c^3*arctan(a*x)*x^5-1/4*a*c^3*arctan(a*x)*x^3-1/4*c^3*x*arctan(a*x)/a+1/8/a^2*c^3*arctan(a*x)^2+1/168*a^4*c^3*x^6+1/35*a^2*x^4*c^3+19/280*x^2*c^3+2/35*c^3*ln(a^2*x^2+1)/a^2","A"
277,1,346,238,0.107000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^2,x)","\frac{a^{6} c^{3} \arctan \left(a x \right)^{2} x^{7}}{7}+\frac{3 a^{4} c^{3} \arctan \left(a x \right)^{2} x^{5}}{5}+a^{2} c^{3} \arctan \left(a x \right)^{2} x^{3}+c^{3} x \arctan \left(a x \right)^{2}-\frac{a^{5} c^{3} \arctan \left(a x \right) x^{6}}{21}-\frac{8 a^{3} c^{3} \arctan \left(a x \right) x^{4}}{35}-\frac{19 a \,c^{3} \arctan \left(a x \right) x^{2}}{35}-\frac{16 c^{3} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{35 a}+\frac{a^{4} c^{3} x^{5}}{105}+\frac{19 a^{2} c^{3} x^{3}}{315}+\frac{38 c^{3} x}{105}-\frac{38 c^{3} \arctan \left(a x \right)}{105 a}-\frac{8 i c^{3} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{35 a}+\frac{8 i c^{3} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{35 a}-\frac{4 i c^{3} \ln \left(a x +i\right)^{2}}{35 a}-\frac{8 i c^{3} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{35 a}+\frac{4 i c^{3} \ln \left(a x -i\right)^{2}}{35 a}+\frac{8 i c^{3} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{35 a}+\frac{8 i c^{3} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{35 a}-\frac{8 i c^{3} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{35 a}"," ",0,"1/7*a^6*c^3*arctan(a*x)^2*x^7+3/5*a^4*c^3*arctan(a*x)^2*x^5+a^2*c^3*arctan(a*x)^2*x^3+c^3*x*arctan(a*x)^2-1/21*a^5*c^3*arctan(a*x)*x^6-8/35*a^3*c^3*arctan(a*x)*x^4-19/35*a*c^3*arctan(a*x)*x^2-16/35/a*c^3*arctan(a*x)*ln(a^2*x^2+1)+1/105*a^4*c^3*x^5+19/315*a^2*c^3*x^3+38/105*c^3*x-38/105/a*c^3*arctan(a*x)-8/35*I/a*c^3*ln(I+a*x)*ln(1/2*I*(a*x-I))+8/35*I/a*c^3*ln(I+a*x)*ln(a^2*x^2+1)-4/35*I/a*c^3*ln(I+a*x)^2-8/35*I/a*c^3*dilog(1/2*I*(a*x-I))+8/35*I/a*c^3*dilog(-1/2*I*(I+a*x))+4/35*I/a*c^3*ln(a*x-I)^2+8/35*I/a*c^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))-8/35*I/a*c^3*ln(a*x-I)*ln(a^2*x^2+1)","A"
278,1,1217,256,11.000000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^2/x,x)","\frac{i c^{3} \pi  \arctan \left(a x \right)^{2}}{2}-2 i c^{3} \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i c^{3} \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+i c^{3} \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)-\frac{11 a \,c^{3} x \arctan \left(a x \right)}{6}-\frac{7 a^{3} c^{3} x^{3} \arctan \left(a x \right)}{18}-\frac{a^{5} c^{3} x^{5} \arctan \left(a x \right)}{15}+\frac{3 a^{2} c^{3} x^{2} \arctan \left(a x \right)^{2}}{2}+\frac{3 a^{4} c^{3} x^{4} \arctan \left(a x \right)^{2}}{4}+\frac{a^{6} c^{3} x^{6} \arctan \left(a x \right)^{2}}{6}+\frac{29 a^{2} c^{3} x^{2}}{180}+\frac{a^{4} c^{3} x^{4}}{60}+\frac{11 c^{3} \arctan \left(a x \right)^{2}}{12}+\frac{i c^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2}-c^{3} \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)+c^{3} \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+c^{3} \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{68 i c^{3} \arctan \left(a x \right)}{45}+\frac{i c^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2}-\frac{i c^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}+\frac{i c^{3} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2}-\frac{68 c^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{45}-\frac{c^{3} \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+2 c^{3} \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 c^{3} \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{i c^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}+\frac{i c^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2}-\frac{i c^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2}-\frac{i c^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2}+\frac{13 c^{3}}{90}+c^{3} \arctan \left(a x \right)^{2} \ln \left(a x \right)"," ",0,"1/2*I*c^3*Pi*arctan(a*x)^2-2*I*c^3*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*c^3*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-11/6*a*c^3*x*arctan(a*x)-7/18*a^3*c^3*x^3*arctan(a*x)-1/15*a^5*c^3*x^5*arctan(a*x)+3/2*a^2*c^3*x^2*arctan(a*x)^2+3/4*a^4*c^3*x^4*arctan(a*x)^2+1/6*a^6*c^3*x^6*arctan(a*x)^2+29/180*a^2*c^3*x^2+1/60*a^4*c^3*x^4-1/2*c^3*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+2*c^3*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*c^3*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-68/45*c^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+11/12*c^3*arctan(a*x)^2+1/2*I*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2+1/2*I*c^3*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2-1/2*I*c^3*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+1/2*I*c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3+I*c^3*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-1/2*I*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+1/2*I*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-1/2*I*c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-1/2*I*c^3*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+13/90*c^3+c^3*arctan(a*x)^2*ln(a*x)-c^3*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+c^3*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+c^3*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+68/45*I*c^3*arctan(a*x)","C"
279,1,388,226,0.109000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^2/x^2,x)","\frac{a^{6} c^{3} x^{5} \arctan \left(a x \right)^{2}}{5}+a^{4} c^{3} x^{3} \arctan \left(a x \right)^{2}+3 a^{2} c^{3} x \arctan \left(a x \right)^{2}-\frac{c^{3} \arctan \left(a x \right)^{2}}{x}-\frac{a^{5} c^{3} x^{4} \arctan \left(a x \right)}{10}-\frac{4 a^{3} c^{3} x^{2} \arctan \left(a x \right)}{5}+2 a \,c^{3} \arctan \left(a x \right) \ln \left(a x \right)-\frac{16 a \,c^{3} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{5}+\frac{a^{4} c^{3} x^{3}}{30}+\frac{7 a^{2} c^{3} x}{10}-\frac{7 a \,c^{3} \arctan \left(a x \right)}{10}+\frac{4 i a \,c^{3} \ln \left(a x -i\right)^{2}}{5}+i a \,c^{3} \dilog \left(i a x +1\right)-\frac{8 i a \,c^{3} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{5}-\frac{8 i a \,c^{3} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{5}-\frac{8 i a \,c^{3} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{5}+\frac{8 i a \,c^{3} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{5}-\frac{4 i a \,c^{3} \ln \left(a x +i\right)^{2}}{5}+i a \,c^{3} \ln \left(a x \right) \ln \left(i a x +1\right)-i a \,c^{3} \ln \left(a x \right) \ln \left(-i a x +1\right)-i a \,c^{3} \dilog \left(-i a x +1\right)+\frac{8 i a \,c^{3} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{5}+\frac{8 i a \,c^{3} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{5}"," ",0,"1/5*a^6*c^3*x^5*arctan(a*x)^2+a^4*c^3*x^3*arctan(a*x)^2+3*a^2*c^3*x*arctan(a*x)^2-c^3*arctan(a*x)^2/x-1/10*a^5*c^3*x^4*arctan(a*x)-4/5*a^3*c^3*x^2*arctan(a*x)+2*a*c^3*arctan(a*x)*ln(a*x)-16/5*a*c^3*arctan(a*x)*ln(a^2*x^2+1)+1/30*a^4*c^3*x^3+7/10*a^2*c^3*x-7/10*a*c^3*arctan(a*x)+I*a*c^3*dilog(1+I*a*x)+8/5*I*a*c^3*dilog(-1/2*I*(I+a*x))-I*a*c^3*dilog(1-I*a*x)+4/5*I*a*c^3*ln(a*x-I)^2-8/5*I*a*c^3*ln(I+a*x)*ln(1/2*I*(a*x-I))-8/5*I*a*c^3*ln(a*x-I)*ln(a^2*x^2+1)+8/5*I*a*c^3*ln(I+a*x)*ln(a^2*x^2+1)-4/5*I*a*c^3*ln(I+a*x)^2+I*a*c^3*ln(a*x)*ln(1+I*a*x)-I*a*c^3*ln(a*x)*ln(1-I*a*x)-8/5*I*a*c^3*dilog(1/2*I*(a*x-I))+8/5*I*a*c^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))","A"
280,1,1333,272,13.522000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^2/x^3,x)","\frac{4 i a^{2} c^{3} \arctan \left(a x \right)}{3}+3 a^{2} c^{3} \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 a^{2} c^{3} \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 a^{2} c^{3} \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)+6 a^{2} c^{3} \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 a^{2} c^{3} \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 a^{2} c^{3} \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-\frac{7 a^{2} c^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{3}+a^{2} c^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+a^{2} c^{3} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)+\frac{3 i a^{2} c^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2}-\frac{3 i a^{2} c^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}-\frac{3 i a^{2} c^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2}-\frac{3 i a^{2} c^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2}+\frac{a^{4} c^{3} x^{2}}{12}+\frac{3 a^{2} c^{3} \arctan \left(a x \right)^{2}}{4}-\frac{c^{3} \arctan \left(a x \right)^{2}}{2 x^{2}}+3 i a^{2} c^{3} \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)-6 i a^{2} c^{3} \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i a^{2} c^{3} \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{3 i a^{2} c^{3} \pi  \arctan \left(a x \right)^{2}}{2}-\frac{a \,c^{3} \arctan \left(a x \right)}{x}+\frac{c^{3} a^{2}}{12}-\frac{5 a^{3} c^{3} x \arctan \left(a x \right)}{2}-\frac{a^{5} c^{3} x^{3} \arctan \left(a x \right)}{6}+\frac{3 a^{4} c^{3} x^{2} \arctan \left(a x \right)^{2}}{2}+\frac{a^{6} c^{3} x^{4} \arctan \left(a x \right)^{2}}{4}+\frac{3 i a^{2} c^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2}-\frac{3 i a^{2} c^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}+\frac{3 i a^{2} c^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2}+\frac{3 i a^{2} c^{3} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2}+3 a^{2} c^{3} \arctan \left(a x \right)^{2} \ln \left(a x \right)"," ",0,"4/3*I*a^2*c^3*arctan(a*x)+1/12*a^4*c^3*x^2+3/4*a^2*c^3*arctan(a*x)^2-1/2*c^3*arctan(a*x)^2/x^2+3*I*a^2*c^3*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+3/2*I*a^2*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-3/2*I*a^2*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-3/2*I*a^2*c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-6*I*a^2*c^3*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*a^2*c^3*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/2*I*a^2*c^3*Pi*arctan(a*x)^2-a*c^3*arctan(a*x)/x-3/2*I*a^2*c^3*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/12*c^3*a^2-5/2*a^3*c^3*x*arctan(a*x)-1/6*a^5*c^3*x^3*arctan(a*x)+3/2*a^4*c^3*x^2*arctan(a*x)^2+1/4*a^6*c^3*x^4*arctan(a*x)^2+3/2*I*a^2*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-3/2*I*a^2*c^3*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+3/2*I*a^2*c^3*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2+3/2*I*a^2*c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3+6*a^2*c^3*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*a^2*c^3*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-7/3*a^2*c^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+a^2*c^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+a^2*c^3*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)-3/2*a^2*c^3*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+3*a^2*c^3*arctan(a*x)^2*ln(a*x)+3*a^2*c^3*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2*c^3*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*a^2*c^3*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)","C"
281,1,417,222,0.115000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^2/x^4,x)","\frac{a^{6} c^{3} x^{3} \arctan \left(a x \right)^{2}}{3}+3 a^{4} c^{3} x \arctan \left(a x \right)^{2}-\frac{c^{3} \arctan \left(a x \right)^{2}}{3 x^{3}}-\frac{3 a^{2} c^{3} \arctan \left(a x \right)^{2}}{x}-\frac{a^{5} c^{3} x^{2} \arctan \left(a x \right)}{3}-\frac{a \,c^{3} \arctan \left(a x \right)}{3 x^{2}}+\frac{16 a^{3} c^{3} \arctan \left(a x \right) \ln \left(a x \right)}{3}-\frac{16 a^{3} c^{3} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3}+\frac{a^{4} c^{3} x}{3}-\frac{a^{2} c^{3}}{3 x}-\frac{2 a^{3} c^{3} \arctan \left(a x \right)}{3}+\frac{8 i a^{3} c^{3} \ln \left(a x \right) \ln \left(i a x +1\right)}{3}-\frac{8 i a^{3} c^{3} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{3}-\frac{8 i a^{3} c^{3} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{3}-\frac{8 i a^{3} c^{3} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{3}-\frac{4 i a^{3} c^{3} \ln \left(a x +i\right)^{2}}{3}+\frac{8 i a^{3} c^{3} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{3}+\frac{4 i a^{3} c^{3} \ln \left(a x -i\right)^{2}}{3}+\frac{8 i a^{3} c^{3} \dilog \left(i a x +1\right)}{3}+\frac{8 i a^{3} c^{3} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{3}-\frac{8 i a^{3} c^{3} \dilog \left(-i a x +1\right)}{3}+\frac{8 i a^{3} c^{3} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{3}-\frac{8 i a^{3} c^{3} \ln \left(a x \right) \ln \left(-i a x +1\right)}{3}"," ",0,"1/3*a^6*c^3*x^3*arctan(a*x)^2+3*a^4*c^3*x*arctan(a*x)^2-1/3*c^3*arctan(a*x)^2/x^3-3*a^2*c^3*arctan(a*x)^2/x-1/3*a^5*c^3*x^2*arctan(a*x)-1/3*a*c^3*arctan(a*x)/x^2+16/3*a^3*c^3*arctan(a*x)*ln(a*x)-16/3*a^3*c^3*arctan(a*x)*ln(a^2*x^2+1)+1/3*a^4*c^3*x-1/3*a^2*c^3/x-2/3*a^3*c^3*arctan(a*x)+8/3*I*a^3*c^3*dilog(-1/2*I*(I+a*x))+8/3*I*a^3*c^3*ln(a*x)*ln(1+I*a*x)-8/3*I*a^3*c^3*dilog(1/2*I*(a*x-I))-8/3*I*a^3*c^3*ln(a*x-I)*ln(a^2*x^2+1)-8/3*I*a^3*c^3*ln(I+a*x)*ln(1/2*I*(a*x-I))-4/3*I*a^3*c^3*ln(I+a*x)^2+8/3*I*a^3*c^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))+4/3*I*a^3*c^3*ln(a*x-I)^2-8/3*I*a^3*c^3*dilog(1-I*a*x)+8/3*I*a^3*c^3*dilog(1+I*a*x)+8/3*I*a^3*c^3*ln(I+a*x)*ln(a^2*x^2+1)-8/3*I*a^3*c^3*ln(a*x)*ln(1-I*a*x)","A"
282,1,284,146,0.101000," ","int(x^4*arctan(a*x)^2/(a^2*c*x^2+c),x)","\frac{x^{3} \arctan \left(a x \right)^{2}}{3 a^{2} c}-\frac{x \arctan \left(a x \right)^{2}}{a^{4} c}+\frac{\arctan \left(a x \right)^{3}}{3 a^{5} c}-\frac{x^{2} \arctan \left(a x \right)}{3 a^{3} c}+\frac{4 \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3 a^{5} c}+\frac{x}{3 a^{4} c}-\frac{\arctan \left(a x \right)}{3 a^{5} c}+\frac{2 i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{3 a^{5} c}+\frac{2 i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{3 a^{5} c}-\frac{i \ln \left(a x -i\right)^{2}}{3 a^{5} c}-\frac{2 i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{3 a^{5} c}-\frac{2 i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{3 a^{5} c}-\frac{2 i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{3 a^{5} c}+\frac{2 i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{3 a^{5} c}+\frac{i \ln \left(a x +i\right)^{2}}{3 a^{5} c}"," ",0,"1/3*x^3*arctan(a*x)^2/a^2/c-x*arctan(a*x)^2/a^4/c+1/3*arctan(a*x)^3/a^5/c-1/3*x^2*arctan(a*x)/a^3/c+4/3/a^5/c*arctan(a*x)*ln(a^2*x^2+1)+1/3*x/a^4/c-1/3*arctan(a*x)/a^5/c+2/3*I/a^5/c*ln(I+a*x)*ln(1/2*I*(a*x-I))+2/3*I/a^5/c*ln(a*x-I)*ln(a^2*x^2+1)-1/3*I/a^5/c*ln(a*x-I)^2-2/3*I/a^5/c*ln(I+a*x)*ln(a^2*x^2+1)-2/3*I/a^5/c*ln(a*x-I)*ln(-1/2*I*(I+a*x))-2/3*I/a^5/c*dilog(-1/2*I*(I+a*x))+2/3*I/a^5/c*dilog(1/2*I*(a*x-I))+1/3*I/a^5/c*ln(I+a*x)^2","A"
283,1,1695,154,1.520000," ","int(x^3*arctan(a*x)^2/(a^2*c*x^2+c),x)","-\frac{\arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 a^{4} c}+\frac{\arctan \left(a x \right)^{2}}{2 a^{4} c}-\frac{\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{3} \arctan \left(a x \right)^{2} \pi  x}{8 a^{3} c}+\frac{\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{2} \pi  x}{8 a^{3} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{3} \arctan \left(a x \right)^{2} \pi}{8 a^{4} c}+\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{2} \pi}{8 a^{4} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c}+\frac{\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \arctan \left(a x \right)^{2} \pi  x}{8 a^{3} c}+\frac{\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \arctan \left(a x \right)^{2} \pi  x}{4 a^{3} c}-\frac{\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \arctan \left(a x \right)^{2} \pi  x}{8 a^{3} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)^{2} \pi}{2 a^{4} c}-\frac{\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \arctan \left(a x \right)^{2} \pi  x}{4 a^{3} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c}+\frac{i \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \arctan \left(a x \right)^{2} \pi}{4 a^{4} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \arctan \left(a x \right)^{2} \pi}{8 a^{4} c}-\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \arctan \left(a x \right)^{2} \pi}{4 a^{4} c}-\frac{x \arctan \left(a x \right)}{a^{3} c}+\frac{x^{2} \arctan \left(a x \right)^{2}}{2 a^{2} c}+\frac{\polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{4} c}-\frac{\ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{a^{4} c}+\frac{\arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{4} c}+\frac{i \arctan \left(a x \right)}{a^{4} c}-\frac{i \arctan \left(a x \right)^{3}}{3 a^{4} c}-\frac{i \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{a^{4} c}+\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \arctan \left(a x \right)^{2} \pi}{8 a^{4} c}+\frac{\ln \left(2\right) \arctan \left(a x \right)^{2}}{a^{4} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(a x \right)^{2} \pi}{4 a^{4} c}"," ",0,"1/8/a^3/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2*Pi*x+1/4/a^3/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*arctan(a*x)^2*Pi*x-1/8/a^3/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*arctan(a*x)^2*Pi*x+1/2*I/a^4/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^2*Pi-1/2/a^4/c*arctan(a*x)^2*ln(a^2*x^2+1)+1/a^4/c*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+I/a^4/c*arctan(a*x)-1/3*I/a^4/c*arctan(a*x)^3+1/2*arctan(a*x)^2/a^4/c-1/4/a^3/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2*Pi*x-x*arctan(a*x)/a^3/c+1/2*x^2*arctan(a*x)^2/a^2/c-1/8/a^3/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*arctan(a*x)^2*Pi*x+1/8/a^3/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*Pi*x+1/8*I/a^4/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*arctan(a*x)^2*Pi+1/8*I/a^4/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*Pi-1/4*I/a^4/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*Pi-1/4*I/a^4/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*arctan(a*x)^2*Pi+1/2/a^4/c*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+1/4*I/a^4/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*Pi-1/4*I/a^4/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*arctan(a*x)^2*Pi+1/4*I/a^4/c*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*Pi-1/4*I/a^4/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*arctan(a*x)^2*Pi+1/8*I/a^4/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*arctan(a*x)^2*Pi-1/4*I/a^4/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2*Pi+1/8*I/a^4/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2*Pi-1/a^4/c*ln((1+I*a*x)^2/(a^2*x^2+1)+1)-I/a^4/c*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+1/a^4/c*ln(2)*arctan(a*x)^2-1/4*I/a^4/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*Pi","C"
284,1,230,92,0.094000," ","int(x^2*arctan(a*x)^2/(a^2*c*x^2+c),x)","\frac{x \arctan \left(a x \right)^{2}}{a^{2} c}-\frac{\arctan \left(a x \right)^{3}}{3 a^{3} c}-\frac{\arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{a^{3} c}-\frac{i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{2 a^{3} c}+\frac{i \ln \left(a x -i\right)^{2}}{4 a^{3} c}+\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 a^{3} c}+\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 a^{3} c}+\frac{i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{2 a^{3} c}-\frac{i \ln \left(a x +i\right)^{2}}{4 a^{3} c}-\frac{i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{2 a^{3} c}-\frac{i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{2 a^{3} c}"," ",0,"x*arctan(a*x)^2/a^2/c-1/3*arctan(a*x)^3/a^3/c-1/a^3/c*arctan(a*x)*ln(a^2*x^2+1)-1/2*I/a^3/c*ln(a*x-I)*ln(a^2*x^2+1)+1/4*I/a^3/c*ln(a*x-I)^2+1/2*I/a^3/c*dilog(-1/2*I*(I+a*x))+1/2*I/a^3/c*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/2*I/a^3/c*ln(I+a*x)*ln(a^2*x^2+1)-1/4*I/a^3/c*ln(I+a*x)^2-1/2*I/a^3/c*dilog(1/2*I*(a*x-I))-1/2*I/a^3/c*ln(I+a*x)*ln(1/2*I*(a*x-I))","B"
285,1,897,93,0.576000," ","int(x*arctan(a*x)^2/(a^2*c*x^2+c),x)","\frac{\arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 a^{2} c}-\frac{\arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{2} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(a x \right)^{2} \pi}{4 a^{2} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)^{2} \pi}{2 a^{2} c}-\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \arctan \left(a x \right)^{2} \pi}{4 a^{2} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 a^{2} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 a^{2} c}+\frac{i \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{a^{2} c}-\frac{i \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 a^{2} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \arctan \left(a x \right)^{2} \pi}{4 a^{2} c}-\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{2} \pi}{4 a^{2} c}+\frac{i \arctan \left(a x \right)^{3}}{3 a^{2} c}-\frac{\ln \left(2\right) \arctan \left(a x \right)^{2}}{a^{2} c}+\frac{i \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(a x \right)^{2} \pi}{4 a^{2} c}-\frac{\polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{2} c}+\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \arctan \left(a x \right)^{2} \pi}{2 a^{2} c}"," ",0,"1/2/a^2/c*arctan(a*x)^2*ln(a^2*x^2+1)-1/a^2/c*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+1/4*I/a^2/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*Pi-1/2*I/a^2/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^2*Pi-1/4*I/a^2/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*Pi-1/4*I/a^2/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*Pi+1/4*I/a^2/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*arctan(a*x)^2*Pi-1/4*I/a^2/c*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*Pi+1/4*I/a^2/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*arctan(a*x)^2*Pi+I/a^2/c*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-1/4*I/a^2/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*Pi+1/3*I/a^2/c*arctan(a*x)^3-1/a^2/c*ln(2)*arctan(a*x)^2+1/4*I/a^2/c*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*Pi-1/2/a^2/c*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+1/2*I/a^2/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*Pi","C"
286,1,15,14,0.026000," ","int(arctan(a*x)^2/(a^2*c*x^2+c),x)","\frac{\arctan \left(a x \right)^{3}}{3 a c}"," ",0,"1/3*arctan(a*x)^3/a/c","A"
287,1,1767,82,0.297000," ","int(arctan(a*x)^2/x/(a^2*c*x^2+c),x)","\frac{\arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{\arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c}-\frac{i \arctan \left(a x \right)^{3}}{3 c}+\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4 c}+\frac{i \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2 c}-\frac{i \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c}-\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4 c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2 c}-\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{4 c}-\frac{2 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{\arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 c}+\frac{\arctan \left(a x \right)^{2} \ln \left(a x \right)}{c}+\frac{\arctan \left(a x \right)^{2} \ln \left(2\right)}{c}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c}+\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{4 c}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2 c}-\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 c}+\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2}}{2 c}-\frac{i \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c}+\frac{i \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2 c}-\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{4 c}+\frac{i \pi  \arctan \left(a x \right)^{2}}{2 c}-\frac{2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2 c}+\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c}+\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c}+\frac{2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}"," ",0,"-1/2/c*arctan(a*x)^2*ln(a^2*x^2+1)+1/c*arctan(a*x)^2*ln(a*x)+1/c*arctan(a*x)^2*ln(2)+1/c*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/c*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)-1/3*I*arctan(a*x)^3/c+1/4*I/c*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+1/2*I/c*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2-1/2*I/c*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-1/4*I/c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+1/2*I/c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2-1/4*I/c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3-1/2*I/c*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-1/2*I/c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+1/4*I/c*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+1/2*I/c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-1/4*I/c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))+1/2*I/c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2-1/2*I/c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-1/2*I/c*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+1/4*I/c*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+1/4*I/c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+1/2*I/c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-1/4*I/c*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-2*I/c*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/2*I/c*Pi*arctan(a*x)^2-2*I/c*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+2/c*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2/c*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))","C"
288,1,292,86,0.123000," ","int(arctan(a*x)^2/x^2/(a^2*c*x^2+c),x)","-\frac{\arctan \left(a x \right)^{2}}{c x}-\frac{a \arctan \left(a x \right)^{3}}{3 c}+\frac{2 a \arctan \left(a x \right) \ln \left(a x \right)}{c}-\frac{a \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{c}+\frac{i a \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 c}-\frac{i a \ln \left(a x +i\right)^{2}}{4 c}-\frac{i a \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{2 c}-\frac{i a \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{2 c}-\frac{i a \dilog \left(-i a x +1\right)}{c}+\frac{i a \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 c}+\frac{i a \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{2 c}+\frac{i a \ln \left(a x \right) \ln \left(i a x +1\right)}{c}+\frac{i a \dilog \left(i a x +1\right)}{c}-\frac{i a \ln \left(a x \right) \ln \left(-i a x +1\right)}{c}+\frac{i a \ln \left(a x -i\right)^{2}}{4 c}-\frac{i a \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{2 c}"," ",0,"-arctan(a*x)^2/c/x-1/3*a*arctan(a*x)^3/c+2*a/c*arctan(a*x)*ln(a*x)-a/c*arctan(a*x)*ln(a^2*x^2+1)+1/2*I*a/c*ln(a*x-I)*ln(-1/2*I*(I+a*x))-1/4*I*a/c*ln(I+a*x)^2-1/2*I*a/c*ln(I+a*x)*ln(1/2*I*(a*x-I))+1/2*I*a/c*dilog(-1/2*I*(I+a*x))-1/2*I*a/c*dilog(1/2*I*(a*x-I))+1/2*I*a/c*ln(I+a*x)*ln(a^2*x^2+1)+I*a/c*ln(a*x)*ln(1+I*a*x)+I*a/c*dilog(1+I*a*x)-I*a/c*dilog(1-I*a*x)-I*a/c*ln(a*x)*ln(1-I*a*x)+1/4*I*a/c*ln(a*x-I)^2-1/2*I*a/c*ln(a*x-I)*ln(a^2*x^2+1)","B"
289,1,5491,163,1.038000," ","int(arctan(a*x)^2/x^3/(a^2*c*x^2+c),x)","\text{output too large to display}"," ",0,"result too large to display","C"
290,1,374,146,0.115000," ","int(arctan(a*x)^2/x^4/(a^2*c*x^2+c),x)","-\frac{\arctan \left(a x \right)^{2}}{3 c \,x^{3}}+\frac{a^{2} \arctan \left(a x \right)^{2}}{c x}+\frac{a^{3} \arctan \left(a x \right)^{3}}{3 c}-\frac{a \arctan \left(a x \right)}{3 c \,x^{2}}-\frac{8 a^{3} \arctan \left(a x \right) \ln \left(a x \right)}{3 c}+\frac{4 a^{3} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3 c}-\frac{a^{2}}{3 c x}-\frac{a^{3} \arctan \left(a x \right)}{3 c}-\frac{i a^{3} \ln \left(a x -i\right)^{2}}{3 c}+\frac{4 i a^{3} \ln \left(a x \right) \ln \left(-i a x +1\right)}{3 c}+\frac{4 i a^{3} \dilog \left(-i a x +1\right)}{3 c}-\frac{2 i a^{3} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{3 c}+\frac{2 i a^{3} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{3 c}-\frac{2 i a^{3} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{3 c}+\frac{2 i a^{3} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{3 c}+\frac{2 i a^{3} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{3 c}-\frac{4 i a^{3} \ln \left(a x \right) \ln \left(i a x +1\right)}{3 c}+\frac{i a^{3} \ln \left(a x +i\right)^{2}}{3 c}-\frac{2 i a^{3} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{3 c}-\frac{4 i a^{3} \dilog \left(i a x +1\right)}{3 c}"," ",0,"-1/3*arctan(a*x)^2/c/x^3+a^2*arctan(a*x)^2/c/x+1/3*a^3*arctan(a*x)^3/c-1/3*a*arctan(a*x)/c/x^2-8/3*a^3/c*arctan(a*x)*ln(a*x)+4/3*a^3/c*arctan(a*x)*ln(a^2*x^2+1)-1/3*a^2/c/x-1/3*a^3*arctan(a*x)/c-2/3*I*a^3/c*dilog(-1/2*I*(I+a*x))-1/3*I*a^3/c*ln(a*x-I)^2+4/3*I*a^3/c*ln(a*x)*ln(1-I*a*x)-2/3*I*a^3/c*ln(I+a*x)*ln(a^2*x^2+1)-4/3*I*a^3/c*dilog(1+I*a*x)+2/3*I*a^3/c*ln(a*x-I)*ln(a^2*x^2+1)+2/3*I*a^3/c*ln(I+a*x)*ln(1/2*I*(a*x-I))+4/3*I*a^3/c*dilog(1-I*a*x)-4/3*I*a^3/c*ln(a*x)*ln(1+I*a*x)+1/3*I*a^3/c*ln(I+a*x)^2-2/3*I*a^3/c*ln(a*x-I)*ln(-1/2*I*(I+a*x))+2/3*I*a^3/c*dilog(1/2*I*(a*x-I))","B"
291,1,1092,175,0.855000," ","int(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^2,x)","-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)^{2} \pi}{2 a^{4} c^{2}}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c^{2}}-\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c^{2}}-\frac{\arctan \left(a x \right)^{2}}{4 a^{4} c^{2}}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c^{2}}-\frac{i \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c^{2}}+\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \arctan \left(a x \right)^{2} \pi}{2 a^{4} c^{2}}+\frac{i \arctan \left(a x \right) x}{a^{3} c^{2} \left(8 a x -8 i\right)}-\frac{i \arctan \left(a x \right) x}{a^{3} c^{2} \left(8 a x +8 i\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c^{2}}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c^{2}}-\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{2} \pi}{4 a^{4} c^{2}}-\frac{\arctan \left(a x \right)}{a^{4} c^{2} \left(8 a x +8 i\right)}+\frac{x}{16 a^{3} c^{2} \left(a x -i\right)}+\frac{x}{16 a^{3} c^{2} \left(a x +i\right)}-\frac{\arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{4} c^{2}}+\frac{i \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{a^{4} c^{2}}+\frac{\arctan \left(a x \right)^{2}}{2 a^{4} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 a^{4} c^{2}}-\frac{\ln \left(2\right) \arctan \left(a x \right)^{2}}{a^{4} c^{2}}-\frac{i}{16 a^{4} c^{2} \left(a x +i\right)}+\frac{i \arctan \left(a x \right)^{3}}{3 a^{4} c^{2}}+\frac{i}{16 a^{4} c^{2} \left(a x -i\right)}-\frac{\arctan \left(a x \right)}{a^{4} c^{2} \left(8 a x -8 i\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(a x \right)^{2} \pi}{4 a^{4} c^{2}}-\frac{\polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{4} c^{2}}"," ",0,"-1/a^4/c^2*arctan(a*x)/(8*I+8*a*x)+1/16/a^3/c^2/(a*x-I)*x+1/16/a^3/c^2/(I+a*x)*x-1/a^4/c^2*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+I/a^4/c^2*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-1/2*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^2*Pi+1/4*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*arctan(a*x)^2*Pi-1/4*I/a^4/c^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2*Pi-1/4*arctan(a*x)^2/a^4/c^2+I/a^3/c^2*arctan(a*x)/(8*a*x-8*I)*x-I/a^3/c^2*arctan(a*x)/(8*I+8*a*x)*x+1/4*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*arctan(a*x)^2*Pi+1/4*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*Pi-1/4*I/a^4/c^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*Pi-1/2/a^4/c^2*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+1/2*arctan(a*x)^2/a^4/c^2/(a^2*x^2+1)+1/2/a^4/c^2*arctan(a*x)^2*ln(a^2*x^2+1)-1/16*I/a^4/c^2/(I+a*x)+1/3*I/a^4/c^2*arctan(a*x)^3+1/16*I/a^4/c^2/(a*x-I)-1/a^4/c^2*ln(2)*arctan(a*x)^2-1/a^4/c^2*arctan(a*x)/(8*a*x-8*I)-1/4*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*Pi-1/4*I/a^4/c^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*Pi+1/2*I/a^4/c^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2*Pi+1/4*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*Pi","C"
292,1,97,96,0.040000," ","int(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^2,x)","\frac{x}{4 a^{2} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)}{4 a^{3} c^{2}}-\frac{\arctan \left(a x \right)}{2 a^{3} c^{2} \left(a^{2} x^{2}+1\right)}-\frac{x \arctan \left(a x \right)^{2}}{2 a^{2} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{3}}{6 a^{3} c^{2}}"," ",0,"1/4*x/a^2/c^2/(a^2*x^2+1)+1/4*arctan(a*x)/a^3/c^2-1/2*arctan(a*x)/a^3/c^2/(a^2*x^2+1)-1/2*x*arctan(a*x)^2/a^2/c^2/(a^2*x^2+1)+1/6*arctan(a*x)^3/a^3/c^2","A"
293,1,84,83,0.037000," ","int(x*arctan(a*x)^2/(a^2*c*x^2+c)^2,x)","\frac{1}{4 a^{2} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{x \arctan \left(a x \right)}{2 a \,c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{2}}{4 a^{2} c^{2}}-\frac{\arctan \left(a x \right)^{2}}{2 a^{2} c^{2} \left(a^{2} x^{2}+1\right)}"," ",0,"1/4/a^2/c^2/(a^2*x^2+1)+1/2*x*arctan(a*x)/a/c^2/(a^2*x^2+1)+1/4*arctan(a*x)^2/a^2/c^2-1/2*arctan(a*x)^2/a^2/c^2/(a^2*x^2+1)","A"
294,1,91,90,0.043000," ","int(arctan(a*x)^2/(a^2*c*x^2+c)^2,x)","-\frac{x}{4 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{\arctan \left(a x \right)}{4 a \,c^{2}}+\frac{\arctan \left(a x \right)}{2 a \,c^{2} \left(a^{2} x^{2}+1\right)}+\frac{x \arctan \left(a x \right)^{2}}{2 c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{3}}{6 a \,c^{2}}"," ",0,"-1/4*x/c^2/(a^2*x^2+1)-1/4*arctan(a*x)/a/c^2+1/2*arctan(a*x)/a/c^2/(a^2*x^2+1)+1/2*x*arctan(a*x)^2/c^2/(a^2*x^2+1)+1/6*arctan(a*x)^3/a/c^2","A"
295,1,1936,153,1.102000," ","int(arctan(a*x)^2/x/(a^2*c*x^2+c)^2,x)","\frac{2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{\arctan \left(a x \right)^{2}}{4 c^{2}}+\frac{\arctan \left(a x \right)^{2}}{2 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{i}{16 c^{2} \left(a x +i\right)}+\frac{\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{\arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c^{2}}-\frac{\arctan \left(a x \right)}{c^{2} \left(8 a x -8 i\right)}-\frac{\arctan \left(a x \right)}{c^{2} \left(8 a x +8 i\right)}+\frac{\arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{i}{16 c^{2} \left(a x -i\right)}-\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{4 c^{2}}+\frac{i \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2 c^{2}}+\frac{a x}{16 c^{2} \left(a x -i\right)}+\frac{a x}{16 c^{2} \left(a x +i\right)}-\frac{2 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c^{2}}+\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{4 c^{2}}+\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{2}}+\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{2}}+\frac{i \arctan \left(a x \right) a x}{c^{2} \left(8 a x -8 i\right)}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c^{2}}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2 c^{2}}-\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 c^{2}}-\frac{i \arctan \left(a x \right) a x}{c^{2} \left(8 a x +8 i\right)}+\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2}}{2 c^{2}}-\frac{i \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c^{2}}-\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2 c^{2}}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2 c^{2}}-\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{4 c^{2}}+\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4 c^{2}}+\frac{i \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2 c^{2}}-\frac{i \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c^{2}}-\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4 c^{2}}+\frac{\arctan \left(a x \right)^{2} \ln \left(a x \right)}{c^{2}}-\frac{\arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 c^{2}}-\frac{i \arctan \left(a x \right)^{3}}{3 c^{2}}-\frac{2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{i \pi  \arctan \left(a x \right)^{2}}{2 c^{2}}+\frac{\arctan \left(a x \right)^{2} \ln \left(2\right)}{c^{2}}"," ",0,"1/16/c^2/(a*x-I)*a*x+1/16/c^2/(I+a*x)*a*x-1/4*arctan(a*x)^2/c^2+1/2*arctan(a*x)^2/c^2/(a^2*x^2+1)-1/3*I*arctan(a*x)^3/c^2-1/4*I/c^2*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+1/2*I/c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2+1/2*I/c^2*Pi*arctan(a*x)^2-2*I/c^2*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I/c^2*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/2*I/c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+1/4*I/c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+1/4*I/c^2*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+1/4*I/c^2*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+2/c^2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2/c^2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/2*I/c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2-1/4*I/c^2*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3+1/4*I/c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3-1/16*I/c^2/(I+a*x)+1/c^2*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/c^2*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+1/c^2*arctan(a*x)^2*ln(a*x)-1/2/c^2*arctan(a*x)^2*ln(a^2*x^2+1)-1/c^2*arctan(a*x)/(8*a*x-8*I)-1/c^2*arctan(a*x)/(8*I+8*a*x)+1/c^2*arctan(a*x)^2*ln(2)+1/c^2*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c^2*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/16*I/c^2/(a*x-I)+I/c^2*arctan(a*x)/(8*a*x-8*I)*a*x-1/2*I/c^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+1/2*I/c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-1/4*I/c^2*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))-I/c^2*arctan(a*x)/(8*I+8*a*x)*a*x+1/2*I/c^2*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2-1/2*I/c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-1/2*I/c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+1/2*I/c^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2-1/2*I/c^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-1/4*I/c^2*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3","C"
296,1,369,163,0.122000," ","int(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^2,x)","-\frac{\arctan \left(a x \right)^{2}}{c^{2} x}-\frac{a^{2} x \arctan \left(a x \right)^{2}}{2 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{a \arctan \left(a x \right)^{3}}{2 c^{2}}+\frac{2 a \arctan \left(a x \right) \ln \left(a x \right)}{c^{2}}-\frac{a \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{c^{2}}-\frac{a \arctan \left(a x \right)}{2 c^{2} \left(a^{2} x^{2}+1\right)}+\frac{a^{2} x}{4 c^{2} \left(a^{2} x^{2}+1\right)}+\frac{a \arctan \left(a x \right)}{4 c^{2}}+\frac{i a \ln \left(a x \right) \ln \left(i a x +1\right)}{c^{2}}+\frac{i a \dilog \left(i a x +1\right)}{c^{2}}+\frac{i a \ln \left(a x -i\right)^{2}}{4 c^{2}}+\frac{i a \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 c^{2}}-\frac{i a \ln \left(a x +i\right)^{2}}{4 c^{2}}-\frac{i a \ln \left(a x \right) \ln \left(-i a x +1\right)}{c^{2}}-\frac{i a \dilog \left(-i a x +1\right)}{c^{2}}-\frac{i a \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{2 c^{2}}+\frac{i a \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{2 c^{2}}+\frac{i a \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 c^{2}}-\frac{i a \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{2 c^{2}}-\frac{i a \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{2 c^{2}}"," ",0,"-arctan(a*x)^2/c^2/x-1/2*a^2*x*arctan(a*x)^2/c^2/(a^2*x^2+1)-1/2*a*arctan(a*x)^3/c^2+2*a/c^2*arctan(a*x)*ln(a*x)-a/c^2*arctan(a*x)*ln(a^2*x^2+1)-1/2*a*arctan(a*x)/c^2/(a^2*x^2+1)+1/4*a^2*x/c^2/(a^2*x^2+1)+1/4*a*arctan(a*x)/c^2+I*a/c^2*ln(a*x)*ln(1+I*a*x)+1/4*I*a/c^2*ln(a*x-I)^2-1/4*I*a/c^2*ln(I+a*x)^2-I*a/c^2*ln(a*x)*ln(1-I*a*x)+1/2*I*a/c^2*dilog(-1/2*I*(I+a*x))-1/2*I*a/c^2*dilog(1/2*I*(a*x-I))-I*a/c^2*dilog(1-I*a*x)+1/2*I*a/c^2*ln(I+a*x)*ln(a^2*x^2+1)+1/2*I*a/c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))+I*a/c^2*dilog(1+I*a*x)-1/2*I*a/c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))-1/2*I*a/c^2*ln(a*x-I)*ln(a^2*x^2+1)","B"
297,1,5115,231,7.516000," ","int(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
298,1,444,216,0.173000," ","int(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^2,x)","-\frac{\arctan \left(a x \right)^{2}}{3 c^{2} x^{3}}+\frac{2 a^{2} \arctan \left(a x \right)^{2}}{c^{2} x}+\frac{a^{4} x \arctan \left(a x \right)^{2}}{2 c^{2} \left(a^{2} x^{2}+1\right)}+\frac{5 a^{3} \arctan \left(a x \right)^{3}}{6 c^{2}}-\frac{a \arctan \left(a x \right)}{3 c^{2} x^{2}}-\frac{14 a^{3} \arctan \left(a x \right) \ln \left(a x \right)}{3 c^{2}}+\frac{7 a^{3} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3 c^{2}}+\frac{a^{3} \arctan \left(a x \right)}{2 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{7 i a^{3} \dilog \left(i a x +1\right)}{3 c^{2}}+\frac{7 i a^{3} \dilog \left(-i a x +1\right)}{3 c^{2}}-\frac{7 i a^{3} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{6 c^{2}}+\frac{7 i a^{3} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{6 c^{2}}-\frac{7 i a^{3} \ln \left(a x -i\right)^{2}}{12 c^{2}}+\frac{7 i a^{3} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{6 c^{2}}+\frac{7 i a^{3} \ln \left(a x +i\right)^{2}}{12 c^{2}}+\frac{7 i a^{3} \ln \left(a x \right) \ln \left(-i a x +1\right)}{3 c^{2}}-\frac{7 i a^{3} \ln \left(a x \right) \ln \left(i a x +1\right)}{3 c^{2}}+\frac{7 i a^{3} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{6 c^{2}}-\frac{7 i a^{3} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{6 c^{2}}-\frac{7 i a^{3} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{6 c^{2}}-\frac{a^{2}}{3 c^{2} x}-\frac{a^{4} x}{4 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{7 a^{3} \arctan \left(a x \right)}{12 c^{2}}"," ",0,"-1/3*arctan(a*x)^2/c^2/x^3+2*a^2*arctan(a*x)^2/c^2/x+1/2*a^4*x*arctan(a*x)^2/c^2/(a^2*x^2+1)+5/6*a^3*arctan(a*x)^3/c^2-1/3*a*arctan(a*x)/c^2/x^2-14/3*a^3/c^2*arctan(a*x)*ln(a*x)+7/3*a^3/c^2*arctan(a*x)*ln(a^2*x^2+1)+1/2*a^3*arctan(a*x)/c^2/(a^2*x^2+1)-7/12*I*a^3/c^2*ln(a*x-I)^2+7/3*I*a^3/c^2*dilog(1-I*a*x)-7/3*I*a^3/c^2*dilog(1+I*a*x)+7/6*I*a^3/c^2*ln(a*x-I)*ln(a^2*x^2+1)+7/12*I*a^3/c^2*ln(I+a*x)^2-7/6*I*a^3/c^2*dilog(-1/2*I*(I+a*x))+7/6*I*a^3/c^2*dilog(1/2*I*(a*x-I))+7/3*I*a^3/c^2*ln(a*x)*ln(1-I*a*x)-7/3*I*a^3/c^2*ln(a*x)*ln(1+I*a*x)+7/6*I*a^3/c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))-7/6*I*a^3/c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))-7/6*I*a^3/c^2*ln(I+a*x)*ln(a^2*x^2+1)-1/3*a^2/c^2/x-1/4*a^4*x/c^2/(a^2*x^2+1)-7/12*a^3*arctan(a*x)/c^2","B"
299,1,154,128,0.066000," ","int(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^3,x)","\frac{\arctan \left(a x \right)^{2}}{4 a^{4} c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{\arctan \left(a x \right)^{2}}{2 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{5 x^{3} \arctan \left(a x \right)}{16 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 \arctan \left(a x \right) x}{16 a^{3} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{5 \arctan \left(a x \right)^{2}}{32 a^{4} c^{3}}-\frac{1}{32 a^{4} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{5}{32 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}"," ",0,"1/4/a^4/c^3*arctan(a*x)^2/(a^2*x^2+1)^2-1/2/a^4/c^3*arctan(a*x)^2/(a^2*x^2+1)+5/16*x^3*arctan(a*x)/a/c^3/(a^2*x^2+1)^2+3/16/a^3/c^3*arctan(a*x)*x/(a^2*x^2+1)^2+5/32*arctan(a*x)^2/a^4/c^3-1/32/a^4/c^3/(a^2*x^2+1)^2+5/32/a^4/c^3/(a^2*x^2+1)","A"
300,1,164,165,0.058000," ","int(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^3,x)","\frac{\arctan \left(a x \right)^{2} x^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{x \arctan \left(a x \right)^{2}}{8 a^{2} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{\arctan \left(a x \right)^{3}}{24 a^{3} c^{3}}-\frac{\arctan \left(a x \right)}{8 a^{3} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{\arctan \left(a x \right)}{8 a^{3} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{x^{3}}{64 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{x}{64 a^{2} c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{\arctan \left(a x \right)}{64 a^{3} c^{3}}"," ",0,"1/8/c^3*arctan(a*x)^2/(a^2*x^2+1)^2*x^3-1/8*x*arctan(a*x)^2/a^2/c^3/(a^2*x^2+1)^2+1/24*arctan(a*x)^3/a^3/c^3-1/8*arctan(a*x)/a^3/c^3/(a^2*x^2+1)^2+1/8*arctan(a*x)/a^3/c^3/(a^2*x^2+1)-1/64/c^3/(a^2*x^2+1)^2*x^3+1/64*x/a^2/c^3/(a^2*x^2+1)^2-1/64*arctan(a*x)/a^3/c^3","A"
301,1,127,126,0.054000," ","int(x*arctan(a*x)^2/(a^2*c*x^2+c)^3,x)","\frac{1}{32 a^{2} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3}{32 a^{2} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{x \arctan \left(a x \right)}{8 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 x \arctan \left(a x \right)}{16 a \,c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 \arctan \left(a x \right)^{2}}{32 a^{2} c^{3}}-\frac{\arctan \left(a x \right)^{2}}{4 a^{2} c^{3} \left(a^{2} x^{2}+1\right)^{2}}"," ",0,"1/32/a^2/c^3/(a^2*x^2+1)^2+3/32/a^2/c^3/(a^2*x^2+1)+1/8*x*arctan(a*x)/a/c^3/(a^2*x^2+1)^2+3/16*x*arctan(a*x)/a/c^3/(a^2*x^2+1)+3/32*arctan(a*x)^2/a^2/c^3-1/4*arctan(a*x)^2/a^2/c^3/(a^2*x^2+1)^2","A"
302,1,159,153,0.056000," ","int(arctan(a*x)^2/(a^2*c*x^2+c)^3,x)","\frac{x \arctan \left(a x \right)^{2}}{4 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 x \arctan \left(a x \right)^{2}}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{3}}{8 a \,c^{3}}+\frac{\arctan \left(a x \right)}{8 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 \arctan \left(a x \right)}{8 a \,c^{3} \left(a^{2} x^{2}+1\right)}-\frac{15 a^{2} x^{3}}{64 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{17 x}{64 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{15 \arctan \left(a x \right)}{64 a \,c^{3}}"," ",0,"1/4*x*arctan(a*x)^2/c^3/(a^2*x^2+1)^2+3/8*x*arctan(a*x)^2/c^3/(a^2*x^2+1)+1/8*arctan(a*x)^3/a/c^3+1/8*arctan(a*x)/a/c^3/(a^2*x^2+1)^2+3/8*arctan(a*x)/a/c^3/(a^2*x^2+1)-15/64*a^2/c^3/(a^2*x^2+1)^2*x^3-17/64*x/c^3/(a^2*x^2+1)^2-15/64*arctan(a*x)/a/c^3","A"
303,1,1986,213,1.631000," ","int(arctan(a*x)^2/x/(a^2*c*x^2+c)^3,x)","-\frac{11 \arctan \left(a x \right)^{2}}{32 c^{3}}+\frac{\arctan \left(a x \right)^{2}}{4 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{\arctan \left(a x \right)^{2}}{2 c^{3} \left(a^{2} x^{2}+1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(a x \right)^{2} \pi}{4 c^{3}}+\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{3}}-\frac{3 i \arctan \left(a x \right) a x}{2 c^{3} \left(8 a x +8 i\right)}+\frac{3 i \arctan \left(a x \right) a x}{2 c^{3} \left(8 a x -8 i\right)}-\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}-\frac{\cos \left(4 \arctan \left(a x \right)\right)}{256 c^{3}}-\frac{2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{2 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{3 a x}{32 c^{3} \left(a x +i\right)}+\frac{3 a x}{32 c^{3} \left(a x -i\right)}+\frac{i \arctan \left(a x \right)^{2} \pi}{2 c^{3}}-\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}+\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{3}}-\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{4 c^{3}}-\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4 c^{3}}+\frac{i \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{3}}+\frac{i \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4 c^{3}}-\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}-\frac{i \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2 c^{3}}-\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)^{2} \pi}{2 c^{3}}+\frac{i \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{3}}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(a x \right)^{2} \pi}{4 c^{3}}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \arctan \left(a x \right)^{2} \pi}{4 c^{3}}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{4 c^{3}}+\frac{i \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{4 c^{3}}+\frac{\arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{3 i}{32 c^{3} \left(a x +i\right)}+\frac{3 i}{32 c^{3} \left(a x -i\right)}-\frac{3 \arctan \left(a x \right)}{2 c^{3} \left(8 a x +8 i\right)}-\frac{i \arctan \left(a x \right)^{3}}{3 c^{3}}-\frac{3 \arctan \left(a x \right)}{2 c^{3} \left(8 a x -8 i\right)}+\frac{\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{\arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c^{3}}-\frac{\arctan \left(a x \right) \sin \left(4 \arctan \left(a x \right)\right)}{64 c^{3}}+\frac{\arctan \left(a x \right)^{2} \ln \left(2\right)}{c^{3}}-\frac{\arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 c^{3}}+\frac{\arctan \left(a x \right)^{2} \ln \left(a x \right)}{c^{3}}+\frac{2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}"," ",0,"-11/32*arctan(a*x)^2/c^3+1/4*arctan(a*x)^2/c^3/(a^2*x^2+1)^2+1/2*arctan(a*x)^2/c^3/(a^2*x^2+1)-1/3*I*arctan(a*x)^3/c^3+1/2*I/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))-1/2*I/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-1/2*I/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-1/2*I/c^3*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/2*I/c^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^2*Pi+1/2*I/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+1/4*I/c^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*Pi+1/4*I/c^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*arctan(a*x)^2*Pi-1/4*I/c^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*arctan(a*x)^2*Pi+1/4*I/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-3/2*I/c^3*arctan(a*x)/(8*I+8*a*x)*a*x+2/c^3*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2/c^3*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/256/c^3*cos(4*arctan(a*x))-1/2*I/c^3*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/2*I/c^3*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-1/4*I/c^3*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3-1/4*I/c^3*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+1/2*I/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3+1/4*I/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+3/32/c^3/(I+a*x)*a*x+3/32/c^3/(a*x-I)*a*x-2*I/c^3*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I/c^3*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/2*I/c^3*arctan(a*x)^2*Pi+3/2*I/c^3*arctan(a*x)/(8*a*x-8*I)*a*x-1/2*I/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-3/2/c^3*arctan(a*x)/(8*a*x-8*I)-1/64/c^3*arctan(a*x)*sin(4*arctan(a*x))+1/c^3*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c^3*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/c^3*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+1/c^3*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c^3*arctan(a*x)^2*ln(2)-3/32*I/c^3/(I+a*x)+3/32*I/c^3/(a*x-I)-1/2/c^3*arctan(a*x)^2*ln(a^2*x^2+1)+1/c^3*arctan(a*x)^2*ln(a*x)-3/2/c^3*arctan(a*x)/(8*I+8*a*x)-1/4*I/c^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*Pi","C"
304,1,440,230,0.176000," ","int(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^3,x)","-\frac{\arctan \left(a x \right)^{2}}{c^{3} x}-\frac{7 \arctan \left(a x \right)^{2} a^{4} x^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{9 a^{2} x \arctan \left(a x \right)^{2}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{5 a \arctan \left(a x \right)^{3}}{8 c^{3}}+\frac{2 a \arctan \left(a x \right) \ln \left(a x \right)}{c^{3}}-\frac{a \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{c^{3}}-\frac{a \arctan \left(a x \right)}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{7 a \arctan \left(a x \right)}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{i a \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{2 c^{3}}+\frac{i a \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 c^{3}}+\frac{i a \ln \left(a x -i\right)^{2}}{4 c^{3}}+\frac{i a \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{2 c^{3}}+\frac{i a \dilog \left(i a x +1\right)}{c^{3}}-\frac{i a \ln \left(a x \right) \ln \left(-i a x +1\right)}{c^{3}}-\frac{i a \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{2 c^{3}}-\frac{i a \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{2 c^{3}}+\frac{i a \ln \left(a x \right) \ln \left(i a x +1\right)}{c^{3}}-\frac{i a \ln \left(a x +i\right)^{2}}{4 c^{3}}-\frac{i a \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{2 c^{3}}-\frac{i a \dilog \left(-i a x +1\right)}{c^{3}}+\frac{31 x^{3} a^{4}}{64 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{33 a^{2} x}{64 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{31 a \arctan \left(a x \right)}{64 c^{3}}"," ",0,"-arctan(a*x)^2/c^3/x-7/8/c^3*arctan(a*x)^2/(a^2*x^2+1)^2*a^4*x^3-9/8*a^2*x*arctan(a*x)^2/c^3/(a^2*x^2+1)^2-5/8*a*arctan(a*x)^3/c^3+2*a/c^3*arctan(a*x)*ln(a*x)-a/c^3*arctan(a*x)*ln(a^2*x^2+1)-1/8*a*arctan(a*x)/c^3/(a^2*x^2+1)^2-7/8*a*arctan(a*x)/c^3/(a^2*x^2+1)+I*a/c^3*dilog(1+I*a*x)-I*a/c^3*dilog(1-I*a*x)+1/2*I*a/c^3*ln(I+a*x)*ln(a^2*x^2+1)+1/4*I*a/c^3*ln(a*x-I)^2+1/2*I*a/c^3*dilog(-1/2*I*(I+a*x))+1/2*I*a/c^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))-1/2*I*a/c^3*dilog(1/2*I*(a*x-I))-I*a/c^3*ln(a*x)*ln(1-I*a*x)-1/2*I*a/c^3*ln(I+a*x)*ln(1/2*I*(a*x-I))+I*a/c^3*ln(a*x)*ln(1+I*a*x)-1/4*I*a/c^3*ln(I+a*x)^2-1/2*I*a/c^3*ln(a*x-I)*ln(a^2*x^2+1)+31/64/c^3/(a^2*x^2+1)^2*x^3*a^4+33/64*a^2*x/c^3/(a^2*x^2+1)^2+31/64*a*arctan(a*x)/c^3","A"
305,1,2217,299,5.272000," ","int(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^3,x)","\frac{3 a^{2} \arctan \left(a x \right)^{2}}{32 c^{3}}-\frac{\arctan \left(a x \right)^{2}}{2 c^{3} x^{2}}+\frac{a^{2} \cos \left(4 \arctan \left(a x \right)\right)}{256 c^{3}}+\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}+\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4 c^{3}}-\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{3}}-\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{3}}-\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4 c^{3}}+\frac{3 i a^{2} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{4 c^{3}}+\frac{3 i a^{2} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{4 c^{3}}-\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{3}}-\frac{3 a^{2} \arctan \left(a x \right)^{2} \ln \left(2\right)}{c^{3}}+\frac{a^{2} \arctan \left(a x \right) \sin \left(4 \arctan \left(a x \right)\right)}{64 c^{3}}-\frac{3 a^{2} \arctan \left(a x \right)^{2} \ln \left(a x \right)}{c^{3}}+\frac{i a^{2} \arctan \left(a x \right)^{3}}{c^{3}}-\frac{5 i a^{2}}{32 c^{3} \left(a x -i\right)}-\frac{3 a^{2} \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{3 a^{2} \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{3 a^{2} \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c^{3}}-\frac{3 a^{2} \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{5 a^{3} x}{32 c^{3} \left(a x +i\right)}-\frac{5 a^{3} x}{32 c^{3} \left(a x -i\right)}+\frac{5 a^{2} \arctan \left(a x \right)}{2 c^{3} \left(8 a x +8 i\right)}+\frac{5 a^{2} \arctan \left(a x \right)}{2 c^{3} \left(8 a x -8 i\right)}-\frac{i a^{2} \arctan \left(a x \right)}{c^{3}}+\frac{5 i a^{2}}{32 c^{3} \left(a x +i\right)}-\frac{a^{2} \arctan \left(a x \right)^{2}}{c^{3} \left(a^{2} x^{2}+1\right)}+\frac{6 i a^{2} \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{6 i a^{2} \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{3 i a^{2} \pi  \arctan \left(a x \right)^{2}}{2 c^{3}}+\frac{a^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)}{c^{3}}+\frac{a^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{6 a^{2} \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{6 a^{2} \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 c^{3}}+\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2 c^{3}}-\frac{3 i a^{2} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{3}}-\frac{3 i a^{2} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{4 c^{3}}-\frac{3 i a^{2} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2}}{2 c^{3}}+\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}+\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}-\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{3}}+\frac{3 i a^{2} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}-\frac{3 i a^{2} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{3}}+\frac{5 i a^{3} \arctan \left(a x \right) x}{2 c^{3} \left(8 a x +8 i\right)}-\frac{5 i a^{3} \arctan \left(a x \right) x}{2 c^{3} \left(8 a x -8 i\right)}+\frac{3 a^{2} \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 c^{3}}-\frac{a \arctan \left(a x \right)}{c^{3} x}-\frac{a^{2} \arctan \left(a x \right)^{2}}{4 c^{3} \left(a^{2} x^{2}+1\right)^{2}}"," ",0,"3/32*a^2*arctan(a*x)^2/c^3+3/4*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))+3/2*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-3/4*I*a^2/c^3*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-3/4*I*a^2/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-3/2*I*a^2/c^3*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2+3/2*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+3/2*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-3/4*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-1/2*arctan(a*x)^2/c^3/x^2+I*a^2*arctan(a*x)^3/c^3+a^2/c^3*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)-6*a^2/c^3*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/256*a^2/c^3*cos(4*arctan(a*x))+a^2/c^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*a^2/c^3*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/4*I*a^2/c^3*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-3/2*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))-5/32*I*a^2/c^3/(a*x-I)-3*a^2/c^3*arctan(a*x)^2*ln(2)+1/64*a^2/c^3*arctan(a*x)*sin(4*arctan(a*x))-3*a^2/c^3*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*a^2/c^3*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2/c^3*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)-3*a^2/c^3*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))-5/32*a^3/c^3/(I+a*x)*x-5/32*a^3/c^3/(a*x-I)*x-3*a^2/c^3*arctan(a*x)^2*ln(a*x)+5/2*a^2/c^3*arctan(a*x)/(8*I+8*a*x)+3/2*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-3/2*I*a^2/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))-a^2*arctan(a*x)^2/c^3/(a^2*x^2+1)+6*I*a^2/c^3*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*a^2/c^3*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/2*I*a^2/c^3*Pi*arctan(a*x)^2+5/2*I*a^3/c^3*arctan(a*x)/(8*I+8*a*x)*x-5/2*I*a^3/c^3*arctan(a*x)/(8*a*x-8*I)*x+3/2*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+3/4*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3-3/2*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-3/2*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-3/4*I*a^2/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+3/4*I*a^2/c^3*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3+5/2*a^2/c^3*arctan(a*x)/(8*a*x-8*I)+3/2*a^2/c^3*arctan(a*x)^2*ln(a^2*x^2+1)-I*a^2/c^3*arctan(a*x)+5/32*I*a^2/c^3/(I+a*x)-a*arctan(a*x)/c^3/x-1/4*a^2*arctan(a*x)^2/c^3/(a^2*x^2+1)^2","C"
306,1,517,285,0.149000," ","int(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^3,x)","\frac{13 a^{4} x \arctan \left(a x \right)^{2}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{11 a^{6} \arctan \left(a x \right)^{2} x^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{49 a^{4} x}{64 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{a \arctan \left(a x \right)}{3 c^{3} x^{2}}+\frac{a^{3} \arctan \left(a x \right)}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{11 a^{3} \arctan \left(a x \right)}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 a^{2} \arctan \left(a x \right)^{2}}{c^{3} x}-\frac{a^{2}}{3 c^{3} x}-\frac{205 a^{3} \arctan \left(a x \right)}{192 c^{3}}-\frac{\arctan \left(a x \right)^{2}}{3 c^{3} x^{3}}+\frac{35 a^{3} \arctan \left(a x \right)^{3}}{24 c^{3}}-\frac{5 i a^{3} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{3 c^{3}}-\frac{10 i a^{3} \dilog \left(i a x +1\right)}{3 c^{3}}+\frac{5 i a^{3} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{3 c^{3}}+\frac{5 i a^{3} \ln \left(a x +i\right)^{2}}{6 c^{3}}-\frac{5 i a^{3} \ln \left(a x -i\right)^{2}}{6 c^{3}}+\frac{10 i a^{3} \dilog \left(-i a x +1\right)}{3 c^{3}}-\frac{20 a^{3} \arctan \left(a x \right) \ln \left(a x \right)}{3 c^{3}}+\frac{10 a^{3} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3 c^{3}}-\frac{47 a^{6} x^{3}}{64 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{5 i a^{3} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{3 c^{3}}+\frac{10 i a^{3} \ln \left(a x \right) \ln \left(-i a x +1\right)}{3 c^{3}}-\frac{10 i a^{3} \ln \left(a x \right) \ln \left(i a x +1\right)}{3 c^{3}}-\frac{5 i a^{3} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{3 c^{3}}-\frac{5 i a^{3} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{3 c^{3}}+\frac{5 i a^{3} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{3 c^{3}}"," ",0,"13/8*a^4*x*arctan(a*x)^2/c^3/(a^2*x^2+1)^2+11/8*a^6/c^3*arctan(a*x)^2/(a^2*x^2+1)^2*x^3-49/64*a^4*x/c^3/(a^2*x^2+1)^2-1/3*a*arctan(a*x)/c^3/x^2+1/8*a^3*arctan(a*x)/c^3/(a^2*x^2+1)^2+11/8*a^3*arctan(a*x)/c^3/(a^2*x^2+1)+3*a^2*arctan(a*x)^2/c^3/x-1/3*a^2/c^3/x-205/192*a^3*arctan(a*x)/c^3-1/3*arctan(a*x)^2/c^3/x^3+35/24*a^3*arctan(a*x)^3/c^3-20/3*a^3/c^3*arctan(a*x)*ln(a*x)+10/3*a^3/c^3*arctan(a*x)*ln(a^2*x^2+1)+5/6*I*a^3/c^3*ln(I+a*x)^2+10/3*I*a^3/c^3*dilog(1-I*a*x)-5/3*I*a^3/c^3*dilog(-1/2*I*(I+a*x))-10/3*I*a^3/c^3*dilog(1+I*a*x)-5/6*I*a^3/c^3*ln(a*x-I)^2-47/64*a^6/c^3/(a^2*x^2+1)^2*x^3+5/3*I*a^3/c^3*dilog(1/2*I*(a*x-I))+5/3*I*a^3/c^3*ln(a*x-I)*ln(a^2*x^2+1)+10/3*I*a^3/c^3*ln(a*x)*ln(1-I*a*x)-10/3*I*a^3/c^3*ln(a*x)*ln(1+I*a*x)-5/3*I*a^3/c^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))-5/3*I*a^3/c^3*ln(I+a*x)*ln(a^2*x^2+1)+5/3*I*a^3/c^3*ln(I+a*x)*ln(1/2*I*(a*x-I))","A"
307,1,235,316,2.542000," ","int(x^3*arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(12 \arctan \left(a x \right)^{2} x^{4} a^{4}-6 \arctan \left(a x \right) x^{3} a^{3}+4 \arctan \left(a x \right)^{2} x^{2} a^{2}+2 a^{2} x^{2}+5 \arctan \left(a x \right) x a -8 \arctan \left(a x \right)^{2}-9\right)}{60 a^{4}}-\frac{11 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{60 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/60/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*(12*arctan(a*x)^2*x^4*a^4-6*arctan(a*x)*x^3*a^3+4*arctan(a*x)^2*x^2*a^2+2*a^2*x^2+5*arctan(a*x)*x*a-8*arctan(a*x)^2-9)-11/60*(c*(a*x-I)*(I+a*x))^(1/2)*(I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^4/(a^2*x^2+1)^(1/2)","A"
308,1,302,412,1.774000," ","int(x^2*arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(6 \arctan \left(a x \right)^{2} x^{3} a^{3}-4 \arctan \left(a x \right) a^{2} x^{2}+3 \arctan \left(a x \right)^{2} x a +2 a x +2 \arctan \left(a x \right)\right)}{24 a^{3}}+\frac{i \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(3 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+8 \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{24 a^{3} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/24/a^3*(c*(a*x-I)*(I+a*x))^(1/2)*(6*arctan(a*x)^2*x^3*a^3-4*arctan(a*x)*a^2*x^2+3*arctan(a*x)^2*x*a+2*a*x+2*arctan(a*x))+1/24*I*(c*(a*x-I)*(I+a*x))^(1/2)*(3*I*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+8*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^3/(a^2*x^2+1)^(1/2)","A"
309,1,198,226,1.139000," ","int(x*arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right)^{2} x^{2} a^{2}-\arctan \left(a x \right) x a +\arctan \left(a x \right)^{2}+1\right)}{3 a^{2}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{3 a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/3/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)^2*x^2*a^2-arctan(a*x)*x*a+arctan(a*x)^2+1)+1/3*(c*(a*x-I)*(I+a*x))^(1/2)*(I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^2/(a^2*x^2+1)^(1/2)","A"
310,1,268,342,0.842000," ","int(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \left(\arctan \left(a x \right) x a -2\right)}{2 a}-\frac{i \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-2 \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+4 \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 a \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2/a*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*(arctan(a*x)*x*a-2)-1/2*I*(c*(a*x-I)*(I+a*x))^(1/2)*(I*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2)))/a/(a^2*x^2+1)^(1/2)","A"
311,1,337,423,0.974000," ","int(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x,x)","\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)^{2}-\frac{i \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-2 \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{\sqrt{a^{2} x^{2}+1}}"," ",0,"(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)^2-I*(c*(a*x-I)*(I+a*x))^(1/2)*(I*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
312,1,309,438,0.937000," ","int(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x^2,x)","-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)^{2}}{x}-\frac{a \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-\arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \dilog \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \dilog \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{\sqrt{a^{2} x^{2}+1}}"," ",0,"-(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)^2/x-a*(c*(a*x-I)*(I+a*x))^(1/2)*(-arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*dilog((1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*dilog(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
313,1,255,337,1.352000," ","int(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x^3,x)","-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \left(2 a x +\arctan \left(a x \right)\right)}{2 x^{2}}+\frac{a^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-4 \arctanh \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*(2*a*x+arctan(a*x))/x^2+1/2*a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*arctanh((1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
314,1,195,225,1.530000," ","int(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x^4,x)","-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right)^{2} x^{2} a^{2}+a^{2} x^{2}+\arctan \left(a x \right) x a +\arctan \left(a x \right)^{2}\right)}{3 x^{3}}+\frac{i a^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{3 \sqrt{a^{2} x^{2}+1}}"," ",0,"-1/3*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)^2*x^2*a^2+a^2*x^2+arctan(a*x)*x*a+arctan(a*x)^2)/x^3+1/3*I*a^3*(c*(a*x-I)*(I+a*x))^(1/2)*(I*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
315,1,271,395,2.276000," ","int(x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(360 \arctan \left(a x \right)^{2} x^{6} a^{6}-120 \arctan \left(a x \right) x^{5} a^{5}+576 \arctan \left(a x \right)^{2} x^{4} a^{4}+24 a^{4} x^{4}-138 \arctan \left(a x \right) x^{3} a^{3}+72 \arctan \left(a x \right)^{2} x^{2} a^{2}+14 a^{2} x^{2}+135 \arctan \left(a x \right) x a -144 \arctan \left(a x \right)^{2}-163\right)}{2520 a^{4}}-\frac{17 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{280 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2520*c/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*(360*arctan(a*x)^2*x^6*a^6-120*arctan(a*x)*x^5*a^5+576*arctan(a*x)^2*x^4*a^4+24*a^4*x^4-138*arctan(a*x)*x^3*a^3+72*arctan(a*x)^2*x^2*a^2+14*a^2*x^2+135*arctan(a*x)*x*a-144*arctan(a*x)^2-163)-17/280*c*(c*(a*x-I)*(I+a*x))^(1/2)*(I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^4/(a^2*x^2+1)^(1/2)","A"
316,1,338,495,1.532000," ","int(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(120 \arctan \left(a x \right)^{2} x^{5} a^{5}-48 \arctan \left(a x \right) x^{4} a^{4}+210 \arctan \left(a x \right)^{2} x^{3} a^{3}+12 a^{3} x^{3}-76 \arctan \left(a x \right) a^{2} x^{2}+45 \arctan \left(a x \right)^{2} x a +20 a x +62 \arctan \left(a x \right)\right)}{720 a^{3}}+\frac{i c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(45 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-45 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+90 \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+90 i \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-90 \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-90 i \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+164 \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{720 a^{3} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/720*c/a^3*(c*(a*x-I)*(I+a*x))^(1/2)*(120*arctan(a*x)^2*x^5*a^5-48*arctan(a*x)*x^4*a^4+210*arctan(a*x)^2*x^3*a^3+12*a^3*x^3-76*arctan(a*x)*a^2*x^2+45*arctan(a*x)^2*x*a+20*a*x+62*arctan(a*x))+1/720*I*c*(c*(a*x-I)*(I+a*x))^(1/2)*(45*I*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-45*I*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+90*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+90*I*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-90*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-90*I*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+164*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^3/(a^2*x^2+1)^(1/2)","A"
317,1,237,273,1.059000," ","int(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(12 \arctan \left(a x \right)^{2} x^{4} a^{4}-6 \arctan \left(a x \right) x^{3} a^{3}+24 \arctan \left(a x \right)^{2} x^{2} a^{2}+2 a^{2} x^{2}-15 \arctan \left(a x \right) x a +12 \arctan \left(a x \right)^{2}+11\right)}{60 a^{2}}+\frac{3 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{20 a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/60*c/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(12*arctan(a*x)^2*x^4*a^4-6*arctan(a*x)*x^3*a^3+24*arctan(a*x)^2*x^2*a^2+2*a^2*x^2-15*arctan(a*x)*x*a+12*arctan(a*x)^2+11)+3/20*c*(c*(a*x-I)*(I+a*x))^(1/2)*(I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^2/(a^2*x^2+1)^(1/2)","A"
318,1,304,414,0.711000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(6 \arctan \left(a x \right)^{2} x^{3} a^{3}-4 \arctan \left(a x \right) a^{2} x^{2}+15 \arctan \left(a x \right)^{2} x a +2 a x -22 \arctan \left(a x \right)\right)}{24 a}-\frac{i c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(9 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-9 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+18 i \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-18 i \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+18 \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-18 \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+40 \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{24 a \sqrt{a^{2} x^{2}+1}}"," ",0,"1/24*c/a*(c*(a*x-I)*(I+a*x))^(1/2)*(6*arctan(a*x)^2*x^3*a^3-4*arctan(a*x)*a^2*x^2+15*arctan(a*x)^2*x*a+2*a*x-22*arctan(a*x))-1/24*I*c*(c*(a*x-I)*(I+a*x))^(1/2)*(9*I*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-9*I*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+18*I*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-18*I*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+18*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-18*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+40*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2)))/a/(a^2*x^2+1)^(1/2)","A"
319,1,365,496,0.893000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right)^{2} x^{2} a^{2}-\arctan \left(a x \right) x a +4 \arctan \left(a x \right)^{2}+1\right)}{3}-\frac{i c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(3 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+7 i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-7 i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+7 \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-7 \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{3 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/3*c*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)^2*x^2*a^2-arctan(a*x)*x*a+4*arctan(a*x)^2+1)-1/3*I*c*(c*(a*x-I)*(I+a*x))^(1/2)*(3*I*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+7*I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-7*I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+7*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-7*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
320,1,356,524,0.873000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^2,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \left(\arctan \left(a x \right) a^{2} x^{2}-2 a x -2 \arctan \left(a x \right)\right)}{2 x}-\frac{i a c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(3 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-4 i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+4 \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-4 \dilog \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-4 \dilog \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2*c*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*(arctan(a*x)*a^2*x^2-2*a*x-2*arctan(a*x))/x-1/2*I*a*c*(c*(a*x-I)*(I+a*x))^(1/2)*(3*I*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*I*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))-4*dilog(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*dilog((1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
321,1,412,539,1.346000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^3,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \left(2 \arctan \left(a x \right) a^{2} x^{2}-2 a x -\arctan \left(a x \right)\right)}{2 x^{2}}-\frac{a^{2} c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-6 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+4 i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-4 i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-4 \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+4 \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-2 \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)+6 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2*c*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*(2*arctan(a*x)*a^2*x^2-2*a*x-arctan(a*x))/x^2-1/2*a^2*c*(c*(a*x-I)*(I+a*x))^(1/2)*(-6*I*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)+6*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
322,1,343,541,1.958000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^4,x)","-\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(4 \arctan \left(a x \right)^{2} x^{2} a^{2}+a^{2} x^{2}+\arctan \left(a x \right) x a +\arctan \left(a x \right)^{2}\right)}{3 x^{3}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-6 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+7 i \dilog \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+7 i \dilog \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-7 \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) c \,a^{3}}{3 \sqrt{a^{2} x^{2}+1}}"," ",0,"-1/3*c*(c*(a*x-I)*(I+a*x))^(1/2)*(4*arctan(a*x)^2*x^2*a^2+a^2*x^2+arctan(a*x)*x*a+arctan(a*x)^2)/x^3+1/3*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)*(-6*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+7*I*dilog(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+7*I*dilog((1+I*a*x)/(a^2*x^2+1)^(1/2))-7*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*c*a^3","A"
323,1,309,485,2.638000," ","int(x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(20160 \arctan \left(a x \right)^{2} x^{8} a^{8}-5040 \arctan \left(a x \right) x^{7} a^{7}+54720 \arctan \left(a x \right)^{2} x^{6} a^{6}+720 a^{6} x^{6}-12360 \arctan \left(a x \right) x^{5} a^{5}+43200 \arctan \left(a x \right)^{2} x^{4} a^{4}+1608 a^{4} x^{4}-6150 \arctan \left(a x \right) x^{3} a^{3}+2880 \arctan \left(a x \right)^{2} x^{2} a^{2}-94 a^{2} x^{2}+6345 \arctan \left(a x \right) x a -5760 \arctan \left(a x \right)^{2}-6157\right)}{181440 a^{4}}-\frac{115 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{4032 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/181440*c^2/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*(20160*arctan(a*x)^2*x^8*a^8-5040*arctan(a*x)*x^7*a^7+54720*arctan(a*x)^2*x^6*a^6+720*a^6*x^6-12360*arctan(a*x)*x^5*a^5+43200*arctan(a*x)^2*x^4*a^4+1608*a^4*x^4-6150*arctan(a*x)*x^3*a^3+2880*arctan(a*x)^2*x^2*a^2-94*a^2*x^2+6345*arctan(a*x)*x*a-5760*arctan(a*x)^2-6157)-115/4032*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^4/(a^2*x^2+1)^(1/2)","A"
324,1,376,590,1.760000," ","int(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(5040 \arctan \left(a x \right)^{2} x^{7} a^{7}-1440 \arctan \left(a x \right) x^{6} a^{6}+14280 \arctan \left(a x \right)^{2} x^{5} a^{5}+240 x^{5} a^{5}-3984 \arctan \left(a x \right) x^{4} a^{4}+12390 \arctan \left(a x \right)^{2} x^{3} a^{3}+696 a^{3} x^{3}-2948 \arctan \left(a x \right) a^{2} x^{2}+1575 \arctan \left(a x \right)^{2} x a +430 a x +2746 \arctan \left(a x \right)\right)}{40320 a^{3}}+\frac{i c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(1575 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-1575 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3150 \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3150 i \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3150 \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3150 i \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6352 \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{40320 a^{3} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/40320*c^2/a^3*(c*(a*x-I)*(I+a*x))^(1/2)*(5040*arctan(a*x)^2*x^7*a^7-1440*arctan(a*x)*x^6*a^6+14280*arctan(a*x)^2*x^5*a^5+240*x^5*a^5-3984*arctan(a*x)*x^4*a^4+12390*arctan(a*x)^2*x^3*a^3+696*a^3*x^3-2948*arctan(a*x)*a^2*x^2+1575*arctan(a*x)^2*x*a+430*a*x+2746*arctan(a*x))+1/40320*I*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(1575*I*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-1575*I*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3150*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3150*I*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3150*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3150*I*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6352*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^3/(a^2*x^2+1)^(1/2)","A"
325,1,275,318,1.194000," ","int(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(360 \arctan \left(a x \right)^{2} x^{6} a^{6}-120 \arctan \left(a x \right) x^{5} a^{5}+1080 \arctan \left(a x \right)^{2} x^{4} a^{4}+24 a^{4} x^{4}-390 \arctan \left(a x \right) x^{3} a^{3}+1080 \arctan \left(a x \right)^{2} x^{2} a^{2}+98 a^{2} x^{2}-495 \arctan \left(a x \right) x a +360 \arctan \left(a x \right)^{2}+299\right)}{2520 a^{2}}+\frac{5 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{56 a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2520*c^2/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(360*arctan(a*x)^2*x^6*a^6-120*arctan(a*x)*x^5*a^5+1080*arctan(a*x)^2*x^4*a^4+24*a^4*x^4-390*arctan(a*x)*x^3*a^3+1080*arctan(a*x)^2*x^2*a^2+98*a^2*x^2-495*arctan(a*x)*x*a+360*arctan(a*x)^2+299)+5/56*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^2/(a^2*x^2+1)^(1/2)","A"
326,1,342,480,0.818000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(120 \arctan \left(a x \right)^{2} x^{5} a^{5}-48 \arctan \left(a x \right) x^{4} a^{4}+390 \arctan \left(a x \right)^{2} x^{3} a^{3}+12 a^{3} x^{3}-196 \arctan \left(a x \right) a^{2} x^{2}+495 \arctan \left(a x \right)^{2} x a +80 a x -598 \arctan \left(a x \right)\right)}{720 a}-\frac{i c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(225 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-225 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+450 i \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-450 i \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+450 \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-450 \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+1036 \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{720 a \sqrt{a^{2} x^{2}+1}}"," ",0,"1/720*c^2/a*(c*(a*x-I)*(I+a*x))^(1/2)*(120*arctan(a*x)^2*x^5*a^5-48*arctan(a*x)*x^4*a^4+390*arctan(a*x)^2*x^3*a^3+12*a^3*x^3-196*arctan(a*x)*a^2*x^2+495*arctan(a*x)^2*x*a+80*a*x-598*arctan(a*x))-1/720*I*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(225*I*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-225*I*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+450*I*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-450*I*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+450*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-450*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+1036*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2)))/a/(a^2*x^2+1)^(1/2)","A"
327,1,404,559,1.063000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(12 \arctan \left(a x \right)^{2} x^{4} a^{4}-6 \arctan \left(a x \right) x^{3} a^{3}+44 \arctan \left(a x \right)^{2} x^{2} a^{2}+2 a^{2} x^{2}-35 \arctan \left(a x \right) x a +92 \arctan \left(a x \right)^{2}+31\right)}{60}-\frac{i c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(60 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-60 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+149 i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-149 i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+120 i \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-120 i \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+120 \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-120 \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+149 \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-149 \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{60 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/60*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(12*arctan(a*x)^2*x^4*a^4-6*arctan(a*x)*x^3*a^3+44*arctan(a*x)^2*x^2*a^2+2*a^2*x^2-35*arctan(a*x)*x*a+92*arctan(a*x)^2+31)-1/60*I*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(60*I*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-60*I*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+149*I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-149*I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+120*I*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-120*I*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+120*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-120*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+149*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-149*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
328,1,399,597,1.091000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^2,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(6 \arctan \left(a x \right)^{2} x^{4} a^{4}-4 \arctan \left(a x \right) x^{3} a^{3}+27 \arctan \left(a x \right)^{2} x^{2} a^{2}+2 a^{2} x^{2}-46 \arctan \left(a x \right) x a -24 \arctan \left(a x \right)^{2}\right)}{24 x}-\frac{i a \,c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(45 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-45 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-48 i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+90 i \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-90 i \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+90 \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-90 \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+88 \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-48 \dilog \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-48 \dilog \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{24 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/24*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(6*arctan(a*x)^2*x^4*a^4-4*arctan(a*x)*x^3*a^3+27*arctan(a*x)^2*x^2*a^2+2*a^2*x^2-46*arctan(a*x)*x*a-24*arctan(a*x)^2)/x-1/24*I*a*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(45*I*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-45*I*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-48*I*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+90*I*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-90*I*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+90*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-90*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+88*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))-48*dilog(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-48*dilog((1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
329,1,454,615,1.506000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^3,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 \arctan \left(a x \right)^{2} x^{4} a^{4}-2 \arctan \left(a x \right) x^{3} a^{3}+14 \arctan \left(a x \right)^{2} x^{2} a^{2}+2 a^{2} x^{2}-6 \arctan \left(a x \right) x a -3 \arctan \left(a x \right)^{2}\right)}{6 x^{2}}+\frac{a^{2} c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-15 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+30 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+15 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-30 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-26 i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+26 i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+26 \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-26 \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)-30 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+30 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{6 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/6*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(2*arctan(a*x)^2*x^4*a^4-2*arctan(a*x)*x^3*a^3+14*arctan(a*x)^2*x^2*a^2+2*a^2*x^2-6*arctan(a*x)*x*a-3*arctan(a*x)^2)/x^2+1/6*a^2*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(-15*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+30*I*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+15*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-30*I*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-26*I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+26*I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+26*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-26*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)-30*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+30*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
330,1,401,625,1.814000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^4,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(3 \arctan \left(a x \right)^{2} x^{4} a^{4}-6 \arctan \left(a x \right) x^{3} a^{3}-14 \arctan \left(a x \right)^{2} x^{2} a^{2}-2 a^{2} x^{2}-2 \arctan \left(a x \right) x a -2 \arctan \left(a x \right)^{2}\right)}{6 x^{3}}-\frac{i a^{3} c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(15 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-15 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-26 i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+30 i \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-30 i \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+30 \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-30 \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+12 \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-26 \dilog \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-26 \dilog \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{6 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/6*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(3*arctan(a*x)^2*x^4*a^4-6*arctan(a*x)*x^3*a^3-14*arctan(a*x)^2*x^2*a^2-2*a^2*x^2-2*arctan(a*x)*x*a-2*arctan(a*x)^2)/x^3-1/6*I*a^3*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(15*I*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-15*I*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-26*I*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+30*I*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-30*I*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+30*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-30*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+12*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))-26*dilog(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-26*dilog((1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
331,1,206,258,3.075000," ","int(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(\arctan \left(a x \right)^{2} x^{2} a^{2}-\arctan \left(a x \right) x a -2 \arctan \left(a x \right)^{2}+1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{3 c \,a^{4}}+\frac{5 i \left(i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{3 \sqrt{a^{2} x^{2}+1}\, a^{4} c}"," ",0,"1/3*(arctan(a*x)^2*x^2*a^2-arctan(a*x)*x*a-2*arctan(a*x)^2+1)*(c*(a*x-I)*(I+a*x))^(1/2)/c/a^4+5/3*I*(I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^4/c","A"
332,1,271,346,2.912000," ","int(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(\arctan \left(a x \right) x a -2\right) \arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 c \,a^{3}}-\frac{\left(\arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+4 i \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, a^{3} c}"," ",0,"1/2*(arctan(a*x)*x*a-2)*arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/c/a^3-1/2*(arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*I*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))+2*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^3/c","A"
333,1,180,183,1.071000," ","int(x*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","\frac{\arctan \left(a x \right)^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{a^{2} c}-\frac{2 i \left(i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{2} c}"," ",0,"arctan(a*x)^2*(c*(a*x-I)*(I+a*x))^(1/2)/a^2/c-2*I*(I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^2/c","A"
334,0,0,270,0.579000," ","int(arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{2}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","F"
335,1,197,248,0.766000," ","int(arctan(a*x)^2/x/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}"," ",0,"(arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c","A"
336,1,171,174,0.774000," ","int(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(1/2),x)","-\frac{\arctan \left(a x \right)^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{c x}-\frac{2 i a \left(-i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+i \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}"," ",0,"-arctan(a*x)^2*(c*(a*x-I)*(I+a*x))^(1/2)/c/x-2*I*a*(-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c","A"
337,1,261,337,1.300000," ","int(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^(1/2),x)","-\frac{\left(2 a x +\arctan \left(a x \right)\right) \arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 x^{2} c}-\frac{a^{2} \left(-2 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+4 \arctanh \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, c}"," ",0,"-1/2*(2*a*x+arctan(a*x))*arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/x^2/c-1/2*a^2*(-2*I*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*arctanh((1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c","A"
338,1,206,257,2.183000," ","int(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(2 \arctan \left(a x \right)^{2} x^{2} a^{2}-a^{2} x^{2}-\arctan \left(a x \right) x a -\arctan \left(a x \right)^{2}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{3 c \,x^{3}}+\frac{5 i a^{3} \left(-i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+i \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{3 \sqrt{a^{2} x^{2}+1}\, c}"," ",0,"1/3*(2*arctan(a*x)^2*x^2*a^2-a^2*x^2-arctan(a*x)*x*a-arctan(a*x)^2)*(c*(a*x-I)*(I+a*x))^(1/2)/c/x^3+5/3*I*a^3*(-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c","A"
339,1,294,262,2.784000," ","int(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) a^{4} c^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right)}{2 \left(a^{2} x^{2}+1\right) a^{4} c^{2}}+\frac{\arctan \left(a x \right)^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{a^{4} c^{2}}-\frac{2 i \left(i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{4} c^{2}}"," ",0,"1/2*(arctan(a*x)^2-2+2*I*arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/a^4/c^2-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))/(a^2*x^2+1)/a^4/c^2+arctan(a*x)^2*(c*(a*x-I)*(I+a*x))^(1/2)/a^4/c^2-2*I*(I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a^4/c^2","A"
340,0,0,357,2.720000," ","int(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{2} \arctan \left(a x \right)^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x)","F"
341,1,116,72,0.882000," ","int(x*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x)","-\frac{\left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2} a^{2}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right)}{2 \left(a^{2} x^{2}+1\right) c^{2} a^{2}}"," ",0,"-1/2*(arctan(a*x)^2-2+2*I*arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2/a^2+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))/(a^2*x^2+1)/c^2/a^2","C"
342,1,114,66,0.454000," ","int(arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2} a}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right)}{2 \left(a^{2} x^{2}+1\right) c^{2} a}"," ",0,"1/2*(arctan(a*x)^2-2+2*I*arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2/a+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))/(a^2*x^2+1)/c^2/a","C"
343,1,306,325,0.767000," ","int(arctan(a*x)^2/x/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right)}{2 \left(a^{2} x^{2}+1\right) c^{2}}+\frac{\left(\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{2}}"," ",0,"1/2*(arctan(a*x)^2-2+2*I*arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))/(a^2*x^2+1)/c^2+(arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2","A"
344,1,279,253,0.763000," ","int(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(3/2),x)","-\frac{a \left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right) a}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\arctan \left(a x \right)^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{x \,c^{2}}-\frac{2 i a \left(-i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+i \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{2}}"," ",0,"-1/2*a*(arctan(a*x)^2-2+2*I*arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))*a/(a^2*x^2+1)/c^2-arctan(a*x)^2*(c*(a*x-I)*(I+a*x))^(1/2)/x/c^2-2*I*a*(-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2","A"
345,1,376,425,1.437000," ","int(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^(3/2),x)","-\frac{a^{2} \left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right) a^{2}}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\left(2 a x +\arctan \left(a x \right)\right) \arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 c^{2} x^{2}}-\frac{a^{2} \left(3 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+4 \arctanh \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, c^{2}}"," ",0,"-1/2*a^2*(arctan(a*x)^2-2+2*I*arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))*a^2/(a^2*x^2+1)/c^2-1/2*(2*a*x+arctan(a*x))*arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2/x^2-1/2*a^2*(3*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)-3*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+4*arctanh((1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2","A"
346,1,318,337,2.443000," ","int(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^(3/2),x)","\frac{a^{3} \left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right) a^{3}}{2 \left(a^{2} x^{2}+1\right) c^{2}}+\frac{\left(5 \arctan \left(a x \right)^{2} x^{2} a^{2}-a^{2} x^{2}-\arctan \left(a x \right) x a -\arctan \left(a x \right)^{2}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{3 x^{3} c^{2}}+\frac{11 i a^{3} \left(-i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+i \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{3 \sqrt{a^{2} x^{2}+1}\, c^{2}}"," ",0,"1/2*a^3*(arctan(a*x)^2-2+2*I*arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))*a^3/(a^2*x^2+1)/c^2+1/3*(5*arctan(a*x)^2*x^2*a^2-a^2*x^2-arctan(a*x)*x*a-arctan(a*x)^2)*(c*(a*x-I)*(I+a*x))^(1/2)/x^3/c^2+11/3*I*a^3*(-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2","A"
347,1,454,339,5.709000," ","int(x^5*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{6}}+\frac{7 \left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{6} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{7 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right)}{8 a^{6} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{\left(-6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{6}}+\frac{\arctan \left(a x \right)^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{c^{3} a^{6}}-\frac{2 i \left(i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{6} c^{3}}"," ",0,"1/216*(6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^6+7/8*(arctan(a*x)^2-2+2*I*arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/a^6/c^3/(a^2*x^2+1)-7/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))/a^6/c^3/(a^2*x^2+1)-1/216*(-6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^6+arctan(a*x)^2*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a^6-2*I*(I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a^6/c^3","A"
348,0,0,436,3.118000," ","int(x^4*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{4} \arctan \left(a x \right)^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^4*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x)","F"
349,1,276,148,2.944000," ","int(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x)","-\frac{\left(6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{4}}-\frac{3 \left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right)}{8 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\left(-6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{4}}"," ",0,"-1/216*(6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^4-3/8*(arctan(a*x)^2-2+2*I*arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/a^4/c^3/(a^2*x^2+1)+3/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))/a^4/c^3/(a^2*x^2+1)+1/216*(-6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^4","C"
350,1,272,119,2.804000," ","int(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \left(a^{3} x^{3}-3 i x^{2} a^{2}-3 a x +i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{3}}+\frac{\left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{3} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right)}{8 a^{3} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\left(-6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a^{3} x^{3}+3 i x^{2} a^{2}-3 a x -i\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{3}}"," ",0,"1/216*(6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(a^3*x^3-3*I*x^2*a^2-3*a*x+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^3+1/8*(arctan(a*x)^2-2+2*I*arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/a^3/c^3/(a^2*x^2+1)+1/8*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))/a^3/c^3/(a^2*x^2+1)+1/216*(-6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(c*(a*x-I)*(I+a*x))^(1/2)*(a^3*x^3+3*I*x^2*a^2-3*a*x-I)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^3","C"
351,1,276,117,1.061000," ","int(x*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{2}}-\frac{\left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{2} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right)}{8 a^{2} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{\left(-6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{2}}"," ",0,"1/216*(6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^2-1/8*(arctan(a*x)^2-2+2*I*arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/a^2/c^3/(a^2*x^2+1)+1/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))/a^2/c^3/(a^2*x^2+1)-1/216*(-6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^2","C"
352,1,272,133,0.568000," ","int(arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x)","-\frac{\left(6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \left(a^{3} x^{3}-3 i x^{2} a^{2}-3 a x +i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} a \,c^{3}}+\frac{3 \left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 c^{3} a \left(a^{2} x^{2}+1\right)}+\frac{3 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right)}{8 c^{3} a \left(a^{2} x^{2}+1\right)}-\frac{\left(-6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a^{3} x^{3}+3 i x^{2} a^{2}-3 a x -i\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) a \,c^{3}}"," ",0,"-1/216*(6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(a^3*x^3-3*I*x^2*a^2-3*a*x+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/a/c^3+3/8*(arctan(a*x)^2-2+2*I*arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a/(a^2*x^2+1)+3/8*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))/c^3/a/(a^2*x^2+1)-1/216*(-6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(c*(a*x-I)*(I+a*x))^(1/2)*(a^3*x^3+3*I*x^2*a^2-3*a*x-I)/(a^4*x^4+2*a^2*x^2+1)/a/c^3","C"
353,1,460,388,0.901000," ","int(arctan(a*x)^2/x/(a^2*c*x^2+c)^(5/2),x)","-\frac{\left(6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3}}+\frac{5 \left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 c^{3} \left(a^{2} x^{2}+1\right)}-\frac{5 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right)}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\left(-6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3}}+\frac{\left(\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{3}}"," ",0,"-1/216*(6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3+5/8*(arctan(a*x)^2-2+2*I*arctan(a*x))*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/(a^2*x^2+1)-5/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))/c^3/(a^2*x^2+1)+1/216*(-6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)/(a^4*x^4+2*a^2*x^2+1)/c^3+(arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3","A"
354,1,433,323,0.803000," ","int(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(5/2),x)","\frac{a \left(6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) \left(a^{3} x^{3}-3 i x^{2} a^{2}-3 a x +i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3}}-\frac{7 a \left(\arctan \left(a x \right)^{2}-2+2 i \arctan \left(a x \right)\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 c^{3} \left(a^{2} x^{2}+1\right)}-\frac{7 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{2}-2-2 i \arctan \left(a x \right)\right) a}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a^{3} x^{3}+3 i x^{2} a^{2}-3 a x -i\right) \left(-6 i \arctan \left(a x \right)+9 \arctan \left(a x \right)^{2}-2\right) a}{216 c^{3} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right)}-\frac{\arctan \left(a x \right)^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{x \,c^{3}}-\frac{2 i a \left(-i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+i \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+\polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{3}}"," ",0,"1/216*a*(6*I*arctan(a*x)+9*arctan(a*x)^2-2)*(a^3*x^3-3*I*x^2*a^2-3*a*x+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3-7/8*a*(arctan(a*x)^2-2+2*I*arctan(a*x))*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/(a^2*x^2+1)-7/8*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^2-2-2*I*arctan(a*x))*a/c^3/(a^2*x^2+1)+1/216*(c*(a*x-I)*(I+a*x))^(1/2)*(a^3*x^3+3*I*x^2*a^2-3*a*x-I)*(-6*I*arctan(a*x)+9*arctan(a*x)^2-2)*a/c^3/(a^4*x^4+2*a^2*x^2+1)-arctan(a*x)^2*(c*(a*x-I)*(I+a*x))^(1/2)/x/c^3-2*I*a*(-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3","A"
355,0,0,24,1.587000," ","int(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^2,x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{2}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^2,x)","F"
356,0,0,22,1.543000," ","int(x^m*(a^2*c*x^2+c)*arctan(a*x)^2,x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{2}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)*arctan(a*x)^2,x)","F"
357,0,0,24,0.600000," ","int(x^m*arctan(a*x)^2/(a^2*c*x^2+c),x)","\int \frac{x^{m} \arctan \left(a x \right)^{2}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^m*arctan(a*x)^2/(a^2*c*x^2+c),x)","F"
358,0,0,24,1.618000," ","int(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^2,x)","\int \frac{x^{m} \arctan \left(a x \right)^{2}}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^2,x)","F"
359,0,0,24,1.108000," ","int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{2}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x)","F"
360,0,0,24,1.047000," ","int(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^2,x)","\int x^{m} \sqrt{a^{2} c \,x^{2}+c}\, \arctan \left(a x \right)^{2}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^2,x)","F"
361,0,0,24,1.436000," ","int(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m} \arctan \left(a x \right)^{2}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","F"
362,0,0,24,1.670000," ","int(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{m} \arctan \left(a x \right)^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x)","F"
363,1,313,187,0.151000," ","int(x^3*(a^2*c*x^2+c)*arctan(a*x)^3,x)","\frac{a^{2} c \,x^{6} \arctan \left(a x \right)^{3}}{6}+\frac{c \,x^{4} \arctan \left(a x \right)^{3}}{4}-\frac{a c \,x^{5} \arctan \left(a x \right)^{2}}{10}-\frac{c \,x^{3} \arctan \left(a x \right)^{2}}{12 a}+\frac{c x \arctan \left(a x \right)^{2}}{4 a^{3}}-\frac{c \arctan \left(a x \right)^{3}}{12 a^{4}}+\frac{c \,x^{4} \arctan \left(a x \right)}{20}-\frac{c \,x^{2} \arctan \left(a x \right)}{60 a^{2}}-\frac{7 c \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{30 a^{4}}-\frac{c \,x^{3}}{60 a}+\frac{c x}{15 a^{3}}-\frac{c \arctan \left(a x \right)}{15 a^{4}}-\frac{7 i c \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{60 a^{4}}+\frac{7 i c \ln \left(a x -i\right)^{2}}{120 a^{4}}+\frac{7 i c \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{60 a^{4}}+\frac{7 i c \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{60 a^{4}}-\frac{7 i c \ln \left(a x +i\right)^{2}}{120 a^{4}}+\frac{7 i c \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{60 a^{4}}-\frac{7 i c \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{60 a^{4}}-\frac{7 i c \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{60 a^{4}}"," ",0,"1/6*a^2*c*x^6*arctan(a*x)^3+1/4*c*x^4*arctan(a*x)^3-1/10*a*c*x^5*arctan(a*x)^2-1/12*c*x^3*arctan(a*x)^2/a+1/4*c*x*arctan(a*x)^2/a^3-1/12*c*arctan(a*x)^3/a^4+1/20*c*x^4*arctan(a*x)-1/60*c*x^2*arctan(a*x)/a^2-7/30/a^4*c*arctan(a*x)*ln(a^2*x^2+1)-1/60*c*x^3/a+1/15*c*x/a^3-1/15*c*arctan(a*x)/a^4-7/60*I/a^4*c*ln(I+a*x)*ln(1/2*I*(a*x-I))-7/60*I/a^4*c*dilog(1/2*I*(a*x-I))+7/120*I/a^4*c*ln(a*x-I)^2+7/60*I/a^4*c*ln(I+a*x)*ln(a^2*x^2+1)-7/120*I/a^4*c*ln(I+a*x)^2+7/60*I/a^4*c*ln(a*x-I)*ln(-1/2*I*(I+a*x))-7/60*I/a^4*c*ln(a*x-I)*ln(a^2*x^2+1)+7/60*I/a^4*c*dilog(-1/2*I*(I+a*x))","A"
364,1,2555,182,5.270000," ","int(x^2*(a^2*c*x^2+c)*arctan(a*x)^3,x)","\text{Expression too large to display}"," ",0,"1/3*c*x^3*arctan(a*x)^3-3/40*I/a*c*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*x^2+3/80*I/a*c*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*x^2+3/40*I/a*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*x^2-3/80*I/a*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*x^2+1/10*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))-1/20/a^3*c-1/5/a^3*c*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-7/80*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2-1/5*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/10*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2+3/80*I/a*c*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*x^2-3/80*I/a*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*x^2+3/40/a^2*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2*x-3/80/a^2*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2*x+1/80*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*x^3-1/80*c*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*arctan(a*x)^2*x^3+2/5*I/a^3*c*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-3/80/a^2*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*x+3/80/a^2*c*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*arctan(a*x)^2*x-1/40*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2*x^3+1/80*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2*x^3+1/40*c*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*arctan(a*x)^2*x^3-1/80*c*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*arctan(a*x)^2*x^3-1/80*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+1/10*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3-7/80*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3+1/10*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3-3/40/a^2*c*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*arctan(a*x)^2*x+3/80/a^2*c*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*arctan(a*x)^2*x+1/40*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))-1/80*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2-1/10*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-1/10*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))+7/40*I/a^3*c*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)+1/5/a^3*c*arctan(a*x)^2*ln(a^2*x^2+1)-2/5/a^3*c*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))-2/5/a^3*c*ln(2)*arctan(a*x)^2+2/15*I/a^3*c*arctan(a*x)^3-1/20*c*arctan(a*x)^2/a^3+1/10*c*x*arctan(a*x)/a^2-1/5*c*x^2*arctan(a*x)^2/a-3/20*a*c*x^4*arctan(a*x)^2+1/5*a^2*c*x^5*arctan(a*x)^3-1/20*c*x^2/a+1/10*c*x^3*arctan(a*x)","C"
365,1,276,142,0.122000," ","int(x*(a^2*c*x^2+c)*arctan(a*x)^3,x)","\frac{a^{2} c \arctan \left(a x \right)^{3} x^{4}}{4}+\frac{c \arctan \left(a x \right)^{3} x^{2}}{2}-\frac{a c \arctan \left(a x \right)^{2} x^{3}}{4}-\frac{3 c x \arctan \left(a x \right)^{2}}{4 a}+\frac{c \arctan \left(a x \right)^{3}}{4 a^{2}}+\frac{c \arctan \left(a x \right) x^{2}}{4}+\frac{c \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{2 a^{2}}-\frac{c x}{4 a}+\frac{c \arctan \left(a x \right)}{4 a^{2}}-\frac{i c \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{4 a^{2}}+\frac{i c \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{4 a^{2}}-\frac{i c \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 a^{2}}+\frac{i c \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{4 a^{2}}+\frac{i c \ln \left(a x +i\right)^{2}}{8 a^{2}}-\frac{i c \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{4 a^{2}}+\frac{i c \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{4 a^{2}}-\frac{i c \ln \left(a x -i\right)^{2}}{8 a^{2}}"," ",0,"1/4*a^2*c*arctan(a*x)^3*x^4+1/2*c*arctan(a*x)^3*x^2-1/4*a*c*arctan(a*x)^2*x^3-3/4*c*x*arctan(a*x)^2/a+1/4/a^2*c*arctan(a*x)^3+1/4*c*arctan(a*x)*x^2+1/2/a^2*c*arctan(a*x)*ln(a^2*x^2+1)-1/4*c*x/a+1/4/a^2*c*arctan(a*x)-1/4*I/a^2*c*ln(I+a*x)*ln(a^2*x^2+1)+1/4*I/a^2*c*dilog(1/2*I*(a*x-I))-1/4*I/a^2*c*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/4*I/a^2*c*ln(a*x-I)*ln(a^2*x^2+1)-1/4*I/a^2*c*dilog(-1/2*I*(I+a*x))+1/8*I/a^2*c*ln(I+a*x)^2+1/4*I/a^2*c*ln(I+a*x)*ln(1/2*I*(a*x-I))-1/8*I/a^2*c*ln(a*x-I)^2","A"
366,1,1635,157,3.227000," ","int((a^2*c*x^2+c)*arctan(a*x)^3,x)","\frac{c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \pi  x}{4}-\frac{c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \pi  x}{2}+\frac{c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \pi  x}{2}-\frac{c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \pi  x}{4}+\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \pi}{4 a}-\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \pi}{2 a}-\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \pi}{2 a}+\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{3} \pi}{4 a}-\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \pi}{2 a}+c x \arctan \left(a x \right)^{3}-\frac{i c \arctan \left(a x \right)}{a}+c x \arctan \left(a x \right)+\frac{a^{2} c \arctan \left(a x \right)^{3} x^{3}}{3}-\frac{a c \arctan \left(a x \right)^{2} x^{2}}{2}-\frac{c \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{a}+\frac{2 c \ln \left(2\right) \arctan \left(a x \right)^{2}}{a}+\frac{2 c \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a}-\frac{2 i c \arctan \left(a x \right)^{3}}{3 a}+\frac{c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \pi  x}{4}-\frac{c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{3} \pi  x}{4}-\frac{2 i c \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{a}-\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \pi}{2 a}+\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \pi}{4 a}+\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \pi}{a}+\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \pi}{4 a}-\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \pi}{2 a}-\frac{c \arctan \left(a x \right)^{2}}{2 a}+\frac{c \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{a}+\frac{c \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{a}-\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \pi}{2 a}+\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \pi}{2 a}+\frac{i c \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \pi}{2 a}"," ",0,"-1/2*I/a*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*Pi+c*x*arctan(a*x)^3+c*x*arctan(a*x)+2/a*c*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+1/3*a^2*c*arctan(a*x)^3*x^3-1/2*a*c*arctan(a*x)^2*x^2-1/a*c*arctan(a*x)^2*ln(a^2*x^2+1)+2/a*c*ln(2)*arctan(a*x)^2-2/3*I/a*c*arctan(a*x)^3-I/a*c*arctan(a*x)+1/4*c*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*Pi*x-1/4*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*Pi*x-2*I/a*c*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+1/4*c*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*Pi*x-1/2*c*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*Pi*x+1/2*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*Pi*x-1/4*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*Pi*x+1/4*I/a*c*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*Pi-1/2*I/a*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*Pi-1/2*I/a*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*Pi+1/4*I/a*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*Pi-1/2*I/a*c*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*Pi+1/4*I/a*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*Pi+I/a*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*Pi+1/4*I/a*c*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*Pi-1/2*I/a*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*Pi-1/2*I/a*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*Pi+1/2*I/a*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*Pi+1/2*I/a*c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*Pi+1/a*c*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+1/a*c*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-1/2/a*c*arctan(a*x)^2","C"
367,1,460,239,6.440000," ","int((a^2*c*x^2+c)*arctan(a*x)^3/x,x)","\frac{c \arctan \left(a x \right)^{2} \left(-3-i \arctan \left(a x \right)+\arctan \left(a x \right) x a \right) \left(a x +i\right)}{2}+6 i c \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 c \arctan \left(a x \right) \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)+6 i c \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-c \arctan \left(a x \right)^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)+3 i \arctan \left(a x \right)^{2} c -\frac{3 c \arctan \left(a x \right) \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-3 i c \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+c \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i c \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 c \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 i c \polylog \left(4, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4}+c \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{3 i c \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+6 c \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{3 i c \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}"," ",0,"1/2*c*arctan(a*x)^2*(-3-I*arctan(a*x)+arctan(a*x)*x*a)*(I+a*x)-3*I*c*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*c*arctan(a*x)*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+3*I*arctan(a*x)^2*c-c*arctan(a*x)^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+3/2*I*c*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-3/2*c*arctan(a*x)*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+6*I*c*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))+c*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/2*I*c*arctan(a*x)^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+6*c*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*c*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+c*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/4*I*c*polylog(4,-(1+I*a*x)^2/(a^2*x^2+1))+6*c*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*c*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))","A"
368,1,1826,157,0.602000," ","int((a^2*c*x^2+c)*arctan(a*x)^3/x^2,x)","-3 i a c \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)-6 i a c \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i a c \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{3 i a c \pi  \arctan \left(a x \right)^{2}}{2}+6 a c \arctan \left(a x \right)^{2} \ln \left(2\right)+3 a c \arctan \left(a x \right)^{2} \ln \left(a x \right)-3 a c \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)+3 a c \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 a c \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)+6 a c \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i a c \arctan \left(a x \right)^{3}+6 a c \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 a c \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{3 a c \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-\frac{3 i a c \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}-\frac{3 i a c \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}+3 i a c \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \arctan \left(a x \right)^{2}+\frac{3 i a c \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2}}{2}+\frac{3 i a c \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \arctan \left(a x \right)^{2}}{2}-\frac{3 i a c \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+\frac{3 i a c \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{2}}{2}+\frac{3 i a c \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2}+\frac{3 i a c \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2}-\frac{3 i a c \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}+\frac{3 i a c \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2}-3 i a c \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \arctan \left(a x \right)^{2}+\frac{3 i a c \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2}}{2}-\frac{3 i a c \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(a x \right)^{2}}{2}-\frac{3 i a c \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2}-\frac{3 i a c \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2}+3 a c \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{c \arctan \left(a x \right)^{3}}{x}+a^{2} c x \arctan \left(a x \right)^{3}+\frac{3 i a c \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2}-\frac{3 i a c \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(a x \right)^{2}}{2}"," ",0,"6*a*c*arctan(a*x)^2*ln(2)+3*a*c*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a*c*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a*c*arctan(a*x)^2*ln(a*x)-3*a*c*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+6*a*c*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))-3*a*c*arctan(a*x)^2*ln(a^2*x^2+1)-2*I*a*c*arctan(a*x)^3-3/2*I*a*c*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+3/2*I*a*c*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))-3*I*a*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2+3/2*I*a*c*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2-3/2*I*a*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-3/2*I*a*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+3*I*a*c*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*arctan(a*x)^2+6*a*c*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*a*c*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/2*a*c*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+3/2*I*a*c*Pi*arctan(a*x)^2-3*I*a*c*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-6*I*a*c*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*a*c*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/2*I*a*c*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2+3/2*I*a*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2-3/2*I*a*c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))-3/2*I*a*c*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2-3/2*I*a*c*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-3/2*I*a*c*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*arctan(a*x)^2+3/2*I*a*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2+3/2*I*a*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2+3/2*I*a*c*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2-c*arctan(a*x)^3/x+a^2*c*x*arctan(a*x)^3+3/2*I*a*c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-3/2*I*a*c*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2","C"
369,1,568,273,10.358000," ","int((a^2*c*x^2+c)*arctan(a*x)^3/x^3,x)","-\frac{a^{2} c \arctan \left(a x \right)^{3}}{2}-3 i a^{2} c \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 a c \arctan \left(a x \right)^{2}}{2 x}-\frac{c \arctan \left(a x \right)^{3}}{2 x^{2}}-3 i a^{2} c \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+a^{2} c \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 i a^{2} c \arctan \left(a x \right)^{2}}{2}+6 a^{2} c \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{3 i a^{2} c \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-\frac{3 a^{2} c \arctan \left(a x \right) \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+6 i a^{2} c \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 a^{2} c \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i a^{2} c \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-a^{2} c \arctan \left(a x \right)^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)+6 i a^{2} c \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+a^{2} c \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i a^{2} c \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 a^{2} c \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 a^{2} c \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 i a^{2} c \polylog \left(4, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4}"," ",0,"-1/2*a^2*c*arctan(a*x)^3-3/4*I*a^2*c*polylog(4,-(1+I*a*x)^2/(a^2*x^2+1))-3/2*a*c*arctan(a*x)^2/x-1/2*c*arctan(a*x)^3/x^2-3/2*I*a^2*c*arctan(a*x)^2+a^2*c*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*a^2*c*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*a^2*c*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*a^2*c*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/2*a^2*c*arctan(a*x)*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-3*I*a^2*c*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2*c*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*a^2*c*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-a^2*c*arctan(a*x)^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+3/2*I*a^2*c*arctan(a*x)^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+a^2*c*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*a^2*c*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2*c*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*a^2*c*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*a^2*c*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))","B"
370,1,5426,174,3.709000," ","int((a^2*c*x^2+c)*arctan(a*x)^3/x^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
371,1,411,273,0.158000," ","int(x^3*(a^2*c*x^2+c)^2*arctan(a*x)^3,x)","\frac{a^{4} c^{2} x^{8} \arctan \left(a x \right)^{3}}{8}+\frac{a^{2} c^{2} x^{6} \arctan \left(a x \right)^{3}}{3}+\frac{c^{2} x^{4} \arctan \left(a x \right)^{3}}{4}-\frac{3 a^{3} c^{2} x^{7} \arctan \left(a x \right)^{2}}{56}-\frac{a \,c^{2} x^{5} \arctan \left(a x \right)^{2}}{8}-\frac{c^{2} x^{3} \arctan \left(a x \right)^{2}}{24 a}+\frac{c^{2} x \arctan \left(a x \right)^{2}}{8 a^{3}}-\frac{c^{2} \arctan \left(a x \right)^{3}}{24 a^{4}}+\frac{a^{2} c^{2} x^{6} \arctan \left(a x \right)}{56}+\frac{c^{2} x^{4} \arctan \left(a x \right)}{28}-\frac{5 c^{2} x^{2} \arctan \left(a x \right)}{168 a^{2}}-\frac{2 c^{2} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{21 a^{4}}-\frac{a \,c^{2} x^{5}}{280}-\frac{c^{2} x^{3}}{168 a}+\frac{c^{2} x}{21 a^{3}}-\frac{c^{2} \arctan \left(a x \right)}{21 a^{4}}-\frac{i c^{2} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{21 a^{4}}+\frac{i c^{2} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{21 a^{4}}-\frac{i c^{2} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{21 a^{4}}+\frac{i c^{2} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{21 a^{4}}+\frac{i c^{2} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{21 a^{4}}-\frac{i c^{2} \ln \left(a x +i\right)^{2}}{42 a^{4}}+\frac{i c^{2} \ln \left(a x -i\right)^{2}}{42 a^{4}}-\frac{i c^{2} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{21 a^{4}}"," ",0,"1/8*a^4*c^2*x^8*arctan(a*x)^3+1/3*a^2*c^2*x^6*arctan(a*x)^3+1/4*c^2*x^4*arctan(a*x)^3-3/56*a^3*c^2*x^7*arctan(a*x)^2-1/8*a*c^2*x^5*arctan(a*x)^2-1/24*c^2*x^3*arctan(a*x)^2/a+1/8*c^2*x*arctan(a*x)^2/a^3-1/24*c^2*arctan(a*x)^3/a^4+1/56*a^2*c^2*x^6*arctan(a*x)+1/28*c^2*x^4*arctan(a*x)-5/168*c^2*x^2*arctan(a*x)/a^2-2/21/a^4*c^2*arctan(a*x)*ln(a^2*x^2+1)-1/280*a*c^2*x^5-1/168*c^2*x^3/a+1/21*c^2*x/a^3-1/21*c^2*arctan(a*x)/a^4-1/21*I/a^4*c^2*ln(a*x-I)*ln(a^2*x^2+1)+1/21*I/a^4*c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/21*I/a^4*c^2*dilog(-1/2*I*(I+a*x))+1/21*I/a^4*c^2*ln(I+a*x)*ln(a^2*x^2+1)-1/42*I/a^4*c^2*ln(I+a*x)^2-1/21*I/a^4*c^2*dilog(1/2*I*(a*x-I))+1/42*I/a^4*c^2*ln(a*x-I)^2-1/21*I/a^4*c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))","A"
372,1,1121,282,16.690000," ","int(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^3,x)","\frac{c^{2} \arctan \left(a x \right)^{2}}{140 a^{3}}+\frac{c^{2} x^{3} \arctan \left(a x \right)^{3}}{3}+\frac{2 i c^{2} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{35 a^{3}}-\frac{c^{2} x \arctan \left(a x \right)}{70 a^{2}}-\frac{4 c^{2} x^{2} \arctan \left(a x \right)^{2}}{35 a}-\frac{27 a \,c^{2} x^{4} \arctan \left(a x \right)^{2}}{140}-\frac{a^{3} c^{2} x^{6} \arctan \left(a x \right)^{2}}{14}+\frac{2 a^{2} c^{2} x^{5} \arctan \left(a x \right)^{3}}{5}+\frac{a^{4} c^{2} x^{7} \arctan \left(a x \right)^{3}}{7}-\frac{4 c^{2} \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{35 a^{3}}-\frac{c^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{15 a^{3}}+\frac{8 i c^{2} \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{35 a^{3}}-\frac{2 i c^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2}}{35 a^{3}}-\frac{2 i c^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2}}{35 a^{3}}-\frac{2 i c^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \arctan \left(a x \right)^{2}}{35 a^{3}}+\frac{4 i c^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \arctan \left(a x \right)^{2}}{35 a^{3}}-\frac{4 i c^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \arctan \left(a x \right)^{2}}{35 a^{3}}+\frac{2 i c^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \arctan \left(a x \right)^{2}}{35 a^{3}}+\frac{2 i c^{2} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{35 a^{3}}-\frac{2 i c^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{2}}{35 a^{3}}-\frac{a \,c^{2} x^{4}}{140}-\frac{8 c^{2} \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{35 a^{3}}+\frac{i c^{2} \arctan \left(a x \right)}{15 a^{3}}+\frac{8 i c^{2} \arctan \left(a x \right)^{3}}{105 a^{3}}-\frac{8 c^{2} \arctan \left(a x \right)^{2} \ln \left(2\right)}{35 a^{3}}+\frac{4 c^{2} \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{35 a^{3}}+\frac{a^{2} c^{2} x^{5} \arctan \left(a x \right)}{35}-\frac{2 c^{2}}{105 a^{3}}+\frac{2 i c^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \arctan \left(a x \right)^{2}}{35 a^{3}}-\frac{11 c^{2} x^{2}}{420 a}+\frac{17 c^{2} x^{3} \arctan \left(a x \right)}{210}"," ",0,"1/140*c^2*arctan(a*x)^2/a^3+1/3*c^2*x^3*arctan(a*x)^3-1/70*c^2*x*arctan(a*x)/a^2-4/35*c^2*x^2*arctan(a*x)^2/a-27/140*a*c^2*x^4*arctan(a*x)^2-1/14*a^3*c^2*x^6*arctan(a*x)^2+2/5*a^2*c^2*x^5*arctan(a*x)^3+1/7*a^4*c^2*x^7*arctan(a*x)^3-2/35*I/a^3*c^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2-2/35*I/a^3*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2-2/35*I/a^3*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2+8/35*I/a^3*c^2*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+2/35*I/a^3*c^2*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-1/15/a^3*c^2*ln((1+I*a*x)^2/(a^2*x^2+1)+1)-4/35/a^3*c^2*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+4/35*I/a^3*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2-4/35*I/a^3*c^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*arctan(a*x)^2+2/35*I/a^3*c^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*arctan(a*x)^2+2/35*I/a^3*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*arctan(a*x)^2+2/35*I/a^3*c^2*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3-2/35*I/a^3*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2-1/140*a*c^2*x^4-8/35/a^3*c^2*arctan(a*x)^2*ln(2)+4/35/a^3*c^2*arctan(a*x)^2*ln(a^2*x^2+1)-8/35/a^3*c^2*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+1/15*I/a^3*c^2*arctan(a*x)+8/105*I/a^3*c^2*arctan(a*x)^3+1/35*a^2*c^2*x^5*arctan(a*x)-2/105/a^3*c^2-11/420*c^2*x^2/a+17/210*c^2*x^3*arctan(a*x)","C"
373,1,368,216,0.120000," ","int(x*(a^2*c*x^2+c)^2*arctan(a*x)^3,x)","\frac{a^{4} c^{2} \arctan \left(a x \right)^{3} x^{6}}{6}+\frac{a^{2} c^{2} \arctan \left(a x \right)^{3} x^{4}}{2}+\frac{c^{2} \arctan \left(a x \right)^{3} x^{2}}{2}-\frac{a^{3} c^{2} \arctan \left(a x \right)^{2} x^{5}}{10}-\frac{a \,c^{2} \arctan \left(a x \right)^{2} x^{3}}{3}-\frac{c^{2} x \arctan \left(a x \right)^{2}}{2 a}+\frac{c^{2} \arctan \left(a x \right)^{3}}{6 a^{2}}+\frac{a^{2} c^{2} \arctan \left(a x \right) x^{4}}{20}+\frac{7 c^{2} \arctan \left(a x \right) x^{2}}{30}+\frac{4 c^{2} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{15 a^{2}}-\frac{a \,c^{2} x^{3}}{60}-\frac{11 c^{2} x}{60 a}+\frac{11 c^{2} \arctan \left(a x \right)}{60 a^{2}}+\frac{2 i c^{2} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{15 a^{2}}+\frac{i c^{2} \ln \left(a x +i\right)^{2}}{15 a^{2}}-\frac{i c^{2} \ln \left(a x -i\right)^{2}}{15 a^{2}}+\frac{2 i c^{2} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{15 a^{2}}-\frac{2 i c^{2} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{15 a^{2}}-\frac{2 i c^{2} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{15 a^{2}}+\frac{2 i c^{2} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{15 a^{2}}-\frac{2 i c^{2} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{15 a^{2}}"," ",0,"1/6*a^4*c^2*arctan(a*x)^3*x^6+1/2*a^2*c^2*arctan(a*x)^3*x^4+1/2*c^2*arctan(a*x)^3*x^2-1/10*a^3*c^2*arctan(a*x)^2*x^5-1/3*a*c^2*arctan(a*x)^2*x^3-1/2*c^2*x*arctan(a*x)^2/a+1/6/a^2*c^2*arctan(a*x)^3+1/20*a^2*c^2*arctan(a*x)*x^4+7/30*c^2*arctan(a*x)*x^2+4/15/a^2*c^2*arctan(a*x)*ln(a^2*x^2+1)-1/60*a*c^2*x^3-11/60*c^2*x/a+11/60/a^2*c^2*arctan(a*x)+2/15*I/a^2*c^2*ln(a*x-I)*ln(a^2*x^2+1)+1/15*I/a^2*c^2*ln(I+a*x)^2-2/15*I/a^2*c^2*dilog(-1/2*I*(I+a*x))-1/15*I/a^2*c^2*ln(a*x-I)^2+2/15*I/a^2*c^2*dilog(1/2*I*(a*x-I))-2/15*I/a^2*c^2*ln(I+a*x)*ln(a^2*x^2+1)-2/15*I/a^2*c^2*ln(a*x-I)*ln(-1/2*I*(I+a*x))+2/15*I/a^2*c^2*ln(I+a*x)*ln(1/2*I*(a*x-I))","A"
374,1,2691,260,5.527000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^3,x)","\text{Expression too large to display}"," ",0,"11/10*c^2*x*arctan(a*x)+c^2*x*arctan(a*x)^3-3/20*I*a*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*x^2+4/5*I/a*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^2+2/5*I/a*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2-1/20*a^2*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*x^3+1/10*a^2*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*x^3+1/20*a^2*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*arctan(a*x)^2*x^3-1/10*a^2*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*arctan(a*x)^2*x^3-11/20/a*c^2*arctan(a*x)^2+1/a*c^2*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+4/5/a*c^2*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-1/20*a^2*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*x^3+1/20*a^2*c^2*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*arctan(a*x)^2*x^3+3/20*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*x-3/10*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*x-3/20*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*arctan(a*x)^2*x+3/10*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*arctan(a*x)^2*x+1/20*I/a*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2-2/5*I/a*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*arctan(a*x)^2-2/5*I/a*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2+7/20*I/a*c^2*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*arctan(a*x)^2+3/20*I*a*c^2*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*arctan(a*x)^2*x^2-2/5*I/a*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*arctan(a*x)^2+2/5*I/a*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2-7/10*I/a*c^2*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*arctan(a*x)^2+7/20*I/a*c^2*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*arctan(a*x)^2+1/20*I/a*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2-1/10*I/a*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2+1/10*a^2*c^2*arctan(a*x)*x^3-3/20*a^3*c^2*arctan(a*x)^2*x^4-7/10*a*c^2*arctan(a*x)^2*x^2+1/5*a^4*c^2*arctan(a*x)^3*x^5+2/3*a^2*c^2*arctan(a*x)^3*x^3-4/5/a*c^2*arctan(a*x)^2*ln(a^2*x^2+1)+8/5/a*c^2*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+8/5/a*c^2*ln(2)*arctan(a*x)^2-8/15*I/a*c^2*arctan(a*x)^3-I/a*c^2*arctan(a*x)-3/20*c^2*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*arctan(a*x)^2*x+3/20*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*x-8/5*I/a*c^2*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-1/20/a*c^2-1/20*c^2*x^2*a-2/5*I/a*c^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2-3/20*I*a*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*x^2+3/10*I*a*c^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*x^2-3/10*I*a*c^2*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*arctan(a*x)^2*x^2+3/20*I*a*c^2*Pi*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*arctan(a*x)^2*x^2","C"
375,1,566,329,11.189000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^3/x,x)","\frac{c^{2} \left(-3 i \arctan \left(a x \right)^{3}+3 \arctan \left(a x \right)^{3} a x -i \arctan \left(a x \right)^{3} a^{2} x^{2}+\arctan \left(a x \right)^{3} a^{3} x^{3}-8 \arctan \left(a x \right)^{2}+i \arctan \left(a x \right)^{2} a x -\arctan \left(a x \right)^{2} x^{2} a^{2}-i \arctan \left(a x \right)+\arctan \left(a x \right) x a -1\right) \left(a x +i\right)}{4}+6 i c^{2} \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-4 c^{2} \arctan \left(a x \right) \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)+\frac{3 i c^{2} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+4 i c^{2} \arctan \left(a x \right)^{2}+6 i c^{2} \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i c^{2} \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-c^{2} \arctan \left(a x \right)^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)+2 i c^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)-\frac{3 c^{2} \arctan \left(a x \right) \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+c^{2} \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 i c^{2} \polylog \left(4, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4}+6 c^{2} \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+c^{2} \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i c^{2} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 c^{2} \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)"," ",0,"1/4*c^2*(-3*I*arctan(a*x)^3+3*arctan(a*x)^3*a*x-I*arctan(a*x)^3*a^2*x^2+arctan(a*x)^3*a^3*x^3-8*arctan(a*x)^2+I*arctan(a*x)^2*a*x-arctan(a*x)^2*x^2*a^2-I*arctan(a*x)+arctan(a*x)*x*a-1)*(I+a*x)-3/4*I*c^2*polylog(4,-(1+I*a*x)^2/(a^2*x^2+1))-4*c^2*arctan(a*x)*ln((1+I*a*x)^2/(a^2*x^2+1)+1)-3*I*c^2*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*c^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+4*I*c^2*arctan(a*x)^2+6*I*c^2*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))-c^2*arctan(a*x)^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)-3*I*c^2*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/2*c^2*arctan(a*x)*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+c^2*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*c^2*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*c^2*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+c^2*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/2*I*c^2*arctan(a*x)^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+6*c^2*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))","A"
376,1,5486,261,7.839000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^3/x^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
377,1,682,365,10.274000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^3/x^3,x)","\frac{a^{4} c^{2} x^{2} \arctan \left(a x \right)^{3}}{2}-\frac{3 a^{3} c^{2} x \arctan \left(a x \right)^{2}}{2}-\frac{3 a \,c^{2} \arctan \left(a x \right)^{2}}{2 x}-\frac{c^{2} \arctan \left(a x \right)^{3}}{2 x^{2}}+2 a^{2} c^{2} \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i a^{2} c^{2} \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+12 a^{2} c^{2} \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 i a^{2} c^{2} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)-3 a^{2} c^{2} \arctan \left(a x \right) \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)-6 i a^{2} c^{2} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 a^{2} c^{2} \arctan \left(a x \right) \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)+12 i a^{2} c^{2} \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 a^{2} c^{2} \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{3 i a^{2} c^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-2 a^{2} c^{2} \arctan \left(a x \right)^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)+12 i a^{2} c^{2} \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 a^{2} c^{2} \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i a^{2} c^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 a^{2} c^{2} \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 i a^{2} c^{2} \polylog \left(4, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+12 a^{2} c^{2} \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i a^{2} c^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)"," ",0,"1/2*a^4*c^2*x^2*arctan(a*x)^3-3/2*a^3*c^2*x*arctan(a*x)^2-3/2*a*c^2*arctan(a*x)^2/x-1/2*c^2*arctan(a*x)^3/x^2+2*a^2*c^2*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+12*I*a^2*c^2*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+12*a^2*c^2*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+12*I*a^2*c^2*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*a^2*c^2*arctan(a*x)*ln((1+I*a*x)^2/(a^2*x^2+1)+1)-3*I*a^2*c^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*a^2*c^2*arctan(a*x)*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-6*I*a^2*c^2*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2*c^2*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*I*a^2*c^2*arctan(a*x)^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-2*a^2*c^2*arctan(a*x)^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+3/2*I*a^2*c^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+2*a^2*c^2*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/2*I*a^2*c^2*polylog(4,-(1+I*a*x)^2/(a^2*x^2+1))+3*a^2*c^2*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*a^2*c^2*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+12*a^2*c^2*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*a^2*c^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))","A"
378,1,5651,288,11.291000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^3/x^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
379,1,471,333,0.132000," ","int(x^3*(a^2*c*x^2+c)^3*arctan(a*x)^3,x)","\frac{13 i c^{3} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{525 a^{4}}-\frac{13 i c^{3} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{525 a^{4}}-\frac{13 i c^{3} \ln \left(a x +i\right)^{2}}{1050 a^{4}}+\frac{13 i c^{3} \ln \left(a x -i\right)^{2}}{1050 a^{4}}-\frac{26 c^{3} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{525 a^{4}}+\frac{389 c^{3} x}{12600 a^{3}}-\frac{17 c^{3} x^{3}}{9450 a}-\frac{a \,c^{3} x^{5}}{252}-\frac{a^{3} c^{3} x^{7}}{840}-\frac{389 c^{3} \arctan \left(a x \right)}{12600 a^{4}}+\frac{53 c^{3} x^{4} \arctan \left(a x \right)}{2100}-\frac{c^{3} \arctan \left(a x \right)^{3}}{40 a^{4}}+\frac{c^{3} x^{4} \arctan \left(a x \right)^{3}}{4}+\frac{71 a^{2} c^{3} x^{6} \arctan \left(a x \right)}{2520}+\frac{a^{4} c^{3} x^{8} \arctan \left(a x \right)}{120}-\frac{107 c^{3} x^{2} \arctan \left(a x \right)}{4200 a^{2}}+\frac{3 c^{3} x \arctan \left(a x \right)^{2}}{40 a^{3}}-\frac{c^{3} x^{3} \arctan \left(a x \right)^{2}}{40 a}-\frac{27 a \,c^{3} x^{5} \arctan \left(a x \right)^{2}}{200}-\frac{33 a^{3} c^{3} x^{7} \arctan \left(a x \right)^{2}}{280}-\frac{a^{5} c^{3} x^{9} \arctan \left(a x \right)^{2}}{30}+\frac{a^{2} c^{3} x^{6} \arctan \left(a x \right)^{3}}{2}+\frac{3 a^{4} c^{3} x^{8} \arctan \left(a x \right)^{3}}{8}+\frac{a^{6} c^{3} x^{10} \arctan \left(a x \right)^{3}}{10}-\frac{13 i c^{3} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{525 a^{4}}-\frac{13 i c^{3} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{525 a^{4}}+\frac{13 i c^{3} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{525 a^{4}}+\frac{13 i c^{3} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{525 a^{4}}"," ",0,"-13/525*I/a^4*c^3*ln(a*x-I)*ln(a^2*x^2+1)-26/525/a^4*c^3*arctan(a*x)*ln(a^2*x^2+1)-13/1050*I/a^4*c^3*ln(I+a*x)^2+13/1050*I/a^4*c^3*ln(a*x-I)^2+13/525*I/a^4*c^3*dilog(-1/2*I*(I+a*x))-13/525*I/a^4*c^3*dilog(1/2*I*(a*x-I))+389/12600*c^3*x/a^3-17/9450*c^3*x^3/a-1/252*a*c^3*x^5-1/840*a^3*c^3*x^7-389/12600*c^3*arctan(a*x)/a^4+53/2100*c^3*x^4*arctan(a*x)-1/40*c^3*arctan(a*x)^3/a^4+1/4*c^3*x^4*arctan(a*x)^3+71/2520*a^2*c^3*x^6*arctan(a*x)+1/120*a^4*c^3*x^8*arctan(a*x)-107/4200*c^3*x^2*arctan(a*x)/a^2+3/40*c^3*x*arctan(a*x)^2/a^3-1/40*c^3*x^3*arctan(a*x)^2/a-27/200*a*c^3*x^5*arctan(a*x)^2-33/280*a^3*c^3*x^7*arctan(a*x)^2-1/30*a^5*c^3*x^9*arctan(a*x)^2+1/2*a^2*c^3*x^6*arctan(a*x)^3+3/8*a^4*c^3*x^8*arctan(a*x)^3+1/10*a^6*c^3*x^10*arctan(a*x)^3-13/525*I/a^4*c^3*ln(I+a*x)*ln(1/2*I*(a*x-I))+13/525*I/a^4*c^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))+13/525*I/a^4*c^3*ln(I+a*x)*ln(a^2*x^2+1)","A"
380,1,1181,342,24.348000," ","int(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^3,x)","-\frac{107 c^{3} x^{2}}{7560 a}-\frac{11 a \,c^{3} x^{4}}{1260}-\frac{a^{3} c^{3} x^{6}}{504}+\frac{239 c^{3} x^{3} \arctan \left(a x \right)}{3780}+\frac{c^{3} x^{3} \arctan \left(a x \right)^{3}}{3}+\frac{47 c^{3} \arctan \left(a x \right)^{2}}{2520 a^{3}}-\frac{47 c^{3} x \arctan \left(a x \right)}{1260 a^{2}}-\frac{8 c^{3} x^{2} \arctan \left(a x \right)^{2}}{105 a}-\frac{89 a \,c^{3} x^{4} \arctan \left(a x \right)^{2}}{420}-\frac{10 a^{3} c^{3} x^{6} \arctan \left(a x \right)^{2}}{63}-\frac{a^{5} c^{3} x^{8} \arctan \left(a x \right)^{2}}{24}+\frac{3 a^{2} c^{3} x^{5} \arctan \left(a x \right)^{3}}{5}+\frac{3 a^{4} c^{3} x^{7} \arctan \left(a x \right)^{3}}{7}+\frac{a^{6} c^{3} x^{9} \arctan \left(a x \right)^{3}}{9}+\frac{4 i c^{3} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{105 a^{3}}+\frac{4 i c^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \arctan \left(a x \right)^{2}}{105 a^{3}}+\frac{4 i c^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(a x \right)^{2}}{105 a^{3}}-\frac{4 i c^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{2}}{105 a^{3}}-\frac{c^{3}}{135 a^{3}}-\frac{8 c^{3} \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{105 a^{3}}-\frac{62 c^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{945 a^{3}}+\frac{16 i c^{3} \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{105 a^{3}}-\frac{4 i c^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2}}{105 a^{3}}-\frac{4 i c^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2}}{105 a^{3}}+\frac{8 i c^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \arctan \left(a x \right)^{2}}{105 a^{3}}-\frac{8 i c^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \arctan \left(a x \right)^{2}}{105 a^{3}}+\frac{4 i c^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \arctan \left(a x \right)^{2}}{105 a^{3}}-\frac{4 i c^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \arctan \left(a x \right)^{2}}{105 a^{3}}+\frac{8 c^{3} \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{105 a^{3}}-\frac{16 c^{3} \arctan \left(a x \right)^{2} \ln \left(2\right)}{105 a^{3}}+\frac{59 a^{2} c^{3} x^{5} \arctan \left(a x \right)}{1260}+\frac{a^{4} c^{3} x^{7} \arctan \left(a x \right)}{84}-\frac{16 c^{3} \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{105 a^{3}}+\frac{16 i c^{3} \arctan \left(a x \right)^{3}}{315 a^{3}}+\frac{62 i c^{3} \arctan \left(a x \right)}{945 a^{3}}"," ",0,"-4/105*I/a^3*c^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2-107/7560*c^3*x^2/a-11/1260*a*c^3*x^4-1/504*a^3*c^3*x^6+239/3780*c^3*x^3*arctan(a*x)+1/3*c^3*x^3*arctan(a*x)^3+47/2520*c^3*arctan(a*x)^2/a^3-47/1260*c^3*x*arctan(a*x)/a^2-8/105*c^3*x^2*arctan(a*x)^2/a-89/420*a*c^3*x^4*arctan(a*x)^2-10/63*a^3*c^3*x^6*arctan(a*x)^2-1/24*a^5*c^3*x^8*arctan(a*x)^2+3/5*a^2*c^3*x^5*arctan(a*x)^3+3/7*a^4*c^3*x^7*arctan(a*x)^3+1/9*a^6*c^3*x^9*arctan(a*x)^3+4/105*I/a^3*c^3*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-1/135/a^3*c^3+4/105*I/a^3*c^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*arctan(a*x)^2+4/105*I/a^3*c^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2-4/105*I/a^3*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2+16/105*I/a^3*c^3*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-4/105*I/a^3*c^3*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2+8/105*I/a^3*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2-8/105*I/a^3*c^3*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*arctan(a*x)^2+4/105*I/a^3*c^3*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*arctan(a*x)^2-4/105*I/a^3*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2-16/105/a^3*c^3*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+8/105/a^3*c^3*arctan(a*x)^2*ln(a^2*x^2+1)-16/105/a^3*c^3*arctan(a*x)^2*ln(2)+16/315*I/a^3*c^3*arctan(a*x)^3+62/945*I/a^3*c^3*arctan(a*x)-8/105/a^3*c^3*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-62/945/a^3*c^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+59/1260*a^2*c^3*x^5*arctan(a*x)+1/84*a^4*c^3*x^7*arctan(a*x)","C"
381,1,428,276,0.125000," ","int(x*(a^2*c*x^2+c)^3*arctan(a*x)^3,x)","\frac{3 i c^{3} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{35 a^{2}}-\frac{3 i c^{3} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{35 a^{2}}+\frac{3 i c^{3} \ln \left(a x +i\right)^{2}}{70 a^{2}}-\frac{3 i c^{3} \ln \left(a x -i\right)^{2}}{70 a^{2}}-\frac{9 a^{3} c^{3} \arctan \left(a x \right)^{2} x^{5}}{40}-\frac{3 a \,c^{3} \arctan \left(a x \right)^{2} x^{3}}{8}+\frac{a^{4} c^{3} \arctan \left(a x \right) x^{6}}{56}+\frac{3 a^{2} c^{3} \arctan \left(a x \right) x^{4}}{35}+\frac{6 c^{3} \arctan \left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{35 a^{2}}+\frac{3 a^{2} c^{3} \arctan \left(a x \right)^{3} x^{4}}{4}+\frac{a^{6} c^{3} \arctan \left(a x \right)^{3} x^{8}}{8}+\frac{a^{4} c^{3} \arctan \left(a x \right)^{3} x^{6}}{2}-\frac{3 a^{5} c^{3} \arctan \left(a x \right)^{2} x^{7}}{56}-\frac{a^{3} c^{3} x^{5}}{280}-\frac{19 c^{3} x}{140 a}-\frac{19 a \,c^{3} x^{3}}{840}-\frac{3 c^{3} x \arctan \left(a x \right)^{2}}{8 a}-\frac{3 i c^{3} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{35 a^{2}}+\frac{3 i c^{3} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{35 a^{2}}+\frac{3 i c^{3} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{35 a^{2}}-\frac{3 i c^{3} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{35 a^{2}}+\frac{57 c^{3} \arctan \left(a x \right) x^{2}}{280}+\frac{c^{3} \arctan \left(a x \right)^{3} x^{2}}{2}+\frac{c^{3} \arctan \left(a x \right)^{3}}{8 a^{2}}+\frac{19 c^{3} \arctan \left(a x \right)}{140 a^{2}}"," ",0,"-9/40*a^3*c^3*arctan(a*x)^2*x^5-3/8*a*c^3*arctan(a*x)^2*x^3+1/56*a^4*c^3*arctan(a*x)*x^6+3/35*a^2*c^3*arctan(a*x)*x^4+6/35/a^2*c^3*arctan(a*x)*ln(a^2*x^2+1)+3/4*a^2*c^3*arctan(a*x)^3*x^4+3/35*I/a^2*c^3*dilog(1/2*I*(a*x-I))+3/70*I/a^2*c^3*ln(I+a*x)^2-3/35*I/a^2*c^3*dilog(-1/2*I*(I+a*x))-3/70*I/a^2*c^3*ln(a*x-I)^2+1/8*a^6*c^3*arctan(a*x)^3*x^8+1/2*a^4*c^3*arctan(a*x)^3*x^6-3/56*a^5*c^3*arctan(a*x)^2*x^7-1/280*a^3*c^3*x^5-19/140*c^3*x/a-19/840*a*c^3*x^3-3/8*c^3*x*arctan(a*x)^2/a+3/35*I/a^2*c^3*ln(I+a*x)*ln(1/2*I*(a*x-I))-3/35*I/a^2*c^3*ln(I+a*x)*ln(a^2*x^2+1)-3/35*I/a^2*c^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))+3/35*I/a^2*c^3*ln(a*x-I)*ln(a^2*x^2+1)+57/280*c^3*arctan(a*x)*x^2+1/2*c^3*arctan(a*x)^3*x^2+1/8/a^2*c^3*arctan(a*x)^3+19/140/a^2*c^3*arctan(a*x)","A"
382,1,1134,349,9.655000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^3,x)","-\frac{12 i c^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(a x \right)^{2}}{35 a}+\frac{12 i c^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{2}}{35 a}-\frac{12 i c^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \arctan \left(a x \right)^{2}}{35 a}+\frac{38 c^{3} x \arctan \left(a x \right)}{35}+c^{3} x \arctan \left(a x \right)^{3}-\frac{48 i c^{3} \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{35 a}+\frac{24 i c^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \arctan \left(a x \right)^{2}}{35 a}-\frac{12 i c^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \arctan \left(a x \right)^{2}}{35 a}+\frac{12 i c^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \arctan \left(a x \right)^{2}}{35 a}+\frac{12 i c^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2}}{35 a}+\frac{12 i c^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2}}{35 a}-\frac{24 i c^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \arctan \left(a x \right)^{2}}{35 a}-\frac{12 a^{3} c^{3} \arctan \left(a x \right)^{2} x^{4}}{35}-\frac{57 a \,c^{3} \arctan \left(a x \right)^{2} x^{2}}{70}+\frac{19 a^{2} c^{3} \arctan \left(a x \right) x^{3}}{105}+\frac{a^{4} c^{3} \arctan \left(a x \right) x^{5}}{35}+\frac{a^{6} c^{3} \arctan \left(a x \right)^{3} x^{7}}{7}+\frac{3 a^{4} c^{3} \arctan \left(a x \right)^{3} x^{5}}{5}-\frac{8 a \,c^{3} x^{2}}{105}-\frac{a^{3} x^{4} c^{3}}{140}-\frac{19 c^{3} \arctan \left(a x \right)^{2}}{35 a}-\frac{12 i c^{3} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{35 a}-\frac{29 c^{3}}{420 a}+\frac{14 c^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{15 a}+\frac{24 c^{3} \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{35 a}+a^{2} c^{3} \arctan \left(a x \right)^{3} x^{3}-\frac{a^{5} c^{3} \arctan \left(a x \right)^{2} x^{6}}{14}+\frac{48 c^{3} \arctan \left(a x \right)^{2} \ln \left(2\right)}{35 a}-\frac{24 c^{3} \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{35 a}+\frac{48 c^{3} \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{35 a}-\frac{14 i c^{3} \arctan \left(a x \right)}{15 a}-\frac{16 i c^{3} \arctan \left(a x \right)^{3}}{35 a}"," ",0,"38/35*c^3*x*arctan(a*x)+c^3*x*arctan(a*x)^3+24/35*I/a*c^3*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*arctan(a*x)^2-12/35*I/a*c^3*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*arctan(a*x)^2+12/35*I/a*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2+12/35*I/a*c^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2+12/35*I/a*c^3*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2-24/35*I/a*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2-48/35*I/a*c^3*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-12/35*a^3*c^3*arctan(a*x)^2*x^4-57/70*a*c^3*arctan(a*x)^2*x^2+19/105*a^2*c^3*arctan(a*x)*x^3+1/35*a^4*c^3*arctan(a*x)*x^5+1/7*a^6*c^3*arctan(a*x)^3*x^7+3/5*a^4*c^3*arctan(a*x)^3*x^5-8/105*a*c^3*x^2-1/140*a^3*x^4*c^3-19/35/a*c^3*arctan(a*x)^2+14/15/a*c^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+24/35/a*c^3*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-29/420/a*c^3+a^2*c^3*arctan(a*x)^3*x^3-1/14*a^5*c^3*arctan(a*x)^2*x^6+48/35/a*c^3*arctan(a*x)^2*ln(2)+48/35/a*c^3*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))-24/35/a*c^3*arctan(a*x)^2*ln(a^2*x^2+1)-14/15*I/a*c^3*arctan(a*x)-16/35*I/a*c^3*arctan(a*x)^3-12/35*I/a*c^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2+12/35*I/a*c^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2-12/35*I/a*c^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*arctan(a*x)^2-12/35*I/a*c^3*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)","C"
383,1,664,390,17.054000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^3/x,x)","\frac{c^{3} \left(i a x +55 \arctan \left(a x \right)^{3} a x -3 i \arctan \left(a x \right) a^{2} x^{2}+35 \arctan \left(a x \right)^{3} a^{3} x^{3}-35 i \arctan \left(a x \right)^{3} a^{2} x^{2}+10 \arctan \left(a x \right)^{3} a^{5} x^{5}-136 \arctan \left(a x \right)^{2}-10 i \arctan \left(a x \right)^{3} a^{4} x^{4}-29 \arctan \left(a x \right)^{2} x^{2} a^{2}+6 i \arctan \left(a x \right)^{2} a^{3} x^{3}-6 \arctan \left(a x \right)^{2} x^{4} a^{4}+29 i \arctan \left(a x \right)^{2} a x +26 \arctan \left(a x \right) x a -26 i \arctan \left(a x \right)+3 \arctan \left(a x \right) x^{3} a^{3}-25-55 i \arctan \left(a x \right)^{3}-a^{2} x^{2}\right) \left(a x +i\right)}{60}+\frac{68 i c^{3} \arctan \left(a x \right)^{2}}{15}-\frac{68 c^{3} \arctan \left(a x \right) \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{15}+6 i c^{3} \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-c^{3} \arctan \left(a x \right)^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)-3 i c^{3} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 c^{3} \arctan \left(a x \right) \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-3 i c^{3} \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+c^{3} \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{3 i c^{3} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+6 c^{3} \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{34 i c^{3} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{15}+c^{3} \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i c^{3} \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 c^{3} \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 i c^{3} \polylog \left(4, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4}"," ",0,"1/60*c^3*(I*a*x+55*arctan(a*x)^3*a*x-3*I*arctan(a*x)*a^2*x^2+35*arctan(a*x)^3*a^3*x^3-35*I*arctan(a*x)^3*a^2*x^2+10*arctan(a*x)^3*a^5*x^5-136*arctan(a*x)^2-10*I*arctan(a*x)^3*a^4*x^4-29*arctan(a*x)^2*x^2*a^2+6*I*arctan(a*x)^2*a^3*x^3-6*arctan(a*x)^2*x^4*a^4+29*I*arctan(a*x)^2*a*x+26*arctan(a*x)*x*a-26*I*arctan(a*x)+3*arctan(a*x)*x^3*a^3-25-55*I*arctan(a*x)^3-a^2*x^2)*(I+a*x)+68/15*I*c^3*arctan(a*x)^2-68/15*c^3*arctan(a*x)*ln((1+I*a*x)^2/(a^2*x^2+1)+1)-3/4*I*c^3*polylog(4,-(1+I*a*x)^2/(a^2*x^2+1))-c^3*arctan(a*x)^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+3/2*I*c^3*arctan(a*x)^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-3/2*c^3*arctan(a*x)*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+6*I*c^3*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))+c^3*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*c^3*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*c^3*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+34/15*I*c^3*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+c^3*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*c^3*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*c^3*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*c^3*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))","A"
384,1,10139,321,13.825000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^3/x^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
385,1,790,449,21.299000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^3/x^3,x)","\frac{9 i a^{2} c^{3} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-9 i a^{2} c^{3} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-9 i a^{2} c^{3} \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{a^{3} c^{3} x}{4}+\frac{a^{2} c^{3} \arctan \left(a x \right)}{4}+\frac{3 a^{2} c^{3} \arctan \left(a x \right)^{3}}{4}-\frac{c^{3} \arctan \left(a x \right)^{3}}{2 x^{2}}-\frac{3 a \,c^{3} \arctan \left(a x \right)^{2}}{2 x}-\frac{15 a^{3} c^{3} x \arctan \left(a x \right)^{2}}{4}-\frac{a^{5} c^{3} x^{3} \arctan \left(a x \right)^{2}}{4}+\frac{3 a^{4} c^{3} x^{2} \arctan \left(a x \right)^{3}}{2}+\frac{a^{6} c^{3} x^{4} \arctan \left(a x \right)^{3}}{4}+\frac{a^{4} c^{3} x^{2} \arctan \left(a x \right)}{4}+18 a^{2} c^{3} \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+18 i a^{2} c^{3} \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 a^{2} c^{3} \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-7 a^{2} c^{3} \arctan \left(a x \right) \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)-\frac{9 i a^{2} c^{3} \polylog \left(4, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4}+18 i a^{2} c^{3} \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i a^{2} c^{3} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i a^{2} c^{3} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{7 i a^{2} c^{3} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+18 a^{2} c^{3} \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{9 a^{2} c^{3} \arctan \left(a x \right) \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+3 a^{2} c^{3} \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 a^{2} c^{3} \arctan \left(a x \right)^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)+3 a^{2} c^{3} \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 a^{2} c^{3} \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i a^{2} c^{3} \arctan \left(a x \right)^{2}-\frac{i a^{2} c^{3}}{4}"," ",0,"-1/4*a^3*c^3*x+1/4*a^2*c^3*arctan(a*x)+9/2*I*a^2*c^3*arctan(a*x)^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+3/4*a^2*c^3*arctan(a*x)^3-1/2*c^3*arctan(a*x)^3/x^2-9*I*a^2*c^3*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-9*I*a^2*c^3*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/2*a*c^3*arctan(a*x)^2/x-15/4*a^3*c^3*x*arctan(a*x)^2-1/4*a^5*c^3*x^3*arctan(a*x)^2+3/2*a^4*c^3*x^2*arctan(a*x)^3+1/4*a^6*c^3*x^4*arctan(a*x)^3+1/4*a^4*c^3*x^2*arctan(a*x)+3*a^2*c^3*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*a^2*c^3*arctan(a*x)^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+3*a^2*c^3*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2*c^3*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+18*a^2*c^3*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+18*I*a^2*c^3*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-9/4*I*a^2*c^3*polylog(4,-(1+I*a*x)^2/(a^2*x^2+1))+2*I*a^2*c^3*arctan(a*x)^2+18*I*a^2*c^3*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*a^2*c^3*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*a^2*c^3*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+7/2*I*a^2*c^3*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+3*a^2*c^3*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+18*a^2*c^3*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-7*a^2*c^3*arctan(a*x)*ln((1+I*a*x)^2/(a^2*x^2+1)+1)-9/2*a^2*c^3*arctan(a*x)*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-1/4*I*a^2*c^3","A"
386,1,7948,320,11.110000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^3/x^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
387,1,1740,200,3.073000," ","int(x^4*arctan(a*x)^3/(a^2*c*x^2+c),x)","-\frac{\arctan \left(a x \right)^{2}}{2 a^{5} c}-\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \arctan \left(a x \right)^{2} \pi}{2 a^{5} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \arctan \left(a x \right)^{2} \pi}{2 a^{5} c}+\frac{\arctan \left(a x \right)^{4}}{4 a^{5} c}-\frac{x^{2} \arctan \left(a x \right)^{2}}{2 a^{3} c}-\frac{x \arctan \left(a x \right)^{3}}{a^{4} c}+\frac{x^{3} \arctan \left(a x \right)^{3}}{3 a^{2} c}+\frac{\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{3} \arctan \left(a x \right)^{2} \pi  x}{2 a^{4} c}-\frac{\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{2} \pi  x}{2 a^{4} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \arctan \left(a x \right)^{2} \pi}{a^{5} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(a x \right)^{2} \pi}{a^{5} c}-\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{2} \pi}{2 a^{5} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{3} \arctan \left(a x \right)^{2} \pi}{2 a^{5} c}-\frac{4 \ln \left(2\right) \arctan \left(a x \right)^{2}}{a^{5} c}+\frac{2 \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{a^{5} c}-\frac{i \arctan \left(a x \right)}{a^{5} c}+\frac{4 i \arctan \left(a x \right)^{3}}{3 a^{5} c}-\frac{4 \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{5} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{a^{5} c}-\frac{\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \arctan \left(a x \right)^{2} \pi  x}{a^{4} c}+\frac{\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \arctan \left(a x \right)^{2} \pi  x}{a^{4} c}-\frac{\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \arctan \left(a x \right)^{2} \pi  x}{2 a^{4} c}+\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \arctan \left(a x \right)^{2} \pi}{a^{5} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \arctan \left(a x \right)^{2} \pi}{a^{5} c}+\frac{\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+i\right)^{2} \arctan \left(a x \right)^{2} \pi  x}{2 a^{4} c}-\frac{2 i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)^{2} \pi}{a^{5} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{2} \pi}{a^{5} c}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(a x \right)^{2} \pi}{a^{5} c}+\frac{4 i \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{a^{5} c}+\frac{x \arctan \left(a x \right)}{a^{4} c}-\frac{2 \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{a^{5} c}+\frac{\ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{a^{5} c}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(a x \right)^{2} \pi}{a^{5} c}"," ",0,"-1/2*arctan(a*x)^2/a^5/c+1/4*arctan(a*x)^4/a^5/c-1/2*x^2*arctan(a*x)^2/a^3/c-x*arctan(a*x)^3/a^4/c+1/3*x^3*arctan(a*x)^3/a^2/c+I/a^5/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*arctan(a*x)^2*Pi+1/a^5/c*ln((1+I*a*x)^2/(a^2*x^2+1)+1)-2/a^5/c*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-1/a^4/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*arctan(a*x)^2*Pi*x-I/a^5/c*arctan(a*x)+4/3*I/a^5/c*arctan(a*x)^3-4/a^5/c*ln(2)*arctan(a*x)^2+2/a^5/c*arctan(a*x)^2*ln(a^2*x^2+1)-4/a^5/c*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+1/a^4/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2*Pi*x-1/2/a^4/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2*Pi*x+I/a^5/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2*Pi+I/a^5/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)*arctan(a*x)^2*Pi+4*I/a^5/c*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+1/2/a^4/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*arctan(a*x)^2*Pi*x-2*I/a^5/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^2*Pi-I/a^5/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^2*Pi-I/a^5/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*Pi-1/2*I/a^5/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2*Pi-1/2*I/a^5/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)+I)^2*arctan(a*x)^2*Pi+x*arctan(a*x)/a^4/c+1/2/a^4/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*arctan(a*x)^2*Pi*x-1/2/a^4/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*Pi*x+I/a^5/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*arctan(a*x)^2*Pi+I/a^5/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*Pi-1/2*I/a^5/c*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^2*Pi-1/2*I/a^5/c*csgn(I*(1+I*a*x)^4/(a^2*x^2+1)^2+2*I*(1+I*a*x)^2/(a^2*x^2+1)+I)^3*arctan(a*x)^2*Pi+I/a^5/c*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^2*Pi","C"
388,1,292,231,8.526000," ","int(x^3*arctan(a*x)^3/(a^2*c*x^2+c),x)","-\frac{i \arctan \left(a x \right)^{4}}{4 a^{4} c}+\frac{x^{2} \arctan \left(a x \right)^{3}}{2 a^{2} c}+\frac{\arctan \left(a x \right)^{3}}{2 a^{4} c}-\frac{3 x \arctan \left(a x \right)^{2}}{2 a^{3} c}+\frac{3 i \arctan \left(a x \right)^{2}}{2 a^{4} c}+\frac{\arctan \left(a x \right)^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{a^{4} c}-\frac{3 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{4} c}+\frac{3 \arctan \left(a x \right) \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{4} c}+\frac{3 i \polylog \left(4, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 a^{4} c}-\frac{3 \arctan \left(a x \right) \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)}{a^{4} c}+\frac{3 i \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{4} c}"," ",0,"-1/4*I/a^4/c*arctan(a*x)^4+1/2*x^2*arctan(a*x)^3/a^2/c+1/2*arctan(a*x)^3/a^4/c-3/2*x*arctan(a*x)^2/a^3/c+3/2*I/a^4/c*arctan(a*x)^2+1/a^4/c*arctan(a*x)^3*ln((1+I*a*x)^2/(a^2*x^2+1)+1)-3/2*I/a^4/c*arctan(a*x)^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+3/2/a^4/c*arctan(a*x)*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))+3/4*I/a^4/c*polylog(4,-(1+I*a*x)^2/(a^2*x^2+1))-3/a^4/c*arctan(a*x)*ln((1+I*a*x)^2/(a^2*x^2+1)+1)+3/2*I/a^4/c*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))","A"
389,1,925,121,0.542000," ","int(x^2*arctan(a*x)^3/(a^2*c*x^2+c),x)","\frac{x \arctan \left(a x \right)^{3}}{a^{2} c}-\frac{\arctan \left(a x \right)^{4}}{4 a^{3} c}-\frac{3 \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 a^{3} c}+\frac{3 \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{3} c}-\frac{3 i \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \pi}{4 a^{3} c}+\frac{3 i \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \pi}{4 a^{3} c}+\frac{3 i \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \pi}{2 a^{3} c}+\frac{3 i \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \pi}{4 a^{3} c}-\frac{i \arctan \left(a x \right)^{3}}{a^{3} c}+\frac{3 i \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \pi}{4 a^{3} c}-\frac{3 i \arctan \left(a x \right) \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{a^{3} c}-\frac{3 i \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \pi}{4 a^{3} c}+\frac{3 i \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \pi}{4 a^{3} c}-\frac{3 i \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \pi}{2 a^{3} c}+\frac{3 \ln \left(2\right) \arctan \left(a x \right)^{2}}{a^{3} c}-\frac{3 i \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \pi}{4 a^{3} c}+\frac{3 \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{3} c}-\frac{3 i \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \pi}{4 a^{3} c}"," ",0,"x*arctan(a*x)^3/a^2/c-1/4*arctan(a*x)^4/a^3/c-3/2/a^3/c*arctan(a*x)^2*ln(a^2*x^2+1)+3/a^3/c*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))-3/4*I/a^3/c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*Pi+3/4*I/a^3/c*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*Pi+3/2*I/a^3/c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*Pi+3/4*I/a^3/c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*Pi-I/a^3/c*arctan(a*x)^3+3/4*I/a^3/c*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*Pi-3/4*I/a^3/c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*Pi+3/4*I/a^3/c*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*Pi-3/2*I/a^3/c*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*Pi-3*I/a^3/c*arctan(a*x)*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+3/a^3/c*ln(2)*arctan(a*x)^2-3/4*I/a^3/c*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*Pi+3/2/a^3/c*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-3/4*I/a^3/c*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*Pi","C"
390,1,936,123,0.731000," ","int(x*arctan(a*x)^3/(a^2*c*x^2+c),x)","\frac{\ln \left(a^{2} x^{2}+1\right) \arctan \left(a x \right)^{3}}{2 a^{2} c}-\frac{\arctan \left(a x \right)^{3} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{2} c}+\frac{i \arctan \left(a x \right)^{3} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \pi}{2 a^{2} c}-\frac{i \arctan \left(a x \right)^{3} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \pi}{4 a^{2} c}+\frac{i \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \pi}{4 a^{2} c}+\frac{i \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \pi}{4 a^{2} c}-\frac{3 i \polylog \left(4, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 a^{2} c}-\frac{i \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \pi}{4 a^{2} c}+\frac{i \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \pi}{4 a^{2} c}+\frac{i \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \pi}{4 a^{2} c}+\frac{3 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{2} c}-\frac{i \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \pi}{2 a^{2} c}-\frac{\ln \left(2\right) \arctan \left(a x \right)^{3}}{a^{2} c}+\frac{i \arctan \left(a x \right)^{4}}{4 a^{2} c}-\frac{3 \arctan \left(a x \right) \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{2} c}-\frac{i \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \pi}{4 a^{2} c}-\frac{i \arctan \left(a x \right)^{3} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \pi}{4 a^{2} c}"," ",0,"1/2/a^2/c*ln(a^2*x^2+1)*arctan(a*x)^3-1/a^2/c*arctan(a*x)^3*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+1/2*I/a^2/c*arctan(a*x)^3*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*Pi-1/4*I/a^2/c*arctan(a*x)^3*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*Pi+1/4*I/a^2/c*arctan(a*x)^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*Pi+1/4*I/a^2/c*arctan(a*x)^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*Pi-3/4*I/a^2/c*polylog(4,-(1+I*a*x)^2/(a^2*x^2+1))-1/4*I/a^2/c*arctan(a*x)^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*Pi+1/4*I/a^2/c*arctan(a*x)^3*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*Pi+1/4*I/a^2/c*arctan(a*x)^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*Pi+3/2*I/a^2/c*arctan(a*x)^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))-1/2*I/a^2/c*arctan(a*x)^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*Pi-1/a^2/c*ln(2)*arctan(a*x)^3+1/4*I/a^2/c*arctan(a*x)^4-3/2/a^2/c*arctan(a*x)*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-1/4*I/a^2/c*arctan(a*x)^3*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*Pi-1/4*I/a^2/c*arctan(a*x)^3*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*Pi","C"
391,1,15,14,0.033000," ","int(arctan(a*x)^3/(a^2*c*x^2+c),x)","\frac{\arctan \left(a x \right)^{4}}{4 a c}"," ",0,"1/4*arctan(a*x)^4/a/c","A"
392,1,1834,109,0.538000," ","int(arctan(a*x)^3/x/(a^2*c*x^2+c),x)","-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c}-\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 c}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c}-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2 c}+\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{4 c}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2}}{2 c}-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c}-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c}-\frac{i \arctan \left(a x \right)^{4}}{4 c}-\frac{\arctan \left(a x \right)^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c}+\frac{6 \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{4 c}+\frac{\arctan \left(a x \right)^{3} \ln \left(a x \right)}{c}-\frac{3 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{3 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c}+\frac{i \arctan \left(a x \right)^{3} \pi}{2 c}-\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{4 c}+\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4 c}+\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c}+\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c}-\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4 c}+\frac{\arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{6 i \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{6 i \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{6 \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{\arctan \left(a x \right)^{3} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{\arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{\ln \left(a^{2} x^{2}+1\right) \arctan \left(a x \right)^{3}}{2 c}+\frac{\arctan \left(a x \right)^{3} \ln \left(2\right)}{c}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c}"," ",0,"-1/4*I*arctan(a*x)^4/c-1/4*I/c*arctan(a*x)^3*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+1/c*arctan(a*x)^3*ln(a*x)+1/2*I/c*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+1/2*I/c*arctan(a*x)^3*Pi-3*I/c*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I/c*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/4*I/c*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3-1/c*arctan(a*x)^3*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+1/4*I/c*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+1/2*I/c*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3+1/2*I/c*arctan(a*x)^3*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-1/2*I/c*arctan(a*x)^3*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-1/4*I/c*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+6*I/c*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I/c*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6/c*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c*arctan(a*x)^3*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+6/c*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/2/c*ln(a^2*x^2+1)*arctan(a*x)^3+1/c*arctan(a*x)^3*ln(2)+1/c*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/2*I/c*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))-1/2*I/c*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+1/4*I/c*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+1/2*I/c*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2-1/2*I/c*arctan(a*x)^3*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/4*I/c*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-1/2*I/c*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-1/2*I/c*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/4*I/c*arctan(a*x)^3*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-1/4*I/c*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))","C"
393,1,1829,113,0.342000," ","int(arctan(a*x)^3/x^2/(a^2*c*x^2+c),x)","\frac{3 i a \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2 c}+\frac{3 i a \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3} \arctan \left(a x \right)^{2}}{2 c}+\frac{3 i a \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4 c}-\frac{3 i a \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{4 c}-\frac{3 i a \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4 c}-\frac{3 i a \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c}-\frac{3 i a \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{4 c}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{3 a \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{i a \arctan \left(a x \right)^{3}}{c}-\frac{\arctan \left(a x \right)^{3}}{c x}-\frac{a \arctan \left(a x \right)^{4}}{4 c}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(2\right)}{c}-\frac{3 a \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 c}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(a x \right)}{c}+\frac{3 i a \pi  \arctan \left(a x \right)^{2}}{2 c}-\frac{6 i a \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{6 i a \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{3 i a \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c}-\frac{3 i a \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2 c}-\frac{3 i a \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c}+\frac{6 a \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{6 a \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{3 i a \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2 c}+\frac{3 i a \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2}}{2 c}-\frac{3 i a \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2} \arctan \left(a x \right)^{2}}{2 c}-\frac{3 i a \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 c}+\frac{3 i a \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c}+\frac{3 i a \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{4 c}+\frac{3 i a \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c}+\frac{3 i a \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \arctan \left(a x \right)^{2}}{2 c}"," ",0,"3/2*I*a/c*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2+3/2*I*a/c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3*arctan(a*x)^2+3/4*I*a/c*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3-3/4*I*a/c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3-3/4*I*a/c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3-3/2*I*a/c*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2+3*a/c*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^3/c/x-1/4*a*arctan(a*x)^4/c+3*a/c*arctan(a*x)^2*ln(2)-3/2*a/c*arctan(a*x)^2*ln(a^2*x^2+1)+3*a/c*arctan(a*x)^2*ln(a*x)-3*a/c*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+3*a/c*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a/c*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/2*I*a/c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2+3/2*I*a/c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2-3/2*I*a/c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-3/4*I*a/c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))+3/4*I*a/c*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+3/4*I*a/c*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+3/4*I*a/c*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-3/2*I*a/c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-3/2*I*a/c*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-3/2*I*a/c*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^2-6*I*a/c*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*a/c*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/2*I*a/c*Pi*arctan(a*x)^2+3/2*I*a/c*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^2-3/4*I*a/c*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+6*a/c*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*a/c*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*a*arctan(a*x)^3/c","C"
394,1,479,233,11.508000," ","int(arctan(a*x)^3/x^3/(a^2*c*x^2+c),x)","\frac{3 i a^{2} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{a^{2} \arctan \left(a x \right)^{3}}{2 c}+\frac{3 i a^{2} \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{3 a \arctan \left(a x \right)^{2}}{2 c x}-\frac{\arctan \left(a x \right)^{3}}{2 c \,x^{2}}-\frac{3 i a^{2} \arctan \left(a x \right)^{2}}{2 c}-\frac{a^{2} \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{6 a^{2} \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{i a^{2} \arctan \left(a x \right)^{4}}{4 c}-\frac{a^{2} \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{6 i a^{2} \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{6 a^{2} \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{3 i a^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{3 i a^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{3 a^{2} \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}-\frac{6 i a^{2} \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}+\frac{3 a^{2} \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c}"," ",0,"-3*I*a^2/c*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/2*a^2*arctan(a*x)^3/c-3*I*a^2/c*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/2*a*arctan(a*x)^2/c/x-1/2*arctan(a*x)^3/c/x^2-6*I*a^2/c*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))-a^2/c*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*a^2/c*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*a^2/c*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-a^2/c*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/2*I*a^2*arctan(a*x)^2/c-6*a^2/c*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/4*I*a^2*arctan(a*x)^4/c+3*I*a^2/c*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2/c*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*I*a^2/c*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2/c*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))","B"
395,1,5574,210,3.806000," ","int(arctan(a*x)^3/x^4/(a^2*c*x^2+c),x)","\text{output too large to display}"," ",0,"result too large to display","C"
396,1,1227,243,1.007000," ","int(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^2,x)","-\frac{3 \arctan \left(a x \right) \polylog \left(3, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{4} c^{2}}-\frac{3 i \polylog \left(4, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 a^{4} c^{2}}-\frac{3 \arctan \left(a x \right)^{2}}{2 a^{4} c^{2} \left(8 a x -8 i\right)}-\frac{3 \arctan \left(a x \right)^{2}}{2 a^{4} c^{2} \left(8 a x +8 i\right)}-\frac{\arctan \left(a x \right)^{3} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{4} c^{2}}+\frac{i \arctan \left(a x \right)^{4}}{4 a^{4} c^{2}}+\frac{3 i \arctan \left(a x \right)^{2} x}{2 a^{3} c^{2} \left(8 a x -8 i\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \arctan \left(a x \right)^{3} \pi}{4 a^{4} c^{2}}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(a x \right)^{3} \pi}{4 a^{4} c^{2}}-\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(a x \right)^{3} \pi}{4 a^{4} c^{2}}-\frac{3 i \arctan \left(a x \right)^{2} x}{2 a^{3} c^{2} \left(8 a x +8 i\right)}+\frac{\arctan \left(a x \right)^{3} \ln \left(a^{2} x^{2}+1\right)}{2 a^{4} c^{2}}-\frac{\arctan \left(a x \right)^{3} \ln \left(2\right)}{a^{4} c^{2}}-\frac{\arctan \left(a x \right)^{3}}{4 a^{4} c^{2}}+\frac{3}{2 a^{4} c^{2} \left(16 a x -16 i\right)}+\frac{3}{2 a^{4} c^{2} \left(16 a x +16 i\right)}+\frac{3 \arctan \left(a x \right) x}{16 a^{3} c^{2} \left(a x +i\right)}+\frac{3 i \arctan \left(a x \right)}{16 a^{4} c^{2} \left(a x -i\right)}-\frac{3 i \arctan \left(a x \right)}{16 a^{4} c^{2} \left(a x +i\right)}+\frac{3 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 a^{4} c^{2}}-\frac{3 i x}{2 a^{3} c^{2} \left(16 a x -16 i\right)}+\frac{3 i x}{2 a^{3} c^{2} \left(16 a x +16 i\right)}+\frac{3 \arctan \left(a x \right) x}{16 a^{3} c^{2} \left(a x -i\right)}+\frac{\arctan \left(a x \right)^{3}}{2 a^{4} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(a x \right)^{3} \pi}{4 a^{4} c^{2}}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)^{3} \pi}{2 a^{4} c^{2}}+\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \arctan \left(a x \right)^{3} \pi}{4 a^{4} c^{2}}-\frac{i \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{3} \pi}{4 a^{4} c^{2}}-\frac{i \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(a x \right)^{3} \pi}{4 a^{4} c^{2}}+\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \arctan \left(a x \right)^{3} \pi}{2 a^{4} c^{2}}-\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \arctan \left(a x \right)^{3} \pi}{4 a^{4} c^{2}}"," ",0,"3/2*I/a^3/c^2/(16*I+16*a*x)*x-3/2/a^4/c^2*arctan(a*x)^2/(8*a*x-8*I)-3/2/a^4/c^2*arctan(a*x)^2/(8*I+8*a*x)+1/2/a^4/c^2*arctan(a*x)^3*ln(a^2*x^2+1)-1/a^4/c^2*arctan(a*x)^3*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))-3/2/a^4/c^2*arctan(a*x)*polylog(3,-(1+I*a*x)^2/(a^2*x^2+1))-1/a^4/c^2*arctan(a*x)^3*ln(2)+1/4*I/a^4/c^2*arctan(a*x)^4-3/4*I/a^4/c^2*polylog(4,-(1+I*a*x)^2/(a^2*x^2+1))-1/4*arctan(a*x)^3/a^4/c^2+3/2*I/a^3/c^2*arctan(a*x)^2/(8*a*x-8*I)*x+1/4*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3*arctan(a*x)^3*Pi+1/4*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^3*Pi-1/4*I/a^4/c^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3*arctan(a*x)^3*Pi-3/2*I/a^3/c^2*arctan(a*x)^2/(8*I+8*a*x)*x+3/2/a^4/c^2/(16*a*x-16*I)+3/2/a^4/c^2/(16*I+16*a*x)+3/16/a^3/c^2*arctan(a*x)/(a*x-I)*x+3/16/a^3/c^2*arctan(a*x)/(I+a*x)*x+3/2*I/a^4/c^2*arctan(a*x)^2*polylog(2,-(1+I*a*x)^2/(a^2*x^2+1))+3/16*I/a^4/c^2*arctan(a*x)/(a*x-I)-3/16*I/a^4/c^2*arctan(a*x)/(I+a*x)+1/2*arctan(a*x)^3/a^4/c^2/(a^2*x^2+1)-3/2*I/a^3/c^2/(16*a*x-16*I)*x+1/4*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*arctan(a*x)^3*Pi-1/2*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^3*Pi+1/4*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*arctan(a*x)^3*Pi-1/4*I/a^4/c^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^3*Pi-1/4*I/a^4/c^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*arctan(a*x)^3*Pi+1/2*I/a^4/c^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*arctan(a*x)^3*Pi-1/4*I/a^4/c^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*arctan(a*x)^3*Pi","C"
397,1,124,123,0.058000," ","int(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^2,x)","\frac{3}{8 a^{3} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{3 x \arctan \left(a x \right)}{4 a^{2} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{3 \arctan \left(a x \right)^{2}}{8 a^{3} c^{2}}-\frac{3 \arctan \left(a x \right)^{2}}{4 a^{3} c^{2} \left(a^{2} x^{2}+1\right)}-\frac{x \arctan \left(a x \right)^{3}}{2 a^{2} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{4}}{8 a^{3} c^{2}}"," ",0,"3/8/a^3/c^2/(a^2*x^2+1)+3/4*x*arctan(a*x)/a^2/c^2/(a^2*x^2+1)+3/8*arctan(a*x)^2/a^3/c^2-3/4*arctan(a*x)^2/a^3/c^2/(a^2*x^2+1)-1/2*x*arctan(a*x)^3/a^2/c^2/(a^2*x^2+1)+1/8*arctan(a*x)^4/a^3/c^2","A"
398,1,122,121,0.046000," ","int(x*arctan(a*x)^3/(a^2*c*x^2+c)^2,x)","-\frac{3 x}{8 a \,c^{2} \left(a^{2} x^{2}+1\right)}-\frac{3 \arctan \left(a x \right)}{8 a^{2} c^{2}}+\frac{3 \arctan \left(a x \right)}{4 a^{2} c^{2} \left(a^{2} x^{2}+1\right)}+\frac{3 x \arctan \left(a x \right)^{2}}{4 a \,c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{3}}{4 a^{2} c^{2}}-\frac{\arctan \left(a x \right)^{3}}{2 a^{2} c^{2} \left(a^{2} x^{2}+1\right)}"," ",0,"-3/8*x/a/c^2/(a^2*x^2+1)-3/8*arctan(a*x)/a^2/c^2+3/4*arctan(a*x)/a^2/c^2/(a^2*x^2+1)+3/4*x*arctan(a*x)^2/a/c^2/(a^2*x^2+1)+1/4*arctan(a*x)^3/a^2/c^2-1/2*arctan(a*x)^3/a^2/c^2/(a^2*x^2+1)","A"
399,1,118,117,0.049000," ","int(arctan(a*x)^3/(a^2*c*x^2+c)^2,x)","-\frac{3}{8 a \,c^{2} \left(a^{2} x^{2}+1\right)}-\frac{3 x \arctan \left(a x \right)}{4 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{3 \arctan \left(a x \right)^{2}}{8 a \,c^{2}}+\frac{3 \arctan \left(a x \right)^{2}}{4 a \,c^{2} \left(a^{2} x^{2}+1\right)}+\frac{x \arctan \left(a x \right)^{3}}{2 c^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{4}}{8 a \,c^{2}}"," ",0,"-3/8/a/c^2/(a^2*x^2+1)-3/4*x*arctan(a*x)/c^2/(a^2*x^2+1)-3/8*arctan(a*x)^2/a/c^2+3/4*arctan(a*x)^2/a/c^2/(a^2*x^2+1)+1/2*x*arctan(a*x)^3/c^2/(a^2*x^2+1)+1/8*arctan(a*x)^4/a/c^2","A"
400,1,2089,213,1.359000," ","int(arctan(a*x)^3/x/(a^2*c*x^2+c)^2,x)","-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{4 c^{2}}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{2}}+\frac{\arctan \left(a x \right)^{3}}{2 c^{2} \left(a^{2} x^{2}+1\right)}+\frac{i \arctan \left(a x \right)^{3} \pi}{2 c^{2}}+\frac{3 i \arctan \left(a x \right)}{16 c^{2} \left(a x -i\right)}-\frac{3 i \arctan \left(a x \right)}{16 c^{2} \left(a x +i\right)}-\frac{i \arctan \left(a x \right)^{4}}{4 c^{2}}-\frac{\arctan \left(a x \right)^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c^{2}}+\frac{\arctan \left(a x \right)^{3} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{\arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{2}}-\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{2}}+\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{2}}-\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{4 c^{2}}-\frac{\arctan \left(a x \right)^{3}}{4 c^{2}}+\frac{3 i a x}{2 c^{2} \left(16 a x +16 i\right)}-\frac{3 i a x}{2 c^{2} \left(16 a x -16 i\right)}+\frac{3 \arctan \left(a x \right) a x}{16 c^{2} \left(a x +i\right)}-\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4 c^{2}}-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{2}}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2}}{2 c^{2}}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{2}}-\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 c^{2}}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{2}}-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{2}}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{2}}-\frac{3 i \arctan \left(a x \right)^{2} a x}{2 c^{2} \left(8 a x +8 i\right)}+\frac{3 i \arctan \left(a x \right)^{2} a x}{2 c^{2} \left(8 a x -8 i\right)}-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{2}}+\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{4 c^{2}}-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2 c^{2}}+\frac{\arctan \left(a x \right)^{3} \ln \left(2\right)}{c^{2}}+\frac{\arctan \left(a x \right)^{3} \ln \left(a x \right)}{c^{2}}-\frac{\arctan \left(a x \right)^{3} \ln \left(a^{2} x^{2}+1\right)}{2 c^{2}}+\frac{\arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{3 \arctan \left(a x \right)^{2}}{2 c^{2} \left(8 a x +8 i\right)}-\frac{3 \arctan \left(a x \right)^{2}}{2 c^{2} \left(8 a x -8 i\right)}+\frac{6 i \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{6 i \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{6 \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{6 \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{3}{2 c^{2} \left(16 a x +16 i\right)}+\frac{3}{2 c^{2} \left(16 a x -16 i\right)}+\frac{3 \arctan \left(a x \right) a x}{16 c^{2} \left(a x -i\right)}+\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4 c^{2}}-\frac{3 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{3 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}"," ",0,"1/2*arctan(a*x)^3/c^2/(a^2*x^2+1)-1/4*I*arctan(a*x)^4/c^2+3/2/c^2/(16*I+16*a*x)+3/2/c^2/(16*a*x-16*I)-1/c^2*arctan(a*x)^3*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+1/c^2*arctan(a*x)^3*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c^2*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/16/c^2*arctan(a*x)/(a*x-I)*a*x-1/4*I/c^2*arctan(a*x)^3*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+1/2*I/c^2*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+1/4*I/c^2*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+3/2*I/c^2/(16*I+16*a*x)*a*x-3/2*I/c^2/(16*a*x-16*I)*a*x-1/4*arctan(a*x)^3/c^2-1/2*I/c^2*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/2*I/c^2*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2+1/4*I/c^2*arctan(a*x)^3*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-1/4*I/c^2*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))+1/2*I/c^2*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))-1/2*I/c^2*arctan(a*x)^3*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/4*I/c^2*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-3/2*I/c^2*arctan(a*x)^2/(8*I+8*a*x)*a*x+3/2*I/c^2*arctan(a*x)^2/(8*a*x-8*I)*a*x+6/c^2*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c^2*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6/c^2*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c^2*arctan(a*x)^3*ln(2)-3/2/c^2*arctan(a*x)^2/(8*I+8*a*x)+3/16/c^2*arctan(a*x)/(I+a*x)*a*x-1/4*I/c^2*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+1/2*I/c^2*arctan(a*x)^3*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-1/2*I/c^2*arctan(a*x)^3*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/2*I/c^2*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-1/4*I/c^2*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3-3/2/c^2*arctan(a*x)^2/(8*a*x-8*I)+1/c^2*arctan(a*x)^3*ln(a*x)-1/2/c^2*arctan(a*x)^3*ln(a^2*x^2+1)-3*I/c^2*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I/c^2*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/2*I/c^2*arctan(a*x)^3*Pi+3/16*I/c^2*arctan(a*x)/(a*x-I)-3/16*I/c^2*arctan(a*x)/(I+a*x)-1/2*I/c^2*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/4*I/c^2*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-1/2*I/c^2*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+6*I/c^2*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I/c^2*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))","C"
401,1,2038,215,1.346000," ","int(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^2,x)","\frac{6 a \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{6 a \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{3 a \arctan \left(a x \right)^{2}}{8 c^{2}}-\frac{\arctan \left(a x \right)^{3}}{c^{2} x}-\frac{3 a \arctan \left(a x \right)^{4}}{8 c^{2}}-\frac{a^{2} x \arctan \left(a x \right)^{3}}{2 c^{2} \left(a^{2} x^{2}+1\right)}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{4 c^{2}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2 c^{2}}-\frac{3 i a \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{2}}-\frac{3 i a \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{2}}+\frac{3 i a \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{2}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4 c^{2}}+\frac{3 i a \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{2}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{4 c^{2}}-\frac{3 a \arctan \left(a x \right)^{2}}{4 c^{2} \left(a^{2} x^{2}+1\right)}-\frac{3 a^{2} x}{32 c^{2} \left(a x -i\right)}-\frac{3 a^{2} x}{32 c^{2} \left(a x +i\right)}+\frac{3 i \arctan \left(a x \right) a^{2} x}{2 c^{2} \left(8 a x +8 i\right)}-\frac{3 i \arctan \left(a x \right) a^{2} x}{2 c^{2} \left(8 a x -8 i\right)}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4 c^{2}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{2}}+\frac{3 i a \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{2}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2}}{2 c^{2}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{2}}-\frac{3 i a \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 c^{2}}-\frac{3 i a \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{2}}-\frac{3 i a \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{2}}-\frac{i a \arctan \left(a x \right)^{3}}{c^{2}}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{3 a \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c^{2}}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{3 i a}{32 c^{2} \left(a x -i\right)}+\frac{3 i a}{32 c^{2} \left(a x +i\right)}-\frac{6 i a \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{6 i a \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{3 i a \arctan \left(a x \right)^{2} \pi}{2 c^{2}}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(2\right)}{c^{2}}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(a x \right)}{c^{2}}-\frac{3 a \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 c^{2}}+\frac{3 a \arctan \left(a x \right)}{2 c^{2} \left(8 a x +8 i\right)}+\frac{3 a \arctan \left(a x \right)}{2 c^{2} \left(8 a x -8 i\right)}+\frac{3 i a \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{2}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{4 c^{2}}"," ",0,"3/4*I*a/c^2*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+3/2*I*a/c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+3/2*I*a/c^2*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2+3/4*I*a/c^2*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-3/4*I*a/c^2*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))+3/8*a*arctan(a*x)^2/c^2-arctan(a*x)^3/c^2/x-3/8*a*arctan(a*x)^4/c^2-1/2*a^2*x*arctan(a*x)^3/c^2/(a^2*x^2+1)+3/2*I/c^2*arctan(a*x)/(8*I+8*a*x)*a^2*x-3/2*I/c^2*arctan(a*x)/(8*a*x-8*I)*a^2*x+3/4*I*a/c^2*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3-3/2*I*a/c^2*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+3/2*I*a/c^2*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-3/4*I*a/c^2*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+3/2*I*a/c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-3/4*I*a/c^2*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3-3/2*I*a/c^2*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-3/2*I*a/c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+3/4*I*a/c^2*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-3/2*I*a/c^2*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-3/2*I*a/c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+3/2*a/c^2*arctan(a*x)/(8*I+8*a*x)+3/2*a/c^2*arctan(a*x)/(8*a*x-8*I)-3/4*a*arctan(a*x)^2/c^2/(a^2*x^2+1)-I*a*arctan(a*x)^3/c^2+6*a/c^2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*a/c^2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a/c^2*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))-3*a/c^2*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+3*a/c^2*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a/c^2*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/32*I*a/c^2/(a*x-I)+3/32*I*a/c^2/(I+a*x)-3/32/c^2/(a*x-I)*a^2*x-3/32/c^2/(I+a*x)*a^2*x+3*a/c^2*arctan(a*x)^2*ln(2)+3*a/c^2*arctan(a*x)^2*ln(a*x)-3/2*a/c^2*arctan(a*x)^2*ln(a^2*x^2+1)+3/2*I*a/c^2*arctan(a*x)^2*Pi-6*I*a/c^2*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*a/c^2*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/2*I*a/c^2*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))-3/4*I*a/c^2*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)","C"
402,1,815,339,13.943000," ","int(arctan(a*x)^3/x^3/(a^2*c*x^2+c)^2,x)","-\frac{3 a^{2}}{32 c^{2} \left(a x +i\right)}-\frac{3 a^{2}}{32 c^{2} \left(a x -i\right)}-\frac{a^{2} \arctan \left(a x \right)^{3}}{2 c^{2}}+\frac{3 i a^{2} \arctan \left(a x \right)}{16 c^{2} \left(a x +i\right)}-\frac{3 i a^{3} x}{32 c^{2} \left(a x +i\right)}+\frac{3 i a^{3} x}{32 c^{2} \left(a x -i\right)}+\frac{i a^{2} \arctan \left(a x \right)^{3}}{8 c^{2} \left(a x -i\right)}-\frac{3 i a^{2} \arctan \left(a x \right)}{16 c^{2} \left(a x -i\right)}-\frac{i a^{2} \arctan \left(a x \right)^{3}}{8 c^{2} \left(a x +i\right)}+\frac{a^{3} \arctan \left(a x \right)^{3} x}{8 c^{2} \left(a x +i\right)}-\frac{3 a^{3} \arctan \left(a x \right) x}{16 c^{2} \left(a x +i\right)}+\frac{a^{3} \arctan \left(a x \right)^{3} x}{8 c^{2} \left(a x -i\right)}-\frac{3 a^{3} \arctan \left(a x \right) x}{16 c^{2} \left(a x -i\right)}+\frac{6 i a^{2} \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{6 i a^{2} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{\arctan \left(a x \right)^{3}}{2 c^{2} x^{2}}-\frac{3 a \arctan \left(a x \right)^{2}}{2 c^{2} x}+\frac{3 i a^{3} \arctan \left(a x \right)^{2} x}{16 c^{2} \left(a x +i\right)}-\frac{3 i a^{3} \arctan \left(a x \right)^{2} x}{16 c^{2} \left(a x -i\right)}-\frac{2 a^{2} \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{2 a^{2} \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{3 a^{2} \arctan \left(a x \right)^{2}}{16 c^{2} \left(a x -i\right)}-\frac{3 i a^{2} \arctan \left(a x \right)^{2}}{2 c^{2}}+\frac{i a^{2} \arctan \left(a x \right)^{4}}{2 c^{2}}-\frac{12 a^{2} \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{12 a^{2} \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{3 i a^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{12 i a^{2} \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{3 i a^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}-\frac{12 i a^{2} \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{3 a^{2} \arctan \left(a x \right)^{2}}{16 c^{2} \left(a x +i\right)}+\frac{3 a^{2} \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}+\frac{3 a^{2} \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{2}}"," ",0,"-3/32*a^2/c^2/(I+a*x)-3/32*a^2/c^2/(a*x-I)-1/2*a^2*arctan(a*x)^3/c^2+3/16*I*a^2/c^2/(I+a*x)*arctan(a*x)-3/32*I*a^3/c^2/(I+a*x)*x+3/32*I*a^3/c^2/(a*x-I)*x+1/8*I*a^2/c^2/(a*x-I)*arctan(a*x)^3-3/16*I*a^2/c^2/(a*x-I)*arctan(a*x)+6*I*a^2/c^2*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*a^2/c^2*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/8*I*a^2/c^2/(I+a*x)*arctan(a*x)^3+1/8*a^3/c^2/(I+a*x)*arctan(a*x)^3*x-3/16*a^3/c^2/(I+a*x)*arctan(a*x)*x+1/8*a^3/c^2/(a*x-I)*arctan(a*x)^3*x-3/16*a^3/c^2/(a*x-I)*arctan(a*x)*x-1/2*arctan(a*x)^3/c^2/x^2-3/2*a*arctan(a*x)^2/c^2/x-3/2*I*a^2*arctan(a*x)^2/c^2+1/2*I*a^2*arctan(a*x)^4/c^2+3/16*I*a^3/c^2/(I+a*x)*arctan(a*x)^2*x-3/16*I*a^3/c^2/(a*x-I)*arctan(a*x)^2*x+3/16*a^2/c^2/(I+a*x)*arctan(a*x)^2+3*a^2/c^2*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2/c^2*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*a^2/c^2*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-12*a^2/c^2*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*a^2/c^2*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-12*a^2/c^2*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*a^2/c^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-12*I*a^2/c^2*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*a^2/c^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-12*I*a^2/c^2*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/16*a^2/c^2/(a*x-I)*arctan(a*x)^2","B"
403,1,5190,305,5.132000," ","int(arctan(a*x)^3/x^4/(a^2*c*x^2+c)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
404,1,220,194,0.064000," ","int(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^3,x)","-\frac{\arctan \left(a x \right)^{3}}{2 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)^{3}}{4 a^{4} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{15 x^{3} \arctan \left(a x \right)^{2}}{32 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{9 \arctan \left(a x \right)^{2} x}{32 a^{3} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{5 \arctan \left(a x \right)^{3}}{32 a^{4} c^{3}}+\frac{15 \arctan \left(a x \right)}{32 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{3 \arctan \left(a x \right)}{32 a^{4} c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{51 x^{3}}{256 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{45 x}{256 a^{3} c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{51 \arctan \left(a x \right)}{256 a^{4} c^{3}}"," ",0,"-1/2/a^4/c^3*arctan(a*x)^3/(a^2*x^2+1)+1/4/a^4/c^3*arctan(a*x)^3/(a^2*x^2+1)^2+15/32*x^3*arctan(a*x)^2/a/c^3/(a^2*x^2+1)^2+9/32/a^3/c^3*arctan(a*x)^2*x/(a^2*x^2+1)^2+5/32*arctan(a*x)^3/a^4/c^3+15/32*arctan(a*x)/a^4/c^3/(a^2*x^2+1)-3/32/a^4/c^3*arctan(a*x)/(a^2*x^2+1)^2-51/256*x^3/a/c^3/(a^2*x^2+1)^2-45/256/a^3/c^3/(a^2*x^2+1)^2*x-51/256*arctan(a*x)/a^4/c^3","A"
405,1,216,217,0.062000," ","int(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^3,x)","\frac{\arctan \left(a x \right)^{3} x^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{x \arctan \left(a x \right)^{3}}{8 a^{2} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{\arctan \left(a x \right)^{4}}{32 a^{3} c^{3}}+\frac{3 \arctan \left(a x \right)^{2}}{16 a^{3} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{3 \arctan \left(a x \right)^{2}}{16 a^{3} c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{3 \arctan \left(a x \right) x^{3}}{64 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 x \arctan \left(a x \right)}{64 a^{2} c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{3 \arctan \left(a x \right)^{2}}{128 a^{3} c^{3}}-\frac{3}{128 a^{3} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3}{128 a^{3} c^{3} \left(a^{2} x^{2}+1\right)^{2}}"," ",0,"1/8/c^3*arctan(a*x)^3/(a^2*x^2+1)^2*x^3-1/8*x*arctan(a*x)^3/a^2/c^3/(a^2*x^2+1)^2+1/32*arctan(a*x)^4/a^3/c^3+3/16*arctan(a*x)^2/a^3/c^3/(a^2*x^2+1)-3/16*arctan(a*x)^2/a^3/c^3/(a^2*x^2+1)^2-3/64/c^3*arctan(a*x)/(a^2*x^2+1)^2*x^3+3/64*x*arctan(a*x)/a^2/c^3/(a^2*x^2+1)^2-3/128*arctan(a*x)^2/a^3/c^3-3/128/a^3/c^3/(a^2*x^2+1)+3/128/a^3/c^3/(a^2*x^2+1)^2","A"
406,1,191,190,0.057000," ","int(x*arctan(a*x)^3/(a^2*c*x^2+c)^3,x)","-\frac{\arctan \left(a x \right)^{3}}{4 a^{2} c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 x \arctan \left(a x \right)^{2}}{16 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{9 x \arctan \left(a x \right)^{2}}{32 a \,c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 \arctan \left(a x \right)^{3}}{32 a^{2} c^{3}}+\frac{9 \arctan \left(a x \right)}{32 a^{2} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 \arctan \left(a x \right)}{32 a^{2} c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{45 a \,x^{3}}{256 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{51 x}{256 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{45 \arctan \left(a x \right)}{256 a^{2} c^{3}}"," ",0,"-1/4*arctan(a*x)^3/a^2/c^3/(a^2*x^2+1)^2+3/16*x*arctan(a*x)^2/a/c^3/(a^2*x^2+1)^2+9/32*x*arctan(a*x)^2/a/c^3/(a^2*x^2+1)+3/32*arctan(a*x)^3/a^2/c^3+9/32*arctan(a*x)/a^2/c^3/(a^2*x^2+1)+3/32*arctan(a*x)/a^2/c^3/(a^2*x^2+1)^2-45/256*a/c^3/(a^2*x^2+1)^2*x^3-51/256*x/a/c^3/(a^2*x^2+1)^2-45/256*arctan(a*x)/a^2/c^3","A"
407,1,211,205,0.069000," ","int(arctan(a*x)^3/(a^2*c*x^2+c)^3,x)","\frac{x \arctan \left(a x \right)^{3}}{4 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 x \arctan \left(a x \right)^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 \arctan \left(a x \right)^{4}}{32 a \,c^{3}}+\frac{9 \arctan \left(a x \right)^{2}}{16 a \,c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 \arctan \left(a x \right)^{2}}{16 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{45 a^{2} \arctan \left(a x \right) x^{3}}{64 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{51 x \arctan \left(a x \right)}{64 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{45 \arctan \left(a x \right)^{2}}{128 a \,c^{3}}-\frac{45}{128 a \,c^{3} \left(a^{2} x^{2}+1\right)}-\frac{3}{128 a \,c^{3} \left(a^{2} x^{2}+1\right)^{2}}"," ",0,"1/4*x*arctan(a*x)^3/c^3/(a^2*x^2+1)^2+3/8*x*arctan(a*x)^3/c^3/(a^2*x^2+1)+3/32*arctan(a*x)^4/a/c^3+9/16*arctan(a*x)^2/a/c^3/(a^2*x^2+1)+3/16*arctan(a*x)^2/a/c^3/(a^2*x^2+1)^2-45/64*a^2/c^3*arctan(a*x)/(a^2*x^2+1)^2*x^3-51/64*x*arctan(a*x)/c^3/(a^2*x^2+1)^2-45/128*arctan(a*x)^2/a/c^3-45/128/a/c^3/(a^2*x^2+1)-3/128/a/c^3/(a^2*x^2+1)^2","A"
408,1,2157,297,1.570000," ","int(arctan(a*x)^3/x/(a^2*c*x^2+c)^3,x)","\frac{\arctan \left(a x \right)^{3}}{4 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{\arctan \left(a x \right)^{3}}{2 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{9}{4 c^{3} \left(16 a x +16 i\right)}+\frac{9}{4 c^{3} \left(16 a x -16 i\right)}+\frac{\arctan \left(a x \right)^{3} \ln \left(a x \right)}{c^{3}}-\frac{\arctan \left(a x \right)^{3} \ln \left(a^{2} x^{2}+1\right)}{2 c^{3}}-\frac{9 i \arctan \left(a x \right)}{32 c^{3} \left(a x +i\right)}+\frac{9 i \arctan \left(a x \right)}{32 c^{3} \left(a x -i\right)}+\frac{i \pi  \arctan \left(a x \right)^{3}}{2 c^{3}}-\frac{3 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{3 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{i \arctan \left(a x \right)^{4}}{4 c^{3}}+\frac{\arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{\arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{\arctan \left(a x \right)^{3} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c^{3}}+\frac{\arctan \left(a x \right)^{3} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{9 \arctan \left(a x \right)^{2}}{4 c^{3} \left(8 a x -8 i\right)}-\frac{9 \arctan \left(a x \right)^{2}}{4 c^{3} \left(8 a x +8 i\right)}+\frac{6 \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{6 \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{6 i \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{6 i \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{\arctan \left(a x \right)^{3} \ln \left(2\right)}{c^{3}}-\frac{3 \arctan \left(a x \right) \cos \left(4 \arctan \left(a x \right)\right)}{256 c^{3}}-\frac{3 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}}{128 c^{3}}-\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{4 c^{3}}+\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{3}}-\frac{11 \arctan \left(a x \right)^{3}}{32 c^{3}}+\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{3}}+\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{3}}-\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}+\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{3}}-\frac{i \arctan \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2 c^{3}}+\frac{9 i \arctan \left(a x \right)^{2} a x}{4 c^{3} \left(8 a x -8 i\right)}-\frac{9 i \arctan \left(a x \right)^{2} a x}{4 c^{3} \left(8 a x +8 i\right)}+\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{4 c^{3}}-\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}+\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2}}{2 c^{3}}-\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}-\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 c^{3}}+\frac{3 \sin \left(4 \arctan \left(a x \right)\right)}{1024 c^{3}}+\frac{9 \arctan \left(a x \right) a x}{32 c^{3} \left(a x -i\right)}-\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{4 c^{3}}-\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}-\frac{i \arctan \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4 c^{3}}+\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4 c^{3}}+\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{3}}+\frac{i \pi  \arctan \left(a x \right)^{3} \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{3}}+\frac{9 i a x}{4 c^{3} \left(16 a x +16 i\right)}+\frac{9 \arctan \left(a x \right) a x}{32 c^{3} \left(a x +i\right)}-\frac{9 i a x}{4 c^{3} \left(16 a x -16 i\right)}"," ",0,"1/4*arctan(a*x)^3/c^3/(a^2*x^2+1)^2+1/2*arctan(a*x)^3/c^3/(a^2*x^2+1)-1/4*I*arctan(a*x)^4/c^3+1/c^3*arctan(a*x)^3*ln(a*x)-1/2/c^3*arctan(a*x)^3*ln(a^2*x^2+1)-9/32*I/c^3*arctan(a*x)/(I+a*x)+9/32*I/c^3*arctan(a*x)/(a*x-I)+1/2*I/c^3*Pi*arctan(a*x)^3-3*I/c^3*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I/c^3*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c^3*arctan(a*x)^3*ln(2)+1/c^3*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+6/c^3*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+1/c^3*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6/c^3*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/256/c^3*arctan(a*x)*cos(4*arctan(a*x))-1/c^3*arctan(a*x)^3*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+1/c^3*arctan(a*x)^3*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))-3/128/c^3*sin(4*arctan(a*x))*arctan(a*x)^2-9/4/c^3*arctan(a*x)^2/(8*a*x-8*I)-9/4/c^3*arctan(a*x)^2/(8*I+8*a*x)+6*I/c^3*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I/c^3*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-11/32*arctan(a*x)^3/c^3-1/2*I/c^3*Pi*arctan(a*x)^3*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/4*I/c^3*Pi*arctan(a*x)^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-1/2*I/c^3*arctan(a*x)^3*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+9/4*I/c^3*arctan(a*x)^2/(8*a*x-8*I)*a*x-9/4*I/c^3*arctan(a*x)^2/(8*I+8*a*x)*a*x+1/4*I/c^3*Pi*arctan(a*x)^3*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-1/2*I/c^3*Pi*arctan(a*x)^3*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+1/2*I/c^3*Pi*arctan(a*x)^3*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2-1/2*I/c^3*Pi*arctan(a*x)^3*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-1/4*I/c^3*Pi*arctan(a*x)^3*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))+1/2*I/c^3*Pi*arctan(a*x)^3*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+1/4*I/c^3*arctan(a*x)^3*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+9/4/c^3/(16*I+16*a*x)+9/4/c^3/(16*a*x-16*I)+3/1024/c^3*sin(4*arctan(a*x))+9/32/c^3*arctan(a*x)/(I+a*x)*a*x+9/32/c^3*arctan(a*x)/(a*x-I)*a*x-1/4*I/c^3*Pi*arctan(a*x)^3*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3-1/2*I/c^3*arctan(a*x)^3*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-1/4*I/c^3*arctan(a*x)^3*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+1/4*I/c^3*Pi*arctan(a*x)^3*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3-1/4*I/c^3*Pi*arctan(a*x)^3*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+1/2*I/c^3*Pi*arctan(a*x)^3*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+1/2*I/c^3*Pi*arctan(a*x)^3*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3+1/2*I/c^3*Pi*arctan(a*x)^3*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3+9/4*I/c^3/(16*I+16*a*x)*a*x-9/4*I/c^3/(16*a*x-16*I)*a*x","C"
409,1,2115,305,1.449000," ","int(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^3,x)","\frac{93 a \arctan \left(a x \right)^{2}}{128 c^{3}}-\frac{\arctan \left(a x \right)^{3}}{c^{3} x}-\frac{15 a \arctan \left(a x \right)^{4}}{32 c^{3}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{4 c^{3}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{3}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2}}{2 c^{3}}-\frac{6 i a \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{6 i a \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4 c^{3}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4 c^{3}}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(a x \right)}{c^{3}}+\frac{3 a \arctan \left(a x \right) \sin \left(4 \arctan \left(a x \right)\right)}{256 c^{3}}+\frac{6 a \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{6 a \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{3}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{4 c^{3}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2 c^{3}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2}}{2 c^{3}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{2 c^{3}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4 c^{3}}+\frac{3 a \cos \left(4 \arctan \left(a x \right)\right)}{1024 c^{3}}+\frac{3 a \arctan \left(a x \right)}{8 c^{3} \left(a x +i\right)}-\frac{3 a \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c^{3}}-\frac{7 \arctan \left(a x \right)^{3} a^{4} x^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{3 a \arctan \left(a x \right)}{8 c^{3} \left(a x -i\right)}-\frac{3 a^{2} x}{16 c^{3} \left(a x -i\right)}-\frac{3 a^{2} x}{16 c^{3} \left(a x +i\right)}+\frac{3 i a}{16 c^{3} \left(a x +i\right)}-\frac{3 i a}{16 c^{3} \left(a x -i\right)}-\frac{i a \arctan \left(a x \right)^{3}}{c^{3}}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{3 a \arctan \left(a x \right)^{2} \ln \left(2\right)}{c^{3}}-\frac{3 i \arctan \left(a x \right) a^{2} x}{8 c^{3} \left(a x -i\right)}+\frac{3 i \arctan \left(a x \right) a^{2} x}{8 c^{3} \left(a x +i\right)}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{3}}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{4 c^{3}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{2 c^{3}}-\frac{3 a \arctan \left(a x \right)^{2}}{16 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{21 a \arctan \left(a x \right)^{2}}{16 c^{3} \left(a^{2} x^{2}+1\right)}-\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{4 c^{3}}+\frac{3 i a \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{2 c^{3}}-\frac{9 a^{2} x \arctan \left(a x \right)^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{3 a \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 c^{3}}"," ",0,"93/128*a*arctan(a*x)^2/c^3-arctan(a*x)^3/c^3/x-15/32*a*arctan(a*x)^4/c^3-3/8*I/c^3*arctan(a*x)/(a*x-I)*a^2*x+3/8*I/c^3*arctan(a*x)/(I+a*x)*a^2*x+3/2*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-3/4*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3+3/2*I*a/c^3*Pi*arctan(a*x)^2*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-3/2*I*a/c^3*Pi*arctan(a*x)^2*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+3/4*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3-3/4*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3-3/4*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))+3/8*a/c^3*arctan(a*x)/(I+a*x)+3*a/c^3*arctan(a*x)^2*ln(a*x)-3*a/c^3*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)+3/256*a/c^3*arctan(a*x)*sin(4*arctan(a*x))-3/16/c^3/(a*x-I)*a^2*x-3/16/c^3/(I+a*x)*a^2*x+3/2*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))-3/2*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-3/2*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+3/4*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+3/1024*a/c^3*cos(4*arctan(a*x))+6*a/c^3*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*a/c^3*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*a/c^3*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/2*I*a/c^3*Pi*arctan(a*x)^2-7/8/c^3*arctan(a*x)^3/(a^2*x^2+1)^2*a^4*x^3-6*I*a/c^3*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/4*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-3/2*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+3/2*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2-3/2*I*a/c^3*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+3/4*I*a/c^3*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+3*a/c^3*arctan(a*x)^2*ln(2)+3/16*I*a/c^3/(I+a*x)-3/16*I*a/c^3/(a*x-I)-3/16*a*arctan(a*x)^2/c^3/(a^2*x^2+1)^2-21/16*a*arctan(a*x)^2/c^3/(a^2*x^2+1)-I*a*arctan(a*x)^3/c^3-3/4*I*a/c^3*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+3/2*I*a/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))-9/8*a^2*x*arctan(a*x)^3/c^3/(a^2*x^2+1)^2+3*a/c^3*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))-3/2*a/c^3*arctan(a*x)^2*ln(a^2*x^2+1)+3*a/c^3*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a/c^3*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3/8*a/c^3*arctan(a*x)/(a*x-I)","C"
410,1,891,433,11.529000," ","int(arctan(a*x)^3/x^3/(a^2*c*x^2+c)^3,x)","-\frac{\arctan \left(a x \right)^{3}}{2 c^{3} x^{2}}-\frac{a^{2} \arctan \left(a x \right)^{3}}{2 c^{3}}-\frac{3 a^{2} \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{3 a^{2} \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{3 a^{2} \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{3 a^{2} \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{15 a^{2} \arctan \left(a x \right)^{2}}{32 c^{3} \left(a x +i\right)}+\frac{15 a^{2} \arctan \left(a x \right)^{2}}{32 c^{3} \left(a x -i\right)}-\frac{18 a^{2} \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{18 a^{2} \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{18 i a^{2} \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{3 i a^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{18 i a^{2} \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{3 i a^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{3 i a^{2} \arctan \left(a x \right)^{4}}{4 c^{3}}-\frac{3 i a^{2} \arctan \left(a x \right)^{2}}{2 c^{3}}+\frac{15 i a^{3} x}{64 c^{3} \left(a x -i\right)}+\frac{5 a^{3} \arctan \left(a x \right)^{3} x}{16 c^{3} \left(a x +i\right)}+\frac{9 i a^{2} \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{9 i a^{2} \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{15 a^{3} \arctan \left(a x \right) x}{32 c^{3} \left(a x +i\right)}+\frac{5 a^{3} \arctan \left(a x \right)^{3} x}{16 c^{3} \left(a x -i\right)}-\frac{15 a^{3} \arctan \left(a x \right) x}{32 c^{3} \left(a x -i\right)}-\frac{15 i a^{2} \arctan \left(a x \right)}{32 c^{3} \left(a x -i\right)}-\frac{5 i a^{2} \arctan \left(a x \right)^{3}}{16 c^{3} \left(a x +i\right)}+\frac{15 i a^{2} \arctan \left(a x \right)}{32 c^{3} \left(a x +i\right)}+\frac{5 i a^{2} \arctan \left(a x \right)^{3}}{16 c^{3} \left(a x -i\right)}-\frac{15 i a^{3} x}{64 c^{3} \left(a x +i\right)}+\frac{3 a^{2} \arctan \left(a x \right) \cos \left(4 \arctan \left(a x \right)\right)}{256 c^{3}}-\frac{a^{2} \arctan \left(a x \right)^{3} \cos \left(4 \arctan \left(a x \right)\right)}{32 c^{3}}+\frac{3 a^{2} \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}}{128 c^{3}}-\frac{15 a^{2}}{64 c^{3} \left(a x +i\right)}-\frac{15 a^{2}}{64 c^{3} \left(a x -i\right)}-\frac{3 a^{2} \sin \left(4 \arctan \left(a x \right)\right)}{1024 c^{3}}+\frac{15 i a^{3} \arctan \left(a x \right)^{2} x}{32 c^{3} \left(a x +i\right)}-\frac{15 i a^{3} \arctan \left(a x \right)^{2} x}{32 c^{3} \left(a x -i\right)}-\frac{3 a \arctan \left(a x \right)^{2}}{2 c^{3} x}"," ",0,"-1/2*arctan(a*x)^3/c^3/x^2-1/2*a^2*arctan(a*x)^3/c^3-15/32*a^3/c^3/(I+a*x)*arctan(a*x)*x+5/16*a^3/c^3/(a*x-I)*arctan(a*x)^3*x-15/32*a^3/c^3/(a*x-I)*arctan(a*x)*x-15/32*I*a^2/c^3/(a*x-I)*arctan(a*x)+9*I*a^2/c^3*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+9*I*a^2/c^3*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-5/16*I*a^2/c^3/(I+a*x)*arctan(a*x)^3+15/32*I*a^2/c^3/(I+a*x)*arctan(a*x)+5/16*I*a^2/c^3/(a*x-I)*arctan(a*x)^3-15/64*I*a^3/c^3/(I+a*x)*x+15/64*I*a^3/c^3/(a*x-I)*x+5/16*a^3/c^3/(I+a*x)*arctan(a*x)^3*x+3/256*a^2*arctan(a*x)/c^3*cos(4*arctan(a*x))-3*a^2/c^3*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-18*a^2/c^3*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*a^2/c^3*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-18*a^2/c^3*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2/c^3*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*a^2/c^3*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-1/32*a^2*arctan(a*x)^3/c^3*cos(4*arctan(a*x))+3/128*a^2/c^3*sin(4*arctan(a*x))*arctan(a*x)^2+15/32*a^2/c^3/(I+a*x)*arctan(a*x)^2+15/32*a^2/c^3/(a*x-I)*arctan(a*x)^2-18*I*a^2/c^3*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*a^2/c^3*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-18*I*a^2/c^3*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*a^2/c^3*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+15/32*I*a^3/c^3/(I+a*x)*arctan(a*x)^2*x-15/32*I*a^3/c^3/(a*x-I)*arctan(a*x)^2*x-15/64*a^2/c^3/(I+a*x)-15/64*a^2/c^3/(a*x-I)-3/1024*a^2/c^3*sin(4*arctan(a*x))+3/4*I*a^2*arctan(a*x)^4/c^3-3/2*a*arctan(a*x)^2/c^3/x-3/2*I*a^2*arctan(a*x)^2/c^3","B"
411,1,2319,399,5.109000," ","int(arctan(a*x)^3/x^4/(a^2*c*x^2+c)^3,x)","-\frac{5 i a^{3} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{c^{3}}+\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)}{2 c^{3}}-\frac{a^{2} \arctan \left(a x \right)}{c^{3} x}-\frac{205 a^{3} \arctan \left(a x \right)^{2}}{128 c^{3}}-\frac{\arctan \left(a x \right)^{3}}{3 c^{3} x^{3}}+\frac{11 a^{6} \arctan \left(a x \right)^{3} x^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}-\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{2 c^{3}}-\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{2}}{c^{3}}+\frac{5 i a^{3} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{c^{3}}+\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{c^{3}}-\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)}{c^{3}}+\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)}{2 c^{3}}+\frac{9 i a^{4} \arctan \left(a x \right) x}{8 c^{3} \left(2 a x -2 i\right)}-\frac{9 i a^{4} \arctan \left(a x \right) x}{8 c^{3} \left(2 a x +2 i\right)}+\frac{5 i a^{3} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{c^{3}}-\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{c^{3}}+\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{a^{2} x^{2}+1}\right)^{3}}{2 c^{3}}-\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{3}}{c^{3}}-\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{2 c^{3}}+\frac{9 i a^{3}}{32 c^{3} \left(a x -i\right)}-\frac{9 i a^{3}}{32 c^{3} \left(a x +i\right)}-\frac{i a^{3} \arctan \left(a x \right)}{c^{3}}+\frac{10 a^{3} \arctan \left(a x \right)^{2} \ln \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{c^{3}}-\frac{10 a^{3} \arctan \left(a x \right)^{2} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{10 a^{3} \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{10 a^{3} \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{9 a^{3} \arctan \left(a x \right)}{8 c^{3} \left(2 a x -2 i\right)}-\frac{9 a^{3} \arctan \left(a x \right)}{8 c^{3} \left(2 a x +2 i\right)}+\frac{9 a^{4} x}{32 c^{3} \left(a x -i\right)}+\frac{9 a^{4} x}{32 c^{3} \left(a x +i\right)}+\frac{10 i a^{3} \arctan \left(a x \right)^{3}}{3 c^{3}}-\frac{20 a^{3} \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{20 a^{3} \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{a^{3} \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)}{c^{3}}+\frac{a^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{2 c^{3}}+\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{c^{3}}-\frac{5 i a^{3} \pi  \arctan \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}\right)}{2 c^{3}}+\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1\right)}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}-1}{\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1}\right)^{2}}{c^{3}}-\frac{5 i a^{3} \arctan \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i a x +1\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(i a x +1\right)^{2}}{a^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{2 c^{3}}-\frac{3 a^{3} \cos \left(4 \arctan \left(a x \right)\right)}{1024 c^{3}}+\frac{5 a^{3} \arctan \left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{c^{3}}-\frac{10 a^{3} \arctan \left(a x \right)^{2} \ln \left(a x \right)}{c^{3}}-\frac{3 a^{3} \arctan \left(a x \right) \sin \left(4 \arctan \left(a x \right)\right)}{256 c^{3}}-\frac{10 a^{3} \arctan \left(a x \right)^{2} \ln \left(2\right)}{c^{3}}-\frac{5 i a^{3} \pi  \arctan \left(a x \right)^{2}}{c^{3}}+\frac{20 i a^{3} \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}+\frac{20 i a^{3} \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{c^{3}}-\frac{a \arctan \left(a x \right)^{2}}{2 c^{3} x^{2}}+\frac{3 a^{3} \arctan \left(a x \right)^{2}}{16 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{33 a^{3} \arctan \left(a x \right)^{2}}{16 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 a^{2} \arctan \left(a x \right)^{3}}{c^{3} x}+\frac{13 a^{4} x \arctan \left(a x \right)^{3}}{8 c^{3} \left(a^{2} x^{2}+1\right)^{2}}+\frac{35 a^{3} \arctan \left(a x \right)^{4}}{32 c^{3}}"," ",0,"-5*I*a^3/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+5/2*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)-a^2*arctan(a*x)/c^3/x-205/128*a^3*arctan(a*x)^2/c^3-1/3*arctan(a*x)^3/c^3/x^3-5/2*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-5*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^2+5*I*a^3/c^3*Pi*arctan(a*x)^2*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2+5*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-5*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))+5/2*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))+11/8*a^6/c^3*arctan(a*x)^3/(a^2*x^2+1)^2*x^3+20*I*a^3/c^3*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+20*I*a^3/c^3*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-5*I*a^3/c^3*Pi*arctan(a*x)^2+5*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2-5/2*I*a^3/c^3*Pi*arctan(a*x)^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)+5*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-5/2*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^2+9/32*I*a^3/c^3/(a*x-I)-9/32*I*a^3/c^3/(I+a*x)-I*a^3/c^3*arctan(a*x)+9/8*I*a^4/c^3*arctan(a*x)/(2*a*x-2*I)*x-9/8*I*a^4/c^3*arctan(a*x)/(2*I+2*a*x)*x+5*I*a^3/c^3*Pi*arctan(a*x)^2*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^2-5*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3+5/2*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1))^3-5*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)-1)/((1+I*a*x)^2/(a^2*x^2+1)+1))^3-5/2*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+5/2*I*a^3/c^3*arctan(a*x)^2*Pi*csgn(I*(1+I*a*x)^2/(a^2*x^2+1)/((1+I*a*x)^2/(a^2*x^2+1)+1)^2)^3+a^3/c^3*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)-20*a^3/c^3*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-20*a^3/c^3*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+a^3/c^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3/1024*a^3/c^3*cos(4*arctan(a*x))+5*a^3/c^3*arctan(a*x)^2*ln(a^2*x^2+1)-10*a^3/c^3*arctan(a*x)^2*ln(a*x)+10*a^3/c^3*arctan(a*x)^2*ln((1+I*a*x)^2/(a^2*x^2+1)-1)-3/256*a^3/c^3*arctan(a*x)*sin(4*arctan(a*x))-10*a^3/c^3*arctan(a*x)^2*ln((1+I*a*x)/(a^2*x^2+1)^(1/2))-10*a^3/c^3*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-10*a^3/c^3*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-10*a^3/c^3*arctan(a*x)^2*ln(2)-9/8*a^3/c^3*arctan(a*x)/(2*a*x-2*I)-9/8*a^3/c^3*arctan(a*x)/(2*I+2*a*x)+9/32*a^4/c^3/(a*x-I)*x+9/32*a^4/c^3/(I+a*x)*x-1/2*a*arctan(a*x)^2/c^3/x^2+3/16*a^3*arctan(a*x)^2/c^3/(a^2*x^2+1)^2+33/16*a^3*arctan(a*x)^2/c^3/(a^2*x^2+1)+3*a^2*arctan(a*x)^3/c^3/x+13/8*a^4*x*arctan(a*x)^3/c^3/(a^2*x^2+1)^2+10/3*I*a^3*arctan(a*x)^3/c^3+35/32*a^3*arctan(a*x)^4/c^3","C"
412,1,417,487,2.757000," ","int(x^3*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(24 \arctan \left(a x \right)^{3} x^{4} a^{4}-18 \arctan \left(a x \right)^{2} x^{3} a^{3}+8 \arctan \left(a x \right)^{3} x^{2} a^{2}+12 \arctan \left(a x \right) a^{2} x^{2}+15 \arctan \left(a x \right)^{2} x a -16 \arctan \left(a x \right)^{3}-6 a x -54 \arctan \left(a x \right)\right)}{120 a^{4}}-\frac{11 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \arctan \left(a x \right)^{3}+6 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{120 a^{4} \sqrt{a^{2} x^{2}+1}}+\frac{11 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \arctan \left(a x \right)^{3}-3 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{120 a^{4} \sqrt{a^{2} x^{2}+1}}-\frac{i \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/120/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*(24*arctan(a*x)^3*x^4*a^4-18*arctan(a*x)^2*x^3*a^3+8*arctan(a*x)^3*x^2*a^2+12*arctan(a*x)*a^2*x^2+15*arctan(a*x)^2*x*a-16*arctan(a*x)^3-6*a*x-54*arctan(a*x))-11/120*(c*(a*x-I)*(I+a*x))^(1/2)*(I*arctan(a*x)^3+6*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^4/(a^2*x^2+1)^(1/2)+11/120*(c*(a*x-I)*(I+a*x))^(1/2)*(I*arctan(a*x)^3-3*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^4/(a^2*x^2+1)^(1/2)-I/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)","A"
413,1,460,688,1.803000," ","int(x^2*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 \arctan \left(a x \right)^{3} a^{3} x^{3}-2 \arctan \left(a x \right)^{2} x^{2} a^{2}+\arctan \left(a x \right)^{3} x a +2 \arctan \left(a x \right) x a +\arctan \left(a x \right)^{2}-2\right)}{8 a^{3}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+4 \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-4 \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+4 i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-4 i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{8 a^{3} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/8/a^3*(c*(a*x-I)*(I+a*x))^(1/2)*(2*arctan(a*x)^3*a^3*x^3-2*arctan(a*x)^2*x^2*a^2+arctan(a*x)^3*x*a+2*arctan(a*x)*x*a+arctan(a*x)^2-2)-1/8*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*I*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^3/(a^2*x^2+1)^(1/2)","A"
414,1,370,371,1.332000," ","int(x*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \left(2 \arctan \left(a x \right)^{2} x^{2} a^{2}-3 \arctan \left(a x \right) x a +2 \arctan \left(a x \right)^{2}+6\right)}{6 a^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-i \arctan \left(a x \right)^{3}+3 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{6 a^{2} \sqrt{a^{2} x^{2}+1}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-i \arctan \left(a x \right)^{3}+3 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{6 a^{2} \sqrt{a^{2} x^{2}+1}}+\frac{2 i \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/6/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*(2*arctan(a*x)^2*x^2*a^2-3*arctan(a*x)*x*a+2*arctan(a*x)^2+6)-1/6*(c*(a*x-I)*(I+a*x))^(1/2)*(-I*arctan(a*x)^3+3*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^2/(a^2*x^2+1)^(1/2)+1/6*(c*(a*x-I)*(I+a*x))^(1/2)*(-I*arctan(a*x)^3+3*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^2/(a^2*x^2+1)^(1/2)+2*I/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)","A"
415,1,422,597,0.890000," ","int(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)^{2} \left(\arctan \left(a x \right) x a -3\right)}{2 a}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 a \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2/a*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)^2*(arctan(a*x)*x*a-3)+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*I*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a/(a^2*x^2+1)^(1/2)","A"
416,1,453,640,1.288000," ","int(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x,x)","\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)^{3}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(3 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+\arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{\sqrt{a^{2} x^{2}+1}}"," ",0,"(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)^3+(c*(a*x-I)*(I+a*x))^(1/2)*(3*I*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
417,1,466,659,1.257000," ","int(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x^2,x)","-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)^{3}}{x}-\frac{i a \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{\sqrt{a^{2} x^{2}+1}}"," ",0,"-(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)^3/x-I*a*(c*(a*x-I)*(I+a*x))^(1/2)*(I*arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*I*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
418,1,404,586,1.396000," ","int(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x^3,x)","-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)^{2} \left(3 a x +\arctan \left(a x \right)\right)}{2 x^{2}}+\frac{i a^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)^2*(3*a*x+arctan(a*x))/x^2+1/2*I*a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(I*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
419,1,462,366,1.636000," ","int(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x^4,x)","-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \left(2 \arctan \left(a x \right)^{2} x^{2} a^{2}+6 a^{2} x^{2}+3 \arctan \left(a x \right) x a +2 \arctan \left(a x \right)^{2}\right)}{6 x^{3}}+\frac{a^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2} x^{2}+1}}-\frac{i a^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{\sqrt{a^{2} x^{2}+1}}+\frac{a^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{\sqrt{a^{2} x^{2}+1}}-\frac{a^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2} x^{2}+1}}+\frac{i a^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{\sqrt{a^{2} x^{2}+1}}-\frac{a^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{\sqrt{a^{2} x^{2}+1}}-\frac{2 a^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctanh \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{\sqrt{a^{2} x^{2}+1}}"," ",0,"-1/6*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*(2*arctan(a*x)^2*x^2*a^2+6*a^2*x^2+3*arctan(a*x)*x*a+2*arctan(a*x)^2)/x^3+1/2*a^3*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)-I*a^3*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)+a^3*(c*(a*x-I)*(I+a*x))^(1/2)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)-1/2*a^3*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)+I*a^3*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)-a^3*(c*(a*x-I)*(I+a*x))^(1/2)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)-2*a^3*(c*(a*x-I)*(I+a*x))^(1/2)*arctanh((1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)","A"
420,1,469,600,2.836000," ","int(x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(240 \arctan \left(a x \right)^{3} x^{6} a^{6}-120 \arctan \left(a x \right)^{2} x^{5} a^{5}+384 \arctan \left(a x \right)^{3} x^{4} a^{4}+48 \arctan \left(a x \right) x^{4} a^{4}-138 \arctan \left(a x \right)^{2} x^{3} a^{3}+48 \arctan \left(a x \right)^{3} x^{2} a^{2}-12 a^{3} x^{3}+28 \arctan \left(a x \right) a^{2} x^{2}+135 \arctan \left(a x \right)^{2} x a -96 \arctan \left(a x \right)^{3}+4 a x -326 \arctan \left(a x \right)\right)}{1680 a^{4}}+\frac{17 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-i \arctan \left(a x \right)^{3}+3 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{560 a^{4} \sqrt{a^{2} x^{2}+1}}-\frac{17 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-i \arctan \left(a x \right)^{3}+3 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{560 a^{4} \sqrt{a^{2} x^{2}+1}}-\frac{23 i c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{60 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/1680*c/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*(240*arctan(a*x)^3*x^6*a^6-120*arctan(a*x)^2*x^5*a^5+384*arctan(a*x)^3*x^4*a^4+48*arctan(a*x)*x^4*a^4-138*arctan(a*x)^2*x^3*a^3+48*arctan(a*x)^3*x^2*a^2-12*a^3*x^3+28*arctan(a*x)*a^2*x^2+135*arctan(a*x)^2*x*a-96*arctan(a*x)^3+4*a*x-326*arctan(a*x))+17/560*c*(c*(a*x-I)*(I+a*x))^(1/2)*(-I*arctan(a*x)^3+3*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^4/(a^2*x^2+1)^(1/2)-17/560*c*(c*(a*x-I)*(I+a*x))^(1/2)*(-I*arctan(a*x)^3+3*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^4/(a^2*x^2+1)^(1/2)-23/60*I*c/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)","A"
421,1,514,805,1.865000," ","int(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(40 \arctan \left(a x \right)^{3} x^{5} a^{5}-24 \arctan \left(a x \right)^{2} x^{4} a^{4}+70 \arctan \left(a x \right)^{3} a^{3} x^{3}+12 \arctan \left(a x \right) x^{3} a^{3}-38 \arctan \left(a x \right)^{2} x^{2} a^{2}+15 \arctan \left(a x \right)^{3} x a -4 a^{2} x^{2}+20 \arctan \left(a x \right) x a +31 \arctan \left(a x \right)^{2}-12\right)}{240 a^{3}}-\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(15 \arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-45 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-15 \arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+45 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+82 \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+90 \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+90 i \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-82 \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-90 \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-90 i \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+82 i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-82 i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{240 a^{3} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/240*c/a^3*(c*(a*x-I)*(I+a*x))^(1/2)*(40*arctan(a*x)^3*x^5*a^5-24*arctan(a*x)^2*x^4*a^4+70*arctan(a*x)^3*a^3*x^3+12*arctan(a*x)*x^3*a^3-38*arctan(a*x)^2*x^2*a^2+15*arctan(a*x)^3*x*a-4*a^2*x^2+20*arctan(a*x)*x*a+31*arctan(a*x)^2-12)-1/240*c*(c*(a*x-I)*(I+a*x))^(1/2)*(15*arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-45*I*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-15*arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+45*I*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+82*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+90*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+90*I*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-82*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-90*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-90*I*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+82*I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-82*I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^3/(a^2*x^2+1)^(1/2)","A"
422,1,421,449,1.316000," ","int(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(8 \arctan \left(a x \right)^{3} x^{4} a^{4}-6 \arctan \left(a x \right)^{2} x^{3} a^{3}+16 \arctan \left(a x \right)^{3} x^{2} a^{2}+4 \arctan \left(a x \right) a^{2} x^{2}-15 \arctan \left(a x \right)^{2} x a +8 \arctan \left(a x \right)^{3}-2 a x +22 \arctan \left(a x \right)\right)}{40 a^{2}}-\frac{3 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-i \arctan \left(a x \right)^{3}+3 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{40 a^{2} \sqrt{a^{2} x^{2}+1}}+\frac{3 c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-i \arctan \left(a x \right)^{3}+3 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{40 a^{2} \sqrt{a^{2} x^{2}+1}}+\frac{i c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/40*c/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(8*arctan(a*x)^3*x^4*a^4-6*arctan(a*x)^2*x^3*a^3+16*arctan(a*x)^3*x^2*a^2+4*arctan(a*x)*a^2*x^2-15*arctan(a*x)^2*x*a+8*arctan(a*x)^3-2*a*x+22*arctan(a*x))-3/40*c*(c*(a*x-I)*(I+a*x))^(1/2)*(-I*arctan(a*x)^3+3*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^2/(a^2*x^2+1)^(1/2)+3/40*c*(c*(a*x-I)*(I+a*x))^(1/2)*(-I*arctan(a*x)^3+3*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^2/(a^2*x^2+1)^(1/2)+I*c/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)","A"
423,1,466,701,0.934000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 \arctan \left(a x \right)^{3} a^{3} x^{3}-2 \arctan \left(a x \right)^{2} x^{2} a^{2}+5 \arctan \left(a x \right)^{3} x a +2 \arctan \left(a x \right) x a -11 \arctan \left(a x \right)^{2}-2\right)}{8 a}+\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(3 \arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-9 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+9 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+20 \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+18 \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+18 i \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-20 \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-18 \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-18 i \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+20 i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-20 i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{8 a \sqrt{a^{2} x^{2}+1}}"," ",0,"1/8*c/a*(c*(a*x-I)*(I+a*x))^(1/2)*(2*arctan(a*x)^3*a^3*x^3-2*arctan(a*x)^2*x^2*a^2+5*arctan(a*x)^3*x*a+2*arctan(a*x)*x*a-11*arctan(a*x)^2-2)+1/8*c*(c*(a*x-I)*(I+a*x))^(1/2)*(3*arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-9*I*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+9*I*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+20*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+18*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+18*I*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-20*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-18*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-18*I*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+20*I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-20*I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a/(a^2*x^2+1)^(1/2)","A"
424,1,511,750,1.174000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \left(2 \arctan \left(a x \right)^{2} x^{2} a^{2}-3 \arctan \left(a x \right) x a +8 \arctan \left(a x \right)^{2}+6\right)}{6}+\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+7 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-14 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-7 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+14 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+12 \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+12 i \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-12 \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-12 i \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+4 i \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+14 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-14 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/6*c*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*(2*arctan(a*x)^2*x^2*a^2-3*arctan(a*x)*x*a+8*arctan(a*x)^2+6)+1/2*c*(c*(a*x-I)*(I+a*x))^(1/2)*(2*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+7*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-14*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-7*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+14*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+12*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+12*I*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))-12*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-12*I*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*I*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))+14*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-14*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
425,1,602,891,1.270000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^2,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)^{2} \left(\arctan \left(a x \right) a^{2} x^{2}-3 a x -2 \arctan \left(a x \right)\right)}{2 x}-\frac{3 i a c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-6 i \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+4 i \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-4 i \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+4 \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-4 \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2*c*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)^2*(arctan(a*x)*a^2*x^2-3*a*x-2*arctan(a*x))/x-3/2*I*a*c*(c*(a*x-I)*(I+a*x))^(1/2)*(-I*arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*I*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*I*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+I*arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
426,1,592,915,1.700000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^3,x)","\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right)^{2} \left(2 \arctan \left(a x \right) a^{2} x^{2}-3 a x -\arctan \left(a x \right)\right)}{2 x^{2}}+\frac{3 a^{2} c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(\arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-\arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-4 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+4 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+4 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-4 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/2*c*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)^2*(2*arctan(a*x)*a^2*x^2-3*a*x-arctan(a*x))/x^2+3/2*a^2*c*(c*(a*x-I)*(I+a*x))^(1/2)*(arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*I*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*I*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+4*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
427,1,557,809,1.977000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^4,x)","-\frac{c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \left(8 \arctan \left(a x \right)^{2} x^{2} a^{2}+6 a^{2} x^{2}+3 \arctan \left(a x \right) x a +2 \arctan \left(a x \right)^{2}\right)}{6 x^{3}}+\frac{i a^{3} c \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(14 i \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-12 i \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)-6 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-7 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-14 \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+12 i \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+14 \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-14 i \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+7 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-12 \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+12 \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"-1/6*c*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*(8*arctan(a*x)^2*x^2*a^2+6*a^2*x^2+3*arctan(a*x)*x*a+2*arctan(a*x)^2)/x^3+1/2*I*a^3*c*(c*(a*x-I)*(I+a*x))^(1/2)*(2*I*arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+12*I*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)+6*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-7*I*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-14*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-14*I*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-12*I*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+14*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+7*I*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+14*I*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-12*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+12*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
428,1,525,730,2.848000," ","int(x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(13440 \arctan \left(a x \right)^{3} x^{8} a^{8}-5040 \arctan \left(a x \right)^{2} x^{7} a^{7}+36480 \arctan \left(a x \right)^{3} x^{6} a^{6}+1440 \arctan \left(a x \right) x^{6} a^{6}-12360 \arctan \left(a x \right)^{2} x^{5} a^{5}+28800 \arctan \left(a x \right)^{3} x^{4} a^{4}-240 x^{5} a^{5}+3216 \arctan \left(a x \right) x^{4} a^{4}-6150 \arctan \left(a x \right)^{2} x^{3} a^{3}+1920 \arctan \left(a x \right)^{3} x^{2} a^{2}-504 a^{3} x^{3}-188 \arctan \left(a x \right) a^{2} x^{2}+6345 \arctan \left(a x \right)^{2} x a -3840 \arctan \left(a x \right)^{3}+850 a x -12314 \arctan \left(a x \right)\right)}{120960 a^{4}}+\frac{115 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-i \arctan \left(a x \right)^{3}+3 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{8064 a^{4} \sqrt{a^{2} x^{2}+1}}-\frac{115 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-i \arctan \left(a x \right)^{3}+3 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{8064 a^{4} \sqrt{a^{2} x^{2}+1}}-\frac{1433 i c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{7560 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/120960*c^2/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*(13440*arctan(a*x)^3*x^8*a^8-5040*arctan(a*x)^2*x^7*a^7+36480*arctan(a*x)^3*x^6*a^6+1440*arctan(a*x)*x^6*a^6-12360*arctan(a*x)^2*x^5*a^5+28800*arctan(a*x)^3*x^4*a^4-240*x^5*a^5+3216*arctan(a*x)*x^4*a^4-6150*arctan(a*x)^2*x^3*a^3+1920*arctan(a*x)^3*x^2*a^2-504*a^3*x^3-188*arctan(a*x)*a^2*x^2+6345*arctan(a*x)^2*x*a-3840*arctan(a*x)^3+850*a*x-12314*arctan(a*x))+115/8064*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(-I*arctan(a*x)^3+3*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^4/(a^2*x^2+1)^(1/2)-115/8064*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(-I*arctan(a*x)^3+3*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^4/(a^2*x^2+1)^(1/2)-1433/7560*I*c^2/a^4*(c*(a*x-I)*(I+a*x))^(1/2)*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)","A"
429,1,566,926,2.046000," ","int(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(1680 \arctan \left(a x \right)^{3} x^{7} a^{7}-720 \arctan \left(a x \right)^{2} x^{6} a^{6}+4760 \arctan \left(a x \right)^{3} x^{5} a^{5}+240 \arctan \left(a x \right) x^{5} a^{5}-1992 \arctan \left(a x \right)^{2} x^{4} a^{4}+4130 \arctan \left(a x \right)^{3} a^{3} x^{3}-48 a^{4} x^{4}+696 \arctan \left(a x \right) x^{3} a^{3}-1474 \arctan \left(a x \right)^{2} x^{2} a^{2}+525 \arctan \left(a x \right)^{3} x a -168 a^{2} x^{2}+430 \arctan \left(a x \right) x a +1373 \arctan \left(a x \right)^{2}-94\right)}{13440 a^{3}}-\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(525 \arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-1575 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-525 \arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+1575 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3176 \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3150 \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3150 i \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3176 \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3150 \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3150 i \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3176 i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3176 i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{13440 a^{3} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/13440*c^2/a^3*(c*(a*x-I)*(I+a*x))^(1/2)*(1680*arctan(a*x)^3*x^7*a^7-720*arctan(a*x)^2*x^6*a^6+4760*arctan(a*x)^3*x^5*a^5+240*arctan(a*x)*x^5*a^5-1992*arctan(a*x)^2*x^4*a^4+4130*arctan(a*x)^3*a^3*x^3-48*a^4*x^4+696*arctan(a*x)*x^3*a^3-1474*arctan(a*x)^2*x^2*a^2+525*arctan(a*x)^3*x*a-168*a^2*x^2+430*arctan(a*x)*x*a+1373*arctan(a*x)^2-94)-1/13440*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(525*arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-1575*I*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-525*arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+1575*I*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3176*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3150*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3150*I*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3176*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3150*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3150*I*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3176*I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3176*I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^3/(a^2*x^2+1)^(1/2)","A"
430,1,477,521,1.367000," ","int(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(240 \arctan \left(a x \right)^{3} x^{6} a^{6}-120 \arctan \left(a x \right)^{2} x^{5} a^{5}+720 \arctan \left(a x \right)^{3} x^{4} a^{4}+48 \arctan \left(a x \right) x^{4} a^{4}-390 \arctan \left(a x \right)^{2} x^{3} a^{3}+720 \arctan \left(a x \right)^{3} x^{2} a^{2}-12 a^{3} x^{3}+196 \arctan \left(a x \right) a^{2} x^{2}-495 \arctan \left(a x \right)^{2} x a +240 \arctan \left(a x \right)^{3}-80 a x +598 \arctan \left(a x \right)\right)}{1680 a^{2}}+\frac{5 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i \arctan \left(a x \right)^{3}+6 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{112 a^{2} \sqrt{a^{2} x^{2}+1}}+\frac{5 c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-i \arctan \left(a x \right)^{3}+3 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{112 a^{2} \sqrt{a^{2} x^{2}+1}}+\frac{37 i c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)}{60 a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/1680*c^2/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*(240*arctan(a*x)^3*x^6*a^6-120*arctan(a*x)^2*x^5*a^5+720*arctan(a*x)^3*x^4*a^4+48*arctan(a*x)*x^4*a^4-390*arctan(a*x)^2*x^3*a^3+720*arctan(a*x)^3*x^2*a^2-12*a^3*x^3+196*arctan(a*x)*a^2*x^2-495*arctan(a*x)^2*x*a+240*arctan(a*x)^3-80*a*x+598*arctan(a*x))+5/112*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(I*arctan(a*x)^3+6*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^2/(a^2*x^2+1)^(1/2)+5/112*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(-I*arctan(a*x)^3+3*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a^2/(a^2*x^2+1)^(1/2)+37/60*I*c^2/a^2*(c*(a*x-I)*(I+a*x))^(1/2)*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)","A"
431,1,518,793,0.970000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(40 \arctan \left(a x \right)^{3} x^{5} a^{5}-24 \arctan \left(a x \right)^{2} x^{4} a^{4}+130 \arctan \left(a x \right)^{3} a^{3} x^{3}+12 \arctan \left(a x \right) x^{3} a^{3}-98 \arctan \left(a x \right)^{2} x^{2} a^{2}+165 \arctan \left(a x \right)^{3} x a -4 a^{2} x^{2}+80 \arctan \left(a x \right) x a -299 \arctan \left(a x \right)^{2}-72\right)}{240 a}+\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(75 \arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-225 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-75 \arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+225 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+518 \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+450 \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+450 i \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-518 \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-450 \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-450 i \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+518 i \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-518 i \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{240 a \sqrt{a^{2} x^{2}+1}}"," ",0,"1/240*c^2/a*(c*(a*x-I)*(I+a*x))^(1/2)*(40*arctan(a*x)^3*x^5*a^5-24*arctan(a*x)^2*x^4*a^4+130*arctan(a*x)^3*a^3*x^3+12*arctan(a*x)*x^3*a^3-98*arctan(a*x)^2*x^2*a^2+165*arctan(a*x)^3*x*a-4*a^2*x^2+80*arctan(a*x)*x*a-299*arctan(a*x)^2-72)+1/240*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(75*arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-225*I*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-75*arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+225*I*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+518*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+450*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+450*I*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-518*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-450*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-450*I*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+518*I*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-518*I*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/a/(a^2*x^2+1)^(1/2)","A"
432,1,562,839,1.271000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(24 \arctan \left(a x \right)^{3} x^{4} a^{4}-18 \arctan \left(a x \right)^{2} x^{3} a^{3}+88 \arctan \left(a x \right)^{3} x^{2} a^{2}+12 \arctan \left(a x \right) a^{2} x^{2}-105 \arctan \left(a x \right)^{2} x a +184 \arctan \left(a x \right)^{3}-6 a x +186 \arctan \left(a x \right)\right)}{120}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(40 \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-40 \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-120 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+120 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+149 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-149 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-298 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+298 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+240 \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-240 \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+240 i \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-240 i \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+120 i \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+298 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-298 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) c^{2}}{40 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/120*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(24*arctan(a*x)^3*x^4*a^4-18*arctan(a*x)^2*x^3*a^3+88*arctan(a*x)^3*x^2*a^2+12*arctan(a*x)*a^2*x^2-105*arctan(a*x)^2*x*a+184*arctan(a*x)^3-6*a*x+186*arctan(a*x))+1/40*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)*(40*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-40*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-120*I*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+120*I*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+149*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-149*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-298*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+298*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+240*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-240*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+240*I*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))-240*I*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+120*I*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))+298*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-298*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*c^2","A"
433,1,655,987,1.408000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^2,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(2 \arctan \left(a x \right)^{3} x^{4} a^{4}-2 \arctan \left(a x \right)^{2} x^{3} a^{3}+9 \arctan \left(a x \right)^{3} x^{2} a^{2}+2 \arctan \left(a x \right) a^{2} x^{2}-23 \arctan \left(a x \right)^{2} x a -8 \arctan \left(a x \right)^{3}-2 a x \right)}{8 x}+\frac{i a \,c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(15 i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+48 i \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-90 i \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+24 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-44 i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-45 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+90 i \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+45 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+44 i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-48 i \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-48 \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-15 i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+48 \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-24 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-44 \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+44 \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-90 \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+90 \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{8 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/8*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(2*arctan(a*x)^3*x^4*a^4-2*arctan(a*x)^2*x^3*a^3+9*arctan(a*x)^3*x^2*a^2+2*arctan(a*x)*a^2*x^2-23*arctan(a*x)^2*x*a-8*arctan(a*x)^3-2*a*x)/x+1/8*I*a*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(15*I*arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+24*I*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-44*I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-48*I*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-90*I*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-45*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+48*I*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+45*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+44*I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+90*I*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-48*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-15*I*arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+48*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-24*I*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-44*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+44*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-90*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+90*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
434,1,660,1023,1.739000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^3,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \left(2 \arctan \left(a x \right)^{2} x^{4} a^{4}-3 \arctan \left(a x \right) x^{3} a^{3}+14 \arctan \left(a x \right)^{2} x^{2} a^{2}+6 a^{2} x^{2}-9 \arctan \left(a x \right) x a -3 \arctan \left(a x \right)^{2}\right)}{6 x^{2}}-\frac{a^{2} c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(5 \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-5 \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-30 i \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-4 i \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+13 \arctan \left(a x \right)^{2} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-13 \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-15 i \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+15 i \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+26 i \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-30 \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+30 i \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+30 \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-26 i \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+26 \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-26 \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/6*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*(2*arctan(a*x)^2*x^4*a^4-3*arctan(a*x)*x^3*a^3+14*arctan(a*x)^2*x^2*a^2+6*a^2*x^2-9*arctan(a*x)*x*a-3*arctan(a*x)^2)/x^2-1/2*a^2*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(5*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-5*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-4*I*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))+13*arctan(a*x)^2*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+26*I*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-13*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+30*I*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+15*I*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-26*I*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-30*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-30*I*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))+30*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-15*I*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+26*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-26*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
435,1,699,1035,2.040000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^4,x)","\frac{c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \arctan \left(a x \right) \left(3 \arctan \left(a x \right)^{2} x^{4} a^{4}-9 \arctan \left(a x \right) x^{3} a^{3}-14 \arctan \left(a x \right)^{2} x^{2} a^{2}-6 a^{2} x^{2}-3 \arctan \left(a x \right) x a -2 \arctan \left(a x \right)^{2}\right)}{6 x^{3}}+\frac{i a^{3} c^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(-30 i \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+5 i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+26 i \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+13 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-13 i \arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+30 i \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+15 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-15 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-26 i \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \ln \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}-1\right)-5 i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+26 \arctan \left(a x \right) \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-26 \arctan \left(a x \right) \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+30 \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-30 \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2 \sqrt{a^{2} x^{2}+1}}"," ",0,"1/6*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*arctan(a*x)*(3*arctan(a*x)^2*x^4*a^4-9*arctan(a*x)*x^3*a^3-14*arctan(a*x)^2*x^2*a^2-6*a^2*x^2-3*arctan(a*x)*x*a-2*arctan(a*x)^2)/x^3+1/2*I*a^3*c^2*(c*(a*x-I)*(I+a*x))^(1/2)*(5*I*arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+13*I*arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-13*I*arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-26*I*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-30*I*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+26*I*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+15*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-15*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+30*I*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*ln((1+I*a*x)/(a^2*x^2+1)^(1/2)-1)-5*I*arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+26*arctan(a*x)*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-26*arctan(a*x)*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+30*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-30*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)","A"
436,1,380,402,3.463000," ","int(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(2 \arctan \left(a x \right)^{2} x^{2} a^{2}-3 \arctan \left(a x \right) x a -4 \arctan \left(a x \right)^{2}+6\right) \arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 c \,a^{4}}-\frac{5 i \left(3 i \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)^{2}+\arctan \left(a x \right)^{3}+6 i \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 \sqrt{a^{2} x^{2}+1}\, a^{4} c}+\frac{5 i \left(3 i \arctan \left(a x \right)^{2} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+\arctan \left(a x \right)^{3}+6 i \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \arctan \left(a x \right) \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 \sqrt{a^{2} x^{2}+1}\, a^{4} c}+\frac{2 i \arctan \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, a^{4} c}"," ",0,"1/6*(2*arctan(a*x)^2*x^2*a^2-3*arctan(a*x)*x*a-4*arctan(a*x)^2+6)*arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/c/a^4-5/6*I*(3*I*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^2+arctan(a*x)^3+6*I*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^4/c+5/6*I*(3*I*arctan(a*x)^2*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+arctan(a*x)^3+6*I*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*arctan(a*x)*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^4/c+2*I*arctan((1+I*a*x)/(a^2*x^2+1)^(1/2))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^4/c","A"
437,1,430,596,3.425000," ","int(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(\arctan \left(a x \right) x a -3\right) \arctan \left(a x \right)^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 c \,a^{3}}+\frac{i \left(i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \ln \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(3, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \ln \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(3, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \dilog \left(1+\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \dilog \left(1-\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(4, \frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(4, -\frac{i \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, a^{3} c}"," ",0,"1/2*(arctan(a*x)*x*a-3)*arctan(a*x)^2*(c*(a*x-I)*(I+a*x))^(1/2)/c/a^3+1/2*I*(I*arctan(a*x)^3*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)^3*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*ln(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(3,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*ln(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(3,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*polylog(2,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*polylog(2,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*dilog(1+I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*dilog(1-I*(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(4,I*(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(4,-I*(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/a^3/c","A"
438,0,0,295,1.476000," ","int(x*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x \arctan \left(a x \right)^{3}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","F"
439,0,0,386,0.756000," ","int(arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{3}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","F"
440,1,261,355,0.941000," ","int(arctan(a*x)^3/x/(a^2*c*x^2+c)^(1/2),x)","\frac{i \left(i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}"," ",0,"I*(I*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c","A"
441,1,230,279,0.904000," ","int(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(1/2),x)","-\frac{\arctan \left(a x \right)^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{c x}+\frac{3 a \left(\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)-\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}"," ",0,"-arctan(a*x)^3*(c*(a*x-I)*(I+a*x))^(1/2)/c/x+3*a*(arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)-arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c","A"
442,1,410,581,1.605000," ","int(arctan(a*x)^3/x^3/(a^2*c*x^2+c)^(1/2),x)","-\frac{\left(3 a x +\arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 x^{2} c}+\frac{i a^{2} \left(i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, c}"," ",0,"-1/2*(3*a*x+arctan(a*x))*arctan(a*x)^2*(c*(a*x-I)*(I+a*x))^(1/2)/x^2/c+1/2*I*a^2*(I*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^3-I*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^3-6*I*arctan(a*x)*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+6*I*arctan(a*x)*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)-6*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c","A"
443,1,487,397,2.954000," ","int(arctan(a*x)^3/x^4/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(4 \arctan \left(a x \right)^{2} x^{2} a^{2}-6 a^{2} x^{2}-3 \arctan \left(a x \right) x a -2 \arctan \left(a x \right)^{2}\right) \arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{6 c \,x^{3}}-\frac{2 a^{3} \arctanh \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}-\frac{5 a^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, c}+\frac{5 i a^{3} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}-\frac{5 a^{3} \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}+\frac{5 a^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)^{2} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, c}-\frac{5 i a^{3} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}+\frac{5 a^{3} \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c}"," ",0,"1/6*(4*arctan(a*x)^2*x^2*a^2-6*a^2*x^2-3*arctan(a*x)*x*a-2*arctan(a*x)^2)*arctan(a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/c/x^3-2*a^3*arctanh((1+I*a*x)/(a^2*x^2+1)^(1/2))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c-5/2*a^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^2*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c+5*I*a^3*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c-5*a^3*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c+5/2*a^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)^2*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c-5*I*a^3*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c+5*a^3*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c","A"
444,0,0,407,3.349000," ","int(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{3} \arctan \left(a x \right)^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x)","F"
445,0,0,505,3.398000," ","int(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{2} \arctan \left(a x \right)^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x)","F"
446,1,134,99,1.118000," ","int(x*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x)","-\frac{\left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)+3 i \arctan \left(a x \right)^{2}-6 i\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2} a^{2}}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)-3 i \arctan \left(a x \right)^{2}+6 i\right)}{2 \left(a^{2} x^{2}+1\right) c^{2} a^{2}}"," ",0,"-1/2*(arctan(a*x)^3-6*arctan(a*x)+3*I*arctan(a*x)^2-6*I)*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2/a^2+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^3-6*arctan(a*x)-3*I*arctan(a*x)^2+6*I)/(a^2*x^2+1)/c^2/a^2","C"
447,1,132,92,0.577000," ","int(arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)+3 i \arctan \left(a x \right)^{2}-6 i\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2} a}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)-3 i \arctan \left(a x \right)^{2}+6 i\right)}{2 \left(a^{2} x^{2}+1\right) c^{2} a}"," ",0,"1/2*(arctan(a*x)^3-6*arctan(a*x)+3*I*arctan(a*x)^2-6*I)*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2/a+1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^3-6*arctan(a*x)-3*I*arctan(a*x)^2+6*I)/(a^2*x^2+1)/c^2/a","C"
448,1,388,463,0.984000," ","int(arctan(a*x)^3/x/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)+3 i \arctan \left(a x \right)^{2}-6 i\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)-3 i \arctan \left(a x \right)^{2}+6 i\right)}{2 \left(a^{2} x^{2}+1\right) c^{2}}+\frac{i \left(i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{2}}"," ",0,"1/2*(arctan(a*x)^3-6*arctan(a*x)+3*I*arctan(a*x)^2-6*I)*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^3-6*arctan(a*x)-3*I*arctan(a*x)^2+6*I)/(a^2*x^2+1)/c^2+I*(I*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c^2","A"
449,1,356,388,0.987000," ","int(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(3/2),x)","-\frac{a \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)+3 i \arctan \left(a x \right)^{2}-6 i\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)-3 i \arctan \left(a x \right)^{2}+6 i\right) a}{2 \left(a^{2} x^{2}+1\right) c^{2}}-\frac{\arctan \left(a x \right)^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{x \,c^{2}}+\frac{3 a \left(\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)-\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{2}}"," ",0,"-1/2*a*(arctan(a*x)^3-6*arctan(a*x)+3*I*arctan(a*x)^2-6*I)*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)/c^2-1/2*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^3-6*arctan(a*x)-3*I*arctan(a*x)^2+6*I)*a/(a^2*x^2+1)/c^2-arctan(a*x)^3*(c*(a*x-I)*(I+a*x))^(1/2)/x/c^2+3*a*(arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)-arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2","A"
450,0,0,516,5.800000," ","int(x^5*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{5} \arctan \left(a x \right)^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^5*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x)","F"
451,0,0,610,3.308000," ","int(x^4*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{4} \arctan \left(a x \right)^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^4*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x)","F"
452,1,312,207,2.631000," ","int(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x)","-\frac{\left(9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}-2 i-6 \arctan \left(a x \right)\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{4}}-\frac{3 \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)+3 i \arctan \left(a x \right)^{2}-6 i\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{3 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)-3 i \arctan \left(a x \right)^{2}+6 i\right)}{8 a^{4} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\left(-9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}+2 i-6 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{4}}"," ",0,"-1/216*(9*I*arctan(a*x)^2+9*arctan(a*x)^3-2*I-6*arctan(a*x))*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^4-3/8*(arctan(a*x)^3-6*arctan(a*x)+3*I*arctan(a*x)^2-6*I)*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/a^4/c^3/(a^2*x^2+1)+3/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^3-6*arctan(a*x)-3*I*arctan(a*x)^2+6*I)/a^4/c^3/(a^2*x^2+1)+1/216*(-9*I*arctan(a*x)^2+9*arctan(a*x)^3+2*I-6*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^4","C"
453,1,308,171,2.555000," ","int(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}-2 i-6 \arctan \left(a x \right)\right) \left(a^{3} x^{3}-3 i x^{2} a^{2}-3 a x +i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{3}}+\frac{\left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)+3 i \arctan \left(a x \right)^{2}-6 i\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{3} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)-3 i \arctan \left(a x \right)^{2}+6 i\right)}{8 a^{3} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\left(-9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}+2 i-6 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a^{3} x^{3}+3 i x^{2} a^{2}-3 a x -i\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{3}}"," ",0,"1/216*(9*I*arctan(a*x)^2+9*arctan(a*x)^3-2*I-6*arctan(a*x))*(a^3*x^3-3*I*x^2*a^2-3*a*x+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^3+1/8*(arctan(a*x)^3-6*arctan(a*x)+3*I*arctan(a*x)^2-6*I)*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/a^3/c^3/(a^2*x^2+1)+1/8*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^3-6*arctan(a*x)-3*I*arctan(a*x)^2+6*I)/a^3/c^3/(a^2*x^2+1)+1/216*(-9*I*arctan(a*x)^2+9*arctan(a*x)^3+2*I-6*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)*(a^3*x^3+3*I*x^2*a^2-3*a*x-I)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^3","C"
454,1,312,171,0.993000," ","int(x*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}-2 i-6 \arctan \left(a x \right)\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3} a^{2}}-\frac{\left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)+3 i \arctan \left(a x \right)^{2}-6 i\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 a^{2} c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)-3 i \arctan \left(a x \right)^{2}+6 i\right)}{8 a^{2} c^{3} \left(a^{2} x^{2}+1\right)}-\frac{\left(-9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}+2 i-6 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{2}}"," ",0,"1/216*(9*I*arctan(a*x)^2+9*arctan(a*x)^3-2*I-6*arctan(a*x))*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3/a^2-1/8*(arctan(a*x)^3-6*arctan(a*x)+3*I*arctan(a*x)^2-6*I)*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/a^2/c^3/(a^2*x^2+1)+1/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^3-6*arctan(a*x)-3*I*arctan(a*x)^2+6*I)/a^2/c^3/(a^2*x^2+1)-1/216*(-9*I*arctan(a*x)^2+9*arctan(a*x)^3+2*I-6*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^2","C"
455,1,308,185,0.531000," ","int(arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x)","-\frac{\left(9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}-2 i-6 \arctan \left(a x \right)\right) \left(a^{3} x^{3}-3 i x^{2} a^{2}-3 a x +i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} a \,c^{3}}+\frac{3 \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)+3 i \arctan \left(a x \right)^{2}-6 i\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 c^{3} a \left(a^{2} x^{2}+1\right)}+\frac{3 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)-3 i \arctan \left(a x \right)^{2}+6 i\right)}{8 c^{3} a \left(a^{2} x^{2}+1\right)}-\frac{\left(-9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}+2 i-6 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a^{3} x^{3}+3 i x^{2} a^{2}-3 a x -i\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) a \,c^{3}}"," ",0,"-1/216*(9*I*arctan(a*x)^2+9*arctan(a*x)^3-2*I-6*arctan(a*x))*(a^3*x^3-3*I*x^2*a^2-3*a*x+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/a/c^3+3/8*(arctan(a*x)^3-6*arctan(a*x)+3*I*arctan(a*x)^2-6*I)*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a/(a^2*x^2+1)+3/8*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^3-6*arctan(a*x)-3*I*arctan(a*x)^2+6*I)/c^3/a/(a^2*x^2+1)-1/216*(-9*I*arctan(a*x)^2+9*arctan(a*x)^3+2*I-6*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)*(a^3*x^3+3*I*x^2*a^2-3*a*x-I)/(a^4*x^4+2*a^2*x^2+1)/a/c^3","C"
456,1,560,551,0.877000," ","int(arctan(a*x)^3/x/(a^2*c*x^2+c)^(5/2),x)","-\frac{\left(9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}-2 i-6 \arctan \left(a x \right)\right) \left(i x^{3} a^{3}+3 a^{2} x^{2}-3 i a x -1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3}}+\frac{5 \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)+3 i \arctan \left(a x \right)^{2}-6 i\right) \left(i a x +1\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 c^{3} \left(a^{2} x^{2}+1\right)}-\frac{5 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i a x -1\right) \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)-3 i \arctan \left(a x \right)^{2}+6 i\right)}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\left(-9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}+2 i-6 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(i x^{3} a^{3}-3 a^{2} x^{2}-3 i a x +1\right)}{216 \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3}}+\frac{i \left(i \arctan \left(a x \right)^{3} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-i \arctan \left(a x \right)^{3} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+3 \arctan \left(a x \right)^{2} \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 i \arctan \left(a x \right) \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-3 \arctan \left(a x \right)^{2} \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 i \arctan \left(a x \right) \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-6 \polylog \left(4, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+6 \polylog \left(4, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{3}}"," ",0,"-1/216*(9*I*arctan(a*x)^2+9*arctan(a*x)^3-2*I-6*arctan(a*x))*(I*x^3*a^3+3*a^2*x^2-3*I*a*x-1)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3+5/8*(arctan(a*x)^3-6*arctan(a*x)+3*I*arctan(a*x)^2-6*I)*(1+I*a*x)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/(a^2*x^2+1)-5/8*(c*(a*x-I)*(I+a*x))^(1/2)*(-1+I*a*x)*(arctan(a*x)^3-6*arctan(a*x)-3*I*arctan(a*x)^2+6*I)/c^3/(a^2*x^2+1)+1/216*(-9*I*arctan(a*x)^2+9*arctan(a*x)^3+2*I-6*arctan(a*x))*(c*(a*x-I)*(I+a*x))^(1/2)*(I*x^3*a^3-3*a^2*x^2-3*I*a*x+1)/(a^4*x^4+2*a^2*x^2+1)/c^3+I*(I*arctan(a*x)^3*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))-I*arctan(a*x)^3*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))+3*arctan(a*x)^2*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*I*arctan(a*x)*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2))-3*arctan(a*x)^2*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*I*arctan(a*x)*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-6*polylog(4,-(1+I*a*x)/(a^2*x^2+1)^(1/2))+6*polylog(4,(1+I*a*x)/(a^2*x^2+1)^(1/2)))*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^(1/2)/c^3","A"
457,1,528,482,0.836000," ","int(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(5/2),x)","\frac{a \left(9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}-2 i-6 \arctan \left(a x \right)\right) \left(a^{3} x^{3}-3 i x^{2} a^{2}-3 a x +i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{216 \left(a^{2} x^{2}+1\right)^{2} c^{3}}-\frac{7 a \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)+3 i \arctan \left(a x \right)^{2}-6 i\right) \left(a x -i\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 c^{3} \left(a^{2} x^{2}+1\right)}-\frac{7 \sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a x +i\right) \left(\arctan \left(a x \right)^{3}-6 \arctan \left(a x \right)-3 i \arctan \left(a x \right)^{2}+6 i\right) a}{8 c^{3} \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a x -i\right) \left(a x +i\right)}\, \left(a^{3} x^{3}+3 i x^{2} a^{2}-3 a x -i\right) \left(-9 i \arctan \left(a x \right)^{2}+9 \arctan \left(a x \right)^{3}+2 i-6 \arctan \left(a x \right)\right) a}{216 c^{3} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right)}-\frac{\arctan \left(a x \right)^{3} \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{x \,c^{3}}+\frac{3 a \left(\arctan \left(a x \right)^{2} \ln \left(1-\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 i \polylog \left(2, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)-\arctan \left(a x \right)^{2} \ln \left(1+\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)+2 i \polylog \left(2, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right) \arctan \left(a x \right)+2 \polylog \left(3, \frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)-2 \polylog \left(3, -\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{3}}"," ",0,"1/216*a*(9*I*arctan(a*x)^2+9*arctan(a*x)^3-2*I-6*arctan(a*x))*(a^3*x^3-3*I*x^2*a^2-3*a*x+I)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^2*x^2+1)^2/c^3-7/8*a*(arctan(a*x)^3-6*arctan(a*x)+3*I*arctan(a*x)^2-6*I)*(a*x-I)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/(a^2*x^2+1)-7/8*(c*(a*x-I)*(I+a*x))^(1/2)*(I+a*x)*(arctan(a*x)^3-6*arctan(a*x)-3*I*arctan(a*x)^2+6*I)*a/c^3/(a^2*x^2+1)+1/216*(c*(a*x-I)*(I+a*x))^(1/2)*(a^3*x^3+3*I*x^2*a^2-3*a*x-I)*(-9*I*arctan(a*x)^2+9*arctan(a*x)^3+2*I-6*arctan(a*x))*a/c^3/(a^4*x^4+2*a^2*x^2+1)-arctan(a*x)^3*(c*(a*x-I)*(I+a*x))^(1/2)/x/c^3+3*a*(arctan(a*x)^2*ln(1-(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*I*polylog(2,(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)-arctan(a*x)^2*ln(1+(1+I*a*x)/(a^2*x^2+1)^(1/2))+2*I*polylog(2,-(1+I*a*x)/(a^2*x^2+1)^(1/2))*arctan(a*x)+2*polylog(3,(1+I*a*x)/(a^2*x^2+1)^(1/2))-2*polylog(3,-(1+I*a*x)/(a^2*x^2+1)^(1/2)))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3","A"
458,0,0,24,1.545000," ","int(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^3,x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{3}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^3,x)","F"
459,0,0,22,1.342000," ","int(x^m*(a^2*c*x^2+c)*arctan(a*x)^3,x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{3}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)*arctan(a*x)^3,x)","F"
460,0,0,24,0.512000," ","int(x^m*arctan(a*x)^3/(a^2*c*x^2+c),x)","\int \frac{x^{m} \arctan \left(a x \right)^{3}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^m*arctan(a*x)^3/(a^2*c*x^2+c),x)","F"
461,0,0,24,1.497000," ","int(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^2,x)","\int \frac{x^{m} \arctan \left(a x \right)^{3}}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^2,x)","F"
462,0,0,24,0.949000," ","int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{3}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x)","F"
463,0,0,24,0.989000," ","int(x^m*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x)","\int x^{m} \arctan \left(a x \right)^{3} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^m*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x)","F"
464,0,0,24,1.361000," ","int(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m} \arctan \left(a x \right)^{3}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","F"
465,0,0,24,1.640000," ","int(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{m} \arctan \left(a x \right)^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x)","F"
466,0,0,20,1.497000," ","int(x*(a^2*c*x^2+c)/arctan(a*x),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)}{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)/arctan(a*x),x)","F"
467,0,0,19,1.316000," ","int((a^2*c*x^2+c)/arctan(a*x),x)","\int \frac{a^{2} c \,x^{2}+c}{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)/arctan(a*x),x)","F"
468,0,0,22,2.101000," ","int((a^2*c*x^2+c)/x/arctan(a*x),x)","\int \frac{a^{2} c \,x^{2}+c}{x \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)/x/arctan(a*x),x)","F"
469,0,0,22,1.766000," ","int(x*(a^2*c*x^2+c)^2/arctan(a*x),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^2/arctan(a*x),x)","F"
470,0,0,21,1.615000," ","int((a^2*c*x^2+c)^2/arctan(a*x),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^2/arctan(a*x),x)","F"
471,0,0,24,2.062000," ","int((a^2*c*x^2+c)^2/x/arctan(a*x),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{x \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^2/x/arctan(a*x),x)","F"
472,0,0,22,2.149000," ","int(x*(a^2*c*x^2+c)^3/arctan(a*x),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^3/arctan(a*x),x)","F"
473,0,0,21,1.867000," ","int((a^2*c*x^2+c)^3/arctan(a*x),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^3/arctan(a*x),x)","F"
474,0,0,24,2.105000," ","int((a^2*c*x^2+c)^3/x/arctan(a*x),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{x \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^3/x/arctan(a*x),x)","F"
475,0,0,24,0.760000," ","int(x^2/(a^2*c*x^2+c)/arctan(a*x),x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)/arctan(a*x),x)","F"
476,0,0,22,0.251000," ","int(x/(a^2*c*x^2+c)/arctan(a*x),x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)}\, dx"," ",0,"int(x/(a^2*c*x^2+c)/arctan(a*x),x)","F"
477,1,13,12,0.084000," ","int(1/(a^2*c*x^2+c)/arctan(a*x),x)","\frac{\ln \left(\arctan \left(a x \right)\right)}{a c}"," ",0,"ln(arctan(a*x))/a/c","A"
478,0,0,24,0.251000," ","int(1/x/(a^2*c*x^2+c)/arctan(a*x),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)/arctan(a*x),x)","F"
479,0,0,24,0.536000," ","int(1/x^2/(a^2*c*x^2+c)/arctan(a*x),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)/arctan(a*x),x)","F"
480,0,0,24,1.009000," ","int(x^4/(a^2*c*x^2+c)^2/arctan(a*x),x)","\int \frac{x^{4}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)}\, dx"," ",0,"int(x^4/(a^2*c*x^2+c)^2/arctan(a*x),x)","F"
481,0,0,24,0.682000," ","int(x^3/(a^2*c*x^2+c)^2/arctan(a*x),x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^2/arctan(a*x),x)","F"
482,1,30,29,0.240000," ","int(x^2/(a^2*c*x^2+c)^2/arctan(a*x),x)","-\frac{\Ci \left(2 \arctan \left(a x \right)\right)}{2 a^{3} c^{2}}+\frac{\ln \left(\arctan \left(a x \right)\right)}{2 a^{3} c^{2}}"," ",0,"-1/2*Ci(2*arctan(a*x))/a^3/c^2+1/2*ln(arctan(a*x))/a^3/c^2","A"
483,1,16,15,0.234000," ","int(x/(a^2*c*x^2+c)^2/arctan(a*x),x)","\frac{\Si \left(2 \arctan \left(a x \right)\right)}{2 a^{2} c^{2}}"," ",0,"1/2*Si(2*arctan(a*x))/a^2/c^2","A"
484,1,30,29,0.212000," ","int(1/(a^2*c*x^2+c)^2/arctan(a*x),x)","\frac{\Ci \left(2 \arctan \left(a x \right)\right)}{2 a \,c^{2}}+\frac{\ln \left(\arctan \left(a x \right)\right)}{2 a \,c^{2}}"," ",0,"1/2*Ci(2*arctan(a*x))/a/c^2+1/2*ln(arctan(a*x))/a/c^2","A"
485,0,0,24,0.688000," ","int(1/x/(a^2*c*x^2+c)^2/arctan(a*x),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^2/arctan(a*x),x)","F"
486,0,0,24,0.715000," ","int(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x),x)","F"
487,0,0,24,1.156000," ","int(x^6/(a^2*c*x^2+c)^3/arctan(a*x),x)","\int \frac{x^{6}}{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)}\, dx"," ",0,"int(x^6/(a^2*c*x^2+c)^3/arctan(a*x),x)","F"
488,0,0,24,1.258000," ","int(x^5/(a^2*c*x^2+c)^3/arctan(a*x),x)","\int \frac{x^{5}}{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)}\, dx"," ",0,"int(x^5/(a^2*c*x^2+c)^3/arctan(a*x),x)","F"
489,1,45,44,0.307000," ","int(x^4/(a^2*c*x^2+c)^3/arctan(a*x),x)","-\frac{\Ci \left(2 \arctan \left(a x \right)\right)}{2 a^{5} c^{3}}+\frac{\Ci \left(4 \arctan \left(a x \right)\right)}{8 a^{5} c^{3}}+\frac{3 \ln \left(\arctan \left(a x \right)\right)}{8 a^{5} c^{3}}"," ",0,"-1/2*Ci(2*arctan(a*x))/a^5/c^3+1/8*Ci(4*arctan(a*x))/a^5/c^3+3/8*ln(arctan(a*x))/a^5/c^3","A"
490,1,32,31,0.218000," ","int(x^3/(a^2*c*x^2+c)^3/arctan(a*x),x)","\frac{\Si \left(2 \arctan \left(a x \right)\right)}{4 a^{4} c^{3}}-\frac{\Si \left(4 \arctan \left(a x \right)\right)}{8 a^{4} c^{3}}"," ",0,"1/4*Si(2*arctan(a*x))/a^4/c^3-1/8*Si(4*arctan(a*x))/a^4/c^3","A"
491,1,30,29,0.190000," ","int(x^2/(a^2*c*x^2+c)^3/arctan(a*x),x)","-\frac{\Ci \left(4 \arctan \left(a x \right)\right)}{8 a^{3} c^{3}}+\frac{\ln \left(\arctan \left(a x \right)\right)}{8 a^{3} c^{3}}"," ",0,"-1/8*Ci(4*arctan(a*x))/a^3/c^3+1/8*ln(arctan(a*x))/a^3/c^3","A"
492,1,32,31,0.234000," ","int(x/(a^2*c*x^2+c)^3/arctan(a*x),x)","\frac{\Si \left(2 \arctan \left(a x \right)\right)}{4 a^{2} c^{3}}+\frac{\Si \left(4 \arctan \left(a x \right)\right)}{8 a^{2} c^{3}}"," ",0,"1/4*Si(2*arctan(a*x))/a^2/c^3+1/8*Si(4*arctan(a*x))/a^2/c^3","A"
493,1,45,44,0.265000," ","int(1/(a^2*c*x^2+c)^3/arctan(a*x),x)","\frac{\Ci \left(2 \arctan \left(a x \right)\right)}{2 a \,c^{3}}+\frac{\Ci \left(4 \arctan \left(a x \right)\right)}{8 a \,c^{3}}+\frac{3 \ln \left(\arctan \left(a x \right)\right)}{8 a \,c^{3}}"," ",0,"1/2*Ci(2*arctan(a*x))/a/c^3+1/8*Ci(4*arctan(a*x))/a/c^3+3/8*ln(arctan(a*x))/a/c^3","A"
494,0,0,24,1.269000," ","int(1/x/(a^2*c*x^2+c)^3/arctan(a*x),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^3/arctan(a*x),x)","F"
495,0,0,24,0.843000," ","int(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x),x)","F"
496,0,0,22,1.602000," ","int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x),x)","\int \frac{x \sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x),x)","F"
497,0,0,21,1.250000," ","int((a^2*c*x^2+c)^(1/2)/arctan(a*x),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/arctan(a*x),x)","F"
498,0,0,24,1.661000," ","int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{x \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x),x)","F"
499,0,0,22,1.582000," ","int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","F"
500,0,0,21,1.279000," ","int((a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","F"
501,0,0,24,1.700000," ","int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{x \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x),x)","F"
502,0,0,22,1.746000," ","int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","F"
503,0,0,21,1.429000," ","int((a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","F"
504,0,0,24,1.819000," ","int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{x \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x),x)","F"
505,0,0,22,1.319000," ","int(x/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x}{\arctan \left(a x \right) \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","F"
506,0,0,21,0.737000," ","int(1/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{\arctan \left(a x \right) \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","F"
507,0,0,24,0.950000," ","int(1/x/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{x \arctan \left(a x \right) \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/x/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","F"
508,0,0,24,2.938000," ","int(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","F"
509,0,0,24,3.851000," ","int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","F"
510,1,82,35,0.961000," ","int(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","-\frac{\mathrm{csgn}\left(\arctan \left(a x \right)\right) \pi  \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, c^{2} a^{2}}+\frac{\Si \left(\arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{2} a^{2}}"," ",0,"-1/2*csgn(arctan(a*x))*Pi/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2/a^2+Si(arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2/a^2","C"
511,1,136,35,0.631000," ","int(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","-\frac{i \mathrm{csgn}\left(\arctan \left(a x \right)\right) \mathrm{csgn}\left(i \arctan \left(a x \right)\right) \pi  \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, c^{2} a}+\frac{i \mathrm{csgn}\left(i \arctan \left(a x \right)\right) \pi  \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, c^{2} a}+\frac{\Ci \left(\arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{\sqrt{a^{2} x^{2}+1}\, c^{2} a}"," ",0,"-1/2*I*csgn(arctan(a*x))*csgn(I*arctan(a*x))*Pi/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2/a+1/2*I*csgn(I*arctan(a*x))*Pi/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2/a+Ci(arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^2/a","C"
512,0,0,24,1.046000," ","int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","F"
513,0,0,24,1.088000," ","int(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","F"
514,0,0,24,5.326000," ","int(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","\int \frac{x^{5}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)}\, dx"," ",0,"int(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","F"
515,0,0,24,3.605000," ","int(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","\int \frac{x^{4}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)}\, dx"," ",0,"int(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","F"
516,1,125,75,2.676000," ","int(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","-\frac{\mathrm{csgn}\left(\arctan \left(a x \right)\right) \pi  \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \sqrt{a^{2} x^{2}+1}\, c^{3} a^{4}}-\frac{\Si \left(3 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \sqrt{a^{2} x^{2}+1}\, c^{3} a^{4}}+\frac{3 \Si \left(\arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \sqrt{a^{2} x^{2}+1}\, c^{3} a^{4}}"," ",0,"-1/4*csgn(arctan(a*x))*Pi/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a^4-1/4*Si(3*arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a^4+3/4*Si(arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a^4","C"
517,1,84,75,3.593000," ","int(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","-\frac{\Ci \left(3 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \sqrt{a^{2} x^{2}+1}\, c^{3} a^{3}}+\frac{\Ci \left(\arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \sqrt{a^{2} x^{2}+1}\, c^{3} a^{3}}"," ",0,"-1/4*Ci(3*arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a^3+1/4*Ci(arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a^3","C"
518,1,125,75,0.967000," ","int(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","-\frac{\mathrm{csgn}\left(\arctan \left(a x \right)\right) \pi  \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \sqrt{a^{2} x^{2}+1}\, c^{3} a^{2}}+\frac{\Si \left(3 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \sqrt{a^{2} x^{2}+1}\, c^{3} a^{2}}+\frac{\Si \left(\arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \sqrt{a^{2} x^{2}+1}\, c^{3} a^{2}}"," ",0,"-1/4*csgn(arctan(a*x))*Pi/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a^2+1/4*Si(3*arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a^2+1/4*Si(arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/c^3/a^2","C"
519,1,179,75,0.637000," ","int(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","-\frac{i \mathrm{csgn}\left(\arctan \left(a x \right)\right) \mathrm{csgn}\left(i \arctan \left(a x \right)\right) \pi  \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, a \,c^{3}}+\frac{i \mathrm{csgn}\left(i \arctan \left(a x \right)\right) \pi  \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \sqrt{a^{2} x^{2}+1}\, a \,c^{3}}+\frac{\Ci \left(3 \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \sqrt{a^{2} x^{2}+1}\, a \,c^{3}}+\frac{3 \Ci \left(\arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \sqrt{a^{2} x^{2}+1}\, a \,c^{3}}"," ",0,"-1/2*I*csgn(arctan(a*x))*csgn(I*arctan(a*x))*Pi/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a/c^3+1/2*I*csgn(I*arctan(a*x))*Pi/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a/c^3+1/4*Ci(3*arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a/c^3+3/4*Ci(arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a/c^3","C"
520,0,0,24,1.079000," ","int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","F"
521,0,0,24,1.138000," ","int(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","F"
522,0,0,24,1.544000," ","int(x^m*(a^2*c*x^2+c)^3/arctan(a*x),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^3/arctan(a*x),x)","F"
523,0,0,24,1.431000," ","int(x^m*(a^2*c*x^2+c)^2/arctan(a*x),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2/arctan(a*x),x)","F"
524,0,0,22,1.312000," ","int(x^m*(a^2*c*x^2+c)/arctan(a*x),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)}{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)/arctan(a*x),x)","F"
525,0,0,24,0.482000," ","int(x^m/(a^2*c*x^2+c)/arctan(a*x),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)/arctan(a*x),x)","F"
526,0,0,24,1.416000," ","int(x^m/(a^2*c*x^2+c)^2/arctan(a*x),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^2/arctan(a*x),x)","F"
527,0,0,24,1.559000," ","int(x^m/(a^2*c*x^2+c)^3/arctan(a*x),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^3/arctan(a*x),x)","F"
528,0,0,24,1.033000," ","int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","F"
529,0,0,24,1.007000," ","int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","F"
530,0,0,24,1.064000," ","int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x),x)","\int \frac{x^{m} \sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x),x)","F"
531,0,0,24,1.591000," ","int(x^m/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m}}{\arctan \left(a x \right) \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x)","F"
532,0,0,24,1.691000," ","int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x)","F"
533,0,0,24,1.707000," ","int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x)","F"
534,0,0,20,1.572000," ","int(x*(a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
535,0,0,19,1.521000," ","int((a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{a^{2} c \,x^{2}+c}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
536,0,0,22,2.076000," ","int((a^2*c*x^2+c)/x/arctan(a*x)^2,x)","\int \frac{a^{2} c \,x^{2}+c}{x \arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)/x/arctan(a*x)^2,x)","F"
537,0,0,22,1.730000," ","int(x*(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","F"
538,0,0,21,1.710000," ","int((a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^2/arctan(a*x)^2,x)","F"
539,0,0,24,1.733000," ","int((a^2*c*x^2+c)^2/x/arctan(a*x)^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{x \arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^2/x/arctan(a*x)^2,x)","F"
540,0,0,22,2.090000," ","int(x*(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","F"
541,0,0,21,1.995000," ","int((a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^3/arctan(a*x)^2,x)","F"
542,0,0,24,1.974000," ","int((a^2*c*x^2+c)^3/x/arctan(a*x)^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{x \arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^3/x/arctan(a*x)^2,x)","F"
543,0,0,38,1.799000," ","int(x^3/(a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
544,0,0,36,0.837000," ","int(x^2/(a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
545,0,0,31,0.240000," ","int(x/(a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
546,1,15,14,0.063000," ","int(1/(a^2*c*x^2+c)/arctan(a*x)^2,x)","-\frac{1}{a c \arctan \left(a x \right)}"," ",0,"-1/a/c/arctan(a*x)","A"
547,0,0,38,0.265000," ","int(1/x/(a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
548,0,0,38,0.787000," ","int(1/x^2/(a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
549,0,0,38,2.305000," ","int(1/x^3/(a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
550,0,0,38,2.197000," ","int(1/x^4/(a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
551,0,0,71,0.907000," ","int(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","F"
552,1,37,43,0.300000," ","int(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\frac{2 \Si \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+\cos \left(2 \arctan \left(a x \right)\right)-1}{2 a^{3} c^{2} \arctan \left(a x \right)}"," ",0,"1/2/a^3/c^2*(2*Si(2*arctan(a*x))*arctan(a*x)+cos(2*arctan(a*x))-1)/arctan(a*x)","A"
553,1,38,41,0.246000," ","int(x/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\frac{2 \Ci \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)-\sin \left(2 \arctan \left(a x \right)\right)}{2 a^{2} c^{2} \arctan \left(a x \right)}"," ",0,"1/2/a^2/c^2*(2*Ci(2*arctan(a*x))*arctan(a*x)-sin(2*arctan(a*x)))/arctan(a*x)","A"
554,1,37,41,0.226000," ","int(1/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","-\frac{2 \Si \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+\cos \left(2 \arctan \left(a x \right)\right)+1}{2 a \,c^{2} \arctan \left(a x \right)}"," ",0,"-1/2/a/c^2*(2*Si(2*arctan(a*x))*arctan(a*x)+cos(2*arctan(a*x))+1)/arctan(a*x)","A"
555,0,0,73,0.893000," ","int(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","F"
556,0,0,72,0.933000," ","int(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","F"
557,0,0,109,2.584000," ","int(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","F"
558,0,0,110,2.487000," ","int(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","F"
559,1,58,82,0.235000," ","int(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\frac{4 \Ci \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)-4 \Ci \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)-2 \sin \left(2 \arctan \left(a x \right)\right)+\sin \left(4 \arctan \left(a x \right)\right)}{8 a^{4} c^{3} \arctan \left(a x \right)}"," ",0,"1/8/a^4/c^3*(4*Ci(2*arctan(a*x))*arctan(a*x)-4*Ci(4*arctan(a*x))*arctan(a*x)-2*sin(2*arctan(a*x))+sin(4*arctan(a*x)))/arctan(a*x)","A"
560,1,37,65,0.207000," ","int(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\frac{4 \Si \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)+\cos \left(4 \arctan \left(a x \right)\right)-1}{8 a^{3} c^{3} \arctan \left(a x \right)}"," ",0,"1/8/a^3/c^3*(4*Si(4*arctan(a*x))*arctan(a*x)+cos(4*arctan(a*x))-1)/arctan(a*x)","A"
561,1,60,57,0.218000," ","int(x/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\frac{4 \Ci \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+4 \Ci \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)-2 \sin \left(2 \arctan \left(a x \right)\right)-\sin \left(4 \arctan \left(a x \right)\right)}{8 a^{2} c^{3} \arctan \left(a x \right)}"," ",0,"1/8/a^2/c^3*(4*Ci(2*arctan(a*x))*arctan(a*x)+4*Ci(4*arctan(a*x))*arctan(a*x)-2*sin(2*arctan(a*x))-sin(4*arctan(a*x)))/arctan(a*x)","A"
562,1,59,56,0.280000," ","int(1/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","-\frac{8 \Si \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+4 \Si \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)+4 \cos \left(2 \arctan \left(a x \right)\right)+\cos \left(4 \arctan \left(a x \right)\right)+3}{8 a \,c^{3} \arctan \left(a x \right)}"," ",0,"-1/8/a/c^3*(8*Si(2*arctan(a*x))*arctan(a*x)+4*Si(4*arctan(a*x))*arctan(a*x)+4*cos(2*arctan(a*x))+cos(4*arctan(a*x))+3)/arctan(a*x)","A"
563,0,0,108,1.654000," ","int(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","F"
564,0,0,108,1.135000," ","int(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","F"
565,0,0,153,4.029000," ","int(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","F"
566,0,0,151,2.552000," ","int(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","F"
567,0,0,22,1.714000," ","int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x)","\int \frac{x \sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x)","F"
568,0,0,21,1.096000," ","int((a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x)","F"
569,0,0,24,1.544000," ","int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^2,x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{x \arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^2,x)","F"
570,0,0,22,1.792000," ","int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","F"
571,0,0,21,1.191000," ","int((a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","F"
572,0,0,24,1.690000," ","int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{x \arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^2,x)","F"
573,0,0,22,1.946000," ","int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","F"
574,0,0,21,1.276000," ","int((a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","F"
575,0,0,24,1.539000," ","int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{x \arctan \left(a x \right)^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^2,x)","F"
576,0,0,22,1.306000," ","int(x/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x}{\arctan \left(a x \right)^{2} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","F"
577,0,0,21,0.729000," ","int(1/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{\arctan \left(a x \right)^{2} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","F"
578,0,0,59,0.818000," ","int(1/x/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{x \arctan \left(a x \right)^{2} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/x/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","F"
579,0,0,92,3.204000," ","int(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","F"
580,0,0,89,4.299000," ","int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","F"
581,1,210,63,1.117000," ","int(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","-\frac{\left(\arctan \left(a x \right) \Ei \left(1, -i \arctan \left(a x \right)\right) x^{2} a^{2}+\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a -i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) c^{2} a^{2}}-\frac{\left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}+\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a +i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) c^{2} a^{2}}"," ",0,"-1/2*(arctan(a*x)*Ei(1,-I*arctan(a*x))*x^2*a^2+Ei(1,-I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a-I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/c^2/a^2-1/2*(Ei(1,I*arctan(a*x))*arctan(a*x)*x^2*a^2+Ei(1,I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a+I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/c^2/a^2","C"
582,1,212,63,0.641000," ","int(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\frac{i \left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}+\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a +i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) c^{2} a}-\frac{i \left(\arctan \left(a x \right) \Ei \left(1, -i \arctan \left(a x \right)\right) x^{2} a^{2}+\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a -i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{2 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) c^{2} a}"," ",0,"1/2*I*(Ei(1,I*arctan(a*x))*arctan(a*x)*x^2*a^2+Ei(1,I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a+I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/c^2/a-1/2*I*(arctan(a*x)*Ei(1,-I*arctan(a*x))*x^2*a^2+Ei(1,-I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a-I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/c^2/a","C"
583,0,0,119,1.008000," ","int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","F"
584,0,0,85,1.068000," ","int(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","F"
585,0,0,146,1.816000," ","int(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","F"
586,0,0,123,4.266000," ","int(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","F"
587,0,0,158,5.701000," ","int(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\int \frac{x^{5}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","F"
588,0,0,155,4.047000," ","int(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\int \frac{x^{4}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","F"
589,1,582,104,3.064000," ","int(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\frac{\left(3 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{4} a^{4}+6 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}-\sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 i \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+3 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)+3 \sqrt{a^{2} x^{2}+1}\, x a -i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right) c^{3} a^{4}}+\frac{\left(3 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{4} a^{4}-\sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+6 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}-3 i \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+3 \sqrt{a^{2} x^{2}+1}\, x a +3 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)+i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right) c^{3} a^{4}}-\frac{3 \left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}+\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a +i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) c^{3} a^{4}}-\frac{3 \left(\arctan \left(a x \right) \Ei \left(1, -i \arctan \left(a x \right)\right) x^{2} a^{2}+\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a -i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) c^{3} a^{4}}"," ",0,"1/8*(3*Ei(1,-3*I*arctan(a*x))*arctan(a*x)*x^4*a^4+6*Ei(1,-3*I*arctan(a*x))*arctan(a*x)*x^2*a^2-(a^2*x^2+1)^(1/2)*x^3*a^3+3*I*(a^2*x^2+1)^(1/2)*x^2*a^2+3*Ei(1,-3*I*arctan(a*x))*arctan(a*x)+3*(a^2*x^2+1)^(1/2)*x*a-I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)/c^3/a^4+1/8*(3*Ei(1,3*I*arctan(a*x))*arctan(a*x)*x^4*a^4-(a^2*x^2+1)^(1/2)*x^3*a^3+6*Ei(1,3*I*arctan(a*x))*arctan(a*x)*x^2*a^2-3*I*(a^2*x^2+1)^(1/2)*x^2*a^2+3*(a^2*x^2+1)^(1/2)*x*a+3*Ei(1,3*I*arctan(a*x))*arctan(a*x)+I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)/c^3/a^4-3/8*(Ei(1,I*arctan(a*x))*arctan(a*x)*x^2*a^2+Ei(1,I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a+I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/c^3/a^4-3/8*(arctan(a*x)*Ei(1,-I*arctan(a*x))*x^2*a^2+Ei(1,-I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a-I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/c^3/a^4","C"
590,1,586,126,4.126000," ","int(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","-\frac{i \left(3 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{4} a^{4}-\sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+6 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}-3 i \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+3 \sqrt{a^{2} x^{2}+1}\, x a +3 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)+i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right) c^{3} a^{3}}+\frac{i \left(3 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{4} a^{4}+6 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}-\sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 i \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+3 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)+3 \sqrt{a^{2} x^{2}+1}\, x a -i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right) c^{3} a^{3}}+\frac{i \left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}+\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a +i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) c^{3} a^{3}}-\frac{i \left(\arctan \left(a x \right) \Ei \left(1, -i \arctan \left(a x \right)\right) x^{2} a^{2}+\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a -i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) c^{3} a^{3}}"," ",0,"-1/8*I*(3*Ei(1,3*I*arctan(a*x))*arctan(a*x)*x^4*a^4-(a^2*x^2+1)^(1/2)*x^3*a^3+6*Ei(1,3*I*arctan(a*x))*arctan(a*x)*x^2*a^2-3*I*(a^2*x^2+1)^(1/2)*x^2*a^2+3*(a^2*x^2+1)^(1/2)*x*a+3*Ei(1,3*I*arctan(a*x))*arctan(a*x)+I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)/c^3/a^3+1/8*I*(3*Ei(1,-3*I*arctan(a*x))*arctan(a*x)*x^4*a^4+6*Ei(1,-3*I*arctan(a*x))*arctan(a*x)*x^2*a^2-(a^2*x^2+1)^(1/2)*x^3*a^3+3*I*(a^2*x^2+1)^(1/2)*x^2*a^2+3*Ei(1,-3*I*arctan(a*x))*arctan(a*x)+3*(a^2*x^2+1)^(1/2)*x*a-I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)/c^3/a^3+1/8*I*(Ei(1,I*arctan(a*x))*arctan(a*x)*x^2*a^2+Ei(1,I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a+I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/c^3/a^3-1/8*I*(arctan(a*x)*Ei(1,-I*arctan(a*x))*x^2*a^2+Ei(1,-I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a-I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/c^3/a^3","C"
591,1,601,102,1.220000," ","int(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","-\frac{\left(\arctan \left(a x \right) \Ei \left(1, -i \arctan \left(a x \right)\right) x^{2} a^{2}+\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a -i \sqrt{a^{2} x^{2}+1}\right) \sqrt{a^{2} x^{2}+1}\, \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \arctan \left(a x \right) \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{2}}-\frac{\left(3 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{4} a^{4}+6 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}-\sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 i \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+3 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)+3 \sqrt{a^{2} x^{2}+1}\, x a -i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \sqrt{a^{2} x^{2}+1}\, a^{2} c^{3} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right)}-\frac{\left(3 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{4} a^{4}-\sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+6 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}-3 i \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+3 \sqrt{a^{2} x^{2}+1}\, x a +3 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)+i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \sqrt{a^{2} x^{2}+1}\, a^{2} c^{3} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right)}-\frac{\left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}+\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a +i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) c^{3} a^{2}}"," ",0,"-1/8*(arctan(a*x)*Ei(1,-I*arctan(a*x))*x^2*a^2+Ei(1,-I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a-I*(a^2*x^2+1)^(1/2))*(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/(a^4*x^4+2*a^2*x^2+1)/c^3/a^2-1/8*(3*Ei(1,-3*I*arctan(a*x))*arctan(a*x)*x^4*a^4+6*Ei(1,-3*I*arctan(a*x))*arctan(a*x)*x^2*a^2-(a^2*x^2+1)^(1/2)*x^3*a^3+3*I*(a^2*x^2+1)^(1/2)*x^2*a^2+3*Ei(1,-3*I*arctan(a*x))*arctan(a*x)+3*(a^2*x^2+1)^(1/2)*x*a-I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a^2/c^3/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)-1/8*(3*Ei(1,3*I*arctan(a*x))*arctan(a*x)*x^4*a^4-(a^2*x^2+1)^(1/2)*x^3*a^3+6*Ei(1,3*I*arctan(a*x))*arctan(a*x)*x^2*a^2-3*I*(a^2*x^2+1)^(1/2)*x^2*a^2+3*(a^2*x^2+1)^(1/2)*x*a+3*Ei(1,3*I*arctan(a*x))*arctan(a*x)+I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a^2/c^3/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)-1/8*(Ei(1,I*arctan(a*x))*arctan(a*x)*x^2*a^2+Ei(1,I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a+I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/c^3/a^2","C"
592,1,586,101,0.766000," ","int(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\frac{i \left(3 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{4} a^{4}-\sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+6 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}-3 i \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+3 \sqrt{a^{2} x^{2}+1}\, x a +3 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)+i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right) a \,c^{3}}-\frac{i \left(3 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{4} a^{4}+6 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}-\sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 i \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+3 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)+3 \sqrt{a^{2} x^{2}+1}\, x a -i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right) a \,c^{3}}+\frac{3 i \left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right) x^{2} a^{2}+\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a +i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) a \,c^{3}}-\frac{3 i \left(\arctan \left(a x \right) \Ei \left(1, -i \arctan \left(a x \right)\right) x^{2} a^{2}+\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sqrt{a^{2} x^{2}+1}\, x a -i \sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{8 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right) a \,c^{3}}"," ",0,"1/8*I*(3*Ei(1,3*I*arctan(a*x))*arctan(a*x)*x^4*a^4-(a^2*x^2+1)^(1/2)*x^3*a^3+6*Ei(1,3*I*arctan(a*x))*arctan(a*x)*x^2*a^2-3*I*(a^2*x^2+1)^(1/2)*x^2*a^2+3*(a^2*x^2+1)^(1/2)*x*a+3*Ei(1,3*I*arctan(a*x))*arctan(a*x)+I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)/a/c^3-1/8*I*(3*Ei(1,-3*I*arctan(a*x))*arctan(a*x)*x^4*a^4+6*Ei(1,-3*I*arctan(a*x))*arctan(a*x)*x^2*a^2-(a^2*x^2+1)^(1/2)*x^3*a^3+3*I*(a^2*x^2+1)^(1/2)*x^2*a^2+3*Ei(1,-3*I*arctan(a*x))*arctan(a*x)+3*(a^2*x^2+1)^(1/2)*x*a-I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)/a/c^3+3/8*I*(Ei(1,I*arctan(a*x))*arctan(a*x)*x^2*a^2+Ei(1,I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a+I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/a/c^3-3/8*I*(arctan(a*x)*Ei(1,-I*arctan(a*x))*x^2*a^2+Ei(1,-I*arctan(a*x))*arctan(a*x)+(a^2*x^2+1)^(1/2)*x*a-I*(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)/a/c^3","C"
593,0,0,178,1.106000," ","int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","F"
594,0,0,145,1.116000," ","int(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","F"
595,0,0,214,1.968000," ","int(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","F"
596,0,0,187,3.883000," ","int(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","F"
597,0,0,30,1.404000," ","int((f*x)^(1/2)/(c^2*d*x^2+d)^2/(a+b*arctan(c*x))^2,x)","\int \frac{\sqrt{f x}}{\left(c^{2} d \,x^{2}+d \right)^{2} \left(a +b \arctan \left(c x \right)\right)^{2}}\, dx"," ",0,"int((f*x)^(1/2)/(c^2*d*x^2+d)^2/(a+b*arctan(c*x))^2,x)","F"
598,0,0,24,1.663000," ","int(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","F"
599,0,0,24,1.509000," ","int(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","F"
600,0,0,22,1.328000," ","int(x^m*(a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
601,0,0,40,0.545000," ","int(x^m/(a^2*c*x^2+c)/arctan(a*x)^2,x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)/arctan(a*x)^2,x)","F"
602,0,0,24,1.580000," ","int(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^2,x)","F"
603,0,0,24,1.711000," ","int(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^2,x)","F"
604,0,0,24,1.098000," ","int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","F"
605,0,0,24,1.044000," ","int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","F"
606,0,0,24,1.116000," ","int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x)","\int \frac{x^{m} \sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x)","F"
607,0,0,24,1.527000," ","int(x^m/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m}}{\arctan \left(a x \right)^{2} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x)","F"
608,0,0,24,1.732000," ","int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x)","F"
609,0,0,24,1.707000," ","int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x)","F"
610,0,0,20,1.695000," ","int(x*(a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
611,0,0,19,1.462000," ","int((a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{a^{2} c \,x^{2}+c}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
612,0,0,22,2.316000," ","int((a^2*c*x^2+c)/x/arctan(a*x)^3,x)","\int \frac{a^{2} c \,x^{2}+c}{x \arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)/x/arctan(a*x)^3,x)","F"
613,0,0,22,1.954000," ","int(x*(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","F"
614,0,0,21,1.686000," ","int((a^2*c*x^2+c)^2/arctan(a*x)^3,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)^2/arctan(a*x)^3,x)","F"
615,0,0,24,1.885000," ","int((a^2*c*x^2+c)^2/x/arctan(a*x)^3,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{x \arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)^2/x/arctan(a*x)^3,x)","F"
616,0,0,22,2.315000," ","int(x*(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","F"
617,0,0,21,2.044000," ","int((a^2*c*x^2+c)^3/arctan(a*x)^3,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)^3/arctan(a*x)^3,x)","F"
618,0,0,24,2.214000," ","int((a^2*c*x^2+c)^3/x/arctan(a*x)^3,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{x \arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)^3/x/arctan(a*x)^3,x)","F"
619,0,0,38,1.940000," ","int(x^3/(a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
620,0,0,35,0.882000," ","int(x^2/(a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
621,0,0,32,0.283000," ","int(x/(a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
622,1,15,14,0.064000," ","int(1/(a^2*c*x^2+c)/arctan(a*x)^3,x)","-\frac{1}{2 a c \arctan \left(a x \right)^{2}}"," ",0,"-1/2/a/c/arctan(a*x)^2","A"
623,0,0,38,0.263000," ","int(1/x/(a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
624,0,0,38,0.865000," ","int(1/x^2/(a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
625,0,0,38,2.562000," ","int(1/x^3/(a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
626,0,0,38,2.104000," ","int(1/x^4/(a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
627,0,0,107,0.852000," ","int(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","F"
628,1,52,69,0.266000," ","int(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","\frac{4 \Ci \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-2 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+\cos \left(2 \arctan \left(a x \right)\right)-1}{4 a^{3} c^{2} \arctan \left(a x \right)^{2}}"," ",0,"1/4/a^3/c^2*(4*Ci(2*arctan(a*x))*arctan(a*x)^2-2*sin(2*arctan(a*x))*arctan(a*x)+cos(2*arctan(a*x))-1)/arctan(a*x)^2","A"
629,1,51,76,0.268000," ","int(x/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","-\frac{4 \Si \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+2 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sin \left(2 \arctan \left(a x \right)\right)}{4 a^{2} c^{2} \arctan \left(a x \right)^{2}}"," ",0,"-1/4/a^2/c^2*(4*Si(2*arctan(a*x))*arctan(a*x)^2+2*cos(2*arctan(a*x))*arctan(a*x)+sin(2*arctan(a*x)))/arctan(a*x)^2","A"
630,1,52,63,0.235000," ","int(1/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","-\frac{4 \Ci \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-2 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+\cos \left(2 \arctan \left(a x \right)\right)+1}{4 a \,c^{2} \arctan \left(a x \right)^{2}}"," ",0,"-1/4/a/c^2*(4*Ci(2*arctan(a*x))*arctan(a*x)^2-2*sin(2*arctan(a*x))*arctan(a*x)+cos(2*arctan(a*x))+1)/arctan(a*x)^2","A"
631,0,0,105,0.820000," ","int(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","F"
632,0,0,99,0.924000," ","int(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","F"
633,0,0,147,2.687000," ","int(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","F"
634,0,0,135,1.944000," ","int(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","F"
635,1,90,166,0.233000," ","int(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","-\frac{8 \Si \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-16 \Si \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+4 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)-4 \cos \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)+2 \sin \left(2 \arctan \left(a x \right)\right)-\sin \left(4 \arctan \left(a x \right)\right)}{16 a^{4} c^{3} \arctan \left(a x \right)^{2}}"," ",0,"-1/16/a^4/c^3*(8*Si(2*arctan(a*x))*arctan(a*x)^2-16*Si(4*arctan(a*x))*arctan(a*x)^2+4*cos(2*arctan(a*x))*arctan(a*x)-4*cos(4*arctan(a*x))*arctan(a*x)+2*sin(2*arctan(a*x))-sin(4*arctan(a*x)))/arctan(a*x)^2","A"
636,1,52,116,0.233000," ","int(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","\frac{16 \Ci \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-4 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)+\cos \left(4 \arctan \left(a x \right)\right)-1}{16 a^{3} c^{3} \arctan \left(a x \right)^{2}}"," ",0,"1/16/a^3/c^3*(16*Ci(4*arctan(a*x))*arctan(a*x)^2-4*sin(4*arctan(a*x))*arctan(a*x)+cos(4*arctan(a*x))-1)/arctan(a*x)^2","A"
637,1,88,107,0.247000," ","int(x/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","-\frac{8 \Si \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+16 \Si \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+4 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+4 \cos \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)+2 \sin \left(2 \arctan \left(a x \right)\right)+\sin \left(4 \arctan \left(a x \right)\right)}{16 a^{2} c^{3} \arctan \left(a x \right)^{2}}"," ",0,"-1/16/a^2/c^3*(8*Si(2*arctan(a*x))*arctan(a*x)^2+16*Si(4*arctan(a*x))*arctan(a*x)^2+4*cos(2*arctan(a*x))*arctan(a*x)+4*cos(4*arctan(a*x))*arctan(a*x)+2*sin(2*arctan(a*x))+sin(4*arctan(a*x)))/arctan(a*x)^2","A"
638,1,89,79,0.292000," ","int(1/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","-\frac{16 \Ci \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+16 \Ci \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-8 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)-4 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)+4 \cos \left(2 \arctan \left(a x \right)\right)+\cos \left(4 \arctan \left(a x \right)\right)+3}{16 a \,c^{3} \arctan \left(a x \right)^{2}}"," ",0,"-1/16/a/c^3*(16*Ci(2*arctan(a*x))*arctan(a*x)^2+16*Ci(4*arctan(a*x))*arctan(a*x)^2-8*sin(2*arctan(a*x))*arctan(a*x)-4*sin(4*arctan(a*x))*arctan(a*x)+4*cos(2*arctan(a*x))+cos(4*arctan(a*x))+3)/arctan(a*x)^2","A"
639,0,0,185,1.603000," ","int(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","F"
640,0,0,161,1.099000," ","int(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","F"
641,0,0,236,4.448000," ","int(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","F"
642,0,0,202,2.513000," ","int(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","F"
643,0,0,14,2.444000," ","int(x^3/(a^2*x^2+1)/arctan(a*x)^3-3/2*x^2/a/arctan(a*x)^2,x)","\int \frac{x^{3}}{\left(a^{2} x^{2}+1\right) \arctan \left(a x \right)^{3}}-\frac{3 x^{2}}{2 a \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x^3/(a^2*x^2+1)/arctan(a*x)^3-3/2*x^2/a/arctan(a*x)^2,x)","F"
644,0,0,22,1.751000," ","int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x)","\int \frac{x \sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x)","F"
645,0,0,21,1.405000," ","int((a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x)","F"
646,0,0,24,1.854000," ","int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^3,x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{x \arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^3,x)","F"
647,0,0,22,2.012000," ","int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","F"
648,0,0,21,1.629000," ","int((a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","F"
649,0,0,24,1.922000," ","int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^3,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{x \arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^3,x)","F"
650,0,0,22,2.159000," ","int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","F"
651,0,0,21,1.575000," ","int((a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","F"
652,0,0,24,1.857000," ","int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^3,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{x \arctan \left(a x \right)^{3}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^3,x)","F"
653,0,0,22,1.506000," ","int(x/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x}{\arctan \left(a x \right)^{3} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","F"
654,0,0,21,0.930000," ","int(1/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{\arctan \left(a x \right)^{3} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","F"
655,0,0,59,1.054000," ","int(1/x/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{x \arctan \left(a x \right)^{3} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/x/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","F"
656,0,0,24,1.048000," ","int(1/x^2/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{x^{2} \arctan \left(a x \right)^{3} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/x^2/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","F"
657,0,0,24,2.064000," ","int(1/x^3/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{x^{3} \arctan \left(a x \right)^{3} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/x^3/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","F"
658,0,0,119,3.495000," ","int(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","F"
659,0,0,118,3.449000," ","int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","F"
660,1,313,90,1.174000," ","int(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","-\frac{i \left(\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-i \sqrt{a^{2} x^{2}+1}\, x a -\sqrt{a^{2} x^{2}+1}-i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)\right) \sqrt{a^{2} x^{2}+1}\, \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \arctan \left(a x \right)^{2} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{2} a^{2}}+\frac{i \left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +i \sqrt{a^{2} x^{2}+1}\, x a +\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)-\sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right)^{2} c^{2} a^{2}}"," ",0,"-1/4*I*(Ei(1,-I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+Ei(1,-I*arctan(a*x))*arctan(a*x)^2-I*(a^2*x^2+1)^(1/2)*x*a-(a^2*x^2+1)^(1/2)-I*(a^2*x^2+1)^(1/2)*arctan(a*x))*(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/(a^4*x^4+2*a^2*x^2+1)/c^2/a^2+1/4*I*(Ei(1,I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+I*(a^2*x^2+1)^(1/2)*x*a+Ei(1,I*arctan(a*x))*arctan(a*x)^2+I*(a^2*x^2+1)^(1/2)*arctan(a*x)-(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/c^2/a^2","C"
661,1,292,87,0.648000," ","int(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\frac{\left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +i \sqrt{a^{2} x^{2}+1}\, x a +\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)-\sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right)^{2} c^{2} a}+\frac{\left(\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-i \sqrt{a^{2} x^{2}+1}\, x a -\sqrt{a^{2} x^{2}+1}-i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{4 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right)^{2} c^{2} a}"," ",0,"1/4*(Ei(1,I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+I*(a^2*x^2+1)^(1/2)*x*a+Ei(1,I*arctan(a*x))*arctan(a*x)^2+I*(a^2*x^2+1)^(1/2)*arctan(a*x)-(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/c^2/a+1/4*(Ei(1,-I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+Ei(1,-I*arctan(a*x))*arctan(a*x)^2-I*(a^2*x^2+1)^(1/2)*x*a-(a^2*x^2+1)^(1/2)-I*(a^2*x^2+1)^(1/2)*arctan(a*x))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/c^2/a","C"
662,0,0,143,1.036000," ","int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","F"
663,0,0,114,1.176000," ","int(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","F"
664,0,0,175,2.260000," ","int(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","F"
665,0,0,150,4.023000," ","int(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","F"
666,0,0,212,6.644000," ","int(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","\int \frac{x^{5}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","F"
667,0,0,208,4.834000," ","int(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","\int \frac{x^{4}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","F"
668,1,848,156,3.612000," ","int(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","\frac{i \left(9 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{4} a^{4}-3 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{3} a^{3}+18 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+i \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+9 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{2} a^{2}+9 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a -3 i \sqrt{a^{2} x^{2}+1}\, x a +9 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-3 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)-\sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right)^{2} c^{3} a^{4}}-\frac{i \left(9 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{4} a^{4}-3 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{3} a^{3}+18 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}-i \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}-9 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{2} a^{2}+9 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +9 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+3 i \sqrt{a^{2} x^{2}+1}\, x a -\sqrt{a^{2} x^{2}+1}+3 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right)^{2} c^{3} a^{4}}+\frac{3 i \left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +i \sqrt{a^{2} x^{2}+1}\, x a +\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)-\sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right)^{2} c^{3} a^{4}}-\frac{3 i \left(\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-i \sqrt{a^{2} x^{2}+1}\, x a -\sqrt{a^{2} x^{2}+1}-i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right)^{2} c^{3} a^{4}}"," ",0,"1/16*I*(9*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2*x^4*a^4-3*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^3*a^3+18*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+I*(a^2*x^2+1)^(1/2)*x^3*a^3+3*(a^2*x^2+1)^(1/2)*x^2*a^2+9*I*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^2*a^2+9*(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a-3*I*(a^2*x^2+1)^(1/2)*x*a+9*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2-3*I*(a^2*x^2+1)^(1/2)*arctan(a*x)-(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)^2/c^3/a^4-1/16*I*(9*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2*x^4*a^4-3*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^3*a^3+18*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2*x^2*a^2-I*(a^2*x^2+1)^(1/2)*x^3*a^3+3*(a^2*x^2+1)^(1/2)*x^2*a^2-9*I*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^2*a^2+9*(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+9*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2+3*I*(a^2*x^2+1)^(1/2)*x*a-(a^2*x^2+1)^(1/2)+3*I*(a^2*x^2+1)^(1/2)*arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)^2/c^3/a^4+3/16*I*(Ei(1,I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+I*(a^2*x^2+1)^(1/2)*x*a+Ei(1,I*arctan(a*x))*arctan(a*x)^2+I*(a^2*x^2+1)^(1/2)*arctan(a*x)-(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/c^3/a^4-3/16*I*(Ei(1,-I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+Ei(1,-I*arctan(a*x))*arctan(a*x)^2-I*(a^2*x^2+1)^(1/2)*x*a-(a^2*x^2+1)^(1/2)-I*(a^2*x^2+1)^(1/2)*arctan(a*x))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/c^3/a^4","C"
669,1,844,181,3.333000," ","int(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","-\frac{\left(9 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{4} a^{4}-3 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{3} a^{3}+18 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}-i \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}-9 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{2} a^{2}+9 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +9 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+3 i \sqrt{a^{2} x^{2}+1}\, x a -\sqrt{a^{2} x^{2}+1}+3 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right)^{2} c^{3} a^{3}}-\frac{\left(9 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{4} a^{4}-3 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{3} a^{3}+18 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+i \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+9 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{2} a^{2}+9 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a -3 i \sqrt{a^{2} x^{2}+1}\, x a +9 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-3 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)-\sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right)^{2} c^{3} a^{3}}+\frac{\left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +i \sqrt{a^{2} x^{2}+1}\, x a +\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)-\sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right)^{2} c^{3} a^{3}}+\frac{\left(\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-i \sqrt{a^{2} x^{2}+1}\, x a -\sqrt{a^{2} x^{2}+1}-i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right)^{2} c^{3} a^{3}}"," ",0,"-1/16*(9*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2*x^4*a^4-3*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^3*a^3+18*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2*x^2*a^2-I*(a^2*x^2+1)^(1/2)*x^3*a^3+3*(a^2*x^2+1)^(1/2)*x^2*a^2-9*I*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^2*a^2+9*(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+9*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2+3*I*(a^2*x^2+1)^(1/2)*x*a-(a^2*x^2+1)^(1/2)+3*I*(a^2*x^2+1)^(1/2)*arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)^2/c^3/a^3-1/16*(9*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2*x^4*a^4-3*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^3*a^3+18*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+I*(a^2*x^2+1)^(1/2)*x^3*a^3+3*(a^2*x^2+1)^(1/2)*x^2*a^2+9*I*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^2*a^2+9*(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a-3*I*(a^2*x^2+1)^(1/2)*x*a+9*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2-3*I*(a^2*x^2+1)^(1/2)*arctan(a*x)-(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)^2/c^3/a^3+1/16*(Ei(1,I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+I*(a^2*x^2+1)^(1/2)*x*a+Ei(1,I*arctan(a*x))*arctan(a*x)^2+I*(a^2*x^2+1)^(1/2)*arctan(a*x)-(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/c^3/a^3+1/16*(Ei(1,-I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+Ei(1,-I*arctan(a*x))*arctan(a*x)^2-I*(a^2*x^2+1)^(1/2)*x*a-(a^2*x^2+1)^(1/2)-I*(a^2*x^2+1)^(1/2)*arctan(a*x))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/c^3/a^3","C"
670,1,867,153,1.300000," ","int(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","-\frac{i \left(\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-i \sqrt{a^{2} x^{2}+1}\, x a -\sqrt{a^{2} x^{2}+1}-i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)\right) \sqrt{a^{2} x^{2}+1}\, \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \arctan \left(a x \right)^{2} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) c^{3} a^{2}}-\frac{i \left(9 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{4} a^{4}-3 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{3} a^{3}+18 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+i \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+9 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{2} a^{2}+9 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a -3 i \sqrt{a^{2} x^{2}+1}\, x a +9 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-3 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)-\sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \sqrt{a^{2} x^{2}+1}\, a^{2} c^{3} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right)^{2}}+\frac{i \left(9 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{4} a^{4}-3 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{3} a^{3}+18 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}-i \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}-9 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{2} a^{2}+9 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +9 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+3 i \sqrt{a^{2} x^{2}+1}\, x a -\sqrt{a^{2} x^{2}+1}+3 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \sqrt{a^{2} x^{2}+1}\, a^{2} c^{3} \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right)^{2}}+\frac{i \left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +i \sqrt{a^{2} x^{2}+1}\, x a +\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)-\sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right)^{2} c^{3} a^{2}}"," ",0,"-1/16*I*(Ei(1,-I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+Ei(1,-I*arctan(a*x))*arctan(a*x)^2-I*(a^2*x^2+1)^(1/2)*x*a-(a^2*x^2+1)^(1/2)-I*(a^2*x^2+1)^(1/2)*arctan(a*x))*(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/(a^4*x^4+2*a^2*x^2+1)/c^3/a^2-1/16*I*(9*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2*x^4*a^4-3*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^3*a^3+18*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+I*(a^2*x^2+1)^(1/2)*x^3*a^3+3*(a^2*x^2+1)^(1/2)*x^2*a^2+9*I*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^2*a^2+9*(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a-3*I*(a^2*x^2+1)^(1/2)*x*a+9*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2-3*I*(a^2*x^2+1)^(1/2)*arctan(a*x)-(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a^2/c^3/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)^2+1/16*I*(9*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2*x^4*a^4-3*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^3*a^3+18*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2*x^2*a^2-I*(a^2*x^2+1)^(1/2)*x^3*a^3+3*(a^2*x^2+1)^(1/2)*x^2*a^2-9*I*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^2*a^2+9*(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+9*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2+3*I*(a^2*x^2+1)^(1/2)*x*a-(a^2*x^2+1)^(1/2)+3*I*(a^2*x^2+1)^(1/2)*arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/a^2/c^3/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)^2+1/16*I*(Ei(1,I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+I*(a^2*x^2+1)^(1/2)*x*a+Ei(1,I*arctan(a*x))*arctan(a*x)^2+I*(a^2*x^2+1)^(1/2)*arctan(a*x)-(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/c^3/a^2","C"
671,1,844,125,0.790000," ","int(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","\frac{\left(9 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{4} a^{4}-3 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{3} a^{3}+18 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}-i \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}-9 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{2} a^{2}+9 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +9 \Ei \left(1, 3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+3 i \sqrt{a^{2} x^{2}+1}\, x a -\sqrt{a^{2} x^{2}+1}+3 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right)^{2} a \,c^{3}}+\frac{\left(9 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{4} a^{4}-3 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{3} a^{3}+18 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+i \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+3 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+9 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x^{2} a^{2}+9 \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a -3 i \sqrt{a^{2} x^{2}+1}\, x a +9 \Ei \left(1, -3 i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-3 i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)-\sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \sqrt{a^{2} x^{2}+1}\, \left(a^{4} x^{4}+2 a^{2} x^{2}+1\right) \arctan \left(a x \right)^{2} a \,c^{3}}+\frac{3 \left(\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +i \sqrt{a^{2} x^{2}+1}\, x a +\Ei \left(1, i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}+i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)-\sqrt{a^{2} x^{2}+1}\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right)^{2} a \,c^{3}}+\frac{3 \left(\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2} x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right) x a +\Ei \left(1, -i \arctan \left(a x \right)\right) \arctan \left(a x \right)^{2}-i \sqrt{a^{2} x^{2}+1}\, x a -\sqrt{a^{2} x^{2}+1}-i \sqrt{a^{2} x^{2}+1}\, \arctan \left(a x \right)\right) \sqrt{c \left(a x -i\right) \left(a x +i\right)}}{16 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctan \left(a x \right)^{2} a \,c^{3}}"," ",0,"1/16*(9*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2*x^4*a^4-3*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^3*a^3+18*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2*x^2*a^2-I*(a^2*x^2+1)^(1/2)*x^3*a^3+3*(a^2*x^2+1)^(1/2)*x^2*a^2-9*I*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^2*a^2+9*(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+9*Ei(1,3*I*arctan(a*x))*arctan(a*x)^2+3*I*(a^2*x^2+1)^(1/2)*x*a-(a^2*x^2+1)^(1/2)+3*I*(a^2*x^2+1)^(1/2)*arctan(a*x))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)^2/a/c^3+1/16*(9*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2*x^4*a^4-3*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^3*a^3+18*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+I*(a^2*x^2+1)^(1/2)*x^3*a^3+3*(a^2*x^2+1)^(1/2)*x^2*a^2+9*I*(a^2*x^2+1)^(1/2)*arctan(a*x)*x^2*a^2+9*(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a-3*I*(a^2*x^2+1)^(1/2)*x*a+9*Ei(1,-3*I*arctan(a*x))*arctan(a*x)^2-3*I*(a^2*x^2+1)^(1/2)*arctan(a*x)-(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(1/2)*(c*(a*x-I)*(I+a*x))^(1/2)/(a^4*x^4+2*a^2*x^2+1)/arctan(a*x)^2/a/c^3+3/16*(Ei(1,I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+I*(a^2*x^2+1)^(1/2)*x*a+Ei(1,I*arctan(a*x))*arctan(a*x)^2+I*(a^2*x^2+1)^(1/2)*arctan(a*x)-(a^2*x^2+1)^(1/2))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/a/c^3+3/16*(Ei(1,-I*arctan(a*x))*arctan(a*x)^2*x^2*a^2+(a^2*x^2+1)^(1/2)*arctan(a*x)*x*a+Ei(1,-I*arctan(a*x))*arctan(a*x)^2-I*(a^2*x^2+1)^(1/2)*x*a-(a^2*x^2+1)^(1/2)-I*(a^2*x^2+1)^(1/2)*arctan(a*x))/(a^2*x^2+1)^(3/2)*(c*(a*x-I)*(I+a*x))^(1/2)/arctan(a*x)^2/a/c^3","C"
672,0,0,226,1.156000," ","int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","F"
673,0,0,201,1.194000," ","int(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","F"
674,0,0,24,1.821000," ","int(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","F"
675,0,0,24,1.775000," ","int(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","F"
676,0,0,22,1.503000," ","int(x^m*(a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
677,0,0,41,0.523000," ","int(x^m/(a^2*c*x^2+c)/arctan(a*x)^3,x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)/arctan(a*x)^3,x)","F"
678,0,0,24,1.567000," ","int(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^3,x)","F"
679,0,0,24,1.926000," ","int(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^3,x)","F"
680,0,0,24,1.326000," ","int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","F"
681,0,0,24,1.264000," ","int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","F"
682,0,0,24,1.438000," ","int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x)","\int \frac{x^{m} \sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x)","F"
683,0,0,24,1.823000," ","int(x^m/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m}}{\arctan \left(a x \right)^{3} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","F"
684,0,0,24,2.174000," ","int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x)","F"
685,0,0,24,2.085000," ","int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{3}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x)","F"
686,0,0,22,4.569000," ","int(x^m*(a^2*c*x^2+c)*arctan(a*x)^(1/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right) \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)*arctan(a*x)^(1/2),x)","F"
687,0,0,48,2.002000," ","int(x*(a^2*c*x^2+c)*arctan(a*x)^(1/2),x)","\int x \left(a^{2} c \,x^{2}+c \right) \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)*arctan(a*x)^(1/2),x)","F"
688,0,0,19,1.621000," ","int((a^2*c*x^2+c)*arctan(a*x)^(1/2),x)","\int \left(a^{2} c \,x^{2}+c \right) \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)*arctan(a*x)^(1/2),x)","F"
689,0,0,22,2.842000," ","int((a^2*c*x^2+c)*arctan(a*x)^(1/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right) \sqrt{\arctan \left(a x \right)}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)*arctan(a*x)^(1/2)/x,x)","F"
690,0,0,24,4.505000," ","int(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(1/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{2} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(1/2),x)","F"
691,0,0,52,2.433000," ","int(x*(a^2*c*x^2+c)^2*arctan(a*x)^(1/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{2} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^2*arctan(a*x)^(1/2),x)","F"
692,0,0,21,2.689000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^(1/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{2} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^2*arctan(a*x)^(1/2),x)","F"
693,0,0,24,3.185000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^(1/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2} \sqrt{\arctan \left(a x \right)}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)^2*arctan(a*x)^(1/2)/x,x)","F"
694,0,0,24,5.605000," ","int(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(1/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{3} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(1/2),x)","F"
695,0,0,52,3.145000," ","int(x*(a^2*c*x^2+c)^3*arctan(a*x)^(1/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{3} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^3*arctan(a*x)^(1/2),x)","F"
696,0,0,21,2.754000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^(1/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{3} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^3*arctan(a*x)^(1/2),x)","F"
697,0,0,24,3.967000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^(1/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3} \sqrt{\arctan \left(a x \right)}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)^3*arctan(a*x)^(1/2)/x,x)","F"
698,0,0,24,1.298000," ","int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x)","\int \frac{x^{m} \sqrt{\arctan \left(a x \right)}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x)","F"
699,0,0,49,3.701000," ","int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x)","\int \frac{x^{3} \sqrt{\arctan \left(a x \right)}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x)","F"
700,0,0,30,1.596000," ","int(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x)","\int \frac{x^{2} \sqrt{\arctan \left(a x \right)}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x)","F"
701,0,0,32,0.429000," ","int(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x)","\int \frac{x \sqrt{\arctan \left(a x \right)}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x)","F"
702,1,15,14,0.166000," ","int(arctan(a*x)^(1/2)/(a^2*c*x^2+c),x)","\frac{2 \arctan \left(a x \right)^{\frac{3}{2}}}{3 a c}"," ",0,"2/3*arctan(a*x)^(3/2)/a/c","A"
703,0,0,39,0.595000," ","int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c),x)","F"
704,0,0,29,1.266000," ","int(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x^{2} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c),x)","F"
705,0,0,61,5.982000," ","int(arctan(a*x)^(1/2)/x^3/(a^2*c*x^2+c),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x^{3} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x^3/(a^2*c*x^2+c),x)","F"
706,0,0,51,3.789000," ","int(arctan(a*x)^(1/2)/x^4/(a^2*c*x^2+c),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x^{4} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x^4/(a^2*c*x^2+c),x)","F"
707,0,0,24,3.033000," ","int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x)","\int \frac{x^{m} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x)","F"
708,0,0,24,2.362000," ","int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x)","\int \frac{x^{3} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x)","F"
709,1,60,64,0.507000," ","int(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x)","\frac{3 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+8 \arctan \left(a x \right)^{2}-6 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{24 a^{3} c^{2} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/24/a^3/c^2*(3*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))+8*arctan(a*x)^2-6*sin(2*arctan(a*x))*arctan(a*x))/arctan(a*x)^(1/2)","A"
710,1,46,63,0.392000," ","int(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x)","-\frac{\sqrt{\arctan \left(a x \right)}\, \cos \left(2 \arctan \left(a x \right)\right)}{4 a^{2} c^{2}}+\frac{\FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{8 a^{2} c^{2}}"," ",0,"-1/4/a^2/c^2*arctan(a*x)^(1/2)*cos(2*arctan(a*x))+1/8*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^2/c^2","A"
711,1,60,61,0.572000," ","int(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x)","\frac{8 \arctan \left(a x \right)^{2}+6 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)-3 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)}{24 a \,c^{2} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/24/a/c^2/arctan(a*x)^(1/2)*(8*arctan(a*x)^2+6*sin(2*arctan(a*x))*arctan(a*x)-3*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2)))","A"
712,0,0,24,3.160000," ","int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^2,x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x \left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^2,x)","F"
713,0,0,24,4.287000," ","int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x)","\int \frac{x^{m} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x)","F"
714,0,0,24,4.191000," ","int(x^5*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x)","\int \frac{x^{5} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(x^5*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x)","F"
715,1,102,109,0.703000," ","int(x^4*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x)","\frac{-\sqrt{2}\, \sqrt{\pi}\, \sqrt{\arctan \left(a x \right)}\, \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+16 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+32 \arctan \left(a x \right)^{2}+4 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)-32 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{128 a^{5} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/128/a^5/c^3/arctan(a*x)^(1/2)*(-2^(1/2)*Pi^(1/2)*arctan(a*x)^(1/2)*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))+16*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))+32*arctan(a*x)^2+4*sin(4*arctan(a*x))*arctan(a*x)-32*sin(2*arctan(a*x))*arctan(a*x))","A"
716,1,94,92,0.490000," ","int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x)","\frac{-\sqrt{2}\, \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+4 \cos \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)-16 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+8 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)}{128 a^{4} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/128/a^4/c^3/arctan(a*x)^(1/2)*(-2^(1/2)*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))+4*cos(4*arctan(a*x))*arctan(a*x)-16*cos(2*arctan(a*x))*arctan(a*x)+8*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2)))","A"
717,1,66,65,0.626000," ","int(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x)","\frac{3 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\arctan \left(a x \right)}\, \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+32 \arctan \left(a x \right)^{2}-12 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{384 a^{3} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/384/a^3/c^3*(3*2^(1/2)*Pi^(1/2)*arctan(a*x)^(1/2)*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))+32*arctan(a*x)^2-12*sin(4*arctan(a*x))*arctan(a*x))/arctan(a*x)^(1/2)","A"
718,1,94,92,0.517000," ","int(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x)","-\frac{-\sqrt{2}\, \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-8 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+16 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+4 \cos \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{128 a^{2} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"-1/128/a^2/c^3/arctan(a*x)^(1/2)*(-2^(1/2)*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))-8*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))+16*cos(2*arctan(a*x))*arctan(a*x)+4*cos(4*arctan(a*x))*arctan(a*x))","A"
719,1,102,109,0.660000," ","int(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x)","\frac{-\sqrt{2}\, \sqrt{\pi}\, \sqrt{\arctan \left(a x \right)}\, \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-16 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+32 \arctan \left(a x \right)^{2}+32 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+4 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{128 a \,c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/128/a/c^3/arctan(a*x)^(1/2)*(-2^(1/2)*Pi^(1/2)*arctan(a*x)^(1/2)*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))-16*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))+32*arctan(a*x)^2+32*sin(2*arctan(a*x))*arctan(a*x)+4*sin(4*arctan(a*x))*arctan(a*x))","A"
720,0,0,24,5.487000," ","int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^3,x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x \left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^3,x)","F"
721,0,0,24,3.652000," ","int(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x)","\int x^{m} \sqrt{a^{2} c \,x^{2}+c}\, \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x)","F"
722,0,0,24,4.554000," ","int(x^2*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x)","\int x^{2} \sqrt{a^{2} c \,x^{2}+c}\, \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x)","F"
723,0,0,53,3.383000," ","int(x*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x)","\int x \sqrt{a^{2} c \,x^{2}+c}\, \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x)","F"
724,0,0,21,1.657000," ","int((a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x)","\int \sqrt{a^{2} c \,x^{2}+c}\, \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x)","F"
725,0,0,24,3.321000," ","int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x)","F"
726,0,0,24,4.586000," ","int(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x)","F"
727,0,0,53,3.154000," ","int(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x)","F"
728,0,0,21,1.588000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x)","F"
729,0,0,24,3.422000," ","int(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x)","F"
730,0,0,24,4.849000," ","int(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x)","F"
731,0,0,53,3.299000," ","int(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x)","F"
732,0,0,21,1.834000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x)","F"
733,0,0,24,3.615000," ","int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m} \sqrt{\arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","F"
734,0,0,111,10.347000," ","int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{3} \sqrt{\arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","F"
735,0,0,81,10.028000," ","int(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{2} \sqrt{\arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","F"
736,0,0,52,3.768000," ","int(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x \sqrt{\arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","F"
737,0,0,21,1.534000," ","int(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","F"
738,0,0,24,1.727000," ","int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(1/2),x)","F"
739,0,0,54,1.979000," ","int(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x^{2} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c)^(1/2),x)","F"
740,0,0,83,5.081000," ","int(arctan(a*x)^(1/2)/x^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x^{3} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x^3/(a^2*c*x^2+c)^(1/2),x)","F"
741,0,0,112,8.637000," ","int(arctan(a*x)^(1/2)/x^4/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x^{4} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x^4/(a^2*c*x^2+c)^(1/2),x)","F"
742,0,0,24,3.365000," ","int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{m} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","F"
743,0,0,24,10.059000," ","int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{3} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","F"
744,0,0,24,10.100000," ","int(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{2} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","F"
745,0,0,78,3.644000," ","int(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","F"
746,0,0,75,1.538000," ","int(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","F"
747,0,0,24,1.839000," ","int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(3/2),x)","F"
748,0,0,24,2.191000," ","int(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c)^(3/2),x)","F"
749,0,0,24,3.614000," ","int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{m} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","F"
750,0,0,24,11.629000," ","int(x^4*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{4} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^4*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","F"
751,0,0,173,9.937000," ","int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{3} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","F"
752,0,0,129,9.891000," ","int(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{2} \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","F"
753,0,0,129,3.567000," ","int(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x \sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","F"
754,0,0,171,1.613000," ","int(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","F"
755,0,0,24,1.894000," ","int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(5/2),x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(5/2),x)","F"
756,0,0,22,4.495000," ","int(x^m*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x)","F"
757,0,0,22,3.761000," ","int(x^2*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x)","F"
758,0,0,48,2.189000," ","int(x*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x)","\int x \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x)","F"
759,0,0,63,1.796000," ","int((a^2*c*x^2+c)*arctan(a*x)^(3/2),x)","\int \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)*arctan(a*x)^(3/2),x)","F"
760,0,0,22,3.114000," ","int((a^2*c*x^2+c)*arctan(a*x)^(3/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)*arctan(a*x)^(3/2)/x,x)","F"
761,0,0,22,1.116000," ","int((a^2*c*x^2+c)*arctan(a*x)^(3/2)/x^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)*arctan(a*x)^(3/2)/x^2,x)","F"
762,0,0,24,4.754000," ","int(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x)","F"
763,0,0,24,4.524000," ","int(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x)","F"
764,0,0,52,2.482000," ","int(x*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x)","F"
765,0,0,141,2.150000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x)","F"
766,0,0,24,3.130000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x,x)","F"
767,0,0,24,2.869000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x^2,x)","F"
768,0,0,24,5.405000," ","int(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x)","F"
769,0,0,24,5.713000," ","int(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x)","F"
770,0,0,52,3.303000," ","int(x*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x)","F"
771,0,0,215,2.797000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x)","F"
772,0,0,24,4.036000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x,x)","F"
773,0,0,24,3.298000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x^2,x)","F"
774,0,0,24,1.402000," ","int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{3}{2}}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x)","F"
775,0,0,49,3.566000," ","int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x)","\int \frac{x^{3} \arctan \left(a x \right)^{\frac{3}{2}}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x)","F"
776,0,0,30,1.346000," ","int(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x)","\int \frac{x^{2} \arctan \left(a x \right)^{\frac{3}{2}}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x)","F"
777,0,0,32,0.402000," ","int(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x)","\int \frac{x \arctan \left(a x \right)^{\frac{3}{2}}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x)","F"
778,1,15,14,0.139000," ","int(arctan(a*x)^(3/2)/(a^2*c*x^2+c),x)","\frac{2 \arctan \left(a x \right)^{\frac{5}{2}}}{5 a c}"," ",0,"2/5*arctan(a*x)^(5/2)/a/c","A"
779,0,0,39,0.549000," ","int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c),x)","F"
780,0,0,29,1.280000," ","int(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x^{2} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c),x)","F"
781,0,0,61,5.788000," ","int(arctan(a*x)^(3/2)/x^3/(a^2*c*x^2+c),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x^{3} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x^3/(a^2*c*x^2+c),x)","F"
782,0,0,51,3.510000," ","int(arctan(a*x)^(3/2)/x^4/(a^2*c*x^2+c),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x^{4} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x^4/(a^2*c*x^2+c),x)","F"
783,0,0,24,2.879000," ","int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x)","F"
784,0,0,24,2.354000," ","int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x)","\int \frac{x^{3} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x)","F"
785,1,75,103,0.487000," ","int(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x)","\frac{32 \arctan \left(a x \right)^{3}-40 \arctan \left(a x \right)^{2} \sin \left(2 \arctan \left(a x \right)\right)+15 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-30 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{160 a^{3} c^{2} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/160/a^3/c^2*(32*arctan(a*x)^3-40*arctan(a*x)^2*sin(2*arctan(a*x))+15*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))-30*cos(2*arctan(a*x))*arctan(a*x))/arctan(a*x)^(1/2)","A"
786,1,67,89,0.313000," ","int(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x)","-\frac{8 \arctan \left(a x \right)^{2} \cos \left(2 \arctan \left(a x \right)\right)+3 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-6 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{32 a^{2} c^{2} \sqrt{\arctan \left(a x \right)}}"," ",0,"-1/32/a^2/c^2*(8*arctan(a*x)^2*cos(2*arctan(a*x))+3*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))-6*sin(2*arctan(a*x))*arctan(a*x))/arctan(a*x)^(1/2)","A"
787,1,75,100,0.530000," ","int(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x)","\frac{32 \arctan \left(a x \right)^{3}+40 \arctan \left(a x \right)^{2} \sin \left(2 \arctan \left(a x \right)\right)+30 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)-15 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)}{160 a \,c^{2} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/160/a/c^2/arctan(a*x)^(1/2)*(32*arctan(a*x)^3+40*arctan(a*x)^2*sin(2*arctan(a*x))+30*cos(2*arctan(a*x))*arctan(a*x)-15*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2)))","A"
788,0,0,24,2.603000," ","int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^2,x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x \left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^2,x)","F"
789,0,0,24,3.486000," ","int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x)","F"
790,0,0,24,3.462000," ","int(x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x)","\int \frac{x^{5} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x)","F"
791,1,132,188,0.710000," ","int(x^4*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x)","\frac{-15 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+768 \arctan \left(a x \right)^{3}-1280 \arctan \left(a x \right)^{2} \sin \left(2 \arctan \left(a x \right)\right)+160 \arctan \left(a x \right)^{2} \sin \left(4 \arctan \left(a x \right)\right)+480 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-960 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+60 \cos \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{5120 a^{5} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/5120/a^5/c^3*(-15*2^(1/2)*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))+768*arctan(a*x)^3-1280*arctan(a*x)^2*sin(2*arctan(a*x))+160*arctan(a*x)^2*sin(4*arctan(a*x))+480*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))-960*cos(2*arctan(a*x))*arctan(a*x)+60*cos(4*arctan(a*x))*arctan(a*x))/arctan(a*x)^(1/2)","A"
792,1,124,134,0.565000," ","int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x)","-\frac{-3 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\arctan \left(a x \right)}\, \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+128 \arctan \left(a x \right)^{2} \cos \left(2 \arctan \left(a x \right)\right)-32 \arctan \left(a x \right)^{2} \cos \left(4 \arctan \left(a x \right)\right)+48 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-96 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+12 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{1024 a^{4} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"-1/1024/a^4/c^3*(-3*2^(1/2)*Pi^(1/2)*arctan(a*x)^(1/2)*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))+128*arctan(a*x)^2*cos(2*arctan(a*x))-32*arctan(a*x)^2*cos(4*arctan(a*x))+48*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))-96*sin(2*arctan(a*x))*arctan(a*x)+12*sin(4*arctan(a*x))*arctan(a*x))/arctan(a*x)^(1/2)","A"
793,1,81,86,0.502000," ","int(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x)","\frac{15 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+256 \arctan \left(a x \right)^{3}-160 \arctan \left(a x \right)^{2} \sin \left(4 \arctan \left(a x \right)\right)-60 \cos \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{5120 a^{3} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/5120/a^3/c^3*(15*2^(1/2)*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))+256*arctan(a*x)^3-160*arctan(a*x)^2*sin(4*arctan(a*x))-60*cos(4*arctan(a*x))*arctan(a*x))/arctan(a*x)^(1/2)","A"
794,1,124,134,0.457000," ","int(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x)","-\frac{3 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\arctan \left(a x \right)}\, \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+128 \arctan \left(a x \right)^{2} \cos \left(2 \arctan \left(a x \right)\right)+32 \arctan \left(a x \right)^{2} \cos \left(4 \arctan \left(a x \right)\right)+48 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-96 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)-12 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{1024 a^{2} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"-1/1024/a^2/c^3*(3*2^(1/2)*Pi^(1/2)*arctan(a*x)^(1/2)*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))+128*arctan(a*x)^2*cos(2*arctan(a*x))+32*arctan(a*x)^2*cos(4*arctan(a*x))+48*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))-96*sin(2*arctan(a*x))*arctan(a*x)-12*sin(4*arctan(a*x))*arctan(a*x))/arctan(a*x)^(1/2)","A"
795,1,132,177,0.766000," ","int(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x)","\frac{-15 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+768 \arctan \left(a x \right)^{3}+1280 \arctan \left(a x \right)^{2} \sin \left(2 \arctan \left(a x \right)\right)+160 \arctan \left(a x \right)^{2} \sin \left(4 \arctan \left(a x \right)\right)-480 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+960 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+60 \cos \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{5120 a \,c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/5120/a/c^3/arctan(a*x)^(1/2)*(-15*2^(1/2)*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))+768*arctan(a*x)^3+1280*arctan(a*x)^2*sin(2*arctan(a*x))+160*arctan(a*x)^2*sin(4*arctan(a*x))-480*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))+960*cos(2*arctan(a*x))*arctan(a*x)+60*cos(4*arctan(a*x))*arctan(a*x))","A"
796,0,0,24,4.676000," ","int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^3,x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x \left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^3,x)","F"
797,0,0,24,3.084000," ","int(x^m*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x)","\int x^{m} \arctan \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^m*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x)","F"
798,0,0,24,3.964000," ","int(x^2*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x)","\int x^{2} \arctan \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^2*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x)","F"
799,0,0,53,2.964000," ","int(x*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x)","\int x \arctan \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x)","F"
800,0,0,93,1.424000," ","int(arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x)","\int \arctan \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x)","F"
801,0,0,24,1.720000," ","int(arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2)/x,x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}}{x}\, dx"," ",0,"int(arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2)/x,x)","F"
802,0,0,24,2.888000," ","int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x)","F"
803,0,0,24,3.846000," ","int(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x)","F"
804,0,0,53,2.703000," ","int(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x)","F"
805,0,0,167,1.505000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x)","F"
806,0,0,24,1.714000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)/x,x)","F"
807,0,0,24,2.939000," ","int(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x)","F"
808,0,0,24,4.241000," ","int(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x)","F"
809,0,0,53,2.979000," ","int(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x)","F"
810,0,0,243,1.592000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x)","F"
811,0,0,24,1.862000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2)/x,x)","F"
812,0,0,24,3.180000," ","int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{3}{2}}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","F"
813,0,0,136,9.118000," ","int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{3} \arctan \left(a x \right)^{\frac{3}{2}}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","F"
814,0,0,106,8.597000," ","int(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{2} \arctan \left(a x \right)^{\frac{3}{2}}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","F"
815,0,0,52,3.366000," ","int(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x \arctan \left(a x \right)^{\frac{3}{2}}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","F"
816,0,0,21,1.315000," ","int(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","F"
817,0,0,24,1.620000," ","int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(1/2),x)","F"
818,0,0,54,1.964000," ","int(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x^{2} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(1/2),x)","F"
819,0,0,112,4.767000," ","int(arctan(a*x)^(3/2)/x^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x^{3} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x^3/(a^2*c*x^2+c)^(1/2),x)","F"
820,0,0,141,8.197000," ","int(arctan(a*x)^(3/2)/x^4/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x^{4} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x^4/(a^2*c*x^2+c)^(1/2),x)","F"
821,0,0,24,2.743000," ","int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","F"
822,0,0,24,8.815000," ","int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{3} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","F"
823,0,0,24,8.642000," ","int(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{2} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","F"
824,0,0,105,3.104000," ","int(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","F"
825,0,0,101,1.424000," ","int(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","F"
826,0,0,24,1.643000," ","int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(3/2),x)","F"
827,0,0,24,1.874000," ","int(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(3/2),x)","F"
828,0,0,24,3.149000," ","int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","F"
829,0,0,24,18.467000," ","int(x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{5} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","F"
830,0,0,24,10.702000," ","int(x^4*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{4} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^4*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","F"
831,0,0,213,8.963000," ","int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{3} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","F"
832,0,0,199,8.990000," ","int(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{2} \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","F"
833,0,0,200,3.164000," ","int(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x \arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","F"
834,0,0,202,1.556000," ","int(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x)","F"
835,0,0,24,1.731000," ","int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(5/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(5/2),x)","F"
836,0,0,24,1.899000," ","int(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(5/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(5/2),x)","F"
837,0,0,22,3.885000," ","int(x^m*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x)","F"
838,0,0,22,3.271000," ","int(x^2*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x)","F"
839,0,0,95,1.773000," ","int(x*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x)","\int x \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x)","F"
840,0,0,63,1.599000," ","int((a^2*c*x^2+c)*arctan(a*x)^(5/2),x)","\int \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)*arctan(a*x)^(5/2),x)","F"
841,0,0,22,2.838000," ","int((a^2*c*x^2+c)*arctan(a*x)^(5/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{5}{2}}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)*arctan(a*x)^(5/2)/x,x)","F"
842,0,0,22,0.954000," ","int((a^2*c*x^2+c)*arctan(a*x)^(5/2)/x^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)*arctan(a*x)^(5/2)/x^2,x)","F"
843,0,0,24,4.288000," ","int(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x)","F"
844,0,0,24,3.999000," ","int(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x)","F"
845,0,0,181,2.353000," ","int(x*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x)","F"
846,0,0,141,1.991000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x)","F"
847,0,0,24,2.843000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x,x)","F"
848,0,0,24,2.505000," ","int((a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x^2,x)","F"
849,0,0,24,4.763000," ","int(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x)","F"
850,0,0,24,4.802000," ","int(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x)","F"
851,0,0,261,2.949000," ","int(x*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x)","F"
852,0,0,215,2.546000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x)","F"
853,0,0,24,3.458000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x,x)","F"
854,0,0,24,2.987000," ","int((a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x^2,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x^2,x)","F"
855,0,0,24,1.294000," ","int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{5}{2}}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x)","F"
856,0,0,49,3.207000," ","int(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x)","\int \frac{x^{3} \arctan \left(a x \right)^{\frac{5}{2}}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x)","F"
857,0,0,30,1.142000," ","int(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x)","\int \frac{x^{2} \arctan \left(a x \right)^{\frac{5}{2}}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x)","F"
858,0,0,32,0.397000," ","int(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x)","\int \frac{x \arctan \left(a x \right)^{\frac{5}{2}}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x)","F"
859,1,15,14,0.126000," ","int(arctan(a*x)^(5/2)/(a^2*c*x^2+c),x)","\frac{2 \arctan \left(a x \right)^{\frac{7}{2}}}{7 a c}"," ",0,"2/7*arctan(a*x)^(7/2)/a/c","A"
860,0,0,39,0.466000," ","int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c),x)","F"
861,0,0,29,1.178000," ","int(arctan(a*x)^(5/2)/x^2/(a^2*c*x^2+c),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x^{2} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x^2/(a^2*c*x^2+c),x)","F"
862,0,0,61,5.168000," ","int(arctan(a*x)^(5/2)/x^3/(a^2*c*x^2+c),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x^{3} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x^3/(a^2*c*x^2+c),x)","F"
863,0,0,51,3.168000," ","int(arctan(a*x)^(5/2)/x^4/(a^2*c*x^2+c),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x^{4} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x^4/(a^2*c*x^2+c),x)","F"
864,0,0,24,2.620000," ","int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x)","F"
865,0,0,24,2.132000," ","int(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x)","\int \frac{x^{3} \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x)","F"
866,1,102,129,0.487000," ","int(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x)","\frac{\arctan \left(a x \right)^{\frac{7}{2}}}{7 a^{3} c^{2}}-\frac{\arctan \left(a x \right)^{\frac{5}{2}} \sin \left(2 \arctan \left(a x \right)\right)}{4 a^{3} c^{2}}-\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \cos \left(2 \arctan \left(a x \right)\right)}{16 a^{3} c^{2}}+\frac{15 \sqrt{\arctan \left(a x \right)}\, \sin \left(2 \arctan \left(a x \right)\right)}{64 a^{3} c^{2}}-\frac{15 \,\mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{128 a^{3} c^{2}}"," ",0,"1/7*arctan(a*x)^(7/2)/a^3/c^2-1/4/a^3/c^2*arctan(a*x)^(5/2)*sin(2*arctan(a*x))-5/16/a^3/c^2*arctan(a*x)^(3/2)*cos(2*arctan(a*x))+15/64/a^3/c^2*arctan(a*x)^(1/2)*sin(2*arctan(a*x))-15/128*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^3/c^2","A"
867,1,88,128,0.338000," ","int(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x)","-\frac{\arctan \left(a x \right)^{\frac{5}{2}} \cos \left(2 \arctan \left(a x \right)\right)}{4 a^{2} c^{2}}+\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \sin \left(2 \arctan \left(a x \right)\right)}{16 a^{2} c^{2}}+\frac{15 \sqrt{\arctan \left(a x \right)}\, \cos \left(2 \arctan \left(a x \right)\right)}{64 a^{2} c^{2}}-\frac{15 \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{128 a^{2} c^{2}}"," ",0,"-1/4/a^2/c^2*arctan(a*x)^(5/2)*cos(2*arctan(a*x))+5/16/a^2/c^2*arctan(a*x)^(3/2)*sin(2*arctan(a*x))+15/64/a^2/c^2*arctan(a*x)^(1/2)*cos(2*arctan(a*x))-15/128*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^2/c^2","A"
868,1,102,123,0.503000," ","int(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x)","\frac{\arctan \left(a x \right)^{\frac{7}{2}}}{7 a \,c^{2}}+\frac{\arctan \left(a x \right)^{\frac{5}{2}} \sin \left(2 \arctan \left(a x \right)\right)}{4 a \,c^{2}}+\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \cos \left(2 \arctan \left(a x \right)\right)}{16 a \,c^{2}}-\frac{15 \sqrt{\arctan \left(a x \right)}\, \sin \left(2 \arctan \left(a x \right)\right)}{64 a \,c^{2}}+\frac{15 \,\mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{128 a \,c^{2}}"," ",0,"1/7*arctan(a*x)^(7/2)/a/c^2+1/4/a/c^2*arctan(a*x)^(5/2)*sin(2*arctan(a*x))+5/16/a/c^2*arctan(a*x)^(3/2)*cos(2*arctan(a*x))-15/64/a/c^2*arctan(a*x)^(1/2)*sin(2*arctan(a*x))+15/128*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a/c^2","A"
869,0,0,24,2.650000," ","int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^2,x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x \left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^2,x)","F"
870,0,0,24,3.506000," ","int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x)","F"
871,0,0,24,3.465000," ","int(x^5*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x)","\int \frac{x^{5} \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(x^5*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x)","F"
872,1,194,256,0.686000," ","int(x^4*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x)","\frac{3 \arctan \left(a x \right)^{\frac{7}{2}}}{28 a^{5} c^{3}}-\frac{\arctan \left(a x \right)^{\frac{5}{2}} \sin \left(2 \arctan \left(a x \right)\right)}{4 a^{5} c^{3}}+\frac{\arctan \left(a x \right)^{\frac{5}{2}} \sin \left(4 \arctan \left(a x \right)\right)}{32 a^{5} c^{3}}-\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \cos \left(2 \arctan \left(a x \right)\right)}{16 a^{5} c^{3}}+\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \cos \left(4 \arctan \left(a x \right)\right)}{256 a^{5} c^{3}}+\frac{15 \,\mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{8192 a^{5} c^{3}}+\frac{15 \sin \left(2 \arctan \left(a x \right)\right) \sqrt{\arctan \left(a x \right)}}{64 a^{5} c^{3}}-\frac{15 \sin \left(4 \arctan \left(a x \right)\right) \sqrt{\arctan \left(a x \right)}}{2048 a^{5} c^{3}}-\frac{15 \,\mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{128 a^{5} c^{3}}"," ",0,"3/28*arctan(a*x)^(7/2)/a^5/c^3-1/4/a^5/c^3*arctan(a*x)^(5/2)*sin(2*arctan(a*x))+1/32/a^5/c^3*arctan(a*x)^(5/2)*sin(4*arctan(a*x))-5/16/a^5/c^3*arctan(a*x)^(3/2)*cos(2*arctan(a*x))+5/256/a^5/c^3*arctan(a*x)^(3/2)*cos(4*arctan(a*x))+15/8192*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*2^(1/2)*Pi^(1/2)/a^5/c^3+15/64*sin(2*arctan(a*x))*arctan(a*x)^(1/2)/a^5/c^3-15/2048*sin(4*arctan(a*x))*arctan(a*x)^(1/2)/a^5/c^3-15/128*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^5/c^3","A"
873,1,180,210,0.570000," ","int(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x)","-\frac{\arctan \left(a x \right)^{\frac{5}{2}} \cos \left(2 \arctan \left(a x \right)\right)}{8 a^{4} c^{3}}+\frac{\arctan \left(a x \right)^{\frac{5}{2}} \cos \left(4 \arctan \left(a x \right)\right)}{32 a^{4} c^{3}}+\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \sin \left(2 \arctan \left(a x \right)\right)}{32 a^{4} c^{3}}-\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \sin \left(4 \arctan \left(a x \right)\right)}{256 a^{4} c^{3}}+\frac{15 \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{8192 a^{4} c^{3}}+\frac{15 \sqrt{\arctan \left(a x \right)}\, \cos \left(2 \arctan \left(a x \right)\right)}{128 a^{4} c^{3}}-\frac{15 \sqrt{\arctan \left(a x \right)}\, \cos \left(4 \arctan \left(a x \right)\right)}{2048 a^{4} c^{3}}-\frac{15 \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{256 a^{4} c^{3}}"," ",0,"-1/8/a^4/c^3*arctan(a*x)^(5/2)*cos(2*arctan(a*x))+1/32/a^4/c^3*arctan(a*x)^(5/2)*cos(4*arctan(a*x))+5/32/a^4/c^3*arctan(a*x)^(3/2)*sin(2*arctan(a*x))-5/256/a^4/c^3*arctan(a*x)^(3/2)*sin(4*arctan(a*x))+15/8192*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*2^(1/2)*Pi^(1/2)/a^4/c^3+15/128/a^4/c^3*arctan(a*x)^(1/2)*cos(2*arctan(a*x))-15/2048/a^4/c^3*arctan(a*x)^(1/2)*cos(4*arctan(a*x))-15/256*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^4/c^3","A"
874,1,96,107,0.579000," ","int(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x)","\frac{2048 \arctan \left(a x \right)^{4}-1792 \arctan \left(a x \right)^{3} \sin \left(4 \arctan \left(a x \right)\right)-105 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\arctan \left(a x \right)}\, \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-1120 \arctan \left(a x \right)^{2} \cos \left(4 \arctan \left(a x \right)\right)+420 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)}{57344 a^{3} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/57344/a^3/c^3*(2048*arctan(a*x)^4-1792*arctan(a*x)^3*sin(4*arctan(a*x))-105*2^(1/2)*Pi^(1/2)*arctan(a*x)^(1/2)*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))-1120*arctan(a*x)^2*cos(4*arctan(a*x))+420*sin(4*arctan(a*x))*arctan(a*x))/arctan(a*x)^(1/2)","A"
875,1,180,208,0.530000," ","int(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x)","-\frac{\arctan \left(a x \right)^{\frac{5}{2}} \cos \left(2 \arctan \left(a x \right)\right)}{8 a^{2} c^{3}}-\frac{\arctan \left(a x \right)^{\frac{5}{2}} \cos \left(4 \arctan \left(a x \right)\right)}{32 a^{2} c^{3}}+\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \sin \left(2 \arctan \left(a x \right)\right)}{32 a^{2} c^{3}}+\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \sin \left(4 \arctan \left(a x \right)\right)}{256 a^{2} c^{3}}-\frac{15 \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{8192 a^{2} c^{3}}+\frac{15 \sqrt{\arctan \left(a x \right)}\, \cos \left(2 \arctan \left(a x \right)\right)}{128 a^{2} c^{3}}+\frac{15 \sqrt{\arctan \left(a x \right)}\, \cos \left(4 \arctan \left(a x \right)\right)}{2048 a^{2} c^{3}}-\frac{15 \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{256 a^{2} c^{3}}"," ",0,"-1/8/a^2/c^3*arctan(a*x)^(5/2)*cos(2*arctan(a*x))-1/32/a^2/c^3*arctan(a*x)^(5/2)*cos(4*arctan(a*x))+5/32/a^2/c^3*arctan(a*x)^(3/2)*sin(2*arctan(a*x))+5/256/a^2/c^3*arctan(a*x)^(3/2)*sin(4*arctan(a*x))-15/8192*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*2^(1/2)*Pi^(1/2)/a^2/c^3+15/128/a^2/c^3*arctan(a*x)^(1/2)*cos(2*arctan(a*x))+15/2048/a^2/c^3*arctan(a*x)^(1/2)*cos(4*arctan(a*x))-15/256*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^2/c^3","A"
876,1,194,242,0.721000," ","int(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x)","\frac{3 \arctan \left(a x \right)^{\frac{7}{2}}}{28 a \,c^{3}}+\frac{\arctan \left(a x \right)^{\frac{5}{2}} \sin \left(2 \arctan \left(a x \right)\right)}{4 a \,c^{3}}+\frac{\arctan \left(a x \right)^{\frac{5}{2}} \sin \left(4 \arctan \left(a x \right)\right)}{32 a \,c^{3}}+\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \cos \left(2 \arctan \left(a x \right)\right)}{16 a \,c^{3}}+\frac{5 \arctan \left(a x \right)^{\frac{3}{2}} \cos \left(4 \arctan \left(a x \right)\right)}{256 a \,c^{3}}+\frac{15 \,\mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{8192 a \,c^{3}}-\frac{15 \sin \left(2 \arctan \left(a x \right)\right) \sqrt{\arctan \left(a x \right)}}{64 a \,c^{3}}-\frac{15 \sin \left(4 \arctan \left(a x \right)\right) \sqrt{\arctan \left(a x \right)}}{2048 a \,c^{3}}+\frac{15 \,\mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{128 a \,c^{3}}"," ",0,"3/28*arctan(a*x)^(7/2)/a/c^3+1/4/a/c^3*arctan(a*x)^(5/2)*sin(2*arctan(a*x))+1/32/a/c^3*arctan(a*x)^(5/2)*sin(4*arctan(a*x))+5/16/a/c^3*arctan(a*x)^(3/2)*cos(2*arctan(a*x))+5/256/a/c^3*arctan(a*x)^(3/2)*cos(4*arctan(a*x))+15/8192*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*2^(1/2)*Pi^(1/2)/a/c^3-15/64*sin(2*arctan(a*x))*arctan(a*x)^(1/2)/a/c^3-15/2048*sin(4*arctan(a*x))*arctan(a*x)^(1/2)/a/c^3+15/128*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a/c^3","A"
877,0,0,24,4.901000," ","int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^3,x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x \left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^3,x)","F"
878,0,0,24,3.102000," ","int(x^m*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x)","\int x^{m} \arctan \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^m*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x)","F"
879,0,0,24,4.040000," ","int(x^2*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x)","\int x^{2} \arctan \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x^2*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x)","F"
880,0,0,128,2.820000," ","int(x*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x)","\int x \arctan \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x)","F"
881,0,0,93,1.519000," ","int(arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x)","\int \arctan \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x)","F"
882,0,0,24,1.770000," ","int(arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2)/x,x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}}{x}\, dx"," ",0,"int(arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2)/x,x)","F"
883,0,0,24,2.905000," ","int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x)","F"
884,0,0,24,4.106000," ","int(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x)","F"
885,0,0,208,2.810000," ","int(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x)","F"
886,0,0,167,1.501000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x)","F"
887,0,0,24,1.850000," ","int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2)/x,x)","F"
888,0,0,24,3.004000," ","int(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x)","\int x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x)","F"
889,0,0,24,4.221000," ","int(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x)","\int x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x)","F"
890,0,0,290,2.977000," ","int(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x)","\int x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x)","F"
891,0,0,243,1.618000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x)","F"
892,0,0,24,1.839000," ","int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2)/x,x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}{x}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2)/x,x)","F"
893,0,0,24,2.999000," ","int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{5}{2}}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","F"
894,0,0,161,9.252000," ","int(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{3} \arctan \left(a x \right)^{\frac{5}{2}}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","F"
895,0,0,106,8.686000," ","int(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{2} \arctan \left(a x \right)^{\frac{5}{2}}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","F"
896,0,0,52,3.229000," ","int(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x \arctan \left(a x \right)^{\frac{5}{2}}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","F"
897,0,0,21,1.375000," ","int(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","F"
898,0,0,24,1.661000," ","int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(1/2),x)","F"
899,0,0,54,1.627000," ","int(arctan(a*x)^(5/2)/x^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x^{2} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x^2/(a^2*c*x^2+c)^(1/2),x)","F"
900,0,0,112,4.427000," ","int(arctan(a*x)^(5/2)/x^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x^{3} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x^3/(a^2*c*x^2+c)^(1/2),x)","F"
901,0,0,170,7.523000," ","int(arctan(a*x)^(5/2)/x^4/(a^2*c*x^2+c)^(1/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x^{4} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x^4/(a^2*c*x^2+c)^(1/2),x)","F"
902,0,0,24,2.923000," ","int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","F"
903,0,0,24,8.872000," ","int(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x^{2} \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","F"
904,0,0,131,3.013000," ","int(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{x \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","F"
905,0,0,125,1.359000," ","int(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","F"
906,0,0,24,1.470000," ","int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(3/2),x)","F"
907,0,0,24,2.911000," ","int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{m} \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","F"
908,0,0,24,10.175000," ","int(x^4*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{4} \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^4*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","F"
909,0,0,284,8.893000," ","int(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{3} \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","F"
910,0,0,237,8.793000," ","int(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x^{2} \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","F"
911,0,0,235,3.083000," ","int(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{x \arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","F"
912,0,0,271,1.470000," ","int(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x)","F"
913,0,0,24,1.568000," ","int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(5/2),x)","\int \frac{\arctan \left(a x \right)^{\frac{5}{2}}}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(5/2),x)","F"
914,0,0,22,3.392000," ","int(x^m*(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","F"
915,0,0,20,1.691000," ","int(x*(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","F"
916,0,0,19,1.408000," ","int((a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","\int \frac{a^{2} c \,x^{2}+c}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","F"
917,0,0,22,2.935000," ","int((a^2*c*x^2+c)/x/arctan(a*x)^(1/2),x)","\int \frac{a^{2} c \,x^{2}+c}{x \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)/x/arctan(a*x)^(1/2),x)","F"
918,0,0,24,3.779000," ","int(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{2}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","F"
919,0,0,22,2.076000," ","int(x*(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{2}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","F"
920,0,0,21,1.965000," ","int((a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","F"
921,0,0,24,2.862000," ","int((a^2*c*x^2+c)^2/x/arctan(a*x)^(1/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{x \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^2/x/arctan(a*x)^(1/2),x)","F"
922,0,0,24,4.689000," ","int(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{3}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","F"
923,0,0,22,2.813000," ","int(x*(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{3}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","F"
924,0,0,21,2.434000," ","int((a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","F"
925,0,0,24,3.263000," ","int((a^2*c*x^2+c)^3/x/arctan(a*x)^(1/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{x \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^3/x/arctan(a*x)^(1/2),x)","F"
926,0,0,24,0.951000," ","int(x^m/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right) \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","F"
927,0,0,32,0.352000," ","int(x/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right) \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","F"
928,1,15,14,0.118000," ","int(1/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","\frac{2 \sqrt{\arctan \left(a x \right)}}{a c}"," ",0,"2*arctan(a*x)^(1/2)/a/c","A"
929,0,0,24,0.464000," ","int(1/x/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right) \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x)","F"
930,0,0,24,2.222000," ","int(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{2} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","F"
931,0,0,24,1.361000," ","int(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{2} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","F"
932,1,38,37,0.433000," ","int(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","-\frac{\FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{2 a^{3} c^{2}}+\frac{\sqrt{\arctan \left(a x \right)}}{a^{3} c^{2}}"," ",0,"-1/2*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^3/c^2+arctan(a*x)^(1/2)/a^3/c^2","A"
933,1,24,23,0.167000," ","int(x/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","\frac{\mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{2 a^{2} c^{2}}"," ",0,"1/2*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^2/c^2","A"
934,1,38,37,0.449000," ","int(1/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","\frac{\FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{2 a \,c^{2}}+\frac{\sqrt{\arctan \left(a x \right)}}{a \,c^{2}}"," ",0,"1/2*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a/c^2+arctan(a*x)^(1/2)/a/c^2","A"
935,0,0,24,2.431000," ","int(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{2} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x)","F"
936,0,0,24,3.345000," ","int(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{3} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","F"
937,0,0,24,2.703000," ","int(x^5/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","\int \frac{x^{5}}{\left(a^{2} c \,x^{2}+c \right)^{3} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^5/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","F"
938,1,68,67,0.561000," ","int(x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","\frac{\FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{16 a^{5} c^{3}}-\frac{\FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{2 a^{5} c^{3}}+\frac{3 \sqrt{\arctan \left(a x \right)}}{4 a^{5} c^{3}}"," ",0,"1/16*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*2^(1/2)*Pi^(1/2)/a^5/c^3-1/2*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^5/c^3+3/4*arctan(a*x)^(1/2)/a^5/c^3","A"
939,1,54,53,0.409000," ","int(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","-\frac{\mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{16 a^{4} c^{3}}+\frac{\mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{4 a^{4} c^{3}}"," ",0,"-1/16*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*2^(1/2)*Pi^(1/2)/a^4/c^3+1/4*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^4/c^3","A"
940,1,45,44,0.500000," ","int(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","-\frac{\FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{16 a^{3} c^{3}}+\frac{\sqrt{\arctan \left(a x \right)}}{4 a^{3} c^{3}}"," ",0,"-1/16*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*2^(1/2)*Pi^(1/2)/a^3/c^3+1/4*arctan(a*x)^(1/2)/a^3/c^3","A"
941,1,54,53,0.343000," ","int(x/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","\frac{\mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{16 a^{2} c^{3}}+\frac{\mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{4 a^{2} c^{3}}"," ",0,"1/16*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*2^(1/2)*Pi^(1/2)/a^2/c^3+1/4*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a^2/c^3","A"
942,1,68,67,0.537000," ","int(1/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","\frac{\FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{16 a \,c^{3}}+\frac{\FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \sqrt{\pi}}{2 a \,c^{3}}+\frac{3 \sqrt{\arctan \left(a x \right)}}{4 a \,c^{3}}"," ",0,"1/16*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*2^(1/2)*Pi^(1/2)/a/c^3+1/2*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*Pi^(1/2)/a/c^3+3/4*arctan(a*x)^(1/2)/a/c^3","A"
943,0,0,24,4.319000," ","int(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{3} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x)","F"
944,0,0,24,3.008000," ","int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","\int \frac{x^{m} \sqrt{a^{2} c \,x^{2}+c}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","F"
945,0,0,22,2.711000," ","int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","\int \frac{x \sqrt{a^{2} c \,x^{2}+c}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","F"
946,0,0,21,1.522000," ","int((a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","F"
947,0,0,24,1.681000," ","int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^(1/2),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{x \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^(1/2),x)","F"
948,0,0,24,2.893000," ","int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","F"
949,0,0,22,2.689000," ","int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","F"
950,0,0,21,1.370000," ","int((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","F"
951,0,0,24,1.609000," ","int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(1/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{x \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(1/2),x)","F"
952,0,0,24,2.852000," ","int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","F"
953,0,0,22,2.865000," ","int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","F"
954,0,0,21,1.537000," ","int((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","F"
955,0,0,24,1.638000," ","int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(1/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{x \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(1/2),x)","F"
956,0,0,24,2.949000," ","int(x^m/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","\int \frac{x^{m}}{\sqrt{a^{2} c \,x^{2}+c}\, \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","F"
957,0,0,22,3.276000," ","int(x/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","\int \frac{x}{\sqrt{a^{2} c \,x^{2}+c}\, \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","F"
958,0,0,21,1.377000," ","int(1/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","\int \frac{1}{\sqrt{a^{2} c \,x^{2}+c}\, \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","F"
959,0,0,24,1.668000," ","int(1/x/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","\int \frac{1}{x \sqrt{a^{2} c \,x^{2}+c}\, \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x)","F"
960,0,0,24,2.961000," ","int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","F"
961,0,0,24,9.868000," ","int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","F"
962,0,0,50,3.256000," ","int(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","F"
963,0,0,50,1.458000," ","int(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","F"
964,0,0,24,1.627000," ","int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x)","F"
965,0,0,24,2.967000," ","int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","F"
966,0,0,24,11.140000," ","int(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","\int \frac{x^{4}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","F"
967,0,0,103,8.793000," ","int(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","F"
968,0,0,103,9.915000," ","int(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","F"
969,0,0,103,3.257000," ","int(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","F"
970,0,0,103,1.615000," ","int(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","F"
971,0,0,24,1.668000," ","int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x)","F"
972,0,0,22,4.037000," ","int(x^m*(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","F"
973,0,0,20,1.738000," ","int(x*(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","F"
974,0,0,19,1.428000," ","int((a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","\int \frac{a^{2} c \,x^{2}+c}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","F"
975,0,0,22,2.811000," ","int((a^2*c*x^2+c)/x/arctan(a*x)^(3/2),x)","\int \frac{a^{2} c \,x^{2}+c}{x \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)/x/arctan(a*x)^(3/2),x)","F"
976,0,0,24,4.207000," ","int(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","F"
977,0,0,22,2.247000," ","int(x*(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","F"
978,0,0,21,2.094000," ","int((a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","F"
979,0,0,24,2.921000," ","int((a^2*c*x^2+c)^2/x/arctan(a*x)^(3/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{x \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^2/x/arctan(a*x)^(3/2),x)","F"
980,0,0,24,4.738000," ","int(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","F"
981,0,0,22,3.122000," ","int(x*(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","F"
982,0,0,21,2.583000," ","int((a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","F"
983,0,0,24,3.408000," ","int((a^2*c*x^2+c)^3/x/arctan(a*x)^(3/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{x \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^3/x/arctan(a*x)^(3/2),x)","F"
984,0,0,41,1.329000," ","int(x^m/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","F"
985,0,0,32,0.356000," ","int(x/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","F"
986,1,15,14,0.118000," ","int(1/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","-\frac{2}{a c \sqrt{\arctan \left(a x \right)}}"," ",0,"-2/a/c/arctan(a*x)^(1/2)","A"
987,0,0,38,0.426000," ","int(1/x/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x)","F"
988,0,0,24,2.605000," ","int(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","F"
989,0,0,85,2.446000," ","int(x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\int \frac{x^{4}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","F"
990,0,0,93,1.612000," ","int(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","F"
991,1,46,52,0.381000," ","int(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\frac{2 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+\cos \left(2 \arctan \left(a x \right)\right)-1}{a^{3} c^{2} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/a^3/c^2*(2*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))+cos(2*arctan(a*x))-1)/arctan(a*x)^(1/2)","A"
992,1,47,124,0.270000," ","int(x/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\frac{2 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-\sin \left(2 \arctan \left(a x \right)\right)}{a^{2} c^{2} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/a^2/c^2*(2*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))-sin(2*arctan(a*x)))/arctan(a*x)^(1/2)","A"
993,1,47,49,0.540000," ","int(1/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","-\frac{2 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+\cos \left(2 \arctan \left(a x \right)\right)+1}{a \,c^{2} \sqrt{\arctan \left(a x \right)}}"," ",0,"-1/a/c^2*(2*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))+cos(2*arctan(a*x))+1)/arctan(a*x)^(1/2)","A"
994,0,0,89,2.577000," ","int(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","F"
995,0,0,85,2.120000," ","int(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","F"
996,0,0,85,5.431000," ","int(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","F"
997,0,0,85,3.658000," ","int(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x)","F"
998,0,0,24,3.411000," ","int(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","F"
999,1,86,80,0.504000," ","int(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","-\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-4 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+2 \sin \left(2 \arctan \left(a x \right)\right)-\sin \left(4 \arctan \left(a x \right)\right)}{4 a^{4} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"-1/4/a^4/c^3*(2*2^(1/2)*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))-4*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))+2*sin(2*arctan(a*x))-sin(4*arctan(a*x)))/arctan(a*x)^(1/2)","A"
1000,1,53,58,0.516000," ","int(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","\frac{2 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\arctan \left(a x \right)}\, \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+\cos \left(4 \arctan \left(a x \right)\right)-1}{4 a^{3} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"1/4/a^3/c^3*(2*2^(1/2)*Pi^(1/2)*arctan(a*x)^(1/2)*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))+cos(4*arctan(a*x))-1)/arctan(a*x)^(1/2)","A"
1001,1,84,78,0.439000," ","int(x/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","-\frac{-2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)-4 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+2 \sin \left(2 \arctan \left(a x \right)\right)+\sin \left(4 \arctan \left(a x \right)\right)}{4 a^{2} c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"-1/4/a^2/c^3/arctan(a*x)^(1/2)*(-2*2^(1/2)*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))-4*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))+2*sin(2*arctan(a*x))+sin(4*arctan(a*x)))","A"
1002,1,85,78,0.645000," ","int(1/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","-\frac{2 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\arctan \left(a x \right)}\, \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+8 \sqrt{\arctan \left(a x \right)}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right)+4 \cos \left(2 \arctan \left(a x \right)\right)+\cos \left(4 \arctan \left(a x \right)\right)+3}{4 a \,c^{3} \sqrt{\arctan \left(a x \right)}}"," ",0,"-1/4/a/c^3*(2*2^(1/2)*Pi^(1/2)*arctan(a*x)^(1/2)*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))+8*arctan(a*x)^(1/2)*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))+4*cos(2*arctan(a*x))+cos(4*arctan(a*x))+3)/arctan(a*x)^(1/2)","A"
1003,0,0,115,4.595000," ","int(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","F"
1004,0,0,85,2.710000," ","int(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","F"
1005,0,0,85,9.060000," ","int(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","F"
1006,0,0,85,4.612000," ","int(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x)","F"
1007,0,0,24,3.360000," ","int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(3/2),x)","\int \frac{x^{m} \sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(3/2),x)","F"
1008,0,0,22,3.022000," ","int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(3/2),x)","\int \frac{x \sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(3/2),x)","F"
1009,0,0,21,1.417000," ","int((a^2*c*x^2+c)^(1/2)/arctan(a*x)^(3/2),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/arctan(a*x)^(3/2),x)","F"
1010,0,0,24,1.842000," ","int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^(3/2),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{x \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^(3/2),x)","F"
1011,0,0,24,3.021000," ","int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1012,0,0,22,2.786000," ","int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1013,0,0,21,1.500000," ","int((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1014,0,0,24,1.620000," ","int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(3/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{x \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(3/2),x)","F"
1015,0,0,24,2.934000," ","int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1016,0,0,22,2.956000," ","int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1017,0,0,21,1.608000," ","int((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1018,0,0,24,1.770000," ","int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(3/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{x \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(3/2),x)","F"
1019,0,0,24,3.139000," ","int(x^m/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m}}{\arctan \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","F"
1020,0,0,22,3.401000," ","int(x/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x}{\arctan \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","F"
1021,0,0,21,1.339000," ","int(1/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{\arctan \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","F"
1022,0,0,59,1.664000," ","int(1/x/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{x \arctan \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/x/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","F"
1023,0,0,24,1.787000," ","int(1/x^2/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{x^{2} \arctan \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/x^2/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","F"
1024,0,0,24,2.938000," ","int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1025,0,0,86,9.269000," ","int(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1026,0,0,108,9.004000," ","int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1027,0,0,79,3.327000," ","int(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1028,0,0,78,1.432000," ","int(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1029,0,0,107,1.678000," ","int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1030,0,0,86,1.826000," ","int(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1031,0,0,86,3.948000," ","int(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1032,0,0,86,7.954000," ","int(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x)","F"
1033,0,0,24,3.070000," ","int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1034,0,0,132,9.163000," ","int(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1035,0,0,132,9.169000," ","int(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1036,0,0,130,3.364000," ","int(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1037,0,0,129,1.654000," ","int(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1038,0,0,155,1.724000," ","int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1039,0,0,86,1.907000," ","int(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1040,0,0,86,3.904000," ","int(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1041,0,0,86,7.942000," ","int(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x)","F"
1042,0,0,22,3.989000," ","int(x^m*(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","F"
1043,0,0,20,1.729000," ","int(x*(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","F"
1044,0,0,19,1.553000," ","int((a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","\int \frac{a^{2} c \,x^{2}+c}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","F"
1045,0,0,22,3.021000," ","int((a^2*c*x^2+c)/x/arctan(a*x)^(5/2),x)","\int \frac{a^{2} c \,x^{2}+c}{x \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)/x/arctan(a*x)^(5/2),x)","F"
1046,0,0,24,4.302000," ","int(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","F"
1047,0,0,22,2.251000," ","int(x*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","F"
1048,0,0,21,1.986000," ","int((a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","F"
1049,0,0,24,2.740000," ","int((a^2*c*x^2+c)^2/x/arctan(a*x)^(5/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{2}}{x \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^2/x/arctan(a*x)^(5/2),x)","F"
1050,0,0,24,4.541000," ","int(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","F"
1051,0,0,22,2.844000," ","int(x*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","F"
1052,0,0,21,2.496000," ","int((a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","F"
1053,0,0,24,3.411000," ","int((a^2*c*x^2+c)^3/x/arctan(a*x)^(5/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{3}}{x \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^3/x/arctan(a*x)^(5/2),x)","F"
1054,0,0,41,1.472000," ","int(x^m/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","F"
1055,0,0,32,0.374000," ","int(x/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","F"
1056,1,15,14,0.168000," ","int(1/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","-\frac{2}{3 a c \arctan \left(a x \right)^{\frac{3}{2}}}"," ",0,"-2/3/a/c/arctan(a*x)^(3/2)","A"
1057,0,0,38,0.448000," ","int(1/x/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right) \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x)","F"
1058,0,0,24,2.708000," ","int(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","F"
1059,0,0,160,1.615000," ","int(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","F"
1060,1,62,152,0.475000," ","int(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","-\frac{-8 \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \arctan \left(a x \right)^{\frac{3}{2}}+4 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)-\cos \left(2 \arctan \left(a x \right)\right)+1}{3 a^{3} c^{2} \arctan \left(a x \right)^{\frac{3}{2}}}"," ",0,"-1/3/a^3/c^2*(-8*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*arctan(a*x)^(3/2)+4*sin(2*arctan(a*x))*arctan(a*x)-cos(2*arctan(a*x))+1)/arctan(a*x)^(3/2)","A"
1061,1,59,85,0.317000," ","int(x/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","-\frac{8 \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \arctan \left(a x \right)^{\frac{3}{2}}+4 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+\sin \left(2 \arctan \left(a x \right)\right)}{3 a^{2} c^{2} \arctan \left(a x \right)^{\frac{3}{2}}}"," ",0,"-1/3/a^2/c^2*(8*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))*arctan(a*x)^(3/2)+4*cos(2*arctan(a*x))*arctan(a*x)+sin(2*arctan(a*x)))/arctan(a*x)^(3/2)","A"
1062,1,62,146,0.473000," ","int(1/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","\frac{-8 \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \arctan \left(a x \right)^{\frac{3}{2}}+4 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)-\cos \left(2 \arctan \left(a x \right)\right)-1}{3 a \,c^{2} \arctan \left(a x \right)^{\frac{3}{2}}}"," ",0,"1/3/a/c^2*(-8*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*arctan(a*x)^(3/2)+4*sin(2*arctan(a*x))*arctan(a*x)-cos(2*arctan(a*x))-1)/arctan(a*x)^(3/2)","A"
1063,0,0,154,2.673000," ","int(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","F"
1064,0,0,170,2.402000," ","int(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","F"
1065,0,0,166,5.524000," ","int(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","F"
1066,0,0,166,3.868000," ","int(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{2} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x)","F"
1067,0,0,24,3.377000," ","int(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","F"
1068,1,112,134,0.551000," ","int(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","-\frac{-16 \sqrt{2}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \arctan \left(a x \right)^{\frac{3}{2}}+16 \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \arctan \left(a x \right)^{\frac{3}{2}}+8 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)-8 \cos \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)+2 \sin \left(2 \arctan \left(a x \right)\right)-\sin \left(4 \arctan \left(a x \right)\right)}{12 a^{4} c^{3} \arctan \left(a x \right)^{\frac{3}{2}}}"," ",0,"-1/12/a^4/c^3*(-16*2^(1/2)*Pi^(1/2)*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*arctan(a*x)^(3/2)+16*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))*arctan(a*x)^(3/2)+8*cos(2*arctan(a*x))*arctan(a*x)-8*cos(4*arctan(a*x))*arctan(a*x)+2*sin(2*arctan(a*x))-sin(4*arctan(a*x)))/arctan(a*x)^(3/2)","A"
1069,1,68,109,0.498000," ","int(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","-\frac{-16 \sqrt{2}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \arctan \left(a x \right)^{\frac{3}{2}}+8 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)-\cos \left(4 \arctan \left(a x \right)\right)+1}{12 a^{3} c^{3} \arctan \left(a x \right)^{\frac{3}{2}}}"," ",0,"-1/12/a^3/c^3*(-16*2^(1/2)*Pi^(1/2)*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*arctan(a*x)^(3/2)+8*sin(4*arctan(a*x))*arctan(a*x)-cos(4*arctan(a*x))+1)/arctan(a*x)^(3/2)","A"
1070,1,110,129,0.456000," ","int(x/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","-\frac{16 \sqrt{2}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \arctan \left(a x \right)^{\frac{3}{2}}+16 \sqrt{\pi}\, \mathrm{S}\left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \arctan \left(a x \right)^{\frac{3}{2}}+8 \cos \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+8 \cos \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)+2 \sin \left(2 \arctan \left(a x \right)\right)+\sin \left(4 \arctan \left(a x \right)\right)}{12 a^{2} c^{3} \arctan \left(a x \right)^{\frac{3}{2}}}"," ",0,"-1/12/a^2/c^3*(16*2^(1/2)*Pi^(1/2)*FresnelS(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*arctan(a*x)^(3/2)+16*Pi^(1/2)*FresnelS(2*arctan(a*x)^(1/2)/Pi^(1/2))*arctan(a*x)^(3/2)+8*cos(2*arctan(a*x))*arctan(a*x)+8*cos(4*arctan(a*x))*arctan(a*x)+2*sin(2*arctan(a*x))+sin(4*arctan(a*x)))/arctan(a*x)^(3/2)","A"
1071,1,113,101,0.696000," ","int(1/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","\frac{-16 \sqrt{2}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \arctan \left(a x \right)^{\frac{3}{2}}-32 \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{\arctan \left(a x \right)}}{\sqrt{\pi}}\right) \arctan \left(a x \right)^{\frac{3}{2}}+16 \sin \left(2 \arctan \left(a x \right)\right) \arctan \left(a x \right)+8 \sin \left(4 \arctan \left(a x \right)\right) \arctan \left(a x \right)-4 \cos \left(2 \arctan \left(a x \right)\right)-\cos \left(4 \arctan \left(a x \right)\right)-3}{12 a \,c^{3} \arctan \left(a x \right)^{\frac{3}{2}}}"," ",0,"1/12/a/c^3*(-16*2^(1/2)*Pi^(1/2)*FresnelC(2*2^(1/2)/Pi^(1/2)*arctan(a*x)^(1/2))*arctan(a*x)^(3/2)-32*Pi^(1/2)*FresnelC(2*arctan(a*x)^(1/2)/Pi^(1/2))*arctan(a*x)^(3/2)+16*sin(2*arctan(a*x))*arctan(a*x)+8*sin(4*arctan(a*x))*arctan(a*x)-4*cos(2*arctan(a*x))-cos(4*arctan(a*x))-3)/arctan(a*x)^(3/2)","A"
1072,0,0,180,3.806000," ","int(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","F"
1073,0,0,197,2.766000," ","int(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","F"
1074,0,0,166,8.636000," ","int(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","F"
1075,0,0,166,4.392000," ","int(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{3} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x)","F"
1076,0,0,24,2.937000," ","int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),x)","\int \frac{x^{m} \sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),x)","F"
1077,0,0,22,2.829000," ","int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),x)","\int \frac{x \sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),x)","F"
1078,0,0,21,1.470000," ","int((a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),x)","F"
1079,0,0,24,1.724000," ","int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^(5/2),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{x \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^(5/2),x)","F"
1080,0,0,24,2.819000," ","int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1081,0,0,22,2.658000," ","int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1082,0,0,21,1.419000," ","int((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1083,0,0,24,1.611000," ","int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(5/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{x \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(5/2),x)","F"
1084,0,0,24,2.767000," ","int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{x^{m} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1085,0,0,22,2.888000," ","int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1086,0,0,21,1.507000," ","int((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1087,0,0,24,1.788000," ","int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(5/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{x \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(5/2),x)","F"
1088,0,0,24,2.992000," ","int(x^m/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m}}{\arctan \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x^m/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","F"
1089,0,0,22,3.424000," ","int(x/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{x}{\arctan \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(x/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","F"
1090,0,0,21,1.313000," ","int(1/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{\arctan \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","F"
1091,0,0,59,1.623000," ","int(1/x/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{x \arctan \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/x/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","F"
1092,0,0,24,1.778000," ","int(1/x^2/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\int \frac{1}{x^{2} \arctan \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/x^2/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","F"
1093,0,0,24,2.875000," ","int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1094,0,0,191,8.881000," ","int(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1095,0,0,189,8.763000," ","int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1096,0,0,105,3.125000," ","int(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1097,0,0,102,1.399000," ","int(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1098,0,0,185,1.605000," ","int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1099,0,0,189,1.880000," ","int(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1100,0,0,169,3.976000," ","int(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1101,0,0,169,7.534000," ","int(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x)","F"
1102,0,0,24,3.022000," ","int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1103,0,0,160,8.673000," ","int(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{x^{3}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1104,0,0,184,8.924000," ","int(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{x^{2}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1105,0,0,182,3.164000," ","int(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{x}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1106,0,0,153,1.430000," ","int(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1107,0,0,233,1.592000," ","int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{1}{x \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1108,0,0,238,1.806000," ","int(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1109,0,0,169,3.810000," ","int(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{3} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1110,0,0,169,7.450000," ","int(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","\int \frac{1}{x^{4} \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arctan \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x)","F"
1111,0,0,45,0.803000," ","int(x*arctan(a*x)^n/(a^2*c*x^2+c),x)","\int \frac{x \arctan \left(a x \right)^{n}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(x*arctan(a*x)^n/(a^2*c*x^2+c),x)","F"
1112,1,21,20,0.067000," ","int(arctan(a*x)^n/(a^2*c*x^2+c),x)","\frac{\arctan \left(a x \right)^{1+n}}{a c \left(1+n \right)}"," ",0,"arctan(a*x)^(1+n)/a/c/(1+n)","A"
1113,0,0,30,7.556000," ","int((f*x)^m*(c^2*d*x^2+d)^q*(a+b*arctan(c*x))^p,x)","\int \left(f x \right)^{m} \left(c^{2} d \,x^{2}+d \right)^{q} \left(a +b \arctan \left(c x \right)\right)^{p}\, dx"," ",0,"int((f*x)^m*(c^2*d*x^2+d)^q*(a+b*arctan(c*x))^p,x)","F"
1114,1,106,95,0.043000," ","int(x^3*(e*x^2+d)*(a+b*arctan(c*x)),x)","\frac{a e \,x^{6}}{6}+\frac{a \,x^{4} d}{4}+\frac{b \arctan \left(c x \right) e \,x^{6}}{6}+\frac{b \arctan \left(c x \right) x^{4} d}{4}-\frac{b e \,x^{5}}{30 c}-\frac{b d \,x^{3}}{12 c}+\frac{b \,x^{3} e}{18 c^{3}}+\frac{b d x}{4 c^{3}}-\frac{b e x}{6 c^{5}}-\frac{b d \arctan \left(c x \right)}{4 c^{4}}+\frac{b \arctan \left(c x \right) e}{6 c^{6}}"," ",0,"1/6*a*e*x^6+1/4*a*x^4*d+1/6*b*arctan(c*x)*e*x^6+1/4*b*arctan(c*x)*x^4*d-1/30*b*e*x^5/c-1/12*b*d*x^3/c+1/18/c^3*b*x^3*e+1/4*b*d*x/c^3-1/6/c^5*b*e*x-1/4*b*d*arctan(c*x)/c^4+1/6/c^6*b*arctan(c*x)*e","A"
1115,1,102,84,0.054000," ","int(x^2*(e*x^2+d)*(a+b*arctan(c*x)),x)","\frac{a e \,x^{5}}{5}+\frac{a d \,x^{3}}{3}+\frac{b e \,x^{5} \arctan \left(c x \right)}{5}+\frac{b \arctan \left(c x \right) d \,x^{3}}{3}-\frac{b d \,x^{2}}{6 c}-\frac{b e \,x^{4}}{20 c}+\frac{b e \,x^{2}}{10 c^{3}}+\frac{b d \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}-\frac{b e \ln \left(c^{2} x^{2}+1\right)}{10 c^{5}}"," ",0,"1/5*a*e*x^5+1/3*a*d*x^3+1/5*b*e*x^5*arctan(c*x)+1/3*b*arctan(c*x)*d*x^3-1/6*b*d*x^2/c-1/20*b*e*x^4/c+1/10*b*e*x^2/c^3+1/6*b*d*ln(c^2*x^2+1)/c^3-1/10*b*e*ln(c^2*x^2+1)/c^5","A"
1116,1,86,74,0.041000," ","int(x*(e*x^2+d)*(a+b*arctan(c*x)),x)","\frac{a e \,x^{4}}{4}+\frac{a \,x^{2} d}{2}+\frac{b \arctan \left(c x \right) e \,x^{4}}{4}+\frac{b \arctan \left(c x \right) d \,x^{2}}{2}-\frac{b e \,x^{3}}{12 c}-\frac{b d x}{2 c}+\frac{b e x}{4 c^{3}}+\frac{b d \arctan \left(c x \right)}{2 c^{2}}-\frac{b e \arctan \left(c x \right)}{4 c^{4}}"," ",0,"1/4*a*e*x^4+1/2*a*x^2*d+1/4*b*arctan(c*x)*e*x^4+1/2*b*arctan(c*x)*d*x^2-1/12*b*e*x^3/c-1/2*b*d*x/c+1/4*b*e*x/c^3+1/2*b*d*arctan(c*x)/c^2-1/4*b*e*arctan(c*x)/c^4","A"
1117,1,76,62,0.040000," ","int((e*x^2+d)*(a+b*arctan(c*x)),x)","\frac{a e \,x^{3}}{3}+a d x +\frac{b e \,x^{3} \arctan \left(c x \right)}{3}+b \arctan \left(c x \right) d x -\frac{b e \,x^{2}}{6 c}-\frac{b d \ln \left(c^{2} x^{2}+1\right)}{2 c}+\frac{b e \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}"," ",0,"1/3*a*e*x^3+a*d*x+1/3*b*e*x^3*arctan(c*x)+b*arctan(c*x)*d*x-1/6*b*e*x^2/c-1/2*b*d*ln(c^2*x^2+1)/c+1/6*b*e*ln(c^2*x^2+1)/c^3","A"
1118,1,117,63,0.059000," ","int((e*x^2+d)*(a+b*arctan(c*x))/x,x)","\frac{a \,x^{2} e}{2}+d a \ln \left(c x \right)+\frac{\arctan \left(c x \right) b e \,x^{2}}{2}+b \arctan \left(c x \right) d \ln \left(c x \right)+\frac{b e \arctan \left(c x \right)}{2 c^{2}}-\frac{b e x}{2 c}+\frac{i b d \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i b d \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{i b d \dilog \left(i c x +1\right)}{2}-\frac{i b d \dilog \left(-i c x +1\right)}{2}"," ",0,"1/2*a*x^2*e+d*a*ln(c*x)+1/2*arctan(c*x)*b*e*x^2+b*arctan(c*x)*d*ln(c*x)+1/2*b*e*arctan(c*x)/c^2-1/2*b*e*x/c+1/2*I*b*d*ln(c*x)*ln(1+I*c*x)-1/2*I*b*d*ln(c*x)*ln(1-I*c*x)+1/2*I*b*d*dilog(1+I*c*x)-1/2*I*b*d*dilog(1-I*c*x)","A"
1119,1,72,55,0.043000," ","int((e*x^2+d)*(a+b*arctan(c*x))/x^2,x)","a e x -\frac{a d}{x}+b e x \arctan \left(c x \right)-\frac{b \arctan \left(c x \right) d}{x}+c b d \ln \left(c x \right)-\frac{b c d \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{b e \ln \left(c^{2} x^{2}+1\right)}{2 c}"," ",0,"a*e*x-a*d/x+b*e*x*arctan(c*x)-b*arctan(c*x)*d/x+c*b*d*ln(c*x)-1/2*b*c*d*ln(c^2*x^2+1)-1/2*b*e*ln(c^2*x^2+1)/c","A"
1120,1,117,63,0.066000," ","int((e*x^2+d)*(a+b*arctan(c*x))/x^3,x)","a e \ln \left(c x \right)-\frac{d a}{2 x^{2}}+b \arctan \left(c x \right) e \ln \left(c x \right)-\frac{b \arctan \left(c x \right) d}{2 x^{2}}+\frac{i b e \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i b e \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{i b e \dilog \left(i c x +1\right)}{2}-\frac{i b e \dilog \left(-i c x +1\right)}{2}-\frac{b c d}{2 x}-\frac{b \,c^{2} d \arctan \left(c x \right)}{2}"," ",0,"a*e*ln(c*x)-1/2*d*a/x^2+b*arctan(c*x)*e*ln(c*x)-1/2*b*arctan(c*x)*d/x^2+1/2*I*b*e*ln(c*x)*ln(1+I*c*x)-1/2*I*b*e*ln(c*x)*ln(1-I*c*x)+1/2*I*b*e*dilog(1+I*c*x)-1/2*I*b*e*dilog(1-I*c*x)-1/2*b*c*d/x-1/2*b*c^2*d*arctan(c*x)","A"
1121,1,97,75,0.057000," ","int((e*x^2+d)*(a+b*arctan(c*x))/x^4,x)","-\frac{a d}{3 x^{3}}-\frac{a e}{x}-\frac{b \arctan \left(c x \right) d}{3 x^{3}}-\frac{b \arctan \left(c x \right) e}{x}-\frac{c^{3} b d \ln \left(c x \right)}{3}+c b \ln \left(c x \right) e -\frac{b c d}{6 x^{2}}+\frac{c^{3} b \ln \left(c^{2} x^{2}+1\right) d}{6}-\frac{c b \ln \left(c^{2} x^{2}+1\right) e}{2}"," ",0,"-1/3*a*d/x^3-a*e/x-1/3*b*arctan(c*x)*d/x^3-b*arctan(c*x)*e/x-1/3*c^3*b*d*ln(c*x)+c*b*ln(c*x)*e-1/6*b*c*d/x^2+1/6*c^3*b*ln(c^2*x^2+1)*d-1/2*c*b*ln(c^2*x^2+1)*e","A"
1122,1,86,72,0.049000," ","int((e*x^2+d)*(a+b*arctan(c*x))/x^5,x)","-\frac{a d}{4 x^{4}}-\frac{a e}{2 x^{2}}-\frac{b \arctan \left(c x \right) d}{4 x^{4}}-\frac{b \arctan \left(c x \right) e}{2 x^{2}}+\frac{b \,c^{3} d}{4 x}-\frac{c b e}{2 x}-\frac{b c d}{12 x^{3}}+\frac{c^{4} b \arctan \left(c x \right) d}{4}-\frac{b \,c^{2} e \arctan \left(c x \right)}{2}"," ",0,"-1/4*a*d/x^4-1/2*a*e/x^2-1/4*b*arctan(c*x)*d/x^4-1/2*b*arctan(c*x)*e/x^2+1/4*b*c^3*d/x-1/2*c*b*e/x-1/12*b*c*d/x^3+1/4*c^4*b*arctan(c*x)*d-1/2*b*c^2*e*arctan(c*x)","A"
1123,1,120,98,0.068000," ","int((e*x^2+d)*(a+b*arctan(c*x))/x^6,x)","-\frac{a e}{3 x^{3}}-\frac{a d}{5 x^{5}}-\frac{b \arctan \left(c x \right) e}{3 x^{3}}-\frac{b \arctan \left(c x \right) d}{5 x^{5}}+\frac{c^{5} b d \ln \left(c x \right)}{5}-\frac{c^{3} b \ln \left(c x \right) e}{3}+\frac{c^{3} b d}{10 x^{2}}-\frac{c b e}{6 x^{2}}-\frac{b c d}{20 x^{4}}-\frac{c^{5} b \ln \left(c^{2} x^{2}+1\right) d}{10}+\frac{b \,c^{3} e \ln \left(c^{2} x^{2}+1\right)}{6}"," ",0,"-1/3*a*e/x^3-1/5*a*d/x^5-1/3*b*arctan(c*x)*e/x^3-1/5*b*arctan(c*x)*d/x^5+1/5*c^5*b*d*ln(c*x)-1/3*c^3*b*ln(c*x)*e+1/10*c^3*b*d/x^2-1/6*c*b*e/x^2-1/20*b*c*d/x^4-1/10*c^5*b*ln(c^2*x^2+1)*d+1/6*b*c^3*e*ln(c^2*x^2+1)","A"
1124,1,106,93,0.049000," ","int((e*x^2+d)*(a+b*arctan(c*x))/x^7,x)","-\frac{a e}{4 x^{4}}-\frac{a d}{6 x^{6}}-\frac{b \arctan \left(c x \right) e}{4 x^{4}}-\frac{b \arctan \left(c x \right) d}{6 x^{6}}-\frac{c^{5} b d}{6 x}+\frac{b \,c^{3} e}{4 x}+\frac{c^{3} b d}{18 x^{3}}-\frac{c b e}{12 x^{3}}-\frac{b c d}{30 x^{5}}-\frac{c^{6} b \arctan \left(c x \right) d}{6}+\frac{b \,c^{4} e \arctan \left(c x \right)}{4}"," ",0,"-1/4*a*e/x^4-1/6*a*d/x^6-1/4*b*arctan(c*x)*e/x^4-1/6*b*arctan(c*x)*d/x^6-1/6*c^5*b*d/x+1/4*b*c^3*e/x+1/18*c^3*b*d/x^3-1/12*c*b*e/x^3-1/30*b*c*d/x^5-1/6*c^6*b*arctan(c*x)*d+1/4*b*c^4*e*arctan(c*x)","A"
1125,1,203,169,0.043000," ","int(x^3*(e*x^2+d)^2*(a+b*arctan(c*x)),x)","\frac{a \,e^{2} x^{8}}{8}+\frac{a e d \,x^{6}}{3}+\frac{a \,x^{4} d^{2}}{4}+\frac{b \arctan \left(c x \right) e^{2} x^{8}}{8}+\frac{b \arctan \left(c x \right) e d \,x^{6}}{3}+\frac{b \arctan \left(c x \right) d^{2} x^{4}}{4}-\frac{b \,e^{2} x^{7}}{56 c}-\frac{b e d \,x^{5}}{15 c}-\frac{b \,d^{2} x^{3}}{12 c}+\frac{b \,x^{5} e^{2}}{40 c^{3}}+\frac{b \,x^{3} d e}{9 c^{3}}+\frac{b \,d^{2} x}{4 c^{3}}-\frac{b \,x^{3} e^{2}}{24 c^{5}}-\frac{b e d x}{3 c^{5}}+\frac{b x \,e^{2}}{8 c^{7}}-\frac{b \,d^{2} \arctan \left(c x \right)}{4 c^{4}}+\frac{b \arctan \left(c x \right) e d}{3 c^{6}}-\frac{b \arctan \left(c x \right) e^{2}}{8 c^{8}}"," ",0,"1/8*a*e^2*x^8+1/3*a*e*d*x^6+1/4*a*x^4*d^2+1/8*b*arctan(c*x)*e^2*x^8+1/3*b*arctan(c*x)*e*d*x^6+1/4*b*arctan(c*x)*d^2*x^4-1/56*b*e^2*x^7/c-1/15/c*b*e*d*x^5-1/12*b*d^2*x^3/c+1/40/c^3*b*x^5*e^2+1/9/c^3*b*x^3*d*e+1/4*b*d^2*x/c^3-1/24/c^5*b*x^3*e^2-1/3/c^5*b*e*d*x+1/8/c^7*b*x*e^2-1/4*b*d^2*arctan(c*x)/c^4+1/3/c^6*b*arctan(c*x)*e*d-1/8/c^8*b*arctan(c*x)*e^2","A"
1126,1,192,147,0.042000," ","int(x^2*(e*x^2+d)^2*(a+b*arctan(c*x)),x)","\frac{a \,e^{2} x^{7}}{7}+\frac{2 a e d \,x^{5}}{5}+\frac{a \,d^{2} x^{3}}{3}+\frac{b \arctan \left(c x \right) e^{2} x^{7}}{7}+\frac{2 b \arctan \left(c x \right) e d \,x^{5}}{5}+\frac{b \arctan \left(c x \right) d^{2} x^{3}}{3}-\frac{b \,d^{2} x^{2}}{6 c}-\frac{b e d \,x^{4}}{10 c}-\frac{b \,e^{2} x^{6}}{42 c}+\frac{b \,x^{2} d e}{5 c^{3}}+\frac{b \,x^{4} e^{2}}{28 c^{3}}-\frac{b \,x^{2} e^{2}}{14 c^{5}}+\frac{b \,d^{2} \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}-\frac{b \ln \left(c^{2} x^{2}+1\right) e d}{5 c^{5}}+\frac{b \ln \left(c^{2} x^{2}+1\right) e^{2}}{14 c^{7}}"," ",0,"1/7*a*e^2*x^7+2/5*a*e*d*x^5+1/3*a*d^2*x^3+1/7*b*arctan(c*x)*e^2*x^7+2/5*b*arctan(c*x)*e*d*x^5+1/3*b*arctan(c*x)*d^2*x^3-1/6*b*d^2*x^2/c-1/10/c*b*e*d*x^4-1/42*b*e^2*x^6/c+1/5/c^3*b*x^2*d*e+1/28/c^3*b*x^4*e^2-1/14/c^5*b*x^2*e^2+1/6*b*d^2*ln(c^2*x^2+1)/c^3-1/5/c^5*b*ln(c^2*x^2+1)*e*d+1/14/c^7*b*ln(c^2*x^2+1)*e^2","A"
1127,1,168,105,0.038000," ","int(x*(e*x^2+d)^2*(a+b*arctan(c*x)),x)","\frac{a \,e^{2} x^{6}}{6}+\frac{a e d \,x^{4}}{2}+\frac{a \,x^{2} d^{2}}{2}+\frac{b \arctan \left(c x \right) e^{2} x^{6}}{6}+\frac{b \arctan \left(c x \right) e d \,x^{4}}{2}+\frac{b \arctan \left(c x \right) d^{2} x^{2}}{2}-\frac{b \,e^{2} x^{5}}{30 c}-\frac{b \,x^{3} d e}{6 c}-\frac{b \,d^{2} x}{2 c}+\frac{b \,x^{3} e^{2}}{18 c^{3}}+\frac{b e d x}{2 c^{3}}-\frac{b x \,e^{2}}{6 c^{5}}+\frac{b \,d^{2} \arctan \left(c x \right)}{2 c^{2}}-\frac{b \arctan \left(c x \right) e d}{2 c^{4}}+\frac{b \arctan \left(c x \right) e^{2}}{6 c^{6}}"," ",0,"1/6*a*e^2*x^6+1/2*a*e*d*x^4+1/2*a*x^2*d^2+1/6*b*arctan(c*x)*e^2*x^6+1/2*b*arctan(c*x)*e*d*x^4+1/2*b*arctan(c*x)*d^2*x^2-1/30*b*e^2*x^5/c-1/6/c*b*x^3*d*e-1/2*b*d^2*x/c+1/18/c^3*b*x^3*e^2+1/2/c^3*b*e*d*x-1/6/c^5*b*x*e^2+1/2*b*d^2*arctan(c*x)/c^2-1/2/c^4*b*arctan(c*x)*e*d+1/6/c^6*b*arctan(c*x)*e^2","A"
1128,1,151,114,0.043000," ","int((e*x^2+d)^2*(a+b*arctan(c*x)),x)","\frac{a \,x^{5} e^{2}}{5}+\frac{2 a \,x^{3} d e}{3}+a x \,d^{2}+\frac{b \arctan \left(c x \right) x^{5} e^{2}}{5}+\frac{2 b \arctan \left(c x \right) x^{3} d e}{3}+b \arctan \left(c x \right) d^{2} x -\frac{b \,x^{2} d e}{3 c}-\frac{b \,e^{2} x^{4}}{20 c}+\frac{b \,x^{2} e^{2}}{10 c^{3}}-\frac{b \ln \left(c^{2} x^{2}+1\right) d^{2}}{2 c}+\frac{b \ln \left(c^{2} x^{2}+1\right) e d}{3 c^{3}}-\frac{b \ln \left(c^{2} x^{2}+1\right) e^{2}}{10 c^{5}}"," ",0,"1/5*a*x^5*e^2+2/3*a*x^3*d*e+a*x*d^2+1/5*b*arctan(c*x)*x^5*e^2+2/3*b*arctan(c*x)*x^3*d*e+b*arctan(c*x)*d^2*x-1/3/c*b*x^2*d*e-1/20*b*e^2*x^4/c+1/10/c^3*b*x^2*e^2-1/2/c*b*ln(c^2*x^2+1)*d^2+1/3/c^3*b*ln(c^2*x^2+1)*e*d-1/10/c^5*b*ln(c^2*x^2+1)*e^2","A"
1129,1,187,121,0.059000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))/x,x)","\frac{a \,x^{4} e^{2}}{4}+a e d \,x^{2}+a \,d^{2} \ln \left(c x \right)+\frac{b \arctan \left(c x \right) x^{4} e^{2}}{4}+b \arctan \left(c x \right) x^{2} d e +b \arctan \left(c x \right) d^{2} \ln \left(c x \right)-\frac{b \,e^{2} x^{3}}{12 c}-\frac{b d e x}{c}+\frac{b \,e^{2} x}{4 c^{3}}+\frac{b d e \arctan \left(c x \right)}{c^{2}}-\frac{b \,e^{2} \arctan \left(c x \right)}{4 c^{4}}+\frac{i b \,d^{2} \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i b \,d^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{i b \,d^{2} \dilog \left(i c x +1\right)}{2}-\frac{i b \,d^{2} \dilog \left(-i c x +1\right)}{2}"," ",0,"1/4*a*x^4*e^2+a*e*d*x^2+a*d^2*ln(c*x)+1/4*b*arctan(c*x)*x^4*e^2+b*arctan(c*x)*x^2*d*e+b*arctan(c*x)*d^2*ln(c*x)-1/12*b*e^2*x^3/c-b*d*e*x/c+1/4*b*e^2*x/c^3+b*d*e*arctan(c*x)/c^2-1/4*b*e^2*arctan(c*x)/c^4+1/2*I*b*d^2*ln(c*x)*ln(1+I*c*x)-1/2*I*b*d^2*ln(c*x)*ln(1-I*c*x)+1/2*I*b*d^2*dilog(1+I*c*x)-1/2*I*b*d^2*dilog(1-I*c*x)","A"
1130,1,138,103,0.048000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))/x^2,x)","\frac{a \,e^{2} x^{3}}{3}+2 a e d x -\frac{a \,d^{2}}{x}+\frac{b \arctan \left(c x \right) x^{3} e^{2}}{3}+2 b \arctan \left(c x \right) e d x -\frac{b \arctan \left(c x \right) d^{2}}{x}-\frac{b \,e^{2} x^{2}}{6 c}+c b \,d^{2} \ln \left(c x \right)-\frac{c b \ln \left(c^{2} x^{2}+1\right) d^{2}}{2}-\frac{b \ln \left(c^{2} x^{2}+1\right) e d}{c}+\frac{b \ln \left(c^{2} x^{2}+1\right) e^{2}}{6 c^{3}}"," ",0,"1/3*a*e^2*x^3+2*a*e*d*x-a*d^2/x+1/3*b*arctan(c*x)*x^3*e^2+2*b*arctan(c*x)*e*d*x-b*arctan(c*x)*d^2/x-1/6*b*e^2*x^2/c+c*b*d^2*ln(c*x)-1/2*c*b*ln(c^2*x^2+1)*d^2-b/c*ln(c^2*x^2+1)*e*d+1/6*b/c^3*ln(c^2*x^2+1)*e^2","A"
1131,1,178,112,0.068000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))/x^3,x)","\frac{a \,x^{2} e^{2}}{2}+2 a e d \ln \left(c x \right)-\frac{a \,d^{2}}{2 x^{2}}+\frac{b \arctan \left(c x \right) x^{2} e^{2}}{2}+2 b \arctan \left(c x \right) e d \ln \left(c x \right)-\frac{b \arctan \left(c x \right) d^{2}}{2 x^{2}}-\frac{b \,e^{2} x}{2 c}-\frac{b c \,d^{2}}{2 x}-\frac{b \,c^{2} d^{2} \arctan \left(c x \right)}{2}+\frac{b \,e^{2} \arctan \left(c x \right)}{2 c^{2}}+i b e d \ln \left(c x \right) \ln \left(i c x +1\right)-i b e d \ln \left(c x \right) \ln \left(-i c x +1\right)+i b e d \dilog \left(i c x +1\right)-i b e d \dilog \left(-i c x +1\right)"," ",0,"1/2*a*x^2*e^2+2*a*e*d*ln(c*x)-1/2*a*d^2/x^2+1/2*b*arctan(c*x)*x^2*e^2+2*b*arctan(c*x)*e*d*ln(c*x)-1/2*b*arctan(c*x)*d^2/x^2-1/2*b*e^2*x/c-1/2*b*c*d^2/x-1/2*b*c^2*d^2*arctan(c*x)+1/2*b*e^2*arctan(c*x)/c^2+I*b*e*d*ln(c*x)*ln(1+I*c*x)-I*b*e*d*ln(c*x)*ln(1-I*c*x)+I*b*e*d*dilog(1+I*c*x)-I*b*e*d*dilog(1-I*c*x)","A"
1132,1,147,107,0.049000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))/x^4,x)","a x \,e^{2}-\frac{a \,d^{2}}{3 x^{3}}-\frac{2 a e d}{x}+b \arctan \left(c x \right) x \,e^{2}-\frac{b \arctan \left(c x \right) d^{2}}{3 x^{3}}-\frac{2 b \arctan \left(c x \right) e d}{x}-\frac{c^{3} b \,d^{2} \ln \left(c x \right)}{3}+2 c b \ln \left(c x \right) d e -\frac{b c \,d^{2}}{6 x^{2}}+\frac{c^{3} b \ln \left(c^{2} x^{2}+1\right) d^{2}}{6}-c b \ln \left(c^{2} x^{2}+1\right) e d -\frac{b \ln \left(c^{2} x^{2}+1\right) e^{2}}{2 c}"," ",0,"a*x*e^2-1/3*a*d^2/x^3-2*a*e*d/x+b*arctan(c*x)*x*e^2-1/3*b*arctan(c*x)*d^2/x^3-2*b*arctan(c*x)*e*d/x-1/3*c^3*b*d^2*ln(c*x)+2*c*b*ln(c*x)*d*e-1/6*b*c*d^2/x^2+1/6*c^3*b*ln(c^2*x^2+1)*d^2-c*b*ln(c^2*x^2+1)*e*d-1/2/c*b*ln(c^2*x^2+1)*e^2","A"
1133,1,190,123,0.068000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))/x^5,x)","a \,e^{2} \ln \left(c x \right)-\frac{a \,d^{2}}{4 x^{4}}-\frac{a e d}{x^{2}}+b \arctan \left(c x \right) e^{2} \ln \left(c x \right)-\frac{b \arctan \left(c x \right) d^{2}}{4 x^{4}}-\frac{b \arctan \left(c x \right) e d}{x^{2}}+\frac{i b \,e^{2} \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i b \,e^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{i b \,e^{2} \dilog \left(i c x +1\right)}{2}-\frac{i b \,e^{2} \dilog \left(-i c x +1\right)}{2}+\frac{b \,c^{3} d^{2}}{4 x}-\frac{b c d e}{x}-\frac{b c \,d^{2}}{12 x^{3}}+\frac{b \,c^{4} d^{2} \arctan \left(c x \right)}{4}-b \,c^{2} d e \arctan \left(c x \right)"," ",0,"a*e^2*ln(c*x)-1/4*a*d^2/x^4-a*e*d/x^2+b*arctan(c*x)*e^2*ln(c*x)-1/4*b*arctan(c*x)*d^2/x^4-b*arctan(c*x)*e*d/x^2+1/2*I*b*e^2*ln(c*x)*ln(1+I*c*x)-1/2*I*b*e^2*ln(c*x)*ln(1-I*c*x)+1/2*I*b*e^2*dilog(1+I*c*x)-1/2*I*b*e^2*dilog(1-I*c*x)+1/4*b*c^3*d^2/x-b*c*d*e/x-1/12*b*c*d^2/x^3+1/4*b*c^4*d^2*arctan(c*x)-b*c^2*d*e*arctan(c*x)","A"
1134,1,186,138,0.049000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))/x^6,x)","-\frac{2 a e d}{3 x^{3}}-\frac{a \,e^{2}}{x}-\frac{a \,d^{2}}{5 x^{5}}-\frac{2 b \arctan \left(c x \right) e d}{3 x^{3}}-\frac{b \arctan \left(c x \right) e^{2}}{x}-\frac{b \arctan \left(c x \right) d^{2}}{5 x^{5}}+\frac{c^{5} b \,d^{2} \ln \left(c x \right)}{5}-\frac{2 c^{3} b \ln \left(c x \right) d e}{3}+c b \ln \left(c x \right) e^{2}+\frac{b \,c^{3} d^{2}}{10 x^{2}}-\frac{c b e d}{3 x^{2}}-\frac{b c \,d^{2}}{20 x^{4}}-\frac{c^{5} b \ln \left(c^{2} x^{2}+1\right) d^{2}}{10}+\frac{c^{3} b \ln \left(c^{2} x^{2}+1\right) e d}{3}-\frac{c b \ln \left(c^{2} x^{2}+1\right) e^{2}}{2}"," ",0,"-2/3*a*e*d/x^3-a*e^2/x-1/5*a*d^2/x^5-2/3*b*arctan(c*x)*e*d/x^3-b*arctan(c*x)*e^2/x-1/5*b*arctan(c*x)*d^2/x^5+1/5*c^5*b*d^2*ln(c*x)-2/3*c^3*b*ln(c*x)*d*e+c*b*ln(c*x)*e^2+1/10*b*c^3*d^2/x^2-1/3*c*b*e*d/x^2-1/20*b*c*d^2/x^4-1/10*c^5*b*ln(c^2*x^2+1)*d^2+1/3*c^3*b*ln(c^2*x^2+1)*e*d-1/2*c*b*ln(c^2*x^2+1)*e^2","A"
1135,1,168,101,0.047000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))/x^7,x)","-\frac{a e d}{2 x^{4}}-\frac{a \,d^{2}}{6 x^{6}}-\frac{a \,e^{2}}{2 x^{2}}-\frac{b \arctan \left(c x \right) e d}{2 x^{4}}-\frac{b \arctan \left(c x \right) d^{2}}{6 x^{6}}-\frac{b \arctan \left(c x \right) e^{2}}{2 x^{2}}-\frac{c^{5} b \,d^{2}}{6 x}+\frac{c^{3} b e d}{2 x}-\frac{c b \,e^{2}}{2 x}+\frac{c^{3} b \,d^{2}}{18 x^{3}}-\frac{c b e d}{6 x^{3}}-\frac{b c \,d^{2}}{30 x^{5}}-\frac{c^{6} b \arctan \left(c x \right) d^{2}}{6}+\frac{c^{4} b \arctan \left(c x \right) e d}{2}-\frac{c^{2} b \arctan \left(c x \right) e^{2}}{2}"," ",0,"-1/2*a*e*d/x^4-1/6*a*d^2/x^6-1/2*a*e^2/x^2-1/2*b*arctan(c*x)*e*d/x^4-1/6*b*arctan(c*x)*d^2/x^6-1/2*b*arctan(c*x)*e^2/x^2-1/6*c^5*b*d^2/x+1/2*c^3*b*e*d/x-1/2*c*b*e^2/x+1/18*c^3*b*d^2/x^3-1/6*c*b*e*d/x^3-1/30*b*c*d^2/x^5-1/6*c^6*b*arctan(c*x)*d^2+1/2*c^4*b*arctan(c*x)*e*d-1/2*c^2*b*arctan(c*x)*e^2","A"
1136,1,224,170,0.048000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))/x^8,x)","-\frac{a \,d^{2}}{7 x^{7}}-\frac{a \,e^{2}}{3 x^{3}}-\frac{2 a e d}{5 x^{5}}-\frac{b \arctan \left(c x \right) d^{2}}{7 x^{7}}-\frac{b \arctan \left(c x \right) e^{2}}{3 x^{3}}-\frac{2 b \arctan \left(c x \right) e d}{5 x^{5}}-\frac{c^{5} b \,d^{2}}{14 x^{2}}+\frac{c^{3} b e d}{5 x^{2}}-\frac{c b \,e^{2}}{6 x^{2}}-\frac{c^{7} b \,d^{2} \ln \left(c x \right)}{7}+\frac{2 c^{5} b \ln \left(c x \right) d e}{5}-\frac{c^{3} b \ln \left(c x \right) e^{2}}{3}-\frac{b c \,d^{2}}{42 x^{6}}+\frac{c^{3} b \,d^{2}}{28 x^{4}}-\frac{c b e d}{10 x^{4}}+\frac{c^{7} b \ln \left(c^{2} x^{2}+1\right) d^{2}}{14}-\frac{c^{5} b \ln \left(c^{2} x^{2}+1\right) e d}{5}+\frac{c^{3} b \ln \left(c^{2} x^{2}+1\right) e^{2}}{6}"," ",0,"-1/7*a*d^2/x^7-1/3*a*e^2/x^3-2/5*a*e*d/x^5-1/7*b*arctan(c*x)*d^2/x^7-1/3*b*arctan(c*x)*e^2/x^3-2/5*b*arctan(c*x)*e*d/x^5-1/14*c^5*b*d^2/x^2+1/5*c^3*b*e*d/x^2-1/6*c*b*e^2/x^2-1/7*c^7*b*d^2*ln(c*x)+2/5*c^5*b*ln(c*x)*d*e-1/3*c^3*b*ln(c*x)*e^2-1/42*b*c*d^2/x^6+1/28*c^3*b*d^2/x^4-1/10*c*b*e*d/x^4+1/14*c^7*b*ln(c^2*x^2+1)*d^2-1/5*c^5*b*ln(c^2*x^2+1)*e*d+1/6*c^3*b*ln(c^2*x^2+1)*e^2","A"
1137,1,315,224,0.041000," ","int(x^3*(e*x^2+d)^3*(a+b*arctan(c*x)),x)","\frac{b \arctan \left(c x \right) e^{3}}{10 c^{10}}+\frac{b \,x^{3} e^{3}}{30 c^{7}}+\frac{b \arctan \left(c x \right) x^{4} d^{3}}{4}+\frac{b \arctan \left(c x \right) e^{3} x^{10}}{10}-\frac{b \,e^{3} x^{9}}{90 c}+\frac{b \,d^{3} x}{4 c^{3}}-\frac{b \,d^{3} x^{3}}{12 c}-\frac{b \,d^{3} \arctan \left(c x \right)}{4 c^{4}}-\frac{b \,e^{3} x}{10 c^{9}}+\frac{3 a d \,e^{2} x^{8}}{8}+\frac{a \,d^{2} e \,x^{6}}{2}+\frac{b \,x^{7} e^{3}}{70 c^{3}}-\frac{b \,x^{5} e^{3}}{50 c^{5}}-\frac{b \,d^{2} e x}{2 c^{5}}+\frac{b \arctan \left(c x \right) d^{2} e}{2 c^{6}}-\frac{3 b \arctan \left(c x \right) d \,e^{2}}{8 c^{8}}+\frac{3 b d \,e^{2} x}{8 c^{7}}+\frac{b \,x^{3} d^{2} e}{6 c^{3}}-\frac{b \,d^{2} e \,x^{5}}{10 c}+\frac{3 b \,x^{5} d \,e^{2}}{40 c^{3}}-\frac{3 b d \,e^{2} x^{7}}{56 c}-\frac{b \,x^{3} d \,e^{2}}{8 c^{5}}+\frac{3 b \arctan \left(c x \right) d \,e^{2} x^{8}}{8}+\frac{b \arctan \left(c x \right) d^{2} e \,x^{6}}{2}+\frac{a \,e^{3} x^{10}}{10}+\frac{a \,x^{4} d^{3}}{4}"," ",0,"1/10/c^10*b*arctan(c*x)*e^3+1/30/c^7*b*x^3*e^3+1/4*b*arctan(c*x)*x^4*d^3+1/10*b*arctan(c*x)*e^3*x^10-1/90*b*e^3*x^9/c+1/4*b*d^3*x/c^3-1/12*b*d^3*x^3/c-1/4*b*d^3*arctan(c*x)/c^4-1/10/c^9*b*e^3*x+3/8*a*d*e^2*x^8+1/2*a*d^2*e*x^6+1/70/c^3*b*x^7*e^3-1/50/c^5*b*x^5*e^3-1/2/c^5*b*d^2*e*x+1/2/c^6*b*arctan(c*x)*d^2*e-3/8/c^8*b*arctan(c*x)*d*e^2+3/8/c^7*b*d*e^2*x+1/6/c^3*b*x^3*d^2*e-1/10/c*b*d^2*e*x^5+3/40/c^3*b*x^5*d*e^2-3/56/c*b*d*e^2*x^7-1/8/c^5*b*x^3*d*e^2+3/8*b*arctan(c*x)*d*e^2*x^8+1/2*b*arctan(c*x)*d^2*e*x^6+1/10*a*e^3*x^10+1/4*a*x^4*d^3","A"
1138,1,297,221,0.043000," ","int(x^2*(e*x^2+d)^3*(a+b*arctan(c*x)),x)","\frac{a \,e^{3} x^{9}}{9}+\frac{3 a d \,e^{2} x^{7}}{7}+\frac{3 a \,d^{2} e \,x^{5}}{5}+\frac{a \,d^{3} x^{3}}{3}+\frac{b \arctan \left(c x \right) e^{3} x^{9}}{9}+\frac{3 b \arctan \left(c x \right) d \,e^{2} x^{7}}{7}+\frac{3 b \arctan \left(c x \right) d^{2} e \,x^{5}}{5}+\frac{b \arctan \left(c x \right) d^{3} x^{3}}{3}-\frac{b \,d^{3} x^{2}}{6 c}-\frac{3 b \,d^{2} e \,x^{4}}{20 c}-\frac{b d \,e^{2} x^{6}}{14 c}+\frac{3 b \,x^{2} d^{2} e}{10 c^{3}}-\frac{b \,e^{3} x^{8}}{72 c}+\frac{3 b \,x^{4} d \,e^{2}}{28 c^{3}}+\frac{b \,x^{6} e^{3}}{54 c^{3}}-\frac{3 b \,x^{2} d \,e^{2}}{14 c^{5}}-\frac{b \,e^{3} x^{4}}{36 c^{5}}+\frac{b \,x^{2} e^{3}}{18 c^{7}}+\frac{b \,d^{3} \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}-\frac{3 b \ln \left(c^{2} x^{2}+1\right) d^{2} e}{10 c^{5}}+\frac{3 b \ln \left(c^{2} x^{2}+1\right) d \,e^{2}}{14 c^{7}}-\frac{b \ln \left(c^{2} x^{2}+1\right) e^{3}}{18 c^{9}}"," ",0,"1/9*a*e^3*x^9+3/7*a*d*e^2*x^7+3/5*a*d^2*e*x^5+1/3*a*d^3*x^3+1/9*b*arctan(c*x)*e^3*x^9+3/7*b*arctan(c*x)*d*e^2*x^7+3/5*b*arctan(c*x)*d^2*e*x^5+1/3*b*arctan(c*x)*d^3*x^3-1/6*b*d^3*x^2/c-3/20/c*b*d^2*e*x^4-1/14/c*b*d*e^2*x^6+3/10/c^3*b*x^2*d^2*e-1/72*b*e^3*x^8/c+3/28/c^3*b*x^4*d*e^2+1/54/c^3*b*x^6*e^3-3/14/c^5*b*x^2*d*e^2-1/36/c^5*b*e^3*x^4+1/18/c^7*b*x^2*e^3+1/6*b*d^3*ln(c^2*x^2+1)/c^3-3/10/c^5*b*ln(c^2*x^2+1)*d^2*e+3/14/c^7*b*ln(c^2*x^2+1)*d*e^2-1/18/c^9*b*ln(c^2*x^2+1)*e^3","A"
1139,1,265,146,0.041000," ","int(x*(e*x^2+d)^3*(a+b*arctan(c*x)),x)","\frac{a \,e^{3} x^{8}}{8}+\frac{a d \,e^{2} x^{6}}{2}+\frac{3 a \,d^{2} e \,x^{4}}{4}+\frac{a \,x^{2} d^{3}}{2}+\frac{b \arctan \left(c x \right) e^{3} x^{8}}{8}+\frac{b \arctan \left(c x \right) d \,e^{2} x^{6}}{2}+\frac{3 b \arctan \left(c x \right) d^{2} e \,x^{4}}{4}+\frac{b \arctan \left(c x \right) x^{2} d^{3}}{2}-\frac{b \,e^{3} x^{7}}{56 c}-\frac{b \,x^{5} d \,e^{2}}{10 c}-\frac{b \,x^{3} d^{2} e}{4 c}-\frac{b \,d^{3} x}{2 c}+\frac{b \,x^{5} e^{3}}{40 c^{3}}+\frac{b \,x^{3} d \,e^{2}}{6 c^{3}}+\frac{3 b \,d^{2} e x}{4 c^{3}}-\frac{b \,x^{3} e^{3}}{24 c^{5}}-\frac{b d \,e^{2} x}{2 c^{5}}+\frac{b \,e^{3} x}{8 c^{7}}+\frac{b \arctan \left(c x \right) d^{3}}{2 c^{2}}-\frac{3 b \arctan \left(c x \right) d^{2} e}{4 c^{4}}+\frac{b \arctan \left(c x \right) d \,e^{2}}{2 c^{6}}-\frac{b \arctan \left(c x \right) e^{3}}{8 c^{8}}"," ",0,"1/8*a*e^3*x^8+1/2*a*d*e^2*x^6+3/4*a*d^2*e*x^4+1/2*a*x^2*d^3+1/8*b*arctan(c*x)*e^3*x^8+1/2*b*arctan(c*x)*d*e^2*x^6+3/4*b*arctan(c*x)*d^2*e*x^4+1/2*b*arctan(c*x)*x^2*d^3-1/56*b*e^3*x^7/c-1/10/c*b*x^5*d*e^2-1/4/c*b*x^3*d^2*e-1/2*b*d^3*x/c+1/40/c^3*b*x^5*e^3+1/6/c^3*b*x^3*d*e^2+3/4/c^3*b*d^2*e*x-1/24/c^5*b*x^3*e^3-1/2/c^5*b*d*e^2*x+1/8/c^7*b*e^3*x+1/2/c^2*b*arctan(c*x)*d^3-3/4/c^4*b*arctan(c*x)*d^2*e+1/2/c^6*b*arctan(c*x)*d*e^2-1/8/c^8*b*arctan(c*x)*e^3","A"
1140,1,239,176,0.040000," ","int((e*x^2+d)^3*(a+b*arctan(c*x)),x)","\frac{a \,x^{7} e^{3}}{7}+\frac{3 a \,x^{5} d \,e^{2}}{5}+a \,x^{3} d^{2} e +a \,d^{3} x +\frac{b \arctan \left(c x \right) x^{7} e^{3}}{7}+\frac{3 b \arctan \left(c x \right) x^{5} d \,e^{2}}{5}+b \arctan \left(c x \right) x^{3} d^{2} e +b \arctan \left(c x \right) d^{3} x -\frac{b \,x^{2} d^{2} e}{2 c}-\frac{3 b \,x^{4} d \,e^{2}}{20 c}-\frac{b \,e^{3} x^{6}}{42 c}+\frac{3 b \,x^{2} d \,e^{2}}{10 c^{3}}+\frac{b \,e^{3} x^{4}}{28 c^{3}}-\frac{b \,x^{2} e^{3}}{14 c^{5}}-\frac{b \ln \left(c^{2} x^{2}+1\right) d^{3}}{2 c}+\frac{b \ln \left(c^{2} x^{2}+1\right) d^{2} e}{2 c^{3}}-\frac{3 b \ln \left(c^{2} x^{2}+1\right) d \,e^{2}}{10 c^{5}}+\frac{b \ln \left(c^{2} x^{2}+1\right) e^{3}}{14 c^{7}}"," ",0,"1/7*a*x^7*e^3+3/5*a*x^5*d*e^2+a*x^3*d^2*e+a*d^3*x+1/7*b*arctan(c*x)*x^7*e^3+3/5*b*arctan(c*x)*x^5*d*e^2+b*arctan(c*x)*x^3*d^2*e+b*arctan(c*x)*d^3*x-1/2/c*b*x^2*d^2*e-3/20/c*b*x^4*d*e^2-1/42*b*e^3*x^6/c+3/10/c^3*b*x^2*d*e^2+1/28/c^3*b*e^3*x^4-1/14/c^5*b*x^2*e^3-1/2/c*b*ln(c^2*x^2+1)*d^3+1/2/c^3*b*ln(c^2*x^2+1)*d^2*e-3/10/c^5*b*ln(c^2*x^2+1)*d*e^2+1/14/c^7*b*ln(c^2*x^2+1)*e^3","A"
1141,1,272,196,0.061000," ","int((e*x^2+d)^3*(a+b*arctan(c*x))/x,x)","\frac{a \,x^{6} e^{3}}{6}+\frac{3 a \,x^{4} d \,e^{2}}{4}+\frac{3 a \,x^{2} d^{2} e}{2}+d^{3} a \ln \left(c x \right)+\frac{b \arctan \left(c x \right) x^{6} e^{3}}{6}+\frac{3 b \arctan \left(c x \right) x^{4} d \,e^{2}}{4}+\frac{3 b \arctan \left(c x \right) x^{2} d^{2} e}{2}+b \arctan \left(c x \right) d^{3} \ln \left(c x \right)-\frac{b \,e^{3} x^{5}}{30 c}-\frac{b d \,e^{2} x^{3}}{4 c}-\frac{3 b \,d^{2} e x}{2 c}+\frac{b \,e^{3} x^{3}}{18 c^{3}}+\frac{3 b d \,e^{2} x}{4 c^{3}}-\frac{b \,e^{3} x}{6 c^{5}}+\frac{3 b \,d^{2} e \arctan \left(c x \right)}{2 c^{2}}-\frac{3 b d \,e^{2} \arctan \left(c x \right)}{4 c^{4}}+\frac{b \,e^{3} \arctan \left(c x \right)}{6 c^{6}}+\frac{i b \,d^{3} \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i b \,d^{3} \dilog \left(-i c x +1\right)}{2}+\frac{i b \,d^{3} \dilog \left(i c x +1\right)}{2}-\frac{i b \,d^{3} \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}"," ",0,"1/6*a*x^6*e^3+3/4*a*x^4*d*e^2+3/2*a*x^2*d^2*e+d^3*a*ln(c*x)+1/6*b*arctan(c*x)*x^6*e^3+3/4*b*arctan(c*x)*x^4*d*e^2+3/2*b*arctan(c*x)*x^2*d^2*e+b*arctan(c*x)*d^3*ln(c*x)-1/30*b*e^3*x^5/c-1/4*b*d*e^2*x^3/c-3/2*b*d^2*e*x/c+1/18*b*e^3*x^3/c^3+3/4*b*d*e^2*x/c^3-1/6*b*e^3*x/c^5+3/2*b*d^2*e*arctan(c*x)/c^2-3/4*b*d*e^2*arctan(c*x)/c^4+1/6*b*e^3*arctan(c*x)/c^6-1/2*I*b*d^3*dilog(1-I*c*x)+1/2*I*b*d^3*ln(c*x)*ln(1+I*c*x)-1/2*I*b*d^3*ln(c*x)*ln(1-I*c*x)+1/2*I*b*d^3*dilog(1+I*c*x)","A"
1142,1,211,152,0.046000," ","int((e*x^2+d)^3*(a+b*arctan(c*x))/x^2,x)","\frac{a \,x^{5} e^{3}}{5}+a \,x^{3} d \,e^{2}+3 a \,d^{2} e x -\frac{a \,d^{3}}{x}+\frac{b \arctan \left(c x \right) x^{5} e^{3}}{5}+b \arctan \left(c x \right) x^{3} d \,e^{2}+3 b \arctan \left(c x \right) d^{2} e x -\frac{b \arctan \left(c x \right) d^{3}}{x}-\frac{b \,e^{3} x^{4}}{20 c}-\frac{b d \,e^{2} x^{2}}{2 c}+\frac{b \,x^{2} e^{3}}{10 c^{3}}+c b \,d^{3} \ln \left(c x \right)-\frac{b c \,d^{3} \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{3 b \ln \left(c^{2} x^{2}+1\right) d^{2} e}{2 c}+\frac{b \ln \left(c^{2} x^{2}+1\right) d \,e^{2}}{2 c^{3}}-\frac{b \ln \left(c^{2} x^{2}+1\right) e^{3}}{10 c^{5}}"," ",0,"1/5*a*x^5*e^3+a*x^3*d*e^2+3*a*d^2*e*x-a*d^3/x+1/5*b*arctan(c*x)*x^5*e^3+b*arctan(c*x)*x^3*d*e^2+3*b*arctan(c*x)*d^2*e*x-b*arctan(c*x)*d^3/x-1/20*b*e^3*x^4/c-1/2*b*d*e^2*x^2/c+1/10*b/c^3*x^2*e^3+c*b*d^3*ln(c*x)-1/2*b*c*d^3*ln(c^2*x^2+1)-3/2*b/c*ln(c^2*x^2+1)*d^2*e+1/2*b/c^3*ln(c^2*x^2+1)*d*e^2-1/10*b/c^5*ln(c^2*x^2+1)*e^3","A"
1143,1,251,172,0.066000," ","int((e*x^2+d)^3*(a+b*arctan(c*x))/x^3,x)","\frac{a \,e^{3} x^{4}}{4}+\frac{3 a \,x^{2} d \,e^{2}}{2}+3 a \,d^{2} e \ln \left(c x \right)-\frac{a \,d^{3}}{2 x^{2}}+\frac{b \arctan \left(c x \right) e^{3} x^{4}}{4}+\frac{3 b \arctan \left(c x \right) x^{2} d \,e^{2}}{2}+3 b \arctan \left(c x \right) d^{2} e \ln \left(c x \right)-\frac{b \arctan \left(c x \right) d^{3}}{2 x^{2}}-\frac{b \,e^{3} x^{3}}{12 c}-\frac{3 b d \,e^{2} x}{2 c}+\frac{b \,e^{3} x}{4 c^{3}}-\frac{b c \,d^{3}}{2 x}-\frac{b \,c^{2} d^{3} \arctan \left(c x \right)}{2}+\frac{3 b d \,e^{2} \arctan \left(c x \right)}{2 c^{2}}-\frac{b \,e^{3} \arctan \left(c x \right)}{4 c^{4}}-\frac{3 i b \,d^{2} e \dilog \left(-i c x +1\right)}{2}-\frac{3 i b \,d^{2} e \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{3 i b \,d^{2} e \ln \left(c x \right) \ln \left(i c x +1\right)}{2}+\frac{3 i b \,d^{2} e \dilog \left(i c x +1\right)}{2}"," ",0,"1/4*a*e^3*x^4+3/2*a*x^2*d*e^2+3*a*d^2*e*ln(c*x)-1/2*a*d^3/x^2+1/4*b*arctan(c*x)*e^3*x^4+3/2*b*arctan(c*x)*x^2*d*e^2+3*b*arctan(c*x)*d^2*e*ln(c*x)-1/2*b*arctan(c*x)*d^3/x^2-1/12*b*e^3*x^3/c-3/2*b*d*e^2*x/c+1/4*b*e^3*x/c^3-1/2*b*c*d^3/x-1/2*b*c^2*d^3*arctan(c*x)+3/2*b*d*e^2*arctan(c*x)/c^2-1/4*b*e^3*arctan(c*x)/c^4+3/2*I*b*d^2*e*dilog(1+I*c*x)-3/2*I*b*d^2*e*ln(c*x)*ln(1-I*c*x)+3/2*I*b*d^2*e*ln(c*x)*ln(1+I*c*x)-3/2*I*b*d^2*e*dilog(1-I*c*x)","A"
1144,1,213,146,0.049000," ","int((e*x^2+d)^3*(a+b*arctan(c*x))/x^4,x)","\frac{a \,x^{3} e^{3}}{3}+3 a d \,e^{2} x -\frac{a \,d^{3}}{3 x^{3}}-\frac{3 a \,d^{2} e}{x}+\frac{b \arctan \left(c x \right) x^{3} e^{3}}{3}+3 b \arctan \left(c x \right) d \,e^{2} x -\frac{b \arctan \left(c x \right) d^{3}}{3 x^{3}}-\frac{3 b \arctan \left(c x \right) d^{2} e}{x}-\frac{b \,e^{3} x^{2}}{6 c}-\frac{c^{3} b \,d^{3} \ln \left(c x \right)}{3}+3 c b \ln \left(c x \right) d^{2} e -\frac{b c \,d^{3}}{6 x^{2}}+\frac{b \,c^{3} d^{3} \ln \left(c^{2} x^{2}+1\right)}{6}-\frac{3 c b \ln \left(c^{2} x^{2}+1\right) d^{2} e}{2}-\frac{3 b \ln \left(c^{2} x^{2}+1\right) d \,e^{2}}{2 c}+\frac{b \ln \left(c^{2} x^{2}+1\right) e^{3}}{6 c^{3}}"," ",0,"1/3*a*x^3*e^3+3*a*d*e^2*x-1/3*a*d^3/x^3-3*a*d^2*e/x+1/3*b*arctan(c*x)*x^3*e^3+3*b*arctan(c*x)*d*e^2*x-1/3*b*arctan(c*x)*d^3/x^3-3*b*arctan(c*x)*d^2*e/x-1/6*b*e^3*x^2/c-1/3*c^3*b*d^3*ln(c*x)+3*c*b*ln(c*x)*d^2*e-1/6*b*c*d^3/x^2+1/6*b*c^3*d^3*ln(c^2*x^2+1)-3/2*c*b*ln(c^2*x^2+1)*d^2*e-3/2/c*b*ln(c^2*x^2+1)*d*e^2+1/6/c^3*b*ln(c^2*x^2+1)*e^3","A"
1145,1,251,172,0.069000," ","int((e*x^2+d)^3*(a+b*arctan(c*x))/x^5,x)","\frac{a \,x^{2} e^{3}}{2}+3 a d \,e^{2} \ln \left(c x \right)-\frac{a \,d^{3}}{4 x^{4}}-\frac{3 a \,d^{2} e}{2 x^{2}}+\frac{b \arctan \left(c x \right) x^{2} e^{3}}{2}+3 b \arctan \left(c x \right) d \,e^{2} \ln \left(c x \right)-\frac{b \arctan \left(c x \right) d^{3}}{4 x^{4}}-\frac{3 b \arctan \left(c x \right) d^{2} e}{2 x^{2}}-\frac{b \,e^{3} x}{2 c}+\frac{b \,c^{3} d^{3}}{4 x}-\frac{3 b c \,d^{2} e}{2 x}-\frac{b c \,d^{3}}{12 x^{3}}+\frac{b \,c^{4} d^{3} \arctan \left(c x \right)}{4}-\frac{3 b \,c^{2} d^{2} e \arctan \left(c x \right)}{2}+\frac{b \,e^{3} \arctan \left(c x \right)}{2 c^{2}}+\frac{3 i b d \,e^{2} \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{3 i b d \,e^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{3 i b d \,e^{2} \dilog \left(i c x +1\right)}{2}-\frac{3 i b d \,e^{2} \dilog \left(-i c x +1\right)}{2}"," ",0,"1/2*a*x^2*e^3+3*a*d*e^2*ln(c*x)-1/4*a*d^3/x^4-3/2*a*d^2*e/x^2+1/2*b*arctan(c*x)*x^2*e^3+3*b*arctan(c*x)*d*e^2*ln(c*x)-1/4*b*arctan(c*x)*d^3/x^4-3/2*b*arctan(c*x)*d^2*e/x^2-1/2*b*e^3*x/c+1/4*b*c^3*d^3/x-3/2*b*c*d^2*e/x-1/12*b*c*d^3/x^3+1/4*b*c^4*d^3*arctan(c*x)-3/2*b*c^2*d^2*e*arctan(c*x)+1/2*b*e^3*arctan(c*x)/c^2+3/2*I*b*d*e^2*dilog(1+I*c*x)+3/2*I*b*d*e^2*ln(c*x)*ln(1+I*c*x)-3/2*I*b*d*e^2*dilog(1-I*c*x)-3/2*I*b*d*e^2*ln(c*x)*ln(1-I*c*x)","A"
1146,1,236,167,0.054000," ","int((e*x^2+d)^3*(a+b*arctan(c*x))/x^6,x)","a \,e^{3} x -\frac{a \,d^{2} e}{x^{3}}-\frac{3 a d \,e^{2}}{x}-\frac{a \,d^{3}}{5 x^{5}}+b \arctan \left(c x \right) e^{3} x -\frac{b \arctan \left(c x \right) d^{2} e}{x^{3}}-\frac{3 b \arctan \left(c x \right) d \,e^{2}}{x}-\frac{b \arctan \left(c x \right) d^{3}}{5 x^{5}}+\frac{b \,c^{3} d^{3}}{10 x^{2}}-\frac{c b \,d^{2} e}{2 x^{2}}-\frac{b c \,d^{3}}{20 x^{4}}+\frac{c^{5} b \,d^{3} \ln \left(c x \right)}{5}-c^{3} b \ln \left(c x \right) d^{2} e +3 c b \ln \left(c x \right) d \,e^{2}-\frac{c^{5} b \ln \left(c^{2} x^{2}+1\right) d^{3}}{10}+\frac{c^{3} b \ln \left(c^{2} x^{2}+1\right) d^{2} e}{2}-\frac{3 c b \ln \left(c^{2} x^{2}+1\right) d \,e^{2}}{2}-\frac{b \ln \left(c^{2} x^{2}+1\right) e^{3}}{2 c}"," ",0,"a*e^3*x-a*d^2*e/x^3-3*a*d*e^2/x-1/5*a*d^3/x^5+b*arctan(c*x)*e^3*x-b*arctan(c*x)*d^2*e/x^3-3*b*arctan(c*x)*d*e^2/x-1/5*b*arctan(c*x)*d^3/x^5+1/10*b*c^3*d^3/x^2-1/2*c*b*d^2*e/x^2-1/20*b*c*d^3/x^4+1/5*c^5*b*d^3*ln(c*x)-c^3*b*ln(c*x)*d^2*e+3*c*b*ln(c*x)*d*e^2-1/10*c^5*b*ln(c^2*x^2+1)*d^3+1/2*c^3*b*ln(c^2*x^2+1)*d^2*e-3/2*c*b*ln(c^2*x^2+1)*d*e^2-1/2/c*b*ln(c^2*x^2+1)*e^3","A"
1147,1,272,196,0.068000," ","int((e*x^2+d)^3*(a+b*arctan(c*x))/x^7,x)","a \,e^{3} \ln \left(c x \right)-\frac{3 a \,d^{2} e}{4 x^{4}}-\frac{a \,d^{3}}{6 x^{6}}-\frac{3 a d \,e^{2}}{2 x^{2}}+b \arctan \left(c x \right) e^{3} \ln \left(c x \right)-\frac{3 b \arctan \left(c x \right) d^{2} e}{4 x^{4}}-\frac{b \arctan \left(c x \right) d^{3}}{6 x^{6}}-\frac{3 b \arctan \left(c x \right) d \,e^{2}}{2 x^{2}}+\frac{i b \,e^{3} \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i b \,e^{3} \dilog \left(-i c x +1\right)}{2}-\frac{i b \,e^{3} \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{i b \,e^{3} \dilog \left(i c x +1\right)}{2}-\frac{b \,c^{5} d^{3}}{6 x}+\frac{3 b \,c^{3} d^{2} e}{4 x}-\frac{3 b c d \,e^{2}}{2 x}-\frac{b c \,d^{3}}{30 x^{5}}+\frac{b \,c^{3} d^{3}}{18 x^{3}}-\frac{b c \,d^{2} e}{4 x^{3}}-\frac{b \,c^{6} d^{3} \arctan \left(c x \right)}{6}+\frac{3 b \,c^{4} d^{2} e \arctan \left(c x \right)}{4}-\frac{3 b \,c^{2} d \,e^{2} \arctan \left(c x \right)}{2}"," ",0,"a*e^3*ln(c*x)-3/4*a*d^2*e/x^4-1/6*a*d^3/x^6-3/2*a*d*e^2/x^2+b*arctan(c*x)*e^3*ln(c*x)-3/4*b*arctan(c*x)*d^2*e/x^4-1/6*b*arctan(c*x)*d^3/x^6-3/2*b*arctan(c*x)*d*e^2/x^2+1/2*I*b*e^3*dilog(1+I*c*x)-1/2*I*b*e^3*dilog(1-I*c*x)+1/2*I*b*e^3*ln(c*x)*ln(1+I*c*x)-1/2*I*b*e^3*ln(c*x)*ln(1-I*c*x)-1/6*b*c^5*d^3/x+3/4*b*c^3*d^2*e/x-3/2*b*c*d*e^2/x-1/30*b*c*d^3/x^5+1/18*b*c^3*d^3/x^3-1/4*b*c*d^2*e/x^3-1/6*b*c^6*d^3*arctan(c*x)+3/4*b*c^4*d^2*e*arctan(c*x)-3/2*b*c^2*d*e^2*arctan(c*x)","A"
1148,1,290,210,0.051000," ","int((e*x^2+d)^3*(a+b*arctan(c*x))/x^8,x)","-\frac{a \,d^{3}}{7 x^{7}}-\frac{a d \,e^{2}}{x^{3}}-\frac{a \,e^{3}}{x}-\frac{3 a \,d^{2} e}{5 x^{5}}-\frac{b \arctan \left(c x \right) d^{3}}{7 x^{7}}-\frac{b \arctan \left(c x \right) d \,e^{2}}{x^{3}}-\frac{b \arctan \left(c x \right) e^{3}}{x}-\frac{3 b \arctan \left(c x \right) d^{2} e}{5 x^{5}}-\frac{c^{7} b \,d^{3} \ln \left(c x \right)}{7}+\frac{3 c^{5} b \ln \left(c x \right) d^{2} e}{5}-c^{3} b \ln \left(c x \right) d \,e^{2}+c b \ln \left(c x \right) e^{3}+\frac{c^{3} b \,d^{3}}{28 x^{4}}-\frac{3 c b \,d^{2} e}{20 x^{4}}-\frac{b c \,d^{3}}{42 x^{6}}-\frac{c^{5} b \,d^{3}}{14 x^{2}}+\frac{3 c^{3} b \,d^{2} e}{10 x^{2}}-\frac{c b d \,e^{2}}{2 x^{2}}+\frac{c^{7} b \ln \left(c^{2} x^{2}+1\right) d^{3}}{14}-\frac{3 c^{5} b \ln \left(c^{2} x^{2}+1\right) d^{2} e}{10}+\frac{c^{3} b \ln \left(c^{2} x^{2}+1\right) d \,e^{2}}{2}-\frac{c b \ln \left(c^{2} x^{2}+1\right) e^{3}}{2}"," ",0,"-1/7*a*d^3/x^7-a*d*e^2/x^3-a*e^3/x-3/5*a*d^2*e/x^5-1/7*b*arctan(c*x)*d^3/x^7-b*arctan(c*x)*d*e^2/x^3-b*arctan(c*x)*e^3/x-3/5*b*arctan(c*x)*d^2*e/x^5-1/7*c^7*b*d^3*ln(c*x)+3/5*c^5*b*ln(c*x)*d^2*e-c^3*b*ln(c*x)*d*e^2+c*b*ln(c*x)*e^3+1/28*c^3*b*d^3/x^4-3/20*c*b*d^2*e/x^4-1/42*b*c*d^3/x^6-1/14*c^5*b*d^3/x^2+3/10*c^3*b*d^2*e/x^2-1/2*c*b*d*e^2/x^2+1/14*c^7*b*ln(c^2*x^2+1)*d^3-3/10*c^5*b*ln(c^2*x^2+1)*d^2*e+1/2*c^3*b*ln(c^2*x^2+1)*d*e^2-1/2*c*b*ln(c^2*x^2+1)*e^3","A"
1149,1,265,140,0.051000," ","int((e*x^2+d)^3*(a+b*arctan(c*x))/x^9,x)","-\frac{a \,d^{3}}{8 x^{8}}-\frac{3 a d \,e^{2}}{4 x^{4}}-\frac{a \,d^{2} e}{2 x^{6}}-\frac{a \,e^{3}}{2 x^{2}}-\frac{b \arctan \left(c x \right) d^{3}}{8 x^{8}}-\frac{3 b \arctan \left(c x \right) d \,e^{2}}{4 x^{4}}-\frac{b \arctan \left(c x \right) d^{2} e}{2 x^{6}}-\frac{b \arctan \left(c x \right) e^{3}}{2 x^{2}}+\frac{c^{7} b \,d^{3}}{8 x}-\frac{c^{5} b \,d^{2} e}{2 x}+\frac{3 c^{3} b d \,e^{2}}{4 x}-\frac{c b \,e^{3}}{2 x}+\frac{c^{3} b \,d^{3}}{40 x^{5}}-\frac{c b \,d^{2} e}{10 x^{5}}-\frac{b c \,d^{3}}{56 x^{7}}-\frac{c^{5} b \,d^{3}}{24 x^{3}}+\frac{c^{3} b \,d^{2} e}{6 x^{3}}-\frac{c b d \,e^{2}}{4 x^{3}}+\frac{c^{8} b \arctan \left(c x \right) d^{3}}{8}-\frac{c^{6} b \arctan \left(c x \right) d^{2} e}{2}+\frac{3 c^{4} b \arctan \left(c x \right) d \,e^{2}}{4}-\frac{c^{2} b \arctan \left(c x \right) e^{3}}{2}"," ",0,"-1/8*a*d^3/x^8-3/4*a*d*e^2/x^4-1/2*a*d^2*e/x^6-1/2*a*e^3/x^2-1/8*b*arctan(c*x)*d^3/x^8-3/4*b*arctan(c*x)*d*e^2/x^4-1/2*b*arctan(c*x)*d^2*e/x^6-1/2*b*arctan(c*x)*e^3/x^2+1/8*c^7*b*d^3/x-1/2*c^5*b*d^2*e/x+3/4*c^3*b*d*e^2/x-1/2*c*b*e^3/x+1/40*c^3*b*d^3/x^5-1/10*c*b*d^2*e/x^5-1/56*b*c*d^3/x^7-1/24*c^5*b*d^3/x^3+1/6*c^3*b*d^2*e/x^3-1/4*c*b*d*e^2/x^3+1/8*c^8*b*arctan(c*x)*d^3-1/2*c^6*b*arctan(c*x)*d^2*e+3/4*c^4*b*arctan(c*x)*d*e^2-1/2*c^2*b*arctan(c*x)*e^3","A"
1150,1,279,226,0.039000," ","int((d*x^2+c)^4*arctan(a*x),x)","\frac{d^{4} x^{9} \arctan \left(a x \right)}{9}+\frac{4 c \,d^{3} x^{7} \arctan \left(a x \right)}{7}+\frac{6 c^{2} d^{2} x^{5} \arctan \left(a x \right)}{5}+\frac{4 c^{3} d \,x^{3} \arctan \left(a x \right)}{3}+c^{4} x \arctan \left(a x \right)-\frac{2 c^{3} d \,x^{2}}{3 a}-\frac{3 c^{2} d^{2} x^{4}}{10 a}-\frac{2 c \,d^{3} x^{6}}{21 a}+\frac{3 c^{2} d^{2} x^{2}}{5 a^{3}}-\frac{d^{4} x^{8}}{72 a}+\frac{x^{4} c \,d^{3}}{7 a^{3}}+\frac{d^{4} x^{6}}{54 a^{3}}-\frac{2 x^{2} c \,d^{3}}{7 a^{5}}-\frac{d^{4} x^{4}}{36 a^{5}}+\frac{x^{2} d^{4}}{18 a^{7}}-\frac{\ln \left(a^{2} x^{2}+1\right) c^{4}}{2 a}+\frac{2 \ln \left(a^{2} x^{2}+1\right) c^{3} d}{3 a^{3}}-\frac{3 \ln \left(a^{2} x^{2}+1\right) c^{2} d^{2}}{5 a^{5}}+\frac{2 \ln \left(a^{2} x^{2}+1\right) c \,d^{3}}{7 a^{7}}-\frac{\ln \left(a^{2} x^{2}+1\right) d^{4}}{18 a^{9}}"," ",0,"1/9*d^4*x^9*arctan(a*x)+4/7*c*d^3*x^7*arctan(a*x)+6/5*c^2*d^2*x^5*arctan(a*x)+4/3*c^3*d*x^3*arctan(a*x)+c^4*x*arctan(a*x)-2/3/a*c^3*d*x^2-3/10/a*c^2*d^2*x^4-2/21/a*c*d^3*x^6+3/5/a^3*c^2*d^2*x^2-1/72*d^4*x^8/a+1/7/a^3*x^4*c*d^3+1/54/a^3*d^4*x^6-2/7/a^5*x^2*c*d^3-1/36/a^5*d^4*x^4+1/18/a^7*x^2*d^4-1/2/a*ln(a^2*x^2+1)*c^4+2/3/a^3*ln(a^2*x^2+1)*c^3*d-3/5/a^5*ln(a^2*x^2+1)*c^2*d^2+2/7/a^7*ln(a^2*x^2+1)*c*d^3-1/18/a^9*ln(a^2*x^2+1)*d^4","A"
1151,1,703,300,0.464000," ","int(x^3*(a+b*arctan(c*x))/(e*x^2+d),x)","\frac{a \,x^{2}}{2 e}-\frac{a d \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e^{2}}+\frac{b \arctan \left(c x \right) x^{2}}{2 e}-\frac{b \arctan \left(c x \right) d \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e^{2}}-\frac{b x}{2 c e}+\frac{b \arctan \left(c x \right)}{2 c^{2} e}-\frac{i b d \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{2}}+\frac{i b d \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{2}}-\frac{i b d \ln \left(c x -i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 e^{2}}+\frac{i b d \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{2}}+\frac{i b d \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{2}}-\frac{i b d \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{2}}+\frac{i b d \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{2}}-\frac{i b d \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{2}}+\frac{i b d \ln \left(c x +i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 e^{2}}-\frac{i b d \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{2}}"," ",0,"1/2*a/e*x^2-1/2*a*d/e^2*ln(c^2*e*x^2+c^2*d)+1/2*b*arctan(c*x)*x^2/e-1/2*b*arctan(c*x)/e^2*d*ln(c^2*e*x^2+c^2*d)-1/2*b*x/c/e+1/2*b*arctan(c*x)/c^2/e+1/4*I*b/e^2*d*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))+1/4*I*b/e^2*d*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))+1/4*I*b/e^2*d*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))-1/4*I*b/e^2*d*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/e^2*d*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))-1/4*I*b/e^2*d*ln(c*x-I)*ln(c^2*e*x^2+c^2*d)-1/4*I*b/e^2*d*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/e^2*d*ln(I+c*x)*ln(c^2*e*x^2+c^2*d)-1/4*I*b/e^2*d*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/e^2*d*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))","C"
1152,1,646,256,0.361000," ","int(x*(a+b*arctan(c*x))/(e*x^2+d),x)","\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e}+\frac{b \ln \left(c^{2} e \,x^{2}+c^{2} d \right) \arctan \left(c x \right)}{2 e}-\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e}-\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e}+\frac{i b \ln \left(c x -i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 e}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e}+\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e}+\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e}-\frac{i b \ln \left(c x +i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 e}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e}"," ",0,"1/2*a/e*ln(c^2*e*x^2+c^2*d)+1/2*b/e*ln(c^2*e*x^2+c^2*d)*arctan(c*x)-1/4*I*b/e*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/e*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/e*ln(c*x-I)*ln(c^2*e*x^2+c^2*d)-1/4*I*b/e*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/e*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/e*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))+1/4*I*b/e*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))-1/4*I*b/e*ln(I+c*x)*ln(c^2*e*x^2+c^2*d)+1/4*I*b/e*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))+1/4*I*b/e*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))","C"
1153,1,736,290,0.404000," ","int((a+b*arctan(c*x))/x/(e*x^2+d),x)","-\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d}+\frac{a \ln \left(c x \right)}{d}-\frac{b \arctan \left(c x \right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d}+\frac{b \arctan \left(c x \right) \ln \left(c x \right)}{d}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d}+\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d}+\frac{i b \dilog \left(i c x +1\right)}{2 d}-\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d}+\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d}-\frac{i b \dilog \left(-i c x +1\right)}{2 d}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d}-\frac{i b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d}+\frac{i b \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d}-\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d}-\frac{i b \ln \left(c x -i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 d}+\frac{i b \ln \left(c^{2} e \,x^{2}+c^{2} d \right) \ln \left(c x +i\right)}{4 d}"," ",0,"-1/2*a/d*ln(c^2*e*x^2+c^2*d)+a/d*ln(c*x)-1/2*b*arctan(c*x)/d*ln(c^2*e*x^2+c^2*d)+b*arctan(c*x)/d*ln(c*x)+1/4*I*b/d*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))+1/4*I*b/d*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))-1/4*I*b/d*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))-1/4*I*b/d*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))-1/2*I*b/d*dilog(1-I*c*x)+1/4*I*b/d*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-1/2*I*b/d*ln(c*x)*ln(1-I*c*x)+1/2*I*b/d*dilog(1+I*c*x)-1/4*I*b/d*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))+1/2*I*b/d*ln(c*x)*ln(1+I*c*x)+1/4*I*b/d*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))-1/4*I*b/d*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/d*ln(c*x-I)*ln(c^2*e*x^2+c^2*d)+1/4*I*b/d*ln(c^2*e*x^2+c^2*d)*ln(I+c*x)","C"
1154,1,801,343,0.387000," ","int((a+b*arctan(c*x))/x^3/(e*x^2+d),x)","\frac{a e \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{2}}-\frac{a}{2 d \,x^{2}}-\frac{a e \ln \left(c x \right)}{d^{2}}+\frac{b \arctan \left(c x \right) e \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{2}}-\frac{b \arctan \left(c x \right)}{2 d \,x^{2}}-\frac{b \arctan \left(c x \right) e \ln \left(c x \right)}{d^{2}}-\frac{i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{2}}+\frac{i b e \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{2}}+\frac{i b e \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{2}}-\frac{i b e \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d^{2}}+\frac{i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{2}}-\frac{i b e \ln \left(c x +i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 d^{2}}+\frac{i b e \ln \left(c x -i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 d^{2}}-\frac{i b e \dilog \left(i c x +1\right)}{2 d^{2}}-\frac{i b e \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{2}}+\frac{i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{2}}-\frac{b c}{2 d x}-\frac{b \,c^{2} \arctan \left(c x \right)}{2 d}-\frac{i b e \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{2}}+\frac{i b e \dilog \left(-i c x +1\right)}{2 d^{2}}+\frac{i b e \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d^{2}}-\frac{i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{2}}"," ",0,"1/2*a*e/d^2*ln(c^2*e*x^2+c^2*d)-1/2*a/d/x^2-a/d^2*e*ln(c*x)+1/2*b*arctan(c*x)*e/d^2*ln(c^2*e*x^2+c^2*d)-1/2*b*arctan(c*x)/d/x^2-b*arctan(c*x)/d^2*e*ln(c*x)-1/2*I*b/d^2*e*ln(c*x)*ln(1+I*c*x)+1/4*I*b/d^2*e*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/d^2*e*ln(I+c*x)*ln(c^2*e*x^2+c^2*d)-1/4*I*b/d^2*e*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/d^2*e*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/d^2*e*ln(c*x-I)*ln(c^2*e*x^2+c^2*d)-1/4*I*b/d^2*e*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))-1/2*I*b/d^2*e*dilog(1+I*c*x)+1/4*I*b/d^2*e*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))+1/4*I*b/d^2*e*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))-1/2*b*c/d/x-1/2*b*c^2*arctan(c*x)/d+1/2*I*b/d^2*e*ln(c*x)*ln(1-I*c*x)-1/4*I*b/d^2*e*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/d^2*e*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))+1/2*I*b/d^2*e*dilog(1-I*c*x)","C"
1155,1,2409,417,0.848000," ","int(x^2*(a+b*arctan(c*x))/(e*x^2+d),x)","\frac{c^{6} b \sqrt{d e}\, d^{3} \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{8 e^{3} \left(c^{2} d -e \right)^{2}}-\frac{5 c^{2} b \sqrt{d e}\, d \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 e^{2} \left(c^{2} d -e \right)}-\frac{c^{2} b \sqrt{d e}\, d \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{2 e \left(c^{2} d -e \right)^{2}}+\frac{c^{4} b \sqrt{d e}\, d^{2} \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 e^{2} \left(c^{2} d -e \right)^{2}}+\frac{3 b \sqrt{d e}\, e \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{8 c^{2} d \left(c^{2} d -e \right)^{2}}+\frac{b x \arctan \left(c x \right)}{e}-\frac{b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 \left(c^{2} d -e \right)^{2}}+\frac{3 b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 e^{2}}+\frac{b \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 c \left(c^{2} d -e \right)}+\frac{b \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c e}-\frac{b \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{4 c e}+\frac{2 b \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{c \left(c^{2} d -e \right)}+\frac{c^{5} b \,d^{3} \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 e^{2} \left(c^{2} d -e \right)^{2}}-\frac{2 c b d \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{e \left(c^{2} d -e \right)}+\frac{c^{3} b \,d^{2} \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 e^{2} \left(c^{2} d -e \right)}-\frac{c b d \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{4 e \left(c^{2} d -e \right)}+\frac{c^{3} b \,d^{2} \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 e \left(c^{2} d -e \right)^{2}}+\frac{3 b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{8 c^{2} d e}+\frac{3 b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 c^{2} d \left(c^{2} d -e \right)}-\frac{c^{2} b \sqrt{d e}\, d \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{8 e^{3}}-\frac{a d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{e \sqrt{d e}}+\frac{i b \arctan \left(c x \right)}{c e}+\frac{3 b e \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 c \left(c^{2} d -e \right)^{2}}-\frac{5 c b d \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 \left(c^{2} d -e \right)^{2}}-\frac{c b d \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{4 e^{2}}+\frac{b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{2 e \left(c^{2} d -e \right)}+\frac{c b d \left(\munderset{\textit{\_R1} =\RootOf \left(\left(c^{2} d -e \right) \textit{\_Z}^{4}+\left(2 c^{2} d +2 e \right) \textit{\_Z}^{2}+c^{2} d -e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -\textit{\_R1}^{2} e +c^{2} d +3 e \right) \left(i \arctan \left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -\textit{\_R1}^{2} e +c^{2} d +e}\right)}{4 e^{2}}-\frac{c b d \left(\munderset{\textit{\_R1} =\RootOf \left(\left(c^{2} d -e \right) \textit{\_Z}^{4}+\left(2 c^{2} d +2 e \right) \textit{\_Z}^{2}+c^{2} d -e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -\textit{\_R1}^{2} e +c^{2} d -e \right) \left(i \arctan \left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -\textit{\_R1}^{2} e +c^{2} d +e}\right)}{4 e^{2}}+\frac{a x}{e}"," ",0,"1/8*c^6*b*(d*e)^(1/2)/e^3*d^3*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2-5/4*c^2*b*(d*e)^(1/2)/e^2*d*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)-1/2*c^2*b*(d*e)^(1/2)*d/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+1/4*c^4*b*(d*e)^(1/2)/e^2*d^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+b*x*arctan(c*x)/e+1/2*b*(d*e)^(1/2)/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)+1/8*c^5*b/e^2*d^3/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-2*c*b/e*d/(c^2*d-e)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+1/8*c^3*b/e^2*d^2/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+3/8/c^2*b*(d*e)^(1/2)/d/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))+3/4/c^2*b*(d*e)^(1/2)/d*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)-1/4*c*b/e*d/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+1/8*c^3*b/e*d^2/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-1/8*c^2*b*(d*e)^(1/2)/e^3*d*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))+1/8/c*b/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+1/c*b/e*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/4/c*b/e*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+2/c*b/(c^2*d-e)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-1/4*b*(d*e)^(1/2)*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+3/4*b*(d*e)^(1/2)/e^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))+3/8/c^2*b*(d*e)^(1/2)/d*e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2-a*d/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+I/c*b*arctan(c*x)/e+3/8/c*b*e/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+1/4*c*b/e^2*d*sum((_R1^2*c^2*d-_R1^2*e+c^2*d+3*e)/(_R1^2*c^2*d-_R1^2*e+c^2*d+e)*(I*arctan(c*x)*ln((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf((c^2*d-e)*_Z^4+(2*c^2*d+2*e)*_Z^2+c^2*d-e))-1/4*c*b/e^2*d*sum((_R1^2*c^2*d-_R1^2*e+c^2*d-e)/(_R1^2*c^2*d-_R1^2*e+c^2*d+e)*(I*arctan(c*x)*ln((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf((c^2*d-e)*_Z^4+(2*c^2*d+2*e)*_Z^2+c^2*d-e))-5/8*c*b*d/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-1/4*c*b/e^2*d*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+a*x/e","C"
1156,1,886,381,0.665000," ","int((a+b*arctan(c*x))/(e*x^2+d),x)","\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}+\frac{i c^{3} b \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}\, d}{2 e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{i c b \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}}{d^{2} c^{4}-2 c^{2} e d +e^{2}}-\frac{b \sqrt{c^{2} e d}\, \arctan \left(c x \right)^{2}}{2 c e d}-\frac{b \sqrt{c^{2} e d}\, \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right)}{4 c e d}-\frac{i b \sqrt{c^{2} e d}\, \arctan \left(c x \right) \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right)}{2 c e d}+\frac{c^{3} b \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}\, d}{2 e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{c b \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{d^{2} c^{4}-2 c^{2} e d +e^{2}}+\frac{i b \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}\, e}{2 c d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{c^{3} b \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}\, d}{4 e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{c b \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{2 \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{b \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}\, e}{2 c d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{b \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}\, e}{4 c d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}"," ",0,"a/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/2*I*c^3*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/e/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*d-I*c*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)-1/2/c*b*(c^2*e*d)^(1/2)/e/d*arctan(c*x)^2-1/4/c*b*(c^2*e*d)^(1/2)/e/d*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))-1/2*I/c*b*(c^2*e*d)^(1/2)/e/d*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))+1/2*c^3*b/e/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2*(c^2*e*d)^(1/2)*d-c*b/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2*(c^2*e*d)^(1/2)+1/2*I/c*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/d/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*e+1/4*c^3*b/e/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*(c^2*e*d)^(1/2)*d-1/2*c*b/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*(c^2*e*d)^(1/2)+1/2/c*b/d/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2*(c^2*e*d)^(1/2)*e+1/4/c*b/d/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*(c^2*e*d)^(1/2)*e","B"
1157,1,2439,425,0.844000," ","int((a+b*arctan(c*x))/x^2/(e*x^2+d),x)","-\frac{b \,c^{2} \sqrt{d e}\, e \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{2 d \left(c^{2} d -e \right)^{2}}+\frac{b \sqrt{d e}\, e^{3} \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{8 c^{2} d^{3} \left(c^{2} d -e \right)^{2}}+\frac{3 b \,c^{6} \sqrt{d e}\, d \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{8 e \left(c^{2} d -e \right)^{2}}-\frac{b \sqrt{d e}\, e \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{8 c^{2} d^{3}}-\frac{3 b \,c^{4} \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 e \left(c^{2} d -e \right)}+\frac{3 b \,c^{2} \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{8 d e}-\frac{b \,c^{2} \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{2 d \left(c^{2} d -e \right)}+\frac{c b e \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{4 d \left(c^{2} d -e \right)}+\frac{c b \,e^{2} \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 d \left(c^{2} d -e \right)^{2}}+\frac{2 c b e \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d \left(c^{2} d -e \right)}+\frac{b \,e^{3} \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 c \,d^{2} \left(c^{2} d -e \right)^{2}}-\frac{b \,e^{2} \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 c \,d^{2} \left(c^{2} d -e \right)}+\frac{5 b \sqrt{d e}\, e \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 d^{2} \left(c^{2} d -e \right)}+\frac{b \sqrt{d e}\, e^{2} \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 d^{2} \left(c^{2} d -e \right)^{2}}+\frac{3 b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 d^{2}}+\frac{c b \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{c b \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}-1\right)}{d}-\frac{c b \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{4 d}-\frac{2 b \,c^{3} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{2} d -e}-\frac{b \,c^{3} \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 \left(c^{2} d -e \right)}-\frac{b \arctan \left(c x \right)}{x d}-\frac{a}{d x}-\frac{a e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{d \sqrt{d e}}+\frac{b e \left(\munderset{\textit{\_R1} =\RootOf \left(\left(c^{2} d -e \right) \textit{\_Z}^{4}+\left(2 c^{2} d +2 e \right) \textit{\_Z}^{2}+c^{2} d -e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -\textit{\_R1}^{2} e +3 c^{2} d +e \right) \left(i \arctan \left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -\textit{\_R1}^{2} e +c^{2} d +e}\right)}{4 c \,d^{2}}-\frac{b e \left(\munderset{\textit{\_R1} =\RootOf \left(\left(c^{2} d -e \right) \textit{\_Z}^{4}+\left(2 c^{2} d +2 e \right) \textit{\_Z}^{2}+c^{2} d -e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -\textit{\_R1}^{2} e -c^{2} d +e \right) \left(i \arctan \left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -\textit{\_R1}^{2} e +c^{2} d +e}\right)}{4 c \,d^{2}}-\frac{b \,c^{4} \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 \left(c^{2} d -e \right)^{2}}-\frac{b e \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{4 c \,d^{2}}-\frac{5 b \,c^{3} e \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 \left(c^{2} d -e \right)^{2}}+\frac{3 b \,c^{5} d \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{8 \left(c^{2} d -e \right)^{2}}+\frac{i c b \arctan \left(c x \right)}{d}"," ",0,"1/8*b/c^2*(d*e)^(1/2)/d^3*e^3*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+3/8*b*c^6*(d*e)^(1/2)*d/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2-1/2*b*c^2*(d*e)^(1/2)/d*e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+c*b/d*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+c*b/d*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)-1/4*c*b/d*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-2*b*c^3/(c^2*d-e)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-1/8*b*c^3/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+3/4*b*(d*e)^(1/2)/d^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))-b*arctan(c*x)/x/d-a/d/x+5/4*b*(d*e)^(1/2)/d^2*e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)+1/4*b*(d*e)^(1/2)/d^2*e^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2-1/8*b/c^2*(d*e)^(1/2)/d^3*e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))+1/4*c*b/d*e/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+1/8*c*b/d*e^2/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+2*c*b/d*e/(c^2*d-e)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-3/4*b*c^4*(d*e)^(1/2)/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)+3/8*b*c^2*(d*e)^(1/2)/d/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))-1/2*b*c^2*(d*e)^(1/2)/d*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)+1/8*b/c/d^2*e^3/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-1/8*b/c/d^2*e^2/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+1/4*b/c/d^2*e*sum((_R1^2*c^2*d-_R1^2*e+3*c^2*d+e)/(_R1^2*c^2*d-_R1^2*e+c^2*d+e)*(I*arctan(c*x)*ln((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf((c^2*d-e)*_Z^4+(2*c^2*d+2*e)*_Z^2+c^2*d-e))-a*e/d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/4*b/c/d^2*e*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-1/4*b/c/d^2*e*sum((_R1^2*c^2*d-_R1^2*e-c^2*d+e)/(_R1^2*c^2*d-_R1^2*e+c^2*d+e)*(I*arctan(c*x)*ln((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf((c^2*d-e)*_Z^4+(2*c^2*d+2*e)*_Z^2+c^2*d-e))-5/8*b*c^3*e/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-1/4*b*c^4*(d*e)^(1/2)*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+3/8*b*c^5*d/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+I*c*b*arctan(c*x)/d","C"
1158,1,760,334,0.374000," ","int(x^3*(a+b*arctan(c*x))/(e*x^2+d)^2,x)","\frac{c^{2} a d}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e^{2}}+\frac{c^{2} b \arctan \left(c x \right) d}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{b \arctan \left(c x \right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e^{2}}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{2}}+\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{2}}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{2}}-\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{2}}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{2}}+\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{2}}+\frac{i b \ln \left(c x -i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 e^{2}}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{2}}-\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{2}}-\frac{i b \ln \left(c x +i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 e^{2}}+\frac{c b d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 e \left(c^{2} d -e \right) \sqrt{d e}}-\frac{b \,c^{2} d \arctan \left(c x \right)}{2 \left(c^{2} d -e \right) e^{2}}"," ",0,"1/2*c^2*a/e^2*d/(c^2*e*x^2+c^2*d)+1/2*a/e^2*ln(c^2*e*x^2+c^2*d)+1/2*c^2*b*arctan(c*x)/e^2*d/(c^2*e*x^2+c^2*d)+1/2*b*arctan(c*x)/e^2*ln(c^2*e*x^2+c^2*d)-1/4*I*b/e^2*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/e^2*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))+1/4*I*b/e^2*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/e^2*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))-1/4*I*b/e^2*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/e^2*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/e^2*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/e^2*ln(c*x-I)*ln(c^2*e*x^2+c^2*d)-1/4*I*b/e^2*ln(I+c*x)*ln(c^2*e*x^2+c^2*d)+1/4*I*b/e^2*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))+1/2*c*b/e*d/(c^2*d-e)/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/2*b*c^2*d*arctan(c*x)/(c^2*d-e)/e^2","C"
1159,1,109,80,0.045000," ","int(x*(a+b*arctan(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{2} b \arctan \left(c x \right)}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \left(c^{2} d -e \right) \sqrt{d e}}+\frac{b \,c^{2} \arctan \left(c x \right)}{2 \left(c^{2} d -e \right) e}"," ",0,"-1/2*c^2*a/e/(c^2*e*x^2+c^2*d)-1/2*c^2*b/e/(c^2*e*x^2+c^2*d)*arctan(c*x)-1/2*c*b/(c^2*d-e)/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/2*b*c^2*arctan(c*x)/(c^2*d-e)/e","A"
1160,1,847,366,0.305000," ","int((a+b*arctan(c*x))/x/(e*x^2+d)^2,x)","\frac{a \,c^{2}}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{2}}+\frac{a \ln \left(c x \right)}{d^{2}}+\frac{b \,c^{2} \arctan \left(c x \right)}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{b \arctan \left(c x \right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{2}}+\frac{b \arctan \left(c x \right) \ln \left(c x \right)}{d^{2}}+\frac{b c e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 d \left(c^{2} d -e \right) \sqrt{d e}}-\frac{b \,c^{2} \arctan \left(c x \right)}{2 d \left(c^{2} d -e \right)}-\frac{i b \ln \left(c x -i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 d^{2}}+\frac{i b \dilog \left(i c x +1\right)}{2 d^{2}}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{2}}-\frac{i b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d^{2}}+\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{2}}+\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{2}}+\frac{i b \ln \left(c x +i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 d^{2}}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{2}}-\frac{i b \dilog \left(-i c x +1\right)}{2 d^{2}}+\frac{i b \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d^{2}}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{2}}-\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{2}}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{2}}-\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{2}}"," ",0,"1/2*a*c^2/d/(c^2*e*x^2+c^2*d)-1/2*a/d^2*ln(c^2*e*x^2+c^2*d)+a/d^2*ln(c*x)+1/2*b*c^2*arctan(c*x)/d/(c^2*e*x^2+c^2*d)-1/2*b*arctan(c*x)/d^2*ln(c^2*e*x^2+c^2*d)+b*arctan(c*x)/d^2*ln(c*x)+1/2*b*c/d*e/(c^2*d-e)/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/2*b*c^2*arctan(c*x)/d/(c^2*d-e)-1/4*I*b/d^2*ln(c*x-I)*ln(c^2*e*x^2+c^2*d)+1/4*I*b/d^2*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-1/2*I*b/d^2*ln(c*x)*ln(1-I*c*x)-1/4*I*b/d^2*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/d^2*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))-1/2*I*b/d^2*dilog(1-I*c*x)-1/4*I*b/d^2*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/d^2*ln(I+c*x)*ln(c^2*e*x^2+c^2*d)-1/4*I*b/d^2*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/d^2*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))+1/4*I*b/d^2*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))+1/2*I*b/d^2*ln(c*x)*ln(1+I*c*x)+1/4*I*b/d^2*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))+1/2*I*b/d^2*dilog(1+I*c*x)","C"
1161,1,925,419,0.368000," ","int((a+b*arctan(c*x))/x^3/(e*x^2+d)^2,x)","\frac{i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{2 d^{3}}+\frac{i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{2 d^{3}}-\frac{i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{2 d^{3}}-\frac{i b e \dilog \left(i c x +1\right)}{d^{3}}-\frac{i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{2 d^{3}}+\frac{i b e \dilog \left(-i c x +1\right)}{d^{3}}-\frac{c^{4} b \arctan \left(c x \right)}{2 d \left(c^{2} d -e \right)}+\frac{b \arctan \left(c x \right) e \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{d^{3}}-\frac{2 b \arctan \left(c x \right) e \ln \left(c x \right)}{d^{3}}-\frac{i b e \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{2 d^{3}}+\frac{i b e \ln \left(c x -i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{3}}+\frac{i b e \ln \left(c x \right) \ln \left(-i c x +1\right)}{d^{3}}-\frac{a}{2 d^{2} x^{2}}-\frac{c^{2} b \arctan \left(c x \right) e}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c b \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 d^{2} \left(c^{2} d -e \right) \sqrt{d e}}+\frac{b \,c^{2} e \arctan \left(c x \right)}{d^{2} \left(c^{2} d -e \right)}-\frac{c^{2} a e}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{i b e \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{2 d^{3}}+\frac{i b e \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{2 d^{3}}+\frac{i b e \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{2 d^{3}}-\frac{i b e \ln \left(c x \right) \ln \left(i c x +1\right)}{d^{3}}-\frac{i b e \ln \left(c x +i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{3}}+\frac{a e \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{d^{3}}-\frac{2 a e \ln \left(c x \right)}{d^{3}}-\frac{b c}{2 d^{2} x}-\frac{b \arctan \left(c x \right)}{2 d^{2} x^{2}}"," ",0,"-1/2*c^4*b/d/(c^2*d-e)*arctan(c*x)+b*arctan(c*x)*e/d^3*ln(c^2*e*x^2+c^2*d)-2*b*arctan(c*x)/d^3*e*ln(c*x)+I*b/d^3*e*dilog(1-I*c*x)+1/2*I*b/d^3*e*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))+1/2*I*b/d^3*e*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))-1/2*I*b/d^3*e*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))-I*b/d^3*e*dilog(1+I*c*x)-1/2*I*b/d^3*e*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-1/2*a/d^2/x^2-I*b/d^3*e*ln(c*x)*ln(1+I*c*x)-1/2*I*b/d^3*e*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-1/2*I*b/d^3*e*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))-1/2*I*b/d^3*e*ln(I+c*x)*ln(c^2*e*x^2+c^2*d)-1/2*c^2*b*arctan(c*x)*e/d^2/(c^2*e*x^2+c^2*d)+1/2*I*b/d^3*e*ln(c*x-I)*ln(c^2*e*x^2+c^2*d)+1/2*I*b/d^3*e*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))+I*b/d^3*e*ln(c*x)*ln(1-I*c*x)+1/2*I*b/d^3*e*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))-1/2*c*b/d^2*e^2/(c^2*d-e)/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+b*c^2*e*arctan(c*x)/d^2/(c^2*d-e)-1/2*c^2*a*e/d^2/(c^2*e*x^2+c^2*d)+a*e/d^3*ln(c^2*e*x^2+c^2*d)-2*a/d^3*e*ln(c*x)-1/2*b*c/d^2/x-1/2*b*arctan(c*x)/d^2/x^2","C"
1162,1,2315,991,2.371000," ","int(x^2*(a+b*arctan(c*x))/(e*x^2+d)^2,x)","-\frac{3 c b \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{8 \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{c b \sqrt{c^{2} e d}\, \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right)}{8 \left(c^{2} d -e \right) e^{2}}-\frac{c^{2} b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 e^{2} \left(c^{2} d -e \right)}-\frac{c^{3} b d \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{4 \left(c^{2} d -e \right)^{2} e}+\frac{c^{3} b d \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{\left(c^{2} d -e \right)^{2} e}-\frac{b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 d e \left(c^{2} d -e \right)}-\frac{c^{2} a x}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{4} b \arctan \left(c x \right) x d}{2 \left(c^{2} d -e \right) e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{5} b \,d^{2} \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{4 \left(c^{2} d -e \right) e^{2} \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{3 c^{3} b d \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{4 \left(c^{2} d -e \right) e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{b \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}\, e}{4 c \left(c^{2} d -e \right) d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{3 i c^{3} b \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) d \sqrt{c^{2} e d}}{4 \left(c^{2} d -e \right) e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{i c^{5} b \,d^{2} \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}}{4 \left(c^{2} d -e \right) e^{2} \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{i b \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}\, e}{4 c \left(c^{2} d -e \right) d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 d \left(c^{2} d -e \right)^{2}}-\frac{c b \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{\left(c^{2} d -e \right)^{2}}+\frac{c b \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{4 \left(c^{2} d -e \right)^{2}}-\frac{i b \sqrt{c^{2} e d}\, \arctan \left(c x \right) \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right)}{4 c \left(c^{2} d -e \right) d e}-\frac{i c^{3} b \arctan \left(c x \right) x^{2}}{2 \left(c^{2} d -e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{b \sqrt{c^{2} e d}\, \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right)}{8 c \left(c^{2} d -e \right) d e}+\frac{c^{4} b \sqrt{d e}\, d \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 e^{2} \left(c^{2} d -e \right)^{2}}+\frac{c^{2} b \arctan \left(c x \right) x}{2 \left(c^{2} d -e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c b \sqrt{c^{2} e d}\, \arctan \left(c x \right)^{2}}{4 \left(c^{2} d -e \right) e^{2}}-\frac{3 c b \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{4 \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right) \left(c^{2} d -e \right)}-\frac{b \sqrt{c^{2} e d}\, \arctan \left(c x \right)^{2}}{4 c \left(c^{2} d -e \right) d e}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 e \sqrt{d e}}-\frac{i c^{3} b \arctan \left(c x \right) d}{2 \left(c^{2} d -e \right) e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{i c b \sqrt{c^{2} e d}\, \arctan \left(c x \right) \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right)}{4 \left(c^{2} d -e \right) e^{2}}-\frac{3 i c b \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}}{4 \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{c^{5} b \,d^{2} \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{8 \left(c^{2} d -e \right) e^{2} \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{3 c^{3} b d \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{8 \left(c^{2} d -e \right) e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{b \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}\, e}{8 c \left(c^{2} d -e \right) d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}"," ",0,"-1/4*I/c*b*(c^2*e*d)^(1/2)/(c^2*d-e)/d/e*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))-1/2*c^2*a/e*x/(c^2*e*x^2+c^2*d)-1/4*b*(d*e)^(1/2)/d*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+3/4*I*c^3*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)*d/(c^2*d-e)/e/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)-1/4*I*c^5*b*d^2*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^2*d-e)/e^2/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+1/4*I/c*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^2*d-e)/d/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*e-1/2*c^4*b*arctan(c*x)/(c^2*d-e)/e/(c^2*e*x^2+c^2*d)*x*d-1/4*c^5*b*d^2*arctan(c*x)^2/(c^2*d-e)/e^2/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)-1/8*c^5*b*d^2*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/(c^2*d-e)/e^2/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+3/8*c^3*b*d*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/(c^2*d-e)/e/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+1/8/c*b*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/(c^2*d-e)/d/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*e+3/4*c^3*b*d*arctan(c*x)^2/(c^2*d-e)/e/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+1/4/c*b*arctan(c*x)^2/(c^2*d-e)/d/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*e-1/2*I*c^3*b*arctan(c*x)/(c^2*d-e)/e/(c^2*e*x^2+c^2*d)*d+1/4*I*c*b*(c^2*e*d)^(1/2)/(c^2*d-e)/e^2*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))-3/4*I*c*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)-1/4*c^3*b/(c^2*d-e)^2/e*d*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-1/4*b*(d*e)^(1/2)/d/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)-3/8*c*b*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+c^3*b/(c^2*d-e)^2/e*d*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*c^2*b*arctan(c*x)/(c^2*d-e)/(c^2*e*x^2+c^2*d)*x+1/8*c*b*(c^2*e*d)^(1/2)/(c^2*d-e)/e^2*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+1/4*c*b*(c^2*e*d)^(1/2)/(c^2*d-e)/e^2*arctan(c*x)^2-1/4*c^2*b*(d*e)^(1/2)/e^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)-3/4*c*b*arctan(c*x)^2/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)*(c^2*e*d)^(1/2)-1/8/c*b*(c^2*e*d)^(1/2)/(c^2*d-e)/d/e*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))-1/4/c*b*(c^2*e*d)^(1/2)/(c^2*d-e)/d/e*arctan(c*x)^2+1/4*c^4*b*(d*e)^(1/2)*d/e^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2-1/2*I*c^3*b*arctan(c*x)/(c^2*d-e)/(c^2*e*x^2+c^2*d)*x^2+1/2*a/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-c*b/(c^2*d-e)^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+1/4*c*b/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)","B"
1163,1,2315,611,2.022000," ","int((a+b*arctan(c*x))/(e*x^2+d)^2,x)","\frac{c^{2} a x}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{i c^{5} b \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}\, d}{4 \left(c^{2} d -e \right) e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{3 i c b e \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}}{4 d \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{i b \,e^{2} \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}}{4 c \,d^{2} \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{c b \sqrt{c^{2} e d}\, \arctan \left(c x \right)^{2}}{4 \left(c^{2} d -e \right) d e}+\frac{c^{2} b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 d e \left(c^{2} d -e \right)}+\frac{c b \sqrt{c^{2} e d}\, \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right)}{8 \left(c^{2} d -e \right) d e}-\frac{3 c b \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}\, e}{4 \left(c^{2} d -e \right) d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{c^{5} b d \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{4 \left(c^{2} d -e \right) e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{c^{2} b \arctan \left(c x \right) x e}{2 d \left(c^{2} d -e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{b \,e^{2} \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{4 c \,d^{2} \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{3 i c^{3} b \arctan \left(c x \right) \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{4 \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right) \left(c^{2} d -e \right)}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 d \sqrt{d e}}+\frac{3 c^{3} b \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{4 \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right) \left(c^{2} d -e \right)}+\frac{c^{4} b \arctan \left(c x \right) x}{2 \left(c^{2} d -e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{b \sqrt{c^{2} e d}\, \arctan \left(c x \right)^{2}}{4 c \,d^{2} \left(c^{2} d -e \right)}+\frac{c b e \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{d \left(c^{2} d -e \right)^{2}}-\frac{c b e \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{4 d \left(c^{2} d -e \right)^{2}}+\frac{i c^{3} b \arctan \left(c x \right)}{2 \left(c^{2} d -e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{4} b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 e \left(c^{2} d -e \right)^{2}}+\frac{3 c^{3} b \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{8 \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{b \sqrt{c^{2} e d}\, \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right)}{8 c \,d^{2} \left(c^{2} d -e \right)}+\frac{b \sqrt{d e}\, e \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 d^{2} \left(c^{2} d -e \right)^{2}}+\frac{i c b \sqrt{c^{2} e d}\, \arctan \left(c x \right) \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right)}{4 \left(c^{2} d -e \right) d e}+\frac{i c^{3} b \arctan \left(c x \right) x^{2} e}{2 d \left(c^{2} d -e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{i b \sqrt{c^{2} e d}\, \arctan \left(c x \right) \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right)}{4 c \,d^{2} \left(c^{2} d -e \right)}-\frac{c^{5} b d \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{8 \left(c^{2} d -e \right) e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{3 c b \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}\, e}{8 \left(c^{2} d -e \right) d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{b \,e^{2} \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{8 c \,d^{2} \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{b \sqrt{d e}\, \arctanh \left(\frac{\frac{2 \left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+2 c^{2} d +2 e}{4 c \sqrt{d e}}\right)}{4 d^{2} \left(c^{2} d -e \right)}-\frac{c^{3} b \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{\left(c^{2} d -e \right)^{2}}+\frac{c^{3} b \ln \left(\frac{\left(i c x +1\right)^{4} c^{2} d}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 c^{2} d \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-\frac{\left(i c x +1\right)^{4} e}{\left(c^{2} x^{2}+1\right)^{2}}+c^{2} d +\frac{2 \left(i c x +1\right)^{2} e}{c^{2} x^{2}+1}-e \right)}{4 \left(c^{2} d -e \right)^{2}}"," ",0,"1/4*I*c*b*(c^2*e*d)^(1/2)/(c^2*d-e)/d/e*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+1/2*I*c^3*b*arctan(c*x)/d/(c^2*d-e)/(c^2*e*x^2+c^2*d)*x^2*e-1/4*I*c^5*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^2*d-e)/e/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*d+1/2*c^2*a*x/d/(c^2*e*x^2+c^2*d)-3/4*I*c*b*e*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/d/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+1/4*I/c*b*e^2*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/d^2/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+1/4*c^2*b*(d*e)^(1/2)/d/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)+1/4*c*b*(c^2*e*d)^(1/2)/(c^2*d-e)/d/e*arctan(c*x)^2+1/8*c*b*(c^2*e*d)^(1/2)/(c^2*d-e)/d/e*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))-3/4*c*b*arctan(c*x)^2/(c^2*d-e)/d/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*e-1/8*c^5*b*d*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/(c^2*d-e)/e/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)-3/8*c*b*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/(c^2*d-e)/d/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*e-1/4*c^5*b*d*arctan(c*x)^2/(c^2*d-e)/e/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)-1/2*c^2*b*arctan(c*x)/d/(c^2*d-e)/(c^2*e*x^2+c^2*d)*x*e+1/8/c*b*e^2*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/d^2/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+1/4/c*b*e^2*arctan(c*x)^2/d^2/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+3/4*I*c^3*b*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)*(c^2*e*d)^(1/2)-1/4*I/c*b*(c^2*e*d)^(1/2)/d^2/(c^2*d-e)*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+1/2*a/d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/4*c^4*b*(d*e)^(1/2)/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+c*b/d/(c^2*d-e)^2*e*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-1/4*c*b/d/(c^2*d-e)^2*e*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+3/4*c^3*b*arctan(c*x)^2/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)*(c^2*e*d)^(1/2)+3/8*c^3*b*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+1/2*c^4*b*arctan(c*x)/(c^2*d-e)/(c^2*e*x^2+c^2*d)*x-1/8/c*b*(c^2*e*d)^(1/2)/d^2/(c^2*d-e)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))-1/4/c*b*(c^2*e*d)^(1/2)/d^2/(c^2*d-e)*arctan(c*x)^2+1/4*b*(d*e)^(1/2)/d^2*e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+1/2*I*c^3*b*arctan(c*x)/(c^2*d-e)/(c^2*e*x^2+c^2*d)+1/4*b*(d*e)^(1/2)/d^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)-c^3*b/(c^2*d-e)^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+1/4*c^3*b/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)","B"
1164,1,3851,1038,1.040000," ","int((a+b*arctan(c*x))/x^2/(e*x^2+d)^2,x)","\text{output too large to display}"," ",0,"3/8*b*c^7/(c^2*d-e)^3*d*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+b*c^3/(c^2*d-e)/d*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+b*c^3/(c^2*d-e)/d*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)-1/4*b*c^3/(c^2*d-e)/d*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-13/16*b*c^6*(d*e)^(1/2)*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^3+b*c^2*arctan(c*x)/(c^2*d-e)/d/(c^2*e*x^2+c^2*d)/x*e-3/2*I*b*c^3*arctan(c*x)/(c^2*d-e)/d/(c^2*e*x^2+c^2*d)*e+3/2*b*arctan(c*x)/(c^2*d-e)/d^2/(c^2*e*x^2+c^2*d)*c^2*x*e^2-3/2*b*c^4*arctan(c*x)/d/(c^2*d-e)/(c^2*e*x^2+c^2*d)*x*e-3/2*a/d^2*e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/2*a/d^2*e*c^2*x/(c^2*e*x^2+c^2*d)-3/16*b/c^2*(d*e)^(1/2)/d^4*e^4*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^3-19/16*b*c^5/(c^2*d-e)^3*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)*e-1/8*b*c^5/(c^2*d-e)^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-2*b*c^5/(c^2*d-e)^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-1/4*b*(d*e)^(1/2)/d^3*e^3*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^3-9/8*b*(d*e)^(1/2)/d^3*e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)-7/4*b*(d*e)^(1/2)/d^3*e^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+3/8*c*b/(c^2*d-e)/d^2*e*sum((_R1^2*c^2*d-_R1^2*e+3*c^2*d+e)/(_R1^2*c^2*d-_R1^2*e+c^2*d+e)*(I*arctan(c*x)*ln((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf((c^2*d-e)*_Z^4+(2*c^2*d+2*e)*_Z^2+c^2*d-e))-c*b/(c^2*d-e)/d^2*e*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/16*c*b/(c^2*d-e)^3/d^2*e^3*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-3*c*b/(c^2*d-e)^2/d^2*e^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-b*c^4*arctan(c*x)/(c^2*d-e)/(c^2*e*x^2+c^2*d)/x+I*b*c^5*arctan(c*x)/(c^2*d-e)/(c^2*e*x^2+c^2*d)-3/8*c*b/(c^2*d-e)/d^2*e*sum((_R1^2*c^2*d-_R1^2*e-c^2*d+e)/(_R1^2*c^2*d-_R1^2*e+c^2*d+e)*(I*arctan(c*x)*ln((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf((c^2*d-e)*_Z^4+(2*c^2*d+2*e)*_Z^2+c^2*d-e))-3/8*c*b/(c^2*d-e)^2/d^2*e^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-3/16*b/c/(c^2*d-e)^3/d^3*e^4*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+3/8*b/c/(c^2*d-e)/d^3*e^2*sum((_R1^2*c^2*d-_R1^2*e-c^2*d+e)/(_R1^2*c^2*d-_R1^2*e+c^2*d+e)*(I*arctan(c*x)*ln((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf((c^2*d-e)*_Z^4+(2*c^2*d+2*e)*_Z^2+c^2*d-e))+17/16*b*c^3/(c^2*d-e)^3/d*e^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+3/16*b/c/(c^2*d-e)^2/d^3*e^3*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+5/16*b*c^2*(d*e)^(1/2)/d^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)-3/4*b*c^6*(d*e)^(1/2)/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+5*b*c^3/d/(c^2*d-e)^2*e*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+5/16*b*c^3/d/(c^2*d-e)^2*e*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+1/2*b*c^4*(d*e)^(1/2)/d*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2-3/8*b/c/(c^2*d-e)/d^3*e^2*sum((_R1^2*c^2*d-_R1^2*e+3*c^2*d+e)/(_R1^2*c^2*d-_R1^2*e+c^2*d+e)*(I*arctan(c*x)*ln((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-(1+I*c*x)/(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf((c^2*d-e)*_Z^4+(2*c^2*d+2*e)*_Z^2+c^2*d-e))+3/8*b/c/(c^2*d-e)/d^3*e^2*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-c*b/(c^2*d-e)/d^2*e*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)+3/16*b/c^2*(d*e)^(1/2)/d^4*e^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)+b*c^2*(d*e)^(1/2)/d^2*e^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^3-1/8*b*c^4*(d*e)^(1/2)/d*e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^3+3/8*b*c^4*(d*e)^(1/2)/d/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)+2*b*c^2*(d*e)^(1/2)/d^2*e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^2+3/8*b*c^8*(d*e)^(1/2)*d/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^2*d-e)^3+I*b*c^5*arctan(c*x)/(c^2*d-e)/d/(c^2*e*x^2+c^2*d)*x^2*e-3/2*I*b*arctan(c*x)/(c^2*d-e)/d^2/(c^2*e*x^2+c^2*d)*c^3*x^2*e^2-a/d^2/x","C"
1165,1,959,453,0.410000," ","int(x^5*(a+b*arctan(c*x))/(e*x^2+d)^3,x)","-\frac{c^{4} a \,d^{2}}{4 e^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{c^{2} a d}{e^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e^{3}}-\frac{c^{4} b \arctan \left(c x \right) d^{2}}{4 e^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{c^{2} b \arctan \left(c x \right) d}{e^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{b \arctan \left(c x \right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e^{3}}-\frac{c^{5} b \,d^{2} x}{8 e^{2} \left(c^{2} d -e \right)^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{3} b d x}{8 e \left(c^{2} d -e \right)^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{5 c^{3} b \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 e^{2} \left(c^{2} d -e \right)^{2} \sqrt{d e}}-\frac{7 c b d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 e \left(c^{2} d -e \right)^{2} \sqrt{d e}}-\frac{3 b \,c^{4} d^{2} \arctan \left(c x \right)}{4 \left(c^{2} d -e \right)^{2} e^{3}}+\frac{c^{2} b d \arctan \left(c x \right)}{e^{2} \left(c^{2} d -e \right)^{2}}-\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{3}}-\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{3}}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{3}}+\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{3}}+\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{3}}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 e^{3}}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{3}}+\frac{i b \ln \left(c^{2} e \,x^{2}+c^{2} d \right) \ln \left(c x -i\right)}{4 e^{3}}-\frac{i b \ln \left(c^{2} e \,x^{2}+c^{2} d \right) \ln \left(c x +i\right)}{4 e^{3}}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 e^{3}}"," ",0,"-1/4*c^4*a*d^2/e^3/(c^2*e*x^2+c^2*d)^2+c^2*a/e^3*d/(c^2*e*x^2+c^2*d)+1/2*a/e^3*ln(c^2*e*x^2+c^2*d)-1/4*c^4*b*arctan(c*x)*d^2/e^3/(c^2*e*x^2+c^2*d)^2+c^2*b*arctan(c*x)/e^3*d/(c^2*e*x^2+c^2*d)+1/2*b*arctan(c*x)/e^3*ln(c^2*e*x^2+c^2*d)-1/8*c^5*b/e^2*d^2/(c^2*d-e)^2*x/(c^2*e*x^2+c^2*d)+1/8*c^3*b/e*d/(c^2*d-e)^2*x/(c^2*e*x^2+c^2*d)+5/8*c^3*b/e^2*d^2/(c^2*d-e)^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-7/8*c*b/e*d/(c^2*d-e)^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-3/4*b*c^4*d^2*arctan(c*x)/(c^2*d-e)^2/e^3+c^2*b/e^2*d/(c^2*d-e)^2*arctan(c*x)+1/4*I*b/e^3*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))-1/4*I*b/e^3*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/e^3*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))+1/4*I*b/e^3*ln(c^2*e*x^2+c^2*d)*ln(c*x-I)+1/4*I*b/e^3*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/e^3*ln(c^2*e*x^2+c^2*d)*ln(I+c*x)+1/4*I*b/e^3*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))-1/4*I*b/e^3*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))-1/4*I*b/e^3*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/e^3*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))","C"
1166,1,297,114,0.054000," ","int(x^3*(a+b*arctan(c*x))/(e*x^2+d)^3,x)","\frac{c^{4} a d}{4 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{2} a}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{4} b \arctan \left(c x \right) d}{4 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{2} b \arctan \left(c x \right)}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{5} b d x}{8 e \left(c^{2} d -e \right)^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{3} b x}{8 \left(c^{2} d -e \right)^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{3} b d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 e \left(c^{2} d -e \right)^{2} \sqrt{d e}}+\frac{3 c b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \left(c^{2} d -e \right)^{2} \sqrt{d e}}+\frac{c^{4} b d \arctan \left(c x \right)}{4 e^{2} \left(c^{2} d -e \right)^{2}}-\frac{c^{2} b \arctan \left(c x \right)}{2 e \left(c^{2} d -e \right)^{2}}"," ",0,"1/4*c^4*a/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*a/e^2/(c^2*e*x^2+c^2*d)+1/4*c^4*b*arctan(c*x)/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*b*arctan(c*x)/e^2/(c^2*e*x^2+c^2*d)+1/8*c^5*b/e*d/(c^2*d-e)^2*x/(c^2*e*x^2+c^2*d)-1/8*c^3*b/(c^2*d-e)^2*x/(c^2*e*x^2+c^2*d)-1/8*c^3*b/e*d/(c^2*d-e)^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+3/8*c*b/(c^2*d-e)^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/4*c^4*b/e^2*d/(c^2*d-e)^2*arctan(c*x)-1/2*c^2*b/e/(c^2*d-e)^2*arctan(c*x)","B"
1167,1,216,118,0.050000," ","int(x*(a+b*arctan(c*x))/(e*x^2+d)^3,x)","-\frac{c^{4} a}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{4} b \arctan \left(c x \right)}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{5} b x}{8 \left(c^{2} d -e \right)^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{3} b e x}{8 \left(c^{2} d -e \right)^{2} d \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{3 c^{3} b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \left(c^{2} d -e \right)^{2} \sqrt{d e}}+\frac{c b e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \left(c^{2} d -e \right)^{2} d \sqrt{d e}}+\frac{b \,c^{4} \arctan \left(c x \right)}{4 \left(c^{2} d -e \right)^{2} e}"," ",0,"-1/4*c^4*a/e/(c^2*e*x^2+c^2*d)^2-1/4*c^4*b/e/(c^2*e*x^2+c^2*d)^2*arctan(c*x)-1/8*c^5*b/(c^2*d-e)^2*x/(c^2*e*x^2+c^2*d)+1/8*c^3*b*e/(c^2*d-e)^2*x/d/(c^2*e*x^2+c^2*d)-3/8*c^3*b/(c^2*d-e)^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/8*c*b*e/(c^2*d-e)^2/d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/4*b*c^4*arctan(c*x)/(c^2*d-e)^2/e","A"
1168,1,1041,481,0.365000," ","int((a+b*arctan(c*x))/x/(e*x^2+d)^3,x)","\frac{b \,c^{2} \arctan \left(c x \right)}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{b \,c^{4} \arctan \left(c x \right)}{4 d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{3}}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{3}}-\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{3}}-\frac{i b \dilog \left(-i c x +1\right)}{2 d^{3}}-\frac{5 b c \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 d^{2} \left(c^{2} d -e \right)^{2} \sqrt{d e}}+\frac{b \,c^{5} e x}{8 \left(c^{2} d -e \right)^{2} d \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{b \,c^{3} e^{2} x}{8 d^{2} \left(c^{2} d -e \right)^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{7 b \,c^{3} e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \left(c^{2} d -e \right)^{2} d \sqrt{d e}}+\frac{i b \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{3}}+\frac{i b \dilog \left(i c x +1\right)}{2 d^{3}}-\frac{b \arctan \left(c x \right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{3}}+\frac{b \arctan \left(c x \right) \ln \left(c x \right)}{d^{3}}+\frac{a \,c^{2}}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \,c^{4}}{4 d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{a \ln \left(c x \right)}{d^{3}}+\frac{b \,c^{2} \arctan \left(c x \right) e}{2 d^{2} \left(c^{2} d -e \right)^{2}}-\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{3}}-\frac{3 b \,c^{4} \arctan \left(c x \right)}{4 d \left(c^{2} d -e \right)^{2}}+\frac{i b \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d^{3}}-\frac{i b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d^{3}}+\frac{i b \ln \left(c x +i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 d^{3}}-\frac{i b \ln \left(c x -i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 d^{3}}-\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{3}}+\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{3}}-\frac{i b \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{3}}+\frac{i b \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{3}}"," ",0,"-1/4*I*b/d^3*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))+1/4*I*b/d^3*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))+1/2*I*b/d^3*ln(c*x)*ln(1+I*c*x)-1/2*I*b/d^3*ln(c*x)*ln(1-I*c*x)+1/4*I*b/d^3*ln(I+c*x)*ln(c^2*e*x^2+c^2*d)+1/2*b*c^2*arctan(c*x)/d^2/(c^2*e*x^2+c^2*d)+1/4*b*c^4*arctan(c*x)/d/(c^2*e*x^2+c^2*d)^2-1/4*I*b/d^3*ln(c*x-I)*ln(c^2*e*x^2+c^2*d)-1/4*I*b/d^3*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))+1/4*I*b/d^3*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-5/8*b*c/d^2/(c^2*d-e)^2*e^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/8*b*c^5*e/(c^2*d-e)^2*x/d/(c^2*e*x^2+c^2*d)-1/8*b*c^3/d^2*e^2/(c^2*d-e)^2*x/(c^2*e*x^2+c^2*d)+7/8*b*c^3*e/(c^2*d-e)^2/d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/4*I*b/d^3*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))+1/2*I*b/d^3*dilog(1+I*c*x)-1/2*b*arctan(c*x)/d^3*ln(c^2*e*x^2+c^2*d)+b*arctan(c*x)/d^3*ln(c*x)+1/2*a*c^2/d^2/(c^2*e*x^2+c^2*d)+1/4*a*c^4/d/(c^2*e*x^2+c^2*d)^2+1/4*I*b/d^3*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/d^3*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))-1/4*I*b/d^3*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))-1/2*I*b/d^3*dilog(1-I*c*x)+a/d^3*ln(c*x)+1/2*b*c^2/d^2/(c^2*d-e)^2*arctan(c*x)*e-1/2*a/d^3*ln(c^2*e*x^2+c^2*d)-3/4*b*c^4*arctan(c*x)/d/(c^2*d-e)^2","C"
1169,1,1128,539,0.377000," ","int((a+b*arctan(c*x))/x^3/(e*x^2+d)^3,x)","-\frac{c^{4} b \arctan \left(c x \right) e}{4 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{3 c^{2} b \arctan \left(c x \right) e^{2}}{2 d^{3} \left(c^{2} d -e \right)^{2}}-\frac{3 i b e \ln \left(c x \right) \ln \left(i c x +1\right)}{2 d^{4}}+\frac{3 i b e \ln \left(c x -i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 d^{4}}+\frac{3 i b e \ln \left(c x \right) \ln \left(-i c x +1\right)}{2 d^{4}}-\frac{3 i b e \ln \left(c x +i\right) \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{4 d^{4}}+\frac{3 i b e \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{4}}+\frac{3 i b e \ln \left(c x +i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{4}}-\frac{3 i b e \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{4}}-\frac{3 i b e \ln \left(c x -i\right) \ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{4}}+\frac{c^{3} b \,e^{3} x}{8 d^{3} \left(c^{2} d -e \right)^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{5} b \,e^{2} x}{8 d^{2} \left(c^{2} d -e \right)^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{9 c b \,e^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 d^{3} \left(c^{2} d -e \right)^{2} \sqrt{d e}}-\frac{11 c^{3} b \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 d^{2} \left(c^{2} d -e \right)^{2} \sqrt{d e}}+\frac{3 i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{4}}-\frac{3 i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{4}}-\frac{c^{4} a e}{4 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{2} a e}{d^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{6} b \arctan \left(c x \right)}{2 d \left(c^{2} d -e \right)^{2}}+\frac{3 b \arctan \left(c x \right) e \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{4}}-\frac{b \arctan \left(c x \right)}{2 d^{3} x^{2}}-\frac{3 a e \ln \left(c x \right)}{d^{4}}+\frac{3 a e \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{4}}-\frac{3 i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)-c x +i}{\RootOf \left(e \,\textit{\_Z}^{2}+2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =2\right)}\right)}{4 d^{4}}-\frac{b c}{2 d^{3} x}+\frac{9 b \,c^{4} e \arctan \left(c x \right)}{4 d^{2} \left(c^{2} d -e \right)^{2}}-\frac{3 i b e \dilog \left(i c x +1\right)}{2 d^{4}}+\frac{3 i b e \dilog \left(-i c x +1\right)}{2 d^{4}}+\frac{3 i b e \dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)-c x -i}{\RootOf \left(e \,\textit{\_Z}^{2}-2 i \textit{\_Z} e +c^{2} d -e , \mathit{index} =1\right)}\right)}{4 d^{4}}-\frac{c^{2} b \arctan \left(c x \right) e}{d^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{a}{2 d^{3} x^{2}}-\frac{3 b \arctan \left(c x \right) e \ln \left(c x \right)}{d^{4}}"," ",0,"-1/4*c^4*b*arctan(c*x)*e/d^2/(c^2*e*x^2+c^2*d)^2-3/2*c^2*b/d^3/(c^2*d-e)^2*arctan(c*x)*e^2+1/8*c^3*b/d^3*e^3/(c^2*d-e)^2*x/(c^2*e*x^2+c^2*d)-1/8*c^5*b/d^2*e^2/(c^2*d-e)^2*x/(c^2*e*x^2+c^2*d)+9/8*c*b/d^3*e^3/(c^2*d-e)^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-11/8*c^3*b/d^2/(c^2*d-e)^2*e^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+3/4*I*b/d^4*e*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))-3/4*I*b/d^4*e*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))-3/4*I*b/d^4*e*dilog((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))-3/2*I*b/d^4*e*dilog(1+I*c*x)+3/2*I*b/d^4*e*dilog(1-I*c*x)+3/4*I*b/d^4*e*dilog((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))-1/4*c^4*a*e/d^2/(c^2*e*x^2+c^2*d)^2-c^2*a*e/d^3/(c^2*e*x^2+c^2*d)-1/2*c^6*b/d/(c^2*d-e)^2*arctan(c*x)+3/2*b*arctan(c*x)*e/d^4*ln(c^2*e*x^2+c^2*d)-1/2*b*arctan(c*x)/d^3/x^2-3*a/d^4*e*ln(c*x)+3/2*a*e/d^4*ln(c^2*e*x^2+c^2*d)-1/2*b*c/d^3/x+3/4*I*b/d^4*e*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=1))+9/4*b*c^4*e*arctan(c*x)/d^2/(c^2*d-e)^2+3/4*I*b/d^4*e*ln(I+c*x)*ln((RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2)-c*x-I)/RootOf(e*_Z^2-2*I*_Z*e+c^2*d-e,index=2))-3/2*I*b/d^4*e*ln(c*x)*ln(1+I*c*x)-3/4*I*b/d^4*e*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=1))+3/4*I*b/d^4*e*ln(c*x-I)*ln(c^2*e*x^2+c^2*d)-c^2*b*arctan(c*x)*e/d^3/(c^2*e*x^2+c^2*d)-3/4*I*b/d^4*e*ln(c*x-I)*ln((RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2)-c*x+I)/RootOf(e*_Z^2+2*I*_Z*e+c^2*d-e,index=2))+3/2*I*b/d^4*e*ln(c*x)*ln(1-I*c*x)-3/4*I*b/d^4*e*ln(I+c*x)*ln(c^2*e*x^2+c^2*d)-1/2*a/d^3/x^2-3*b*arctan(c*x)/d^4*e*ln(c*x)","C"
1170,1,3801,750,1.080000," ","int(x^2*(a+b*arctan(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"1/16*I*c^3*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/e^2*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+1/16*I/c*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/d^2*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+1/8*a/d/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/8*c^4*a/(c^2*e*x^2+c^2*d)^2/d*x^3-1/16*b*(d*e)^(1/2)*e/d^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)-1/4*c*b/(c^4*d^2-2*c^2*d*e+e^2)*e/d/(c^2*d-e)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-1/16*c^7*b*d^2*arctan(c*x)^2/e^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/32/c*b*e^2*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/d^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/32*c^7*b*d^2*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/e^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+1/32*c^3*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/e^2*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+1/32/c*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/d^2*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+1/16/c*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/d^2*arctan(c*x)^2-1/8*c^7*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*d*x^2-1/8*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e*x^2-1/8*c^7*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e*x^4+1/16*c^3*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/e^2*arctan(c*x)^2-1/16*c^4*b*(d*e)^(1/2)/e^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)+1/4*I*c^5*b*d*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/e/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/8*I*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e^2/d*arctan(c*x)*x^4-1/8*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*d-3/16*c^3*b*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-3/8*c^3*b*arctan(c*x)^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/16*b*(d*e)^(1/2)/d^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)-1/8*c*b*(c^2*e*d)^(1/2)/d/e/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2+1/4*c*b*e*arctan(c*x)^2/d/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/16/c*b*e^2*arctan(c*x)^2/d^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/16*c^2*b*(d*e)^(1/2)/d*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)-1/16*c*b*(c^2*e*d)^(1/2)/d/e/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+1/4*c^5*b*d*arctan(c*x)^2/e/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/8*c^2*b*(d*e)^(1/2)/d/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)+1/4*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/e*d/(c^2*d-e)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+1/8*c^5*b*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/e/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)*d-1/16*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/e*d/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-1/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e*x+1/4*c^6*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*d*arctan(c*x)*x-1/8*c^4*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e*arctan(c*x)*x+1/8*c^8*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*d*arctan(c*x)*x^3-1/4*c^6*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e*arctan(c*x)*x^3+1/16*c^4*b*(d*e)^(1/2)/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)+1/16*c*b/(c^4*d^2-2*c^2*d*e+e^2)*e/d/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+1/8*c*b*e*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/d/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-3/8*I*c^3*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/8*I*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*d*arctan(c*x)-1/8*I*c*b*(c^2*e*d)^(1/2)/d/e/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+1/4*I*c*b*e*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/d/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/16*I/c*b*e^2*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/d^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/16*I*c^7*b*d^2*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/e^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-1/8*c^8*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2/e*d^2*arctan(c*x)*x+1/8*c^4*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e^2/d*arctan(c*x)*x^3+1/16*c^6*b*(d*e)^(1/2)*d/e^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)-1/8*I*c^7*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e*arctan(c*x)*x^4-1/4*I*c^7*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*d*arctan(c*x)*x^2-1/4*I*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e*arctan(c*x)*x^2-1/8*I*c^7*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2/e*d^2*arctan(c*x)","B"
1171,1,4027,681,1.989000," ","int((a+b*arctan(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"1/8*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e+3/8*c^2*a/d^2*x/(c^2*e*x^2+c^2*d)+5/16*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-5/4*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+3/8*c^5*b*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+3/4*c^5*b*arctan(c*x)^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+3/4*c*b*e^2*arctan(c*x)^2/d^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+3/8*c*b*e^2*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/d^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+3/16*c^4*b*(d*e)^(1/2)/d*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)-3/16*b*(d*e)^(1/2)/d^3*e^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)-3/8*I*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e*arctan(c*x)+3/8*a/d^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/8*c^7*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e*x^2-3/16*c*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/d^2*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))-3/8*c*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/d^2*arctan(c*x)^2+1/8*c^2*b*(d*e)^(1/2)/d^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)-3/16*b*(d*e)^(1/2)/d^3*e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)+1/4*c^4*a*x/d/(c^2*e*x^2+c^2*d)^2+5/8*I*c^7*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*d*arctan(c*x)+3/4*I*c^5*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+1/8*c^7*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2/d*x^4*e^2+1/8*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2/d*x^2*e^2+3/32*c^3*b*(c^2*e*d)^(1/2)/d/e/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))-3/16*c^7*b*d*arctan(c*x)^2/e/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+2*c^3*b/(c^4*d^2-2*c^2*d*e+e^2)*e/d/(c^2*d-e)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+3/16/c*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/d^3*e*arctan(c*x)^2-3/16/c*b*e^3*arctan(c*x)^2/d^3/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-3/32/c*b*e^3*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/d^3/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+3/32/c*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/d^3*e*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))-3/32*c^7*b*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/e/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)*d-5/16*c^6*b*(d*e)^(1/2)/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)-1/2*c^3*b/(c^4*d^2-2*c^2*d*e+e^2)*e/d/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)-9/16*c^3*b*e*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))/d/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+3/16*c^3*b*(c^2*e*d)^(1/2)/d/e/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2-9/8*c^3*b*e*arctan(c*x)^2/d/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+5/16*c^4*b*(d*e)^(1/2)/d/e*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)-3/4*c*b/(c^4*d^2-2*c^2*d*e+e^2)/d^2*e^2/(c^2*d-e)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+5/8*c^8*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*d*arctan(c*x)*x-5/4*c^6*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e*arctan(c*x)*x+3/8*c^8*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e*arctan(c*x)*x^3+3/16*c*b/(c^4*d^2-2*c^2*d*e+e^2)/d^2*e^2/(c^2*d-e)*ln((1+I*c*x)^4/(c^2*x^2+1)^2*c^2*d+2*c^2*d*(1+I*c*x)^2/(c^2*x^2+1)-(1+I*c*x)^4/(c^2*x^2+1)^2*e+c^2*d+2*(1+I*c*x)^2/(c^2*x^2+1)*e-e)+3/4*I*c*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)*e^2/d^2/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)-9/8*I*c^3*b*e*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/d/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+3/16*I*c^3*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/e/d*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))-3/16*I*c^7*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/e/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)*d+5/8*I*c^7*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2/d*arctan(c*x)*x^4*e^2-3/8*I*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2/d^2*arctan(c*x)*x^4*e^3-3/4*I*c^5*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2/d*arctan(c*x)*x^2*e^2-3/16*I/c*b*e^3*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/d^3/(c^4*d^2-2*c^2*d*e+e^2)^2*(c^2*e*d)^(1/2)+3/16*I/c*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/d^3*e*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+5/16*c^2*b*(d*e)^(1/2)*e/d^2*arctanh(1/4*(2*(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)+2*c^2*d+2*e)/c/(d*e)^(1/2))/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*d-e)+3/8*c^4*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2/d^2*arctan(c*x)*x^3*e^3+5/8*c^4*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2/d*arctan(c*x)*x*e^2-3/4*c^6*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*e^2/d*arctan(c*x)*x^3-3/8*I*c*b*(c^2*e*d)^(1/2)/(c^4*d^2-2*c^2*d*e+e^2)/d^2*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))+5/4*I*c^7*b/(c^4*d^2-2*c^2*d*e+e^2)/(c^2*e*x^2+c^2*d)^2*arctan(c*x)*x^2*e","B"
1172,1,6655,1166,1.378000," ","int((a+b*arctan(c*x))/x^2/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
1173,0,0,191,1.339000," ","int(x^3*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x)","\int x^{3} \sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^3*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x)","F"
1174,0,0,78,1.132000," ","int(x^2*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x)","\int x^{2} \sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^2*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x)","F"
1175,0,0,116,1.037000," ","int(x*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x)","\int x \sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x)","F"
1176,0,0,20,2.385000," ","int((e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x)","\int \sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int((e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x)","F"
1177,0,0,53,1.172000," ","int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x,x)","\int \frac{\sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)}{x}\, dx"," ",0,"int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x,x)","F"
1178,0,0,57,1.162000," ","int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^2,x)","\int \frac{\sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)}{x^{2}}\, dx"," ",0,"int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^2,x)","F"
1179,0,0,58,1.125000," ","int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^3,x)","\int \frac{\sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)}{x^{3}}\, dx"," ",0,"int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^3,x)","F"
1180,0,0,113,1.199000," ","int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^4,x)","\int \frac{\sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)}{x^{4}}\, dx"," ",0,"int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^4,x)","F"
1181,0,0,79,1.142000," ","int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^5,x)","\int \frac{\sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)}{x^{5}}\, dx"," ",0,"int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^5,x)","F"
1182,0,0,263,1.233000," ","int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^6,x)","\int \frac{\sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)}{x^{6}}\, dx"," ",0,"int((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^6,x)","F"
1183,0,0,243,1.107000," ","int(x^3*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x)","\int x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^3*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x)","F"
1184,0,0,96,1.076000," ","int(x^2*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x)","\int x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^2*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x)","F"
1185,0,0,153,0.967000," ","int(x*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x)","\int x \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x)","F"
1186,0,0,20,2.060000," ","int((e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x)","\int \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x)","F"
1187,0,0,66,1.096000," ","int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)}{x}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x,x)","F"
1188,0,0,73,1.140000," ","int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^2,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)}{x^{2}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^2,x)","F"
1189,0,0,71,1.037000," ","int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^3,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)}{x^{3}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^3,x)","F"
1190,0,0,73,1.089000," ","int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^4,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)}{x^{4}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^4,x)","F"
1191,0,0,76,1.062000," ","int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^5,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)}{x^{5}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^5,x)","F"
1192,0,0,150,1.184000," ","int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^6,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)}{x^{6}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^6,x)","F"
1193,0,0,305,1.154000," ","int(x^3*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x)","\int x^{3} \left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^3*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x)","F"
1194,0,0,114,1.107000," ","int(x^2*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x)","\int x^{2} \left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^2*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x)","F"
1195,0,0,201,0.967000," ","int(x*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x)","\int x \left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x)","F"
1196,0,0,20,2.100000," ","int((e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x)","\int \left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int((e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x)","F"
1197,0,0,81,1.106000," ","int((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arctan \left(c x \right)\right)}{x}\, dx"," ",0,"int((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x,x)","F"
1198,0,0,90,1.111000," ","int((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^2,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arctan \left(c x \right)\right)}{x^{2}}\, dx"," ",0,"int((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^2,x)","F"
1199,0,0,85,1.085000," ","int((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^3,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arctan \left(c x \right)\right)}{x^{3}}\, dx"," ",0,"int((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^3,x)","F"
1200,0,0,91,1.079000," ","int((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^4,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arctan \left(c x \right)\right)}{x^{4}}\, dx"," ",0,"int((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^4,x)","F"
1201,0,0,150,1.224000," ","int(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{3} \left(a +b \arctan \left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x)","F"
1202,0,0,60,1.164000," ","int(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{2} \left(a +b \arctan \left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x)","F"
1203,0,0,89,1.056000," ","int(x*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x \left(a +b \arctan \left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x)","F"
1204,0,0,20,2.128000," ","int((a+b*arctan(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{a +b \arctan \left(c x \right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arctan(c*x))/(e*x^2+d)^(1/2),x)","F"
1205,0,0,42,1.142000," ","int((a+b*arctan(c*x))/x/(e*x^2+d)^(1/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arctan(c*x))/x/(e*x^2+d)^(1/2),x)","F"
1206,0,0,86,1.213000," ","int((a+b*arctan(c*x))/x^2/(e*x^2+d)^(1/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x^{2} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arctan(c*x))/x^2/(e*x^2+d)^(1/2),x)","F"
1207,0,0,61,1.148000," ","int((a+b*arctan(c*x))/x^3/(e*x^2+d)^(1/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x^{3} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arctan(c*x))/x^3/(e*x^2+d)^(1/2),x)","F"
1208,0,0,151,1.256000," ","int((a+b*arctan(c*x))/x^4/(e*x^2+d)^(1/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x^{4} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arctan(c*x))/x^4/(e*x^2+d)^(1/2),x)","F"
1209,0,0,121,1.122000," ","int(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{3} \left(a +b \arctan \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x)","F"
1210,0,0,58,1.127000," ","int(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{2} \left(a +b \arctan \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x)","F"
1211,0,0,65,0.993000," ","int(x*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x \left(a +b \arctan \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x)","F"
1212,0,0,62,2.142000," ","int((a+b*arctan(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{a +b \arctan \left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arctan(c*x))/(e*x^2+d)^(3/2),x)","F"
1213,0,0,56,1.110000," ","int((a+b*arctan(c*x))/x/(e*x^2+d)^(3/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arctan(c*x))/x/(e*x^2+d)^(3/2),x)","F"
1214,0,0,121,1.040000," ","int((a+b*arctan(c*x))/x^2/(e*x^2+d)^(3/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arctan(c*x))/x^2/(e*x^2+d)^(3/2),x)","F"
1215,0,0,77,1.054000," ","int((a+b*arctan(c*x))/x^3/(e*x^2+d)^(3/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arctan(c*x))/x^3/(e*x^2+d)^(3/2),x)","F"
1216,0,0,212,1.095000," ","int((a+b*arctan(c*x))/x^4/(e*x^2+d)^(3/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x^{4} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arctan(c*x))/x^4/(e*x^2+d)^(3/2),x)","F"
1217,0,0,76,1.263000," ","int(x^4*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{4} \left(a +b \arctan \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^4*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","F"
1218,0,0,127,1.041000," ","int(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{3} \left(a +b \arctan \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","F"
1219,0,0,93,1.099000," ","int(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{2} \left(a +b \arctan \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","F"
1220,0,0,97,0.925000," ","int(x*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x \left(a +b \arctan \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","F"
1221,0,0,124,1.995000," ","int((a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{a +b \arctan \left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","F"
1222,0,0,71,1.025000," ","int((a+b*arctan(c*x))/x/(e*x^2+d)^(5/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arctan(c*x))/x/(e*x^2+d)^(5/2),x)","F"
1223,0,0,242,1.041000," ","int((a+b*arctan(c*x))/x^2/(e*x^2+d)^(5/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x^{2} \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arctan(c*x))/x^2/(e*x^2+d)^(5/2),x)","F"
1224,0,0,93,1.019000," ","int((a+b*arctan(c*x))/x^3/(e*x^2+d)^(5/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x^{3} \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arctan(c*x))/x^3/(e*x^2+d)^(5/2),x)","F"
1225,0,0,368,1.064000," ","int((a+b*arctan(c*x))/x^4/(e*x^2+d)^(5/2),x)","\int \frac{a +b \arctan \left(c x \right)}{x^{4} \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arctan(c*x))/x^4/(e*x^2+d)^(5/2),x)","F"
1226,0,0,180,1.283000," ","int(arctan(a*x)/(d*x^2+c)^(7/2),x)","\int \frac{\arctan \left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{7}{2}}}\, dx"," ",0,"int(arctan(a*x)/(d*x^2+c)^(7/2),x)","F"
1227,0,0,257,1.200000," ","int(arctan(a*x)/(d*x^2+c)^(9/2),x)","\int \frac{\arctan \left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{9}{2}}}\, dx"," ",0,"int(arctan(a*x)/(d*x^2+c)^(9/2),x)","F"
1228,0,0,376,1.936000," ","int(x^m*(e*x^2+d)^3*(a+b*arctan(c*x)),x)","\int x^{m} \left(e \,x^{2}+d \right)^{3} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^m*(e*x^2+d)^3*(a+b*arctan(c*x)),x)","F"
1229,0,0,228,1.541000," ","int(x^m*(e*x^2+d)^2*(a+b*arctan(c*x)),x)","\int x^{m} \left(e \,x^{2}+d \right)^{2} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^m*(e*x^2+d)^2*(a+b*arctan(c*x)),x)","F"
1230,0,0,120,1.234000," ","int(x^m*(e*x^2+d)*(a+b*arctan(c*x)),x)","\int x^{m} \left(e \,x^{2}+d \right) \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^m*(e*x^2+d)*(a+b*arctan(c*x)),x)","F"
1231,0,0,60,2.009000," ","int(x^m*(a+b*arctan(c*x))/(e*x^2+d),x)","\int \frac{x^{m} \left(a +b \arctan \left(c x \right)\right)}{e \,x^{2}+d}\, dx"," ",0,"int(x^m*(a+b*arctan(c*x))/(e*x^2+d),x)","F"
1232,0,0,60,1.134000," ","int(x^m*(a+b*arctan(c*x))/(e*x^2+d)^2,x)","\int \frac{x^{m} \left(a +b \arctan \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^m*(a+b*arctan(c*x))/(e*x^2+d)^2,x)","F"
1233,0,0,69,1.102000," ","int(x^m*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x)","\int x^{m} \left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^m*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x)","F"
1234,0,0,69,1.016000," ","int(x^m*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x)","\int x^{m} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^m*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x)","F"
1235,0,0,69,1.107000," ","int(x^m*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x)","\int x^{m} \sqrt{e \,x^{2}+d}\, \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^m*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x)","F"
1236,0,0,69,1.095000," ","int(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{m} \left(a +b \arctan \left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x)","F"
1237,0,0,67,1.027000," ","int(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{m} \left(a +b \arctan \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x)","F"
1238,0,0,69,1.030000," ","int(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{m} \left(a +b \arctan \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x)","F"
1239,0,0,72,1.467000," ","int(x^m*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","\int x^{m} \left(e \,x^{2}+d \right)^{p} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^m*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","F"
1240,0,0,76,1.609000," ","int(x^(-2-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","\int x^{-2-2 p} \left(e \,x^{2}+d \right)^{p} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^(-2-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","F"
1241,0,0,119,1.517000," ","int(x^(-3-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","\int x^{-3-2 p} \left(e \,x^{2}+d \right)^{p} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^(-3-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","F"
1242,0,0,76,1.498000," ","int(x^(-4-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","\int x^{-4-2 p} \left(e \,x^{2}+d \right)^{p} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^(-4-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","F"
1243,0,0,267,1.554000," ","int(x^(-5-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","\int x^{-5-2 p} \left(e \,x^{2}+d \right)^{p} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^(-5-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","F"
1244,0,0,76,1.503000," ","int(x^(-6-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","\int x^{-6-2 p} \left(e \,x^{2}+d \right)^{p} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^(-6-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","F"
1245,0,0,448,1.461000," ","int(x^(-7-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","\int x^{-7-2 p} \left(e \,x^{2}+d \right)^{p} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^(-7-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","F"
1246,0,0,76,1.435000," ","int(x^(-8-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","\int x^{-8-2 p} \left(e \,x^{2}+d \right)^{p} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int(x^(-8-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x)","F"
1247,1,329,239,0.052000," ","int(x^3*(e*x^2+d)*(a+b*arctan(c*x))^2,x)","\frac{b^{2} \arctan \left(c x \right)^{2} e \,x^{6}}{6}+\frac{b^{2} \arctan \left(c x \right)^{2} e}{6 c^{6}}-\frac{b^{2} \arctan \left(c x \right)^{2} d}{4 c^{4}}+\frac{b^{2} \arctan \left(c x \right)^{2} x^{4} d}{4}-\frac{a b d \,x^{3}}{6 c}-\frac{4 b^{2} e \,x^{2}}{45 c^{4}}+\frac{b^{2} e \,x^{4}}{60 c^{2}}+\frac{a b d x}{2 c^{3}}+\frac{b^{2} d x \arctan \left(c x \right)}{2 c^{3}}+\frac{b^{2} d \,x^{2}}{12 c^{2}}-\frac{b^{2} d \ln \left(c^{2} x^{2}+1\right)}{3 c^{4}}+\frac{23 b^{2} e \ln \left(c^{2} x^{2}+1\right)}{90 c^{6}}-\frac{a b e x}{3 c^{5}}-\frac{b^{2} e x \arctan \left(c x \right)}{3 c^{5}}+\frac{a b \arctan \left(c x \right) e \,x^{6}}{3}+\frac{a b \arctan \left(c x \right) x^{4} d}{2}+\frac{b^{2} \arctan \left(c x \right) x^{3} e}{9 c^{3}}-\frac{a b e \,x^{5}}{15 c}+\frac{a b \,x^{3} e}{9 c^{3}}-\frac{b^{2} \arctan \left(c x \right) d \,x^{3}}{6 c}-\frac{b^{2} \arctan \left(c x \right) e \,x^{5}}{15 c}-\frac{a b \arctan \left(c x \right) d}{2 c^{4}}+\frac{a b \arctan \left(c x \right) e}{3 c^{6}}+\frac{a^{2} e \,x^{6}}{6}+\frac{a^{2} x^{4} d}{4}"," ",0,"1/6*b^2*arctan(c*x)^2*e*x^6+1/6/c^6*b^2*arctan(c*x)^2*e-1/4/c^4*b^2*arctan(c*x)^2*d+1/4*b^2*arctan(c*x)^2*x^4*d-1/6/c*a*b*d*x^3-4/45*b^2*e*x^2/c^4+1/60*b^2*e*x^4/c^2+1/2*a*b*d*x/c^3+1/2*b^2*d*x*arctan(c*x)/c^3+1/12*b^2*d*x^2/c^2-1/3*b^2*d*ln(c^2*x^2+1)/c^4+23/90*b^2*e*ln(c^2*x^2+1)/c^6-1/3*a*b*e*x/c^5-1/3*b^2*e*x*arctan(c*x)/c^5+1/3*a*b*arctan(c*x)*e*x^6+1/2*a*b*arctan(c*x)*x^4*d+1/9/c^3*b^2*arctan(c*x)*x^3*e-1/15/c*a*b*e*x^5+1/9/c^3*a*b*x^3*e-1/6/c*b^2*arctan(c*x)*d*x^3-1/15/c*b^2*arctan(c*x)*e*x^5-1/2/c^4*a*b*arctan(c*x)*d+1/3/c^6*a*b*arctan(c*x)*e+1/6*a^2*e*x^6+1/4*a^2*x^4*d","A"
1248,1,667,283,0.169000," ","int(x^2*(e*x^2+d)*(a+b*arctan(c*x))^2,x)","\frac{a^{2} e \,x^{5}}{5}+\frac{a^{2} d \,x^{3}}{3}-\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d}{6 c^{3}}+\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d}{6 c^{3}}-\frac{i b^{2} \ln \left(c x -i\right)^{2} d}{12 c^{3}}+\frac{i b^{2} \ln \left(c x +i\right)^{2} d}{12 c^{3}}-\frac{i b^{2} \ln \left(c x +i\right)^{2} e}{20 c^{5}}+\frac{i b^{2} \ln \left(c x -i\right)^{2} e}{20 c^{5}}+\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) e}{10 c^{5}}-\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) e}{10 c^{5}}-\frac{3 b^{2} e x}{10 c^{4}}+\frac{b^{2} e \,x^{3}}{30 c^{2}}+\frac{3 b^{2} e \arctan \left(c x \right)}{10 c^{5}}-\frac{i b^{2} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right) d}{6 c^{3}}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) e}{10 c^{5}}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d}{6 c^{3}}+\frac{i b^{2} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right) e}{10 c^{5}}+\frac{b^{2} d x}{3 c^{2}}-\frac{b^{2} d \arctan \left(c x \right)}{3 c^{3}}-\frac{b^{2} \arctan \left(c x \right) e \,x^{4}}{10 c}+\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) d}{6 c^{3}}-\frac{i b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right) d}{6 c^{3}}+\frac{i b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right) e}{10 c^{5}}-\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) e}{10 c^{5}}+\frac{b^{2} \arctan \left(c x \right)^{2} d \,x^{3}}{3}+\frac{b^{2} \arctan \left(c x \right)^{2} e \,x^{5}}{5}+\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d}{3 c^{3}}+\frac{b^{2} \arctan \left(c x \right) x^{2} e}{5 c^{3}}+\frac{a b \ln \left(c^{2} x^{2}+1\right) d}{3 c^{3}}-\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) e}{5 c^{5}}-\frac{a b \ln \left(c^{2} x^{2}+1\right) e}{5 c^{5}}-\frac{a b e \,x^{4}}{10 c}+\frac{a b \,x^{2} e}{5 c^{3}}-\frac{a b d \,x^{2}}{3 c}+\frac{2 a b \arctan \left(c x \right) d \,x^{3}}{3}+\frac{2 a b \arctan \left(c x \right) e \,x^{5}}{5}-\frac{b^{2} \arctan \left(c x \right) d \,x^{2}}{3 c}"," ",0,"1/5*a^2*e*x^5+1/3*a^2*d*x^3-3/10*b^2*e*x/c^4+1/30*b^2*e*x^3/c^2+3/10*b^2*e*arctan(c*x)/c^5+1/10*I/c^5*b^2*ln(I+c*x)*ln(c^2*x^2+1)*e-1/10*I/c^5*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*e+1/3*b^2*d*x/c^2+1/6*I/c^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*d-1/3*b^2*d*arctan(c*x)/c^3-1/6*I/c^3*b^2*ln(I+c*x)*ln(c^2*x^2+1)*d-1/6*I/c^3*b^2*ln(-1/2*I*(I+c*x))*ln(c*x-I)*d-1/10*I/c^5*b^2*ln(c^2*x^2+1)*ln(c*x-I)*e+1/6*I/c^3*b^2*ln(c^2*x^2+1)*ln(c*x-I)*d+1/10*I/c^5*b^2*ln(-1/2*I*(I+c*x))*ln(c*x-I)*e-1/10/c*b^2*arctan(c*x)*e*x^4+1/3*b^2*arctan(c*x)^2*d*x^3+1/5*b^2*arctan(c*x)^2*e*x^5+1/3/c^3*b^2*arctan(c*x)*ln(c^2*x^2+1)*d+1/5/c^3*b^2*arctan(c*x)*x^2*e+1/3/c^3*a*b*ln(c^2*x^2+1)*d-1/5/c^5*b^2*arctan(c*x)*ln(c^2*x^2+1)*e-1/5/c^5*a*b*ln(c^2*x^2+1)*e-1/10/c*a*b*e*x^4+1/5/c^3*a*b*x^2*e-1/3/c*a*b*d*x^2+1/10*I/c^5*b^2*dilog(-1/2*I*(I+c*x))*e-1/10*I/c^5*b^2*dilog(1/2*I*(c*x-I))*e+2/3*a*b*arctan(c*x)*d*x^3+2/5*a*b*arctan(c*x)*e*x^5-1/3/c*b^2*arctan(c*x)*d*x^2-1/6*I/c^3*b^2*dilog(-1/2*I*(I+c*x))*d-1/12*I/c^3*b^2*ln(c*x-I)^2*d+1/12*I/c^3*b^2*ln(I+c*x)^2*d+1/6*I/c^3*b^2*dilog(1/2*I*(c*x-I))*d-1/20*I/c^5*b^2*ln(I+c*x)^2*e+1/20*I/c^5*b^2*ln(c*x-I)^2*e","B"
1249,1,249,179,0.052000," ","int(x*(e*x^2+d)*(a+b*arctan(c*x))^2,x)","\frac{a^{2} e \,x^{4}}{4}+\frac{a^{2} x^{2} d}{2}+\frac{b^{2} \arctan \left(c x \right)^{2} e \,x^{4}}{4}+\frac{b^{2} \arctan \left(c x \right)^{2} d \,x^{2}}{2}-\frac{b^{2} \arctan \left(c x \right) x^{3} e}{6 c}-\frac{b^{2} d x \arctan \left(c x \right)}{c}+\frac{b^{2} e x \arctan \left(c x \right)}{2 c^{3}}+\frac{b^{2} \arctan \left(c x \right)^{2} d}{2 c^{2}}-\frac{b^{2} \arctan \left(c x \right)^{2} e}{4 c^{4}}+\frac{b^{2} e \,x^{2}}{12 c^{2}}+\frac{b^{2} d \ln \left(c^{2} x^{2}+1\right)}{2 c^{2}}-\frac{b^{2} e \ln \left(c^{2} x^{2}+1\right)}{3 c^{4}}+\frac{a b \arctan \left(c x \right) e \,x^{4}}{2}+a b \arctan \left(c x \right) d \,x^{2}-\frac{a b \,x^{3} e}{6 c}-\frac{a b d x}{c}+\frac{a b e x}{2 c^{3}}+\frac{a b \arctan \left(c x \right) d}{c^{2}}-\frac{a b \arctan \left(c x \right) e}{2 c^{4}}"," ",0,"1/4*a^2*e*x^4+1/2*a^2*x^2*d+1/4*b^2*arctan(c*x)^2*e*x^4+1/2*b^2*arctan(c*x)^2*d*x^2-1/6/c*b^2*arctan(c*x)*x^3*e-b^2*d*x*arctan(c*x)/c+1/2*b^2*e*x*arctan(c*x)/c^3+1/2/c^2*b^2*arctan(c*x)^2*d-1/4/c^4*b^2*arctan(c*x)^2*e+1/12*b^2*e*x^2/c^2+1/2*b^2*d*ln(c^2*x^2+1)/c^2-1/3*b^2*e*ln(c^2*x^2+1)/c^4+1/2*a*b*arctan(c*x)*e*x^4+a*b*arctan(c*x)*d*x^2-1/6/c*a*b*x^3*e-a*b*d*x/c+1/2*a*b*e*x/c^3+1/c^2*a*b*arctan(c*x)*d-1/2/c^4*a*b*arctan(c*x)*e","A"
1250,1,570,209,0.127000," ","int((e*x^2+d)*(a+b*arctan(c*x))^2,x)","a^{2} d x -\frac{i b^{2} \ln \left(c x -i\right)^{2} e}{12 c^{3}}-\frac{b^{2} e \arctan \left(c x \right)}{3 c^{3}}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) e}{6 c^{3}}+\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right) d}{2 c}-\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) d}{2 c}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d}{2 c}+\frac{b^{2} e x}{3 c^{2}}-\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right) e}{6 c^{3}}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) d}{2 c}+\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) e}{6 c^{3}}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) e}{6 c^{3}}+b^{2} \arctan \left(c x \right)^{2} d x +\frac{b^{2} \arctan \left(c x \right)^{2} x^{3} e}{3}+\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) e}{6 c^{3}}-\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) e}{6 c^{3}}-\frac{i b^{2} \ln \left(c x +i\right)^{2} d}{4 c}+\frac{i b^{2} \ln \left(c x -i\right)^{2} d}{4 c}+\frac{i b^{2} \ln \left(c x +i\right)^{2} e}{12 c^{3}}-\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d}{2 c}+\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d}{2 c}+\frac{a b \ln \left(c^{2} x^{2}+1\right) e}{3 c^{3}}-\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d}{c}-\frac{b^{2} \arctan \left(c x \right) x^{2} e}{3 c}-\frac{a b \ln \left(c^{2} x^{2}+1\right) d}{c}+2 a b \arctan \left(c x \right) d x +\frac{2 a b \arctan \left(c x \right) x^{3} e}{3}+\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) e}{3 c^{3}}-\frac{a b \,x^{2} e}{3 c}+\frac{a^{2} x^{3} e}{3}"," ",0,"a^2*d*x-1/6*I/c^3*b^2*ln(c^2*x^2+1)*ln(I+c*x)*e+1/6*I/c^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*e-1/6*I/c^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))*e-1/3*b^2*e*arctan(c*x)/c^3+1/3*b^2*e*x/c^2-1/2*I/c*b^2*dilog(1/2*I*(c*x-I))*d+b^2*arctan(c*x)^2*d*x+1/3*b^2*arctan(c*x)^2*x^3*e+1/2*I/c*b^2*dilog(-1/2*I*(I+c*x))*d+1/2*I/c*b^2*ln(c^2*x^2+1)*ln(I+c*x)*d-1/2*I/c*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*d-1/2*I/c*b^2*ln(c^2*x^2+1)*ln(c*x-I)*d+1/6*I/c^3*b^2*ln(c^2*x^2+1)*ln(c*x-I)*e+1/2*I/c*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))*d-1/4*I/c*b^2*ln(I+c*x)^2*d+1/4*I/c*b^2*ln(c*x-I)^2*d+1/12*I/c^3*b^2*ln(I+c*x)^2*e+1/6*I/c^3*b^2*dilog(1/2*I*(c*x-I))*e-1/6*I/c^3*b^2*dilog(-1/2*I*(I+c*x))*e-1/12*I/c^3*b^2*ln(c*x-I)^2*e+1/3/c^3*a*b*ln(c^2*x^2+1)*e-1/c*b^2*arctan(c*x)*ln(c^2*x^2+1)*d-1/3/c*b^2*arctan(c*x)*x^2*e-1/c*a*b*ln(c^2*x^2+1)*d+2*a*b*arctan(c*x)*d*x+2/3*a*b*arctan(c*x)*x^3*e+1/3/c^3*b^2*arctan(c*x)*ln(c^2*x^2+1)*e-1/3/c*a*b*x^2*e+1/3*a^2*x^3*e","B"
1251,1,1284,200,4.145000," ","int((e*x^2+d)*(a+b*arctan(c*x))^2/x,x)","-\frac{b^{2} e \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{2}}-b^{2} d \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)+b^{2} d \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+b^{2} d \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+2 b^{2} d \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+2 b^{2} d \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{b^{2} d \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}-i a b d \dilog \left(-i c x +1\right)+\frac{i b^{2} d \pi  \arctan \left(c x \right)^{2}}{2}+\frac{i b^{2} \arctan \left(c x \right) e}{c^{2}}+\frac{a b \arctan \left(c x \right) e}{c^{2}}-\frac{i b^{2} d \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{i b^{2} d \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i b^{2} d \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}-\frac{i b^{2} d \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{b^{2} \arctan \left(c x \right)^{2} e}{2 c^{2}}+\frac{b^{2} \arctan \left(c x \right)^{2} x^{2} e}{2}+b^{2} \arctan \left(c x \right)^{2} d \ln \left(c x \right)+a b \arctan \left(c x \right) x^{2} e +2 a b \arctan \left(c x \right) d \ln \left(c x \right)+\frac{i b^{2} d \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}+a^{2} d \ln \left(c x \right)+\frac{i b^{2} d \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{i b^{2} d \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}-\frac{i b^{2} d \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+i a b d \ln \left(c x \right) \ln \left(i c x +1\right)-i a b d \ln \left(c x \right) \ln \left(-i c x +1\right)-\frac{a b e x}{c}-\frac{b^{2} e x \arctan \left(c x \right)}{c}+i a b d \dilog \left(i c x +1\right)+i b^{2} d \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)-2 i b^{2} d \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 i b^{2} d \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{a^{2} x^{2} e}{2}"," ",0,"a*b/c^2*arctan(c*x)*e+1/2*b^2/c^2*arctan(c*x)^2*e+1/2*b^2*arctan(c*x)^2*x^2*e+b^2*arctan(c*x)^2*d*ln(c*x)-b^2/c^2*e*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-b^2*d*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+b^2*d*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2*d*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I*b^2*d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2*I*b^2*d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-1/2*I*b^2*d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+I*a*b*d*ln(c*x)*ln(1+I*c*x)-1/2*I*b^2*d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2*d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2*d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*I*b^2*d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+a*b*arctan(c*x)*x^2*e+2*a*b*arctan(c*x)*d*ln(c*x)+1/2*I*b^2*d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+a^2*d*ln(c*x)+2*b^2*d*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2*d*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*b^2*d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+I*a*b*d*dilog(1+I*c*x)+1/2*I*b^2*d*Pi*arctan(c*x)^2+I*b^2*d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+I*b^2/c^2*arctan(c*x)*e-2*I*b^2*d*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*b^2*d*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-I*a*b*d*dilog(1-I*c*x)-I*a*b*d*ln(c*x)*ln(1-I*c*x)-a*b*e*x/c-b^2*e*x*arctan(c*x)/c+1/2*a^2*x^2*e","C"
1252,1,597,164,0.145000," ","int((e*x^2+d)*(a+b*arctan(c*x))^2/x^2,x)","a^{2} e x -\frac{a^{2} d}{x}-i c \,b^{2} d \ln \left(c x \right) \ln \left(-i c x +1\right)+\frac{i c \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right) d}{2}+\frac{i c \,b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) d}{2}-\frac{i c \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) d}{2}+\frac{i c \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d}{2}-i c \,b^{2} d \dilog \left(-i c x +1\right)-\frac{i c \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d}{2}+\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) e}{2 c}+i c \,b^{2} d \dilog \left(i c x +1\right)-\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) e}{2 c}+\frac{i c \,b^{2} \ln \left(c x -i\right)^{2} d}{4}-\frac{i c \,b^{2} \ln \left(c x +i\right)^{2} d}{4}+\frac{i b^{2} \ln \left(c x -i\right)^{2} e}{4 c}-\frac{i b^{2} \ln \left(c x +i\right)^{2} e}{4 c}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) e}{2 c}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) e}{2 c}+\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right) e}{2 c}+i c \,b^{2} d \ln \left(c x \right) \ln \left(i c x +1\right)-\frac{i c \,b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d}{2}-\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) e}{2 c}-\frac{b^{2} \arctan \left(c x \right)^{2} d}{x}+b^{2} \arctan \left(c x \right)^{2} e x +2 c a b d \ln \left(c x \right)-c a b \ln \left(c^{2} x^{2}+1\right) d +2 c \,b^{2} \arctan \left(c x \right) d \ln \left(c x \right)-c \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d -\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) e}{c}-\frac{a b \ln \left(c^{2} x^{2}+1\right) e}{c}+2 a b \arctan \left(c x \right) e x -\frac{2 a b \arctan \left(c x \right) d}{x}"," ",0,"a^2*e*x-a^2*d/x-b^2*arctan(c*x)^2*d/x+b^2*arctan(c*x)^2*e*x+1/2*I*b^2/c*ln(c^2*x^2+1)*ln(I+c*x)*e-1/2*I*b^2/c*ln(c^2*x^2+1)*ln(c*x-I)*e+1/2*I*b^2/c*ln(c*x-I)*ln(-1/2*I*(I+c*x))*e+I*c*b^2*d*ln(c*x)*ln(1+I*c*x)-1/2*I*c*b^2*ln(c^2*x^2+1)*ln(c*x-I)*d-1/2*I*b^2/c*ln(I+c*x)*ln(1/2*I*(c*x-I))*e-I*c*b^2*d*ln(c*x)*ln(1-I*c*x)+1/2*I*c*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))*d+1/2*I*c*b^2*ln(c^2*x^2+1)*ln(I+c*x)*d-1/2*I*c*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*d+2*c*a*b*d*ln(c*x)-c*a*b*ln(c^2*x^2+1)*d+2*c*b^2*arctan(c*x)*d*ln(c*x)-c*b^2*arctan(c*x)*ln(c^2*x^2+1)*d-1/2*I*b^2/c*dilog(1/2*I*(c*x-I))*e+1/2*I*c*b^2*dilog(-1/2*I*(I+c*x))*d+1/4*I*c*b^2*ln(c*x-I)^2*d-1/4*I*c*b^2*ln(I+c*x)^2*d-I*c*b^2*d*dilog(1-I*c*x)-1/2*I*c*b^2*dilog(1/2*I*(c*x-I))*d+1/4*I*b^2/c*ln(c*x-I)^2*e+1/2*I*b^2/c*dilog(-1/2*I*(I+c*x))*e-1/4*I*b^2/c*ln(I+c*x)^2*e+I*c*b^2*d*dilog(1+I*c*x)-b^2/c*arctan(c*x)*ln(c^2*x^2+1)*e-a*b/c*ln(c^2*x^2+1)*e+2*a*b*arctan(c*x)*e*x-2*a*b*arctan(c*x)*d/x","B"
1253,1,1313,203,7.809000," ","int((e*x^2+d)*(a+b*arctan(c*x))^2/x^3,x)","a^{2} e \ln \left(c x \right)+i a b e \ln \left(c x \right) \ln \left(i c x +1\right)-i a b e \ln \left(c x \right) \ln \left(-i c x +1\right)+\frac{i b^{2} \arctan \left(c x \right)^{2} e \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3}}{2}+\frac{i b^{2} \arctan \left(c x \right)^{2} e \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3}}{2}-\frac{i b^{2} e \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+c^{2} b^{2} d \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}-1\right)+c^{2} b^{2} d \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-b^{2} e \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)+b^{2} e \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+b^{2} e \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{i b^{2} e \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i b^{2} \arctan \left(c x \right)^{2} e \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2}-\frac{i b^{2} e \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{i b^{2} e \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i b^{2} \arctan \left(c x \right)^{2} e \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)}{2}+i a b e \dilog \left(i c x +1\right)+i b^{2} e \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)-i a b e \dilog \left(-i c x +1\right)-2 i b^{2} e \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 i b^{2} e \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-i c^{2} b^{2} d \arctan \left(c x \right)+\frac{i b^{2} \arctan \left(c x \right)^{2} e \pi}{2}+2 b^{2} e \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+2 b^{2} e \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{b^{2} e \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}-\frac{a^{2} d}{2 x^{2}}-\frac{c a b d}{x}-\frac{c \,b^{2} d \arctan \left(c x \right)}{x}-c^{2} a b \arctan \left(c x \right) d +2 a b \arctan \left(c x \right) e \ln \left(c x \right)-\frac{a b \arctan \left(c x \right) d}{x^{2}}-\frac{c^{2} b^{2} \arctan \left(c x \right)^{2} d}{2}-\frac{b^{2} \arctan \left(c x \right)^{2} d}{2 x^{2}}+b^{2} \arctan \left(c x \right)^{2} e \ln \left(c x \right)"," ",0,"a^2*e*ln(c*x)+2*b^2*e*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2*e*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*b^2*e*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+I*a*b*e*ln(c*x)*ln(1+I*c*x)-I*a*b*e*ln(c*x)*ln(1-I*c*x)+1/2*I*b^2*arctan(c*x)^2*e*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3+1/2*I*b^2*arctan(c*x)^2*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3-1/2*I*b^2*e*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2*arctan(c*x)^2*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))-1/2*I*b^2*e*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2*arctan(c*x)^2*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))-1/2*I*b^2*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*a^2*d/x^2-c*a*b*d/x-c*b^2*d*arctan(c*x)/x-c^2*a*b*arctan(c*x)*d+I*a*b*e*dilog(1+I*c*x)+2*a*b*arctan(c*x)*e*ln(c*x)+I*b^2*e*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-a*b*arctan(c*x)*d/x^2-I*c^2*b^2*d*arctan(c*x)-I*a*b*e*dilog(1-I*c*x)+1/2*I*b^2*arctan(c*x)^2*e*Pi-2*I*b^2*e*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*b^2*e*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+c^2*b^2*d*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)+c^2*b^2*d*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*c^2*b^2*arctan(c*x)^2*d-1/2*b^2*arctan(c*x)^2*d/x^2-b^2*e*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+b^2*e*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2*e*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2*arctan(c*x)^2*e*ln(c*x)","C"
1254,1,621,448,0.058000," ","int(x^3*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x)","\frac{2 a b \,x^{3} d e}{9 c^{3}}-\frac{2 a b e d \,x^{5}}{15 c}+\frac{2 a b \arctan \left(c x \right) e d \,x^{6}}{3}+\frac{2 a b \arctan \left(c x \right) d e}{3 c^{6}}-\frac{2 b^{2} \arctan \left(c x \right) e d \,x^{5}}{15 c}+\frac{2 b^{2} \arctan \left(c x \right) x^{3} d e}{9 c^{3}}-\frac{2 a b d e x}{3 c^{5}}-\frac{2 b^{2} d e x \arctan \left(c x \right)}{3 c^{5}}+\frac{a b \,d^{2} x}{2 c^{3}}+\frac{b^{2} d^{2} x \arctan \left(c x \right)}{2 c^{3}}+\frac{b^{2} d^{2} x^{2}}{12 c^{2}}-\frac{b^{2} d^{2} \ln \left(c^{2} x^{2}+1\right)}{3 c^{4}}-\frac{22 b^{2} e^{2} \ln \left(c^{2} x^{2}+1\right)}{105 c^{8}}-\frac{a b \,e^{2} x^{7}}{28 c}-\frac{b^{2} \arctan \left(c x \right) d^{2} x^{3}}{6 c}-\frac{a b \arctan \left(c x \right) e^{2}}{4 c^{8}}+\frac{a b \arctan \left(c x \right) e^{2} x^{8}}{4}-\frac{a b \,d^{2} x^{3}}{6 c}+\frac{a b \,x^{5} e^{2}}{20 c^{3}}-\frac{a b \,x^{3} e^{2}}{12 c^{5}}+\frac{a b \,e^{2} x}{4 c^{7}}-\frac{8 b^{2} d e \,x^{2}}{45 c^{4}}+\frac{b^{2} d e \,x^{4}}{30 c^{2}}+\frac{b^{2} e^{2} x \arctan \left(c x \right)}{4 c^{7}}+\frac{71 b^{2} e^{2} x^{2}}{840 c^{6}}-\frac{3 b^{2} e^{2} x^{4}}{140 c^{4}}+\frac{b^{2} e^{2} x^{6}}{168 c^{2}}+\frac{b^{2} \arctan \left(c x \right) x^{5} e^{2}}{20 c^{3}}-\frac{b^{2} \arctan \left(c x \right) x^{3} e^{2}}{12 c^{5}}-\frac{a b \arctan \left(c x \right) d^{2}}{2 c^{4}}+\frac{b^{2} \arctan \left(c x \right)^{2} e d \,x^{6}}{3}+\frac{a b \arctan \left(c x \right) d^{2} x^{4}}{2}-\frac{b^{2} \arctan \left(c x \right) e^{2} x^{7}}{28 c}+\frac{b^{2} \arctan \left(c x \right)^{2} d e}{3 c^{6}}+\frac{b^{2} \arctan \left(c x \right)^{2} e^{2} x^{8}}{8}-\frac{b^{2} \arctan \left(c x \right)^{2} d^{2}}{4 c^{4}}-\frac{b^{2} \arctan \left(c x \right)^{2} e^{2}}{8 c^{8}}+\frac{a^{2} e d \,x^{6}}{3}+\frac{b^{2} \arctan \left(c x \right)^{2} d^{2} x^{4}}{4}+\frac{23 b^{2} d e \ln \left(c^{2} x^{2}+1\right)}{45 c^{6}}+\frac{a^{2} e^{2} x^{8}}{8}+\frac{a^{2} x^{4} d^{2}}{4}"," ",0,"2/9/c^3*a*b*x^3*d*e-2/15/c*a*b*e*d*x^5+2/3*a*b*arctan(c*x)*e*d*x^6+2/3/c^6*a*b*arctan(c*x)*d*e-2/15/c*b^2*arctan(c*x)*e*d*x^5+2/9/c^3*b^2*arctan(c*x)*x^3*d*e-2/3*a*b*d*e*x/c^5-2/3*b^2*d*e*x*arctan(c*x)/c^5+1/2*a*b*d^2*x/c^3+1/2*b^2*d^2*x*arctan(c*x)/c^3+1/12*b^2*d^2*x^2/c^2-1/3*b^2*d^2*ln(c^2*x^2+1)/c^4-22/105*b^2*e^2*ln(c^2*x^2+1)/c^8-1/28/c*a*b*e^2*x^7-1/6/c*b^2*arctan(c*x)*d^2*x^3-1/4/c^8*a*b*arctan(c*x)*e^2+1/4*a*b*arctan(c*x)*e^2*x^8-1/6/c*a*b*d^2*x^3+1/20/c^3*a*b*x^5*e^2-1/12/c^5*a*b*x^3*e^2+1/4*a*b*e^2*x/c^7-8/45*b^2*d*e*x^2/c^4+1/30*b^2*d*e*x^4/c^2+1/4*b^2*e^2*x*arctan(c*x)/c^7+71/840*b^2*e^2*x^2/c^6-3/140*b^2*e^2*x^4/c^4+1/168*b^2*e^2*x^6/c^2+1/20/c^3*b^2*arctan(c*x)*x^5*e^2-1/12/c^5*b^2*arctan(c*x)*x^3*e^2-1/2/c^4*a*b*arctan(c*x)*d^2+1/3*b^2*arctan(c*x)^2*e*d*x^6+1/2*a*b*arctan(c*x)*d^2*x^4-1/28/c*b^2*arctan(c*x)*e^2*x^7+1/3/c^6*b^2*arctan(c*x)^2*d*e+1/8*b^2*arctan(c*x)^2*e^2*x^8-1/4/c^4*b^2*arctan(c*x)^2*d^2-1/8/c^8*b^2*arctan(c*x)^2*e^2+1/3*a^2*e*d*x^6+1/4*b^2*arctan(c*x)^2*d^2*x^4+23/45*b^2*d*e*ln(c^2*x^2+1)/c^6+1/8*a^2*e^2*x^8+1/4*a^2*x^4*d^2","A"
1255,1,1158,514,0.137000," ","int(x^2*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x)","\frac{i b^{2} \ln \left(c x -i\right)^{2} d e}{10 c^{5}}+\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d e}{5 c^{5}}-\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d e}{5 c^{5}}-\frac{i b^{2} \ln \left(c x +i\right)^{2} d e}{10 c^{5}}-\frac{i b^{2} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right) d^{2}}{6 c^{3}}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) d^{2}}{6 c^{3}}+\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) d^{2}}{6 c^{3}}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d^{2}}{6 c^{3}}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) e^{2}}{14 c^{7}}-\frac{i b^{2} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right) e^{2}}{14 c^{7}}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) e^{2}}{14 c^{7}}+\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) e^{2}}{14 c^{7}}+\frac{a^{2} e^{2} x^{7}}{7}+\frac{a^{2} d^{2} x^{3}}{3}+\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d^{2}}{6 c^{3}}-\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d^{2}}{6 c^{3}}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) d e}{5 c^{5}}-\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) d e}{5 c^{5}}+\frac{i b^{2} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right) d e}{5 c^{5}}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d e}{5 c^{5}}-\frac{b^{2} \arctan \left(c x \right) e^{2} x^{6}}{21 c}-\frac{b^{2} \arctan \left(c x \right) x^{2} d^{2}}{3 c}-\frac{i b^{2} \ln \left(c x -i\right)^{2} e^{2}}{28 c^{7}}+\frac{i b^{2} \ln \left(c x +i\right)^{2} e^{2}}{28 c^{7}}-\frac{i b^{2} \ln \left(c x -i\right)^{2} d^{2}}{12 c^{3}}+\frac{i b^{2} \ln \left(c x +i\right)^{2} d^{2}}{12 c^{3}}+\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) e^{2}}{14 c^{7}}-\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) e^{2}}{14 c^{7}}-\frac{b^{2} \arctan \left(c x \right) x^{2} e^{2}}{7 c^{5}}+\frac{a b \,x^{4} e^{2}}{14 c^{3}}-\frac{a b \,x^{2} e^{2}}{7 c^{5}}+\frac{2 a b \arctan \left(c x \right) d^{2} x^{3}}{3}+\frac{2 b^{2} \arctan \left(c x \right)^{2} e d \,x^{5}}{5}+\frac{2 a b \arctan \left(c x \right) e^{2} x^{7}}{7}+\frac{b^{2} \arctan \left(c x \right)^{2} e^{2} x^{7}}{7}+\frac{2 a^{2} e d \,x^{5}}{5}+\frac{b^{2} \arctan \left(c x \right)^{2} d^{2} x^{3}}{3}+\frac{b^{2} d^{2} x}{3 c^{2}}+\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) e^{2}}{7 c^{7}}+\frac{a b \ln \left(c^{2} x^{2}+1\right) e^{2}}{7 c^{7}}+\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d^{2}}{3 c^{3}}+\frac{b^{2} \arctan \left(c x \right) x^{4} e^{2}}{14 c^{3}}+\frac{a b \ln \left(c^{2} x^{2}+1\right) d^{2}}{3 c^{3}}-\frac{a b \,x^{2} d^{2}}{3 c}-\frac{a b \,e^{2} x^{6}}{21 c}-\frac{3 b^{2} d e x}{5 c^{4}}+\frac{b^{2} d e \,x^{3}}{15 c^{2}}+\frac{3 b^{2} d e \arctan \left(c x \right)}{5 c^{5}}+\frac{11 b^{2} e^{2} x}{42 c^{6}}-\frac{5 b^{2} e^{2} x^{3}}{126 c^{4}}+\frac{b^{2} e^{2} x^{5}}{105 c^{2}}-\frac{11 b^{2} e^{2} \arctan \left(c x \right)}{42 c^{7}}+\frac{2 b^{2} \arctan \left(c x \right) x^{2} d e}{5 c^{3}}-\frac{b^{2} \arctan \left(c x \right) x^{4} d e}{5 c}-\frac{2 a b \ln \left(c^{2} x^{2}+1\right) d e}{5 c^{5}}+\frac{4 a b \arctan \left(c x \right) e d \,x^{5}}{5}-\frac{2 b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d e}{5 c^{5}}-\frac{a b \,x^{4} d e}{5 c}+\frac{2 a b \,x^{2} d e}{5 c^{3}}-\frac{b^{2} d^{2} \arctan \left(c x \right)}{3 c^{3}}"," ",0,"1/7*a^2*e^2*x^7+1/3*a^2*d^2*x^3+1/5*I/c^5*b^2*ln(c^2*x^2+1)*ln(I+c*x)*d*e-1/5*I/c^5*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*d*e+1/5*I/c^5*b^2*ln(-1/2*I*(I+c*x))*ln(c*x-I)*d*e-1/5*I/c^5*b^2*ln(c^2*x^2+1)*ln(c*x-I)*d*e-1/21/c*b^2*arctan(c*x)*e^2*x^6-1/3/c*b^2*arctan(c*x)*x^2*d^2+1/14*I/c^7*b^2*dilog(1/2*I*(c*x-I))*e^2-1/7/c^5*b^2*arctan(c*x)*x^2*e^2-1/28*I/c^7*b^2*ln(c*x-I)^2*e^2-1/14*I/c^7*b^2*dilog(-1/2*I*(I+c*x))*e^2+1/28*I/c^7*b^2*ln(I+c*x)^2*e^2-1/12*I/c^3*b^2*ln(c*x-I)^2*d^2+1/6*I/c^3*b^2*dilog(1/2*I*(c*x-I))*d^2+1/14/c^3*a*b*x^4*e^2-1/7/c^5*a*b*x^2*e^2+2/3*a*b*arctan(c*x)*d^2*x^3+2/5*b^2*arctan(c*x)^2*e*d*x^5+2/7*a*b*arctan(c*x)*e^2*x^7+1/7*b^2*arctan(c*x)^2*e^2*x^7+2/5*a^2*e*d*x^5+1/3*b^2*arctan(c*x)^2*d^2*x^3+1/3*b^2*d^2*x/c^2+1/7/c^7*b^2*arctan(c*x)*ln(c^2*x^2+1)*e^2+1/7/c^7*a*b*ln(c^2*x^2+1)*e^2+1/3/c^3*b^2*arctan(c*x)*ln(c^2*x^2+1)*d^2+1/14/c^3*b^2*arctan(c*x)*x^4*e^2+1/3/c^3*a*b*ln(c^2*x^2+1)*d^2+1/12*I/c^3*b^2*ln(I+c*x)^2*d^2-1/6*I/c^3*b^2*dilog(-1/2*I*(I+c*x))*d^2-1/3/c*a*b*x^2*d^2-1/21/c*a*b*e^2*x^6-3/5*b^2*d*e*x/c^4+1/15*b^2*d*e*x^3/c^2+3/5*b^2*d*e*arctan(c*x)/c^5+11/42*b^2*e^2*x/c^6-5/126*b^2*e^2*x^3/c^4+1/105*b^2*e^2*x^5/c^2-11/42*b^2*e^2*arctan(c*x)/c^7-1/10*I/c^5*b^2*ln(I+c*x)^2*d*e-1/6*I/c^3*b^2*ln(-1/2*I*(I+c*x))*ln(c*x-I)*d^2-1/6*I/c^3*b^2*ln(c^2*x^2+1)*ln(I+c*x)*d^2+1/6*I/c^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*d^2+1/6*I/c^3*b^2*ln(c^2*x^2+1)*ln(c*x-I)*d^2+1/5*I/c^5*b^2*dilog(-1/2*I*(I+c*x))*d*e+1/14*I/c^7*b^2*ln(c^2*x^2+1)*ln(c*x-I)*e^2-1/14*I/c^7*b^2*ln(-1/2*I*(I+c*x))*ln(c*x-I)*e^2-1/14*I/c^7*b^2*ln(c^2*x^2+1)*ln(I+c*x)*e^2+1/14*I/c^7*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*e^2+2/5/c^3*b^2*arctan(c*x)*x^2*d*e-1/5/c*b^2*arctan(c*x)*x^4*d*e-2/5/c^5*a*b*ln(c^2*x^2+1)*d*e+4/5*a*b*arctan(c*x)*e*d*x^5-2/5/c^5*b^2*arctan(c*x)*ln(c^2*x^2+1)*d*e-1/5/c*a*b*x^4*d*e+2/5/c^3*a*b*x^2*d*e+1/10*I/c^5*b^2*ln(c*x-I)^2*d*e-1/5*I/c^5*b^2*dilog(1/2*I*(c*x-I))*d*e-1/3*b^2*d^2*arctan(c*x)/c^3","B"
1256,1,484,346,0.056000," ","int(x*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x)","\frac{b^{2} \arctan \left(c x \right)^{2} e^{2}}{6 c^{6}}+\frac{b^{2} \arctan \left(c x \right)^{2} e^{2} x^{6}}{6}+\frac{d^{2} b^{2} \arctan \left(c x \right)^{2} x^{2}}{2}+\frac{d^{2} b^{2} \arctan \left(c x \right)^{2}}{2 c^{2}}-\frac{a b \arctan \left(c x \right) d e}{c^{4}}+a b \arctan \left(c x \right) x^{4} d e -\frac{b^{2} \arctan \left(c x \right) x^{3} d e}{3 c}-\frac{a b \,x^{3} d e}{3 c}-\frac{a b \,d^{2} x}{c}-\frac{b^{2} d^{2} x \arctan \left(c x \right)}{c}+\frac{b^{2} d^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{2}}+\frac{23 b^{2} e^{2} \ln \left(c^{2} x^{2}+1\right)}{90 c^{6}}+\frac{a b d e x}{c^{3}}+\frac{b^{2} d e x \arctan \left(c x \right)}{c^{3}}-\frac{a b \,e^{2} x}{3 c^{5}}+\frac{b^{2} d e \,x^{2}}{6 c^{2}}-\frac{b^{2} e^{2} x \arctan \left(c x \right)}{3 c^{5}}-\frac{4 b^{2} e^{2} x^{2}}{45 c^{4}}+\frac{b^{2} e^{2} x^{4}}{60 c^{2}}+d^{2} a b \arctan \left(c x \right) x^{2}+\frac{d^{2} a b \arctan \left(c x \right)}{c^{2}}-\frac{a b \,x^{5} e^{2}}{15 c}+\frac{a b \,x^{3} e^{2}}{9 c^{3}}+\frac{a b \arctan \left(c x \right) e^{2} x^{6}}{3}+\frac{b^{2} \arctan \left(c x \right)^{2} x^{4} d e}{2}+\frac{a b \arctan \left(c x \right) e^{2}}{3 c^{6}}+\frac{b^{2} \arctan \left(c x \right) x^{3} e^{2}}{9 c^{3}}-\frac{b^{2} \arctan \left(c x \right)^{2} d e}{2 c^{4}}-\frac{b^{2} \arctan \left(c x \right) x^{5} e^{2}}{15 c}+\frac{a^{2} x^{4} d e}{2}-\frac{2 b^{2} d e \ln \left(c^{2} x^{2}+1\right)}{3 c^{4}}+\frac{d^{2} a^{2} x^{2}}{2}+\frac{a^{2} e^{2} x^{6}}{6}"," ",0,"1/6/c^6*b^2*arctan(c*x)^2*e^2+1/6*b^2*arctan(c*x)^2*e^2*x^6+1/2*d^2*b^2*arctan(c*x)^2*x^2+1/2/c^2*d^2*b^2*arctan(c*x)^2-1/c^4*a*b*arctan(c*x)*d*e+a*b*arctan(c*x)*x^4*d*e-1/3/c*b^2*arctan(c*x)*x^3*d*e-1/3/c*a*b*x^3*d*e-a*b*d^2*x/c-b^2*d^2*x*arctan(c*x)/c+1/2*b^2*d^2*ln(c^2*x^2+1)/c^2+23/90*b^2*e^2*ln(c^2*x^2+1)/c^6+a*b*d*e*x/c^3+b^2*d*e*x*arctan(c*x)/c^3-1/3*a*b*e^2*x/c^5+1/6*b^2*d*e*x^2/c^2-1/3*b^2*e^2*x*arctan(c*x)/c^5-4/45*b^2*e^2*x^2/c^4+1/60*b^2*e^2*x^4/c^2+d^2*a*b*arctan(c*x)*x^2+1/c^2*d^2*a*b*arctan(c*x)-1/15/c*a*b*x^5*e^2+1/9/c^3*a*b*x^3*e^2+1/3*a*b*arctan(c*x)*e^2*x^6+1/2*b^2*arctan(c*x)^2*x^4*d*e+1/3/c^6*a*b*arctan(c*x)*e^2+1/9/c^3*b^2*arctan(c*x)*x^3*e^2-1/2/c^4*b^2*arctan(c*x)^2*d*e-1/15/c*b^2*arctan(c*x)*x^5*e^2+1/2*a^2*x^4*d*e-2/3*b^2*d*e*ln(c^2*x^2+1)/c^4+1/2*d^2*a^2*x^2+1/6*a^2*e^2*x^6","A"
1257,1,1005,398,0.131000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))^2,x)","\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) e^{2}}{10 c^{5}}-\frac{i b^{2} \ln \left(c x +i\right)^{2} e^{2}}{20 c^{5}}+\frac{i b^{2} \ln \left(c x -i\right)^{2} e^{2}}{20 c^{5}}+a^{2} x \,d^{2}+\frac{a^{2} x^{5} e^{2}}{5}-\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d e}{3 c^{3}}+\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d e}{3 c^{3}}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) e^{2}}{10 c^{5}}+\frac{a b \,x^{2} e^{2}}{5 c^{3}}-\frac{a b \ln \left(c^{2} x^{2}+1\right) e^{2}}{5 c^{5}}-\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) e^{2}}{5 c^{5}}-\frac{b^{2} \arctan \left(c x \right) x^{4} e^{2}}{10 c}+\frac{b^{2} \arctan \left(c x \right) x^{2} e^{2}}{5 c^{3}}+\frac{2 b^{2} \arctan \left(c x \right)^{2} x^{3} d e}{3}+\frac{2 a b \arctan \left(c x \right) x^{5} e^{2}}{5}+\frac{i b^{2} \ln \left(c x -i\right)^{2} d^{2}}{4 c}-\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d^{2}}{2 c}-\frac{a b \,x^{4} e^{2}}{10 c}+\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d^{2}}{2 c}+\frac{3 b^{2} e^{2} \arctan \left(c x \right)}{10 c^{5}}-\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d^{2}}{c}+2 a b \arctan \left(c x \right) x \,d^{2}+\frac{i b^{2} \ln \left(c x +i\right)^{2} d e}{6 c^{3}}-\frac{a b \ln \left(c^{2} x^{2}+1\right) d^{2}}{c}-\frac{i b^{2} \ln \left(c x +i\right)^{2} d^{2}}{4 c}+b^{2} \arctan \left(c x \right)^{2} x \,d^{2}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d^{2}}{2 c}+\frac{i b^{2} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right) d^{2}}{2 c}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) d^{2}}{2 c}-\frac{i b^{2} \ln \left(\frac{i \left(c x -i\right)}{2}\right) \ln \left(c x +i\right) d^{2}}{2 c}-\frac{2 a b \,x^{2} d e}{3 c}-\frac{2 b^{2} \arctan \left(c x \right) x^{2} d e}{3 c}+\frac{2 b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d e}{3 c^{3}}+\frac{2 a b \ln \left(c^{2} x^{2}+1\right) d e}{3 c^{3}}+\frac{4 a b \arctan \left(c x \right) x^{3} d e}{3}-\frac{3 b^{2} e^{2} x}{10 c^{4}}+\frac{b^{2} e^{2} x^{3}}{30 c^{2}}+\frac{2 a^{2} x^{3} d e}{3}+\frac{b^{2} \arctan \left(c x \right)^{2} x^{5} e^{2}}{5}-\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) e^{2}}{10 c^{5}}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) e^{2}}{10 c^{5}}-\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) e^{2}}{10 c^{5}}-\frac{i b^{2} \ln \left(c x -i\right)^{2} d e}{6 c^{3}}+\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right) e^{2}}{10 c^{5}}+\frac{2 b^{2} d e x}{3 c^{2}}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) d e}{3 c^{3}}+\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right) d e}{3 c^{3}}-\frac{2 b^{2} d e \arctan \left(c x \right)}{3 c^{3}}-\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right) d e}{3 c^{3}}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d e}{3 c^{3}}"," ",0,"a^2*x*d^2+1/5*a^2*x^5*e^2+1/5/c^3*a*b*x^2*e^2-1/5/c^5*a*b*ln(c^2*x^2+1)*e^2-1/5/c^5*b^2*arctan(c*x)*ln(c^2*x^2+1)*e^2-1/10/c*b^2*arctan(c*x)*x^4*e^2+1/5/c^3*b^2*arctan(c*x)*x^2*e^2+2/3*b^2*arctan(c*x)^2*x^3*d*e+2/5*a*b*arctan(c*x)*x^5*e^2+1/10*I/c^5*b^2*dilog(-1/2*I*(I+c*x))*e^2-1/20*I/c^5*b^2*ln(I+c*x)^2*e^2-1/10*I/c^5*b^2*dilog(1/2*I*(c*x-I))*e^2+1/20*I/c^5*b^2*ln(c*x-I)^2*e^2+1/4*I/c*b^2*ln(c*x-I)^2*d^2+1/2*I/c*b^2*dilog(-1/2*I*(I+c*x))*d^2-1/2*I/c*b^2*dilog(1/2*I*(c*x-I))*d^2-1/4*I/c*b^2*ln(I+c*x)^2*d^2-1/10/c*a*b*x^4*e^2+3/10*b^2*e^2*arctan(c*x)/c^5-1/c*b^2*arctan(c*x)*ln(c^2*x^2+1)*d^2+2*a*b*arctan(c*x)*x*d^2-1/c*a*b*ln(c^2*x^2+1)*d^2+b^2*arctan(c*x)^2*x*d^2-2/3/c*a*b*x^2*d*e-1/2*I/c*b^2*ln(c^2*x^2+1)*ln(c*x-I)*d^2+1/3*I/c^3*b^2*dilog(1/2*I*(c*x-I))*d*e-2/3/c*b^2*arctan(c*x)*x^2*d*e+2/3/c^3*b^2*arctan(c*x)*ln(c^2*x^2+1)*d*e+2/3/c^3*a*b*ln(c^2*x^2+1)*d*e+4/3*a*b*arctan(c*x)*x^3*d*e-1/10*I/c^5*b^2*ln(c^2*x^2+1)*ln(c*x-I)*e^2-1/10*I/c^5*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*e^2-1/6*I/c^3*b^2*ln(c*x-I)^2*d*e+1/10*I/c^5*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))*e^2+1/2*I/c*b^2*ln(c^2*x^2+1)*ln(I+c*x)*d^2-1/2*I/c*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*d^2+1/2*I/c*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))*d^2+1/6*I/c^3*b^2*ln(I+c*x)^2*d*e-1/3*I/c^3*b^2*dilog(-1/2*I*(I+c*x))*d*e+1/10*I/c^5*b^2*ln(c^2*x^2+1)*ln(I+c*x)*e^2-3/10*b^2*e^2*x/c^4+1/30*b^2*e^2*x^3/c^2+2/3*a^2*x^3*d*e+1/5*b^2*arctan(c*x)^2*x^5*e^2+2/3*b^2*d*e*x/c^2-2/3*b^2*d*e*arctan(c*x)/c^3-1/3*I/c^3*b^2*ln(c^2*x^2+1)*ln(I+c*x)*d*e+1/3*I/c^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))*d*e-1/3*I/c^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))*d*e+1/3*I/c^3*b^2*ln(c^2*x^2+1)*ln(c*x-I)*d*e","B"
1258,1,1549,330,7.829000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))^2/x,x)","-\frac{2 a b d e x}{c}-\frac{2 b^{2} d e x \arctan \left(c x \right)}{c}+2 a b e \arctan \left(c x \right) x^{2} d +\frac{2 a b e \arctan \left(c x \right) d}{c^{2}}+\frac{b^{2} e^{2} x^{2}}{12 c^{2}}+\frac{b^{2} e \arctan \left(c x \right)^{2} d}{c^{2}}+a^{2} e \,x^{2} d +\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}-\frac{b^{2} \arctan \left(c x \right)^{2} e^{2}}{4 c^{4}}+\frac{b^{2} \arctan \left(c x \right)^{2} x^{4} e^{2}}{4}+b^{2} \arctan \left(c x \right)^{2} d^{2} \ln \left(c x \right)+\frac{2 b^{2} e^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{3 c^{4}}+b^{2} d^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+b^{2} d^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-b^{2} d^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)+2 b^{2} d^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+2 b^{2} d^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{b^{2} d^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}-\frac{a b \,x^{3} e^{2}}{6 c}-\frac{b^{2} \arctan \left(c x \right) x^{3} e^{2}}{6 c}-\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}-\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{a^{2} x^{4} e^{2}}{4}+a^{2} d^{2} \ln \left(c x \right)+\frac{i b^{2} d^{2} \pi  \arctan \left(c x \right)^{2}}{2}-\frac{2 i b^{2} \arctan \left(c x \right) e^{2}}{3 c^{4}}-\frac{2 b^{2} e d \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{2}}+i b^{2} d^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)-2 i b^{2} d^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 i b^{2} d^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+i a b \,d^{2} \dilog \left(i c x +1\right)-i a b \,d^{2} \dilog \left(-i c x +1\right)+\frac{b^{2} e^{2}}{12 c^{4}}-\frac{i b^{2} d^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i b^{2} d^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{i b^{2} d^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{2 i b^{2} \arctan \left(c x \right) e d}{c^{2}}+i a b \,d^{2} \ln \left(c x \right) \ln \left(i c x +1\right)-i a b \,d^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)+\frac{a b \arctan \left(c x \right) x^{4} e^{2}}{2}+2 a b \arctan \left(c x \right) d^{2} \ln \left(c x \right)-\frac{a b \arctan \left(c x \right) e^{2}}{2 c^{4}}+\frac{a b \,e^{2} x}{2 c^{3}}+\frac{b^{2} e^{2} x \arctan \left(c x \right)}{2 c^{3}}+b^{2} e \arctan \left(c x \right)^{2} x^{2} d"," ",0,"-2*a*b*d*e*x/c-2*b^2*d*e*x*arctan(c*x)/c+2*a*b*e*arctan(c*x)*x^2*d+2/c^2*a*b*e*arctan(c*x)*d+1/12*b^2*e^2*x^2/c^2+1/c^2*b^2*e*arctan(c*x)^2*d+a^2*e*x^2*d+1/2*I*b^2*d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+I*b^2*d^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-2*I*b^2*d^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*b^2*d^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I*b^2*d^2*Pi*arctan(c*x)^2-2/3*I*b^2/c^4*arctan(c*x)*e^2-1/2*I*b^2*d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2*d^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2*d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-2*b^2/c^2*e*d*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/4*b^2/c^4*arctan(c*x)^2*e^2+1/4*b^2*arctan(c*x)^2*x^4*e^2+2/3*b^2/c^4*e^2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+b^2*arctan(c*x)^2*d^2*ln(c*x)+b^2*d^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2*d^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))-b^2*d^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)-1/6*a*b/c*x^3*e^2-1/6*b^2/c*arctan(c*x)*x^3*e^2-1/2*I*b^2*d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/4*a^2*x^4*e^2+2*b^2*d^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2*d^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*b^2*d^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+a^2*d^2*ln(c*x)+1/12*b^2/c^4*e^2-1/2*I*b^2*d^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2*d^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2*I*b^2*d^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+2*I*b^2/c^2*arctan(c*x)*e*d+I*a*b*d^2*ln(c*x)*ln(1+I*c*x)-I*a*b*d^2*ln(c*x)*ln(1-I*c*x)+1/2*a*b*arctan(c*x)*x^4*e^2+2*a*b*arctan(c*x)*d^2*ln(c*x)+I*a*b*d^2*dilog(1+I*c*x)-I*a*b*d^2*dilog(1-I*c*x)-1/2*a*b/c^4*arctan(c*x)*e^2+1/2*a*b*e^2*x/c^3+1/2*b^2*e^2*x*arctan(c*x)/c^3+b^2*e*arctan(c*x)^2*x^2*d","C"
1259,1,997,317,0.142000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))^2/x^2,x)","-\frac{b^{2} e^{2} \arctan \left(c x \right)}{3 c^{3}}-\frac{i b^{2} \ln \left(c x +i\right)^{2} d e}{2 c}+\frac{i c \,b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) d^{2}}{2}+\frac{i c \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right) d^{2}}{2}-i c \,b^{2} d^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)-\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d e}{c}+\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d e}{c}-\frac{a^{2} d^{2}}{x}+\frac{a^{2} e^{2} x^{3}}{3}-\frac{2 a b \arctan \left(c x \right) d^{2}}{x}+\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right) d e}{c}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) d e}{c}-\frac{i b^{2} \ln \left(\frac{i \left(c x -i\right)}{2}\right) \ln \left(c x +i\right) d e}{c}-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d e}{c}-i c \,b^{2} d^{2} \dilog \left(-i c x +1\right)+\frac{i c \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) d^{2}}{2}-\frac{i c \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) d^{2}}{2}+\frac{i c \,b^{2} \ln \left(c x -i\right)^{2} d^{2}}{4}-\frac{i c \,b^{2} \ln \left(c x +i\right)^{2} d^{2}}{4}+\frac{i b^{2} \ln \left(c x +i\right)^{2} e^{2}}{12 c^{3}}+\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right) e^{2}}{6 c^{3}}-\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right) e^{2}}{6 c^{3}}+\frac{a b \,e^{2} \ln \left(c^{2} x^{2}+1\right)}{3 c^{3}}-\frac{b^{2} e^{2} \arctan \left(c x \right) x^{2}}{3 c}+\frac{2 a b \,e^{2} \arctan \left(c x \right) x^{3}}{3}+\frac{b^{2} e^{2} x}{3 c^{2}}+2 a^{2} e d x -\frac{b^{2} \arctan \left(c x \right)^{2} d^{2}}{x}+\frac{b^{2} e^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{3 c^{3}}-\frac{i b^{2} \ln \left(c x -i\right)^{2} e^{2}}{12 c^{3}}+\frac{b^{2} e^{2} \arctan \left(c x \right)^{2} x^{3}}{3}+i c \,b^{2} d^{2} \dilog \left(i c x +1\right)+2 b^{2} \arctan \left(c x \right)^{2} e d x -c \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d^{2}+2 c \,b^{2} \arctan \left(c x \right) d^{2} \ln \left(c x \right)-c a b \ln \left(c^{2} x^{2}+1\right) d^{2}+2 c a b \,d^{2} \ln \left(c x \right)-\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x +i\right) e^{2}}{6 c^{3}}+\frac{i b^{2} \ln \left(\frac{i \left(c x -i\right)}{2}\right) \ln \left(c x +i\right) e^{2}}{6 c^{3}}+\frac{i b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) e^{2}}{6 c^{3}}-\frac{i b^{2} \ln \left(-\frac{i \left(c x +i\right)}{2}\right) \ln \left(c x -i\right) e^{2}}{6 c^{3}}+4 a b \arctan \left(c x \right) e d x -\frac{i c \,b^{2} \ln \left(\frac{i \left(c x -i\right)}{2}\right) \ln \left(c x +i\right) d^{2}}{2}+\frac{i b^{2} \ln \left(c x -i\right)^{2} d e}{2 c}+i c \,b^{2} d^{2} \ln \left(c x \right) \ln \left(i c x +1\right)-\frac{i c \,b^{2} \ln \left(c^{2} x^{2}+1\right) \ln \left(c x -i\right) d^{2}}{2}-\frac{2 a b \ln \left(c^{2} x^{2}+1\right) d e}{c}-\frac{2 b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right) d e}{c}-\frac{a b \,x^{2} e^{2}}{3 c}"," ",0,"-1/3*b^2*e^2*arctan(c*x)/c^3-a^2*d^2/x+1/3*a^2*e^2*x^3-2*a*b*arctan(c*x)*d^2/x-I*b^2/c*ln(1/2*I*(c*x-I))*ln(I+c*x)*d*e-I*b^2/c*ln(c^2*x^2+1)*ln(c*x-I)*d*e+I*b^2/c*ln(c*x-I)*ln(-1/2*I*(I+c*x))*d*e+I*b^2/c*ln(c^2*x^2+1)*ln(I+c*x)*d*e+1/3/c^3*a*b*e^2*ln(c^2*x^2+1)-1/3/c*b^2*e^2*arctan(c*x)*x^2+2/3*a*b*e^2*arctan(c*x)*x^3+1/3*b^2*e^2*x/c^2+2*a^2*e*d*x-b^2*arctan(c*x)^2*d^2/x+1/3/c^3*b^2*e^2*arctan(c*x)*ln(c^2*x^2+1)+1/3*b^2*e^2*arctan(c*x)^2*x^3+I*c*b^2*d^2*dilog(1+I*c*x)+2*b^2*arctan(c*x)^2*e*d*x-1/6*I*b^2/c^3*dilog(-1/2*I*(I+c*x))*e^2+1/12*I*b^2/c^3*ln(I+c*x)^2*e^2-1/12*I*b^2/c^3*ln(c*x-I)^2*e^2+1/6*I*b^2/c^3*dilog(1/2*I*(c*x-I))*e^2-I*c*b^2*d^2*dilog(1-I*c*x)+1/4*I*c*b^2*ln(c*x-I)^2*d^2+1/2*I*c*b^2*dilog(-1/2*I*(I+c*x))*d^2-1/2*I*c*b^2*dilog(1/2*I*(c*x-I))*d^2-1/4*I*c*b^2*ln(I+c*x)^2*d^2-c*b^2*arctan(c*x)*ln(c^2*x^2+1)*d^2+2*c*b^2*arctan(c*x)*d^2*ln(c*x)-c*a*b*ln(c^2*x^2+1)*d^2+2*c*a*b*d^2*ln(c*x)-1/6*I*b^2/c^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))*e^2-1/6*I*b^2/c^3*ln(c^2*x^2+1)*ln(I+c*x)*e^2+1/6*I*b^2/c^3*ln(1/2*I*(c*x-I))*ln(I+c*x)*e^2-1/2*I*b^2/c*ln(I+c*x)^2*d*e-I*b^2/c*dilog(1/2*I*(c*x-I))*d*e+4*a*b*arctan(c*x)*e*d*x+1/6*I*b^2/c^3*ln(c^2*x^2+1)*ln(c*x-I)*e^2+1/2*I*c*b^2*ln(c^2*x^2+1)*ln(I+c*x)*d^2+1/2*I*c*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))*d^2-I*c*b^2*d^2*ln(c*x)*ln(1-I*c*x)-1/2*I*c*b^2*ln(1/2*I*(c*x-I))*ln(I+c*x)*d^2+1/2*I*b^2/c*ln(c*x-I)^2*d*e+I*c*b^2*d^2*ln(c*x)*ln(1+I*c*x)+I*b^2/c*dilog(-1/2*I*(I+c*x))*d*e-2*a*b/c*ln(c^2*x^2+1)*d*e-2*b^2/c*arctan(c*x)*ln(c^2*x^2+1)*d*e-1/2*I*c*b^2*ln(c^2*x^2+1)*ln(c*x-I)*d^2-1/3/c*a*b*x^2*e^2","B"
1260,1,1511,301,6.777000," ","int((e*x^2+d)^2*(a+b*arctan(c*x))^2/x^3,x)","-\frac{d^{2} a^{2}}{2 x^{2}}+i b^{2} e d \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}+c^{2} d^{2} b^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+c^{2} d^{2} b^{2} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}-1\right)-\frac{c^{2} d^{2} b^{2} \arctan \left(c x \right)^{2}}{2}-\frac{d^{2} b^{2} \arctan \left(c x \right)^{2}}{2 x^{2}}-i c^{2} d^{2} b^{2} \arctan \left(c x \right)-\frac{c \,d^{2} a b}{x}-\frac{d^{2} a b \arctan \left(c x \right)}{x^{2}}-c^{2} d^{2} a b \arctan \left(c x \right)-\frac{c \,d^{2} b^{2} \arctan \left(c x \right)}{x}+i b^{2} e d \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}+i b^{2} e d \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}+2 i a b e d \ln \left(c x \right) \ln \left(i c x +1\right)-2 i a b e d \ln \left(c x \right) \ln \left(-i c x +1\right)-i b^{2} e d \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}+\frac{a b \arctan \left(c x \right) e^{2}}{c^{2}}+2 b^{2} \arctan \left(c x \right)^{2} e d \ln \left(c x \right)+a b \arctan \left(c x \right) x^{2} e^{2}-b^{2} e d \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)+4 b^{2} e d \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+4 b^{2} e d \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{b^{2} e^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{2}}+4 a b \arctan \left(c x \right) e d \ln \left(c x \right)+i b^{2} e d \pi  \arctan \left(c x \right)^{2}+2 i a b e d \dilog \left(i c x +1\right)-2 i a b e d \dilog \left(-i c x +1\right)+\frac{b^{2} \arctan \left(c x \right)^{2} x^{2} e^{2}}{2}+\frac{b^{2} \arctan \left(c x \right)^{2} e^{2}}{2 c^{2}}+2 a^{2} e d \ln \left(c x \right)+\frac{a^{2} x^{2} e^{2}}{2}+\frac{i b^{2} \arctan \left(c x \right) e^{2}}{c^{2}}+2 b^{2} e d \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+2 b^{2} e d \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 b^{2} e d \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)-i b^{2} e d \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}-i b^{2} e d \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}+i b^{2} e d \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}-i b^{2} e d \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}-\frac{a b \,e^{2} x}{c}-\frac{b^{2} e^{2} x \arctan \left(c x \right)}{c}+2 i b^{2} e d \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)-4 i b^{2} e d \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-4 i b^{2} e d \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)"," ",0,"-1/2*d^2*a^2/x^2+I*b^2*e*d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*c^2*d^2*b^2*arctan(c*x)^2-1/2*d^2*b^2/x^2*arctan(c*x)^2-c*d^2*a*b/x-d^2*a*b*arctan(c*x)/x^2-c^2*d^2*a*b*arctan(c*x)-c*d^2*b^2*arctan(c*x)/x+I*b^2*e*d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+I*b^2*e*d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+2*I*a*b*e*d*ln(c*x)*ln(1+I*c*x)-2*I*a*b*e*d*ln(c*x)*ln(1-I*c*x)-I*b^2*e*d*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-I*c^2*b^2*arctan(c*x)*d^2+I/c^2*b^2*arctan(c*x)*e^2+1/c^2*a*b*arctan(c*x)*e^2+2*b^2*arctan(c*x)^2*e*d*ln(c*x)+2*b^2*e*d*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2*e*d*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+a*b*arctan(c*x)*x^2*e^2-2*b^2*e*d*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)-b^2*e*d*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+4*b^2*e*d*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+I*b^2*e*d*Pi*arctan(c*x)^2+4*a*b*arctan(c*x)*e*d*ln(c*x)+2*I*a*b*e*d*dilog(1+I*c*x)-2*I*a*b*e*d*dilog(1-I*c*x)+2*I*b^2*e*d*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-4*I*b^2*e*d*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-4*I*b^2*e*d*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+4*b^2*e*d*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*b^2*arctan(c*x)^2*x^2*e^2+1/2/c^2*b^2*arctan(c*x)^2*e^2-1/c^2*b^2*e^2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+c^2*b^2*d^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2)-1)+c^2*b^2*d^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*a^2*e*d*ln(c*x)+1/2*a^2*x^2*e^2+I*b^2*e*d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-I*b^2*e*d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-I*b^2*e*d*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-I*b^2*e*d*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-a*b*e^2*x/c-b^2*e^2*x*arctan(c*x)/c","C"
1261,0,0,504,56.822000," ","int(x^3*(a+b*arctan(c*x))^2/(e*x^2+d),x)","\int \frac{x^{3} \left(a +b \arctan \left(c x \right)\right)^{2}}{e \,x^{2}+d}\, dx"," ",0,"int(x^3*(a+b*arctan(c*x))^2/(e*x^2+d),x)","F"
1262,0,0,452,6.462000," ","int(x^2*(a+b*arctan(c*x))^2/(e*x^2+d),x)","\int \frac{x^{2} \left(a +b \arctan \left(c x \right)\right)^{2}}{e \,x^{2}+d}\, dx"," ",0,"int(x^2*(a+b*arctan(c*x))^2/(e*x^2+d),x)","F"
1263,0,0,412,19.694000," ","int(x*(a+b*arctan(c*x))^2/(e*x^2+d),x)","\int \frac{x \left(a +b \arctan \left(c x \right)\right)^{2}}{e \,x^{2}+d}\, dx"," ",0,"int(x*(a+b*arctan(c*x))^2/(e*x^2+d),x)","F"
1264,1,2600,362,0.770000," ","int((a+b*arctan(c*x))^2/(e*x^2+d),x)","\frac{i c \,b^{2} \polylog \left(3, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) e}{2 d^{2} c^{4}-4 c^{2} e d +2 e^{2}}-\frac{c a b \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{d^{2} c^{4}-2 c^{2} e d +e^{2}}-\frac{c \,b^{2} \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}}{d^{2} c^{4}-2 c^{2} e d +e^{2}}-\frac{2 c a b \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{d^{2} c^{4}-2 c^{2} e d +e^{2}}-\frac{b^{2} \sqrt{c^{2} e d}\, \arctan \left(c x \right)^{3}}{3 c e d}-\frac{i a b \sqrt{c^{2} e d}\, \arctan \left(c x \right) \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right)}{c e d}-\frac{i b^{2} \sqrt{c^{2} e d}\, \polylog \left(3, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right)}{4 c e d}-\frac{i c \,b^{2} \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{d^{2} c^{4}-2 c^{2} e d +e^{2}}-\frac{a b \sqrt{c^{2} e d}\, \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right)}{2 c e d}-\frac{b^{2} \sqrt{c^{2} e d}\, \arctan \left(c x \right) \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right)}{2 c e d}-\frac{i c \,b^{2} \polylog \left(3, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{2 d^{2} c^{4}-4 c^{2} e d +2 e^{2}}-\frac{i c^{3} b^{2} \polylog \left(3, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) d}{2 \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{i c \,b^{2} \polylog \left(3, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) e}{2 \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{i c^{3} b^{2} \polylog \left(3, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) d}{2 d^{2} c^{4}-4 c^{2} e d +2 e^{2}}+\frac{i c^{3} b^{2} \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}\, d}{2 e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{i b^{2} \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}\, e}{2 c d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{i c^{3} a b \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}\, d}{e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{i a b \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}\, e}{c d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{2 c \,b^{2} \arctan \left(c x \right)^{3} \sqrt{c^{2} e d}}{3 \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{c^{3} b^{2} \arctan \left(c x \right)^{3} \sqrt{c^{2} e d}\, d}{3 e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{b^{2} \arctan \left(c x \right)^{3} \sqrt{c^{2} e d}\, e}{3 c d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{a b \sqrt{c^{2} e d}\, \arctan \left(c x \right)^{2}}{c e d}+\frac{a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}+\frac{i c^{3} b^{2} \polylog \left(3, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}\, d}{4 e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{i b^{2} \polylog \left(3, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}\, e}{4 c d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{c^{3} b^{2} \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}\, d}{2 e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{a b \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}\, e}{2 c d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{c^{3} a b \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}\, d}{2 e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{b^{2} \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}\, e}{2 c d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{i b^{2} \sqrt{c^{2} e d}\, \arctan \left(c x \right)^{2} \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right)}{2 c e d}-\frac{2 i c a b \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}}{d^{2} c^{4}-2 c^{2} e d +e^{2}}+\frac{a b \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}\, e}{c d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{c^{3} a b \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}\, d}{e \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}"," ",0,"-2*I*c*b^2*polylog(3,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))/(2*c^4*d^2-4*c^2*d*e+2*e^2)*(c^2*e*d)^(1/2)-1/2*I*c^3*b^2*polylog(3,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))/(c^4*d^2-2*c^2*d*e+e^2)*d+1/2*I*c*b^2*polylog(3,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)-1/2*I*c*b^2*polylog(3,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))/(c^4*d^2-2*c^2*d*e+e^2)*e+I*c^3*b^2*polylog(3,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))/(2*c^4*d^2-4*c^2*d*e+2*e^2)*d+I*c*b^2*polylog(3,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))/(2*c^4*d^2-4*c^2*d*e+2*e^2)*e-2*c*a*b/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2*(c^2*e*d)^(1/2)-c*a*b/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*(c^2*e*d)^(1/2)-1/3/c*b^2*(c^2*e*d)^(1/2)/e/d*arctan(c*x)^3-c*b^2/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)*(c^2*e*d)^(1/2)+1/2*I*c^3*b^2*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)^2/e/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*d+1/2*I/c*b^2*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)^2/d/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*e-I/c*a*b*(c^2*e*d)^(1/2)/e/d*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))+I*c^3*a*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/e/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*d+I/c*a*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/d/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*e-2/3*c*b^2/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^3*(c^2*e*d)^(1/2)+1/3*c^3*b^2/e/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^3*(c^2*e*d)^(1/2)*d+1/3/c*b^2/d/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^3*(c^2*e*d)^(1/2)*e-1/c*a*b*(c^2*e*d)^(1/2)/e/d*arctan(c*x)^2-1/2/c*a*b*(c^2*e*d)^(1/2)/e/d*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))-1/2/c*b^2*(c^2*e*d)^(1/2)/e/d*arctan(c*x)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))-I*c*b^2*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)^2/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)-1/4*I/c*b^2*(c^2*e*d)^(1/2)/e/d*polylog(3,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))+a^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/2/c*a*b/d/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*(c^2*e*d)^(1/2)*e+1/c*a*b/d/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2*(c^2*e*d)^(1/2)*e+1/2*c^3*a*b/e/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*(c^2*e*d)^(1/2)*d+c^3*a*b/e/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2*(c^2*e*d)^(1/2)*d+1/2/c*b^2/d/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)*(c^2*e*d)^(1/2)*e+1/2*c^3*b^2/e/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)*(c^2*e*d)^(1/2)*d-1/2*I/c*b^2*(c^2*e*d)^(1/2)/e/d*arctan(c*x)^2*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))+1/4*I/c*b^2*polylog(3,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))/d/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*e+1/4*I*c^3*b^2*polylog(3,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))/e/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*d-2*I*c*a*b*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)","B"
1265,0,0,546,24.510000," ","int((a+b*arctan(c*x))^2/x/(e*x^2+d),x)","\int \frac{\left(a +b \arctan \left(c x \right)\right)^{2}}{x \left(e \,x^{2}+d \right)}\, dx"," ",0,"int((a+b*arctan(c*x))^2/x/(e*x^2+d),x)","F"
1266,0,0,451,7.036000," ","int((a+b*arctan(c*x))^2/x^2/(e*x^2+d),x)","\int \frac{\left(a +b \arctan \left(c x \right)\right)^{2}}{x^{2} \left(e \,x^{2}+d \right)}\, dx"," ",0,"int((a+b*arctan(c*x))^2/x^2/(e*x^2+d),x)","F"
1267,0,0,648,74.798000," ","int((a+b*arctan(c*x))^2/x^3/(e*x^2+d),x)","\int \frac{\left(a +b \arctan \left(c x \right)\right)^{2}}{x^{3} \left(e \,x^{2}+d \right)}\, dx"," ",0,"int((a+b*arctan(c*x))^2/x^3/(e*x^2+d),x)","F"
1268,0,0,783,26.505000," ","int(x^3*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x)","\int \frac{x^{3} \left(a +b \arctan \left(c x \right)\right)^{2}}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^3*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x)","F"
1269,1,6575,856,3.099000," ","int(x^2*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
1270,1,1185,377,1.047000," ","int(x*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x)","-\frac{c^{2} a^{2}}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{2} b^{2} \arctan \left(c x \right)^{2}}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{b^{2} \sqrt{c^{2} e d}\, \arctan \left(c x \right)^{2}}{2 e d \left(c^{2} d -e \right)}+\frac{i c^{2} b^{2} \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}}{\left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{i c^{4} b^{2} \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}\, d}{2 e \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{i b^{2} \sqrt{c^{2} e d}\, \arctan \left(c x \right) \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right)}{2 e d \left(c^{2} d -e \right)}+\frac{c^{2} b^{2} \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{\left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{c^{2} b^{2} \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{2 \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{i b^{2} e \ln \left(1-\frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \arctan \left(c x \right) \sqrt{c^{2} e d}}{2 \left(c^{2} d -e \right) d \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}+\frac{c^{2} b^{2} \arctan \left(c x \right)^{2}}{2 e \left(c^{2} d -e \right)}+\frac{b^{2} \sqrt{c^{2} e d}\, \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d +2 \sqrt{c^{2} e d}-e \right)}\right)}{4 e d \left(c^{2} d -e \right)}-\frac{b^{2} e \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}}{2 d \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{b^{2} e \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}}{4 d \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{c^{4} b^{2} \polylog \left(2, \frac{\left(c^{2} d -e \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c^{2} d -2 \sqrt{c^{2} e d}-e \right)}\right) \sqrt{c^{2} e d}\, d}{4 e \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{c^{4} b^{2} \arctan \left(c x \right)^{2} \sqrt{c^{2} e d}\, d}{2 e \left(c^{2} d -e \right) \left(d^{2} c^{4}-2 c^{2} e d +e^{2}\right)}-\frac{c^{2} a b \arctan \left(c x \right)}{e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c a b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(c^{2} d -e \right) \sqrt{d e}}+\frac{c^{2} a b \arctan \left(c x \right)}{e \left(c^{2} d -e \right)}"," ",0,"-1/2*c^2*a^2/e/(c^2*e*x^2+c^2*d)-1/2*c^2*b^2/e/(c^2*e*x^2+c^2*d)*arctan(c*x)^2+1/2*b^2/e*(c^2*e*d)^(1/2)/d/(c^2*d-e)*arctan(c*x)^2+I*c^2*b^2*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)-1/2*I*c^4*b^2/e*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)*d+1/2*I*b^2/e*(c^2*e*d)^(1/2)/d/(c^2*d-e)*arctan(c*x)*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))+c^2*b^2/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2*(c^2*e*d)^(1/2)+1/2*c^2*b^2/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*(c^2*e*d)^(1/2)-1/2*I*b^2*e*ln(1-(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*arctan(c*x)/(c^2*d-e)/d/(c^4*d^2-2*c^2*d*e+e^2)*(c^2*e*d)^(1/2)+1/2*c^2*b^2/e*arctan(c*x)^2/(c^2*d-e)+1/4*b^2/e*(c^2*e*d)^(1/2)/d/(c^2*d-e)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d+2*(c^2*e*d)^(1/2)-e))-1/2*b^2*e/d/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2*(c^2*e*d)^(1/2)-1/4*b^2*e/d/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*(c^2*e*d)^(1/2)-1/4*c^4*b^2/e/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*polylog(2,(c^2*d-e)*(1+I*c*x)^2/(c^2*x^2+1)/(-c^2*d-2*(c^2*e*d)^(1/2)-e))*(c^2*e*d)^(1/2)*d-1/2*c^4*b^2/e/(c^2*d-e)/(c^4*d^2-2*c^2*d*e+e^2)*arctan(c*x)^2*(c^2*e*d)^(1/2)*d-c^2*a*b/e/(c^2*e*x^2+c^2*d)*arctan(c*x)-c*a*b/(c^2*d-e)/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+c^2*a*b/e/(c^2*d-e)*arctan(c*x)","B"
1271,1,6575,862,3.148000," ","int((a+b*arctan(c*x))^2/(e*x^2+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
1272,0,0,916,30.086000," ","int((a+b*arctan(c*x))^2/x/(e*x^2+d)^2,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right)^{2}}{x \left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arctan(c*x))^2/x/(e*x^2+d)^2,x)","F"
1273,0,0,960,8.372000," ","int((a+b*arctan(c*x))^2/x^2/(e*x^2+d)^2,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right)^{2}}{x^{2} \left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arctan(c*x))^2/x^2/(e*x^2+d)^2,x)","F"
1274,0,0,1018,56.759000," ","int((a+b*arctan(c*x))^2/x^3/(e*x^2+d)^2,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right)^{2}}{x^{3} \left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arctan(c*x))^2/x^3/(e*x^2+d)^2,x)","F"
1275,1,3626,89,3.777000," ","int(x^4*arctan(x)*ln(x^2+1),x)","\text{output too large to display}"," ",0,"-2/5*x*arctan(x)+2/15*x^3*arctan(x)-2/25*x^5*arctan(x)+1/10*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi*x^5-1/10*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*arctan(x)*Pi*x^5+1/10*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi*x^5+1/10*I*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi*x^5-1/5*I*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi*x^5+1/40*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*Pi*x^4-1/20*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*Pi*x^2+1/5*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*arctan(x)*Pi*x^5-1/10*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)+1/5*x^2*ln(2)-1/5*ln((1+I*x)^2/(x^2+1)+1)*x^2+1/10*ln((1+I*x)^2/(x^2+1)+1)*x^4+46/75*I*arctan(x)+1/10*(-4*I*arctan(x)+4*x^5*arctan(x)+4*ln((1+I*x)^2/(x^2+1)+1)+3+2*x^2-x^4)*ln((1+I*x)/(x^2+1)^(1/2))-181/600-1/10*csgn(I*(1+I*x)^2/(x^2+1))^3*arctan(x)*Pi-1/10*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi+1/10*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi+2/5*ln(2)*arctan(x)*x^5-3/40*I*Pi*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3+3/40*I*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3-3/40*I*Pi*csgn(I*(1+I*x)^2/(x^2+1))^3-2/5*I*ln(2)*arctan(x)-2/5*ln((1+I*x)^2/(x^2+1)+1)*arctan(x)*x^5+1/5*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*arctan(x)*Pi+1/10*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi-1/10*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*arctan(x)*Pi+1/10*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi+1/10*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi-1/5*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi+3/20*I*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))*csgn(I*(1+I*x)^2/(x^2+1))^2-3/20*I*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2+1/40*I*csgn(I*(1+I*x)^2/(x^2+1))^3*Pi*x^4+1/40*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x^4-1/40*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x^4-1/20*I*csgn(I*(1+I*x)^2/(x^2+1))^3*Pi*x^2-1/20*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x^2+1/20*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x^2+2/5*ln(2)*ln((1+I*x)^2/(x^2+1)+1)-1/10*ln(2)*x^4-1/10*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi*x^5+3/40*I*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)+3/40*I*Pi*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2-3/40*I*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*csgn(I*(1+I*x)^2/(x^2+1))+3/40*I*Pi*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2-1/10*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*(1+I*x)^2/(x^2+1))^3+1/10*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3-1/10*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3+1/10*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2+1/10*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2-1/5*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2-1/10*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*csgn(I*(1+I*x)^2/(x^2+1))-1/40*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x^4+1/40*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*Pi*x^4-1/40*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*Pi*x^4-1/40*I*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*Pi*x^4+1/20*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x^2-1/10*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi+1/20*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*Pi*x^2+1/20*I*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*Pi*x^2-1/10*I*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x^2-3/40*I*Pi*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)-1/10*I*csgn(I*(1+I*x)^2/(x^2+1))^3*arctan(x)*Pi*x^5-1/10*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi*x^5+1/10*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi*x^5-1/20*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*Pi*x^4+1/5*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))*csgn(I*(1+I*x)^2/(x^2+1))^2+1/10*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)+1/20*I*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x^4+1/10*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*Pi*x^2-1/20*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*Pi*x^2-77/300*x^2+3/10*ln(2)-137/150*ln((1+I*x)^2/(x^2+1)+1)-1/5*ln((1+I*x)^2/(x^2+1)+1)^2+9/200*x^4","C"
1276,1,2849,70,3.221000," ","int(x^3*arctan(x)*ln(x^2+1),x)","\text{output too large to display}"," ",0,"1/6*(4+3*I*arctan(x)+I*x-3*x*arctan(x)-x^2-3*I*arctan(x)*x^2+3*x^3*arctan(x))*(x+I)*ln((1+I*x)/(x^2+1)^(1/2))+1/4*x^2*arctan(x)-1/8*x^4*arctan(x)+1/2*ln((1+I*x)^2/(x^2+1)+1)*arctan(x)-1/2*ln(2)*arctan(x)-1/2*ln((1+I*x)^2/(x^2+1)+1)*x+1/6*ln((1+I*x)^2/(x^2+1)+1)*x^3-1/6*x^3*ln(2)+1/6*Pi*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3-1/6*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3+1/6*Pi*csgn(I*(1+I*x)^2/(x^2+1))^3+1/24*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x^3+1/24*I*csgn(I*(1+I*x)^2/(x^2+1))^3*Pi*x^3-1/24*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x^3+1/8*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi-1/8*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x+1/8*I*csgn(I*(1+I*x)^2/(x^2+1))^3*arctan(x)*Pi-1/8*I*csgn(I*(1+I*x)^2/(x^2+1))^3*Pi*x-1/8*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi+1/8*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x+1/24*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*Pi*x^3-1/24*I*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*Pi*x^3+1/12*I*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x^3-1/8*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi+1/8*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x-1/8*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*(1+I*x)^2/(x^2+1))*arctan(x)*Pi+1/8*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*(1+I*x)^2/(x^2+1))*Pi*x-1/4*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*arctan(x)*Pi+1/4*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*Pi*x+1/8*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*arctan(x)*Pi-1/8*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*Pi*x-1/8*I*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi+1/8*I*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*Pi*x+1/4*I*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi-1/4*I*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x-1/8*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*arctan(x)*Pi*x^4+1/2*ln(2)*x+1/6*Pi*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)+1/8*I*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi*x^4-1/4*I*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi*x^4+1/24*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*Pi*x^3+1/8*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*arctan(x)*Pi-1/8*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*Pi*x+2/3*I*ln(2)-41/36*I-1/8*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi*x^4-1/8*I*csgn(I*(1+I*x)^2/(x^2+1))^3*arctan(x)*Pi*x^4+1/8*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi*x^4-1/24*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x^3-1/24*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*(1+I*x)^2/(x^2+1))*Pi*x^3-1/12*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*Pi*x^3-25/24*x+1/6*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*csgn(I*(1+I*x)^2/(x^2+1))-1/3*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))*csgn(I*(1+I*x)^2/(x^2+1))^2-1/6*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)+1/3*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2-1/6*Pi*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2-1/6*Pi*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2-1/2*ln((1+I*x)^2/(x^2+1)+1)*arctan(x)*x^4+1/2*ln(2)*arctan(x)*x^4+7/72*x^3+41/24*arctan(x)+1/8*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi*x^4+1/8*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*(1+I*x)^2/(x^2+1))*arctan(x)*Pi*x^4+1/4*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*arctan(x)*Pi*x^4-1/8*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*arctan(x)*Pi*x^4","C"
1277,1,3039,66,2.686000," ","int(x^2*arctan(x)*ln(x^2+1),x)","\text{output too large to display}"," ",0,"-1/6*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi*x^3+2/3*x*arctan(x)-2/9*x^3*arctan(x)-8/9*I*arctan(x)+5/18-1/3*x^2*ln(2)+1/3*ln((1+I*x)^2/(x^2+1)+1)*x^2-2/3*ln((1+I*x)^2/(x^2+1)+1)*arctan(x)*x^3+2/3*ln(2)*arctan(x)*x^3-1/12*I*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3+2/3*I*ln(2)*arctan(x)+1/12*I*Pi*csgn(I*(1+I*x)^2/(x^2+1))^3+1/12*I*Pi*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3+1/6*csgn(I*(1+I*x)^2/(x^2+1))^3*arctan(x)*Pi+1/6*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi-1/6*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi-1/3*(-2*I*arctan(x)-2*x^3*arctan(x)+2*ln((1+I*x)^2/(x^2+1)+1)+1+x^2)*ln((1+I*x)/(x^2+1)^(1/2))-1/3*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*arctan(x)*Pi-1/6*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi+1/6*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*arctan(x)*Pi-1/6*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi-1/6*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi+1/3*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi-1/6*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi*x^3+1/6*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi*x^3-1/12*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x^2-1/6*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*Pi*x^2-2/3*ln(2)*ln((1+I*x)^2/(x^2+1)+1)+1/6*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi+1/6*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*Pi*ln((1+I*x)^2/(x^2+1)+1)+1/6*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi*x^3+1/3*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*arctan(x)*Pi*x^3+1/6*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi*x^3-1/6*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*arctan(x)*Pi*x^3+1/6*I*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi*x^3-1/3*I*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi*x^3+1/12*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*Pi*x^2+5/18*x^2-1/3*ln(2)+11/9*ln((1+I*x)^2/(x^2+1)+1)+1/3*ln((1+I*x)^2/(x^2+1)+1)^2-1/6*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*Pi*ln((1+I*x)^2/(x^2+1)+1)-1/6*I*csgn(I*(1+I*x)^2/(x^2+1))^3*arctan(x)*Pi*x^3+1/12*I*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*csgn(I*(1+I*x)^2/(x^2+1))-1/12*I*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)+1/6*I*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2+1/12*I*csgn(I*(1+I*x)^2/(x^2+1))^3*Pi*x^2+1/12*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x^2-1/12*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x^2-1/6*I*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))*csgn(I*(1+I*x)^2/(x^2+1))^2-1/12*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*Pi-1/12*I*Pi*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2+1/6*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*ln((1+I*x)^2/(x^2+1)+1)+1/6*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*(1+I*x)^2/(x^2+1))^3-1/6*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3-1/12*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x^2+1/12*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*Pi*x^2-1/12*I*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*Pi*x^2+1/6*I*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x^2+1/12*I*Pi*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)+1/6*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*Pi*ln((1+I*x)^2/(x^2+1)+1)-1/3*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*Pi*ln((1+I*x)^2/(x^2+1)+1)-1/6*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*(1+I*x)^2/(x^2+1))*Pi*ln((1+I*x)^2/(x^2+1)+1)-1/6*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*Pi*ln((1+I*x)^2/(x^2+1)+1)+1/3*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*((1+I*x)^2/(x^2+1)+1))*Pi*ln((1+I*x)^2/(x^2+1)+1)","C"
1278,1,2240,39,1.567000," ","int(x*arctan(x)*ln(x^2+1),x)","\text{Expression too large to display}"," ",0,"-1/2*x^2*arctan(x)-ln((1+I*x)^2/(x^2+1)+1)*arctan(x)+ln(2)*arctan(x)+ln((1+I*x)^2/(x^2+1)+1)*x-1/4*Pi*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3+1/4*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3-1/4*Pi*csgn(I*(1+I*x)^2/(x^2+1))^3+(-1-I*arctan(x)+x*arctan(x))*(x+I)*ln((1+I*x)/(x^2+1)^(1/2))+ln(2)*arctan(x)*x^2-ln((1+I*x)^2/(x^2+1)+1)*arctan(x)*x^2-1/4*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi+1/4*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*Pi*x+1/2*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*arctan(x)*Pi*x^2+1/4*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi*x^2-1/4*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*arctan(x)*Pi*x^2+1/4*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi*x^2-1/2*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*((1+I*x)^2/(x^2+1)+1))*arctan(x)*Pi*x^2+1/4*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*arctan(x)*Pi*x^2-1/4*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi*x^2-ln(2)*x-1/4*Pi*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)+3/2*x-1/4*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*csgn(I*(1+I*x)^2/(x^2+1))+1/2*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))*csgn(I*(1+I*x)^2/(x^2+1))^2+1/4*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)-1/2*Pi*csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2+1/4*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi-1/4*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*Pi*x-1/2*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*((1+I*x)^2/(x^2+1)+1))*arctan(x)*Pi+1/2*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*((1+I*x)^2/(x^2+1)+1))*Pi*x+1/4*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*arctan(x)*Pi-1/4*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*Pi*x+3/2*I-I*ln(2)-1/4*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi+1/4*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x+1/4*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi-1/4*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*x-1/4*I*csgn(I*(1+I*x)^2/(x^2+1))^3*arctan(x)*Pi+1/4*I*csgn(I*(1+I*x)^2/(x^2+1))^3*Pi*x+1/4*Pi*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2+1/4*Pi*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2-5/2*arctan(x)-1/4*I*csgn(I*(1+I*x)^2/(x^2+1))^3*arctan(x)*Pi*x^2-1/4*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi*x^2+1/4*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi*x^2+1/2*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*arctan(x)*Pi-1/2*I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*Pi*x+1/4*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi-1/4*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*Pi*x-1/4*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*arctan(x)*Pi+1/4*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*Pi*x","C"
1279,1,1913,36,1.364000," ","int(arctan(x)*ln(x^2+1),x)","-2 x \arctan \left(x \right)+i \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right) \arctan \left(x \right) \pi  x -\frac{i \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right) \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right)}{2}+\frac{i \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(x \right) \pi  x}{2}-\frac{i \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right)^{2} \arctan \left(x \right) \pi  x}{2}-i \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)\right) \arctan \left(x \right) \pi  x +\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)\right)^{2} \arctan \left(x \right) \pi  x}{2}-\frac{\mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right) \arctan \left(x \right) \pi}{2}+i \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right) \pi  \,\mathrm{csgn}\left(\frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right)^{2}-\frac{i \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right)^{3} \arctan \left(x \right) \pi  x}{2}-\frac{i \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(x \right) \pi  x}{2}+\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(x \right) \pi  x}{2}+\frac{i \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right) \pi  \,\mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right)^{2}}{2}-\frac{i \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right)^{2} \pi  \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)}{2}-i \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)\right) \pi  \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)+\frac{i \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right) \pi  \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)}{2}+\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)\right)^{2} \pi  \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)}{2}-2 \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)-\ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}-\frac{i \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right) \arctan \left(x \right) \pi  x}{2}+2 \left(-i \arctan \left(x \right)+x \arctan \left(x \right)+\ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)\right) \ln \left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)+2 \ln \left(2\right) \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)+\frac{i \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(x \right) \pi  x}{2}+2 i \arctan \left(x \right)+\frac{\mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(x \right) \pi}{2}-2 \arctan \left(x \right) \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right) x -2 i \ln \left(2\right) \arctan \left(x \right)-\frac{\mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right)^{3} \arctan \left(x \right) \pi}{2}-\frac{\mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(x \right) \pi}{2}+\frac{i \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}\right)^{3} \pi  \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)}{2}-\frac{i \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right)^{3} \pi  \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)}{2}-\frac{i \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right)^{3} \pi  \ln \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)}{2}+\mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right) \arctan \left(x \right) \pi +\frac{\mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right)^{2} \arctan \left(x \right) \pi}{2}-\frac{\mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right)^{2} \arctan \left(x \right) \pi}{2}+\frac{\mathrm{csgn}\left(\frac{i \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}}\right) \arctan \left(x \right) \pi}{2}+\frac{\mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}\right) \arctan \left(x \right) \pi}{2}-\mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i x +1\right)^{2}}{x^{2}+1}+1\right)^{2}\right)^{2} \arctan \left(x \right) \pi +2 \arctan \left(x \right) \ln \left(2\right) x"," ",0,"-2*x*arctan(x)+1/2*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*ln((1+I*x)^2/(x^2+1)+1)-1/2*I*csgn(I*(1+I*x)^2/(x^2+1))^3*Pi*ln((1+I*x)^2/(x^2+1)+1)-1/2*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*Pi*ln((1+I*x)^2/(x^2+1)+1)+2*(-I*arctan(x)+x*arctan(x)+ln((1+I*x)^2/(x^2+1)+1))*ln((1+I*x)/(x^2+1)^(1/2))+2*I*arctan(x)-1/2*csgn(I*(1+I*x)^2/(x^2+1))^3*arctan(x)*Pi-1/2*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi+1/2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi+csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*arctan(x)*Pi+1/2*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi-1/2*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*arctan(x)*Pi+1/2*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi+1/2*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi-csgn(I*((1+I*x)^2/(x^2+1)+1))*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi+2*ln(2)*ln((1+I*x)^2/(x^2+1)+1)-1/2*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi-2*ln((1+I*x)^2/(x^2+1)+1)-ln((1+I*x)^2/(x^2+1)+1)^2-1/2*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)*arctan(x)*Pi*x+1/2*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi*x+I*csgn(I*(1+I*x)^2/(x^2+1))^2*csgn(I*(1+I*x)/(x^2+1)^(1/2))*arctan(x)*Pi*x-1/2*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)+1/2*I*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*arctan(x)*Pi*x-1/2*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*arctan(x)*Pi*x-I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*((1+I*x)^2/(x^2+1)+1))*arctan(x)*Pi*x+1/2*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*arctan(x)*Pi*x+I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*(1+I*x)/(x^2+1)^(1/2))*csgn(I*(1+I*x)^2/(x^2+1))^2-1/2*I*csgn(I*(1+I*x)^2/(x^2+1))^3*arctan(x)*Pi*x-1/2*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi*x+1/2*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^3*arctan(x)*Pi*x+1/2*I*ln((1+I*x)^2/(x^2+1)+1)*Pi*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2-2*arctan(x)*ln((1+I*x)^2/(x^2+1)+1)*x+2*arctan(x)*ln(2)*x-2*I*ln(2)*arctan(x)-1/2*I*csgn(I*(1+I*x)^2/(x^2+1))*csgn(I*(1+I*x)/(x^2+1)^(1/2))^2*Pi*ln((1+I*x)^2/(x^2+1)+1)-I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I*((1+I*x)^2/(x^2+1)+1))*Pi*ln((1+I*x)^2/(x^2+1)+1)+1/2*I*csgn(I*(1+I*x)^2/(x^2+1)/((1+I*x)^2/(x^2+1)+1)^2)^2*csgn(I/((1+I*x)^2/(x^2+1)+1)^2)*Pi*ln((1+I*x)^2/(x^2+1)+1)+1/2*I*csgn(I*((1+I*x)^2/(x^2+1)+1)^2)*csgn(I*((1+I*x)^2/(x^2+1)+1))^2*Pi*ln((1+I*x)^2/(x^2+1)+1)","C"
1280,1,5237,157,2.795000," ","int(arctan(x)*ln(x^2+1)/x,x)","\text{output too large to display}"," ",0,"result too large to display","C"
1281,0,0,37,4.415000," ","int(arctan(x)*ln(x^2+1)/x^2,x)","\int \frac{\arctan \left(x \right) \ln \left(x^{2}+1\right)}{x^{2}}\, dx"," ",0,"int(arctan(x)*ln(x^2+1)/x^2,x)","F"
1282,0,0,55,8.365000," ","int(arctan(x)*ln(x^2+1)/x^3,x)","\int \frac{\arctan \left(x \right) \ln \left(x^{2}+1\right)}{x^{3}}\, dx"," ",0,"int(arctan(x)*ln(x^2+1)/x^3,x)","F"
1283,0,0,67,4.932000," ","int(arctan(x)*ln(x^2+1)/x^4,x)","\int \frac{\arctan \left(x \right) \ln \left(x^{2}+1\right)}{x^{4}}\, dx"," ",0,"int(arctan(x)*ln(x^2+1)/x^4,x)","F"
1284,0,0,80,8.097000," ","int(arctan(x)*ln(x^2+1)/x^5,x)","\int \frac{\arctan \left(x \right) \ln \left(x^{2}+1\right)}{x^{5}}\, dx"," ",0,"int(arctan(x)*ln(x^2+1)/x^5,x)","F"
1285,0,0,92,5.148000," ","int(arctan(x)*ln(x^2+1)/x^6,x)","\int \frac{\arctan \left(x \right) \ln \left(x^{2}+1\right)}{x^{6}}\, dx"," ",0,"int(arctan(x)*ln(x^2+1)/x^6,x)","F"
1286,1,4941,246,3.796000," ","int(x^4*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),x)","\text{output too large to display}"," ",0,"-181/600*e/c^5*b-1/10*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)*Pi*x^5*e+1/40*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^4*e-1/20*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^2*e-1/10*I/c^5*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*e*Pi*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+3/40*I/c^5*b*Pi*e*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2+3/20*I/c^5*b*Pi*e*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2-1/10*I/c^5*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3+1/10*I/c^5*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-1/10*I/c^5*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-3/20*I/c^5*b*Pi*e*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-2/25*a*e*x^5-2/5*b*e*x*arctan(c*x)/c^4+2/15*b*e*x^3*arctan(c*x)/c^2+3/10/c^5*b*ln(2)*e-2/5*a*e*x/c^4-77/300*b*e*x^2/c^3+2/15*a*e*x^3/c^2+2/5*a*e*arctan(c*x)/c^5-2/25*b*e*x^5*arctan(c*x)-1/10/c^5*b*arctan(c*x)*Pi*e*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3-1/10/c^5*b*arctan(c*x)*Pi*e*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3+1/10/c^5*b*arctan(c*x)*Pi*e*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3+3/40*I/c^5*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*e-3/40*I/c^5*b*Pi*e*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-3/40*I/c^5*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*e-2/5*I/c^5*b*arctan(c*x)*ln(2)*e+1/5*x^5*a*d+1/10/c^5*b*e*(4*arctan(c*x)*x^5*c^5-c^4*x^4-4*I*arctan(c*x)+2*c^2*x^2+4*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+3)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+1/10*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)*Pi*x^5*e-1/5*I*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)*Pi*x^5*e-1/20/c*b*x^4*d+1/10/c^3*b*d*x^2+1/5*a*e*x^5*ln(c^2*x^2+1)+1/5/c^5*b*arctan(c*x)*Pi*e*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2+1/10/c^5*b*arctan(c*x)*Pi*e*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-137/150/c^5*b*e*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/5/c^5*b*d*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/5/c^5*b*e*ln((1+I*c*x)^2/(c^2*x^2+1)+1)^2+1/5*b*arctan(c*x)*x^5*d-1/5/c^5*b*arctan(c*x)*Pi*e*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2+1/10/c^5*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)*Pi*e+1/10/c*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*x^4*e-1/5/c^3*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*x^2*e-1/10/c*b*ln(2)*x^4*e+1/5/c^3*b*ln(2)*x^2*e+2/5/c^5*b*e*ln(2)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+2/5*b*ln(2)*arctan(c*x)*x^5*e-2/5*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*arctan(c*x)*x^5*e-1/5*I/c^5*b*arctan(c*x)*d+46/75*I/c^5*b*e*arctan(c*x)+1/5*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*arctan(c*x)*Pi*x^5*e-1/10*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*arctan(c*x)*Pi*x^5*e+1/10*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)*Pi*x^5*e+1/10*I*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)*Pi*x^5*e-3/40*I/c^5*b*Pi*e*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)+1/40*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*Pi*x^4*e+1/20*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^4*e-1/20*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*Pi*x^4*e-1/40*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^4*e-1/10*I/c^3*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^2*e+1/10*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*Pi*x^2*e+1/20*I/c^3*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^2*e+1/20*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^2*e+1/20*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^2*e-1/20*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*Pi*x^2*e-1/40*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^4*e-1/40*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^4*e-1/5*I/c^5*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2+1/10*I/c^5*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-1/10*I/c^5*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*e*Pi*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/5*I/c^5*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*e*Pi*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/10*I/c^5*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*e*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/10*I/c^5*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-1/10/c^5*b*arctan(c*x)*Pi*e*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)-3/40*I/c^5*b*Pi*e*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))-1/20*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*x^2*e+1/40*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^4*e+1/40*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*x^4*e-1/40*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^4*e+1/20*I/c^3*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^2*e-1/10*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)*Pi*x^5*e+1/10*I*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)*Pi*x^5*e-1/10*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*arctan(c*x)*Pi*x^5*e+1/10/c^5*b*arctan(c*x)*Pi*e*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)+3/20/c^5*b*d-1/10/c^5*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*arctan(c*x)*Pi*e-1/20*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^2*e+3/40*I/c^5*b*Pi*e*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2+3/40*I/c^5*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*e+9/200*b*e*x^4/c","C"
1287,1,3897,197,4.049000," ","int(x^3*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),x)","\text{output too large to display}"," ",0,"-1/2/c^4*b*arctan(c*x)*ln(2)*e+1/2/c^4*b*e*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/2*b*ln(2)*arctan(c*x)*x^4*e-1/2*b*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*x^4*e-25/24*b*e*x/c^3+41/24*b*e*arctan(c*x)/c^4+1/4*b*d*x/c^3-1/12*b*d*x^3/c-1/4*b*d*arctan(c*x)/c^4+1/24*I/c*b*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*Pi*x^3*e-1/12*I/c*b*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*Pi*x^3*e-1/24*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^3*e-1/24*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^3*e+1/12*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*Pi*x^3*e-1/24*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*x^3*e-1/4*I*b*arctan(c*x)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*Pi*x^4*e+1/8*I*b*arctan(c*x)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*x^4*e-1/8*I/c^3*b*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*Pi*x*e+1/4*I/c^3*b*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*Pi*x*e+1/8*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x*e+1/8*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x*e-1/4*I/c^3*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*Pi*x*e+1/8*I/c^3*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*x*e+1/8*I/c^4*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*Pi*e*arctan(c*x)-1/4*I/c^4*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*Pi*e*arctan(c*x)-1/8*I/c^4*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*Pi*e*arctan(c*x)-1/8*I/c^4*b*Pi*e*arctan(c*x)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2+1/4*I/c^4*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*Pi*e*arctan(c*x)-1/8*I/c^4*b*Pi*e*arctan(c*x)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)-1/8*I*b*arctan(c*x)*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*Pi*x^4*e+1/4*I*b*arctan(c*x)*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*Pi*x^4*e+1/8*I*b*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^4*e+1/8*I*b*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^4*e+1/4*a*e/c^2*x^2-1/4*a*e/c^4*ln(c^2*x^2+1)+1/4*x^4*a*e*ln(c^2*x^2+1)+1/4*b*arctan(c*x)*x^4*d+1/4*x^4*a*d+1/6/c^4*b*e*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))-1/3/c^4*b*e*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2-1/6/c^4*b*e*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-1/6/c^4*b*e*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2+1/3/c^4*b*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-1/6/c^4*b*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)+1/6/c^4*b*e*(3*arctan(c*x)*x^3*c^3-c^2*x^2-3*I*arctan(c*x)*x^2*c^2+I*c*x-3*arctan(c*x)*x*c+4+3*I*arctan(c*x))*(I+c*x)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-1/6/c*b*ln(2)*x^3*e+1/6/c*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*x^3*e+1/4/c^2*b*arctan(c*x)*x^2*e+1/6/c^4*b*e*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3+1/6/c^4*b*e*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-1/6/c^4*b*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3+1/2/c^3*b*ln(2)*x*e-1/2/c^3*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*x*e+2/3*I/c^4*b*e*ln(2)+1/24*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*x^3*e+1/24*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^3*e-1/24*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^3*e-1/8*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*x*e-1/8*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x*e+1/8*I/c^3*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x*e+1/8*I/c^4*b*Pi*e*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3+1/8*I/c^4*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*e*arctan(c*x)-1/8*I/c^4*b*Pi*e*arctan(c*x)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3+1/6/c^4*b*e*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)-1/8*I*b*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*x^4*e-1/8*I*b*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^4*e+1/8*I*b*arctan(c*x)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^4*e+1/24*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^3*e-1/8*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x*e+1/8*I/c^4*b*Pi*e*arctan(c*x)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)-1/8*I*b*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^4*e+7/72*b*e*x^3/c-1/8*a*e*x^4+1/3*I/c^4*b*d-41/36*I/c^4*b*e-1/8*b*arctan(c*x)*e*x^4","C"
1288,1,4145,189,2.797000," ","int(x^2*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),x)","\text{output too large to display}"," ",0,"5/18*e/c^3*b-2/9*a*e*x^3-1/6*b*d*x^2/c+1/3/c^3*b*e*ln((1+I*c*x)^2/(c^2*x^2+1)+1)^2+1/3*b*arctan(c*x)*x^3*d-1/3/c^3*b*d*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+11/9/c^3*b*e*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/3*x^3*a*d+2/3*b*e*x*arctan(c*x)/c^2+1/12*I/c*b*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^2*e+1/6*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*e*Pi*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/6*I*b*arctan(c*x)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^3*e+2/3*a*e*x/c^2-2/3*a*e*arctan(c*x)/c^3-2/9*b*e*x^3*arctan(c*x)-1/3/c*b*ln(2)*x^2*e-2/3/c^3*b*e*ln(2)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-2/3*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*arctan(c*x)*x^3*e+2/3*b*ln(2)*arctan(c*x)*x^3*e+1/3*I/c^3*b*d*arctan(c*x)-8/9*I/c^3*b*e*arctan(c*x)+1/3*x^3*a*e*ln(c^2*x^2+1)+1/3*I/c^3*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*e*Pi*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/12*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*e+1/6*I*b*arctan(c*x)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^3*e+1/3*I*b*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*Pi*x^3*e+1/6*I*b*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^3*e-1/6*I*b*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*Pi*x^3*e+1/6*I*b*arctan(c*x)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^3*e-1/3*I*b*arctan(c*x)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^3*e+1/6/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*e*arctan(c*x)-1/12*I/c*b*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^2*e-1/6*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*Pi*x^2*e-1/12*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^2*e+1/12*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*Pi*x^2*e-1/12*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x^2*e+1/6*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x^2*e-1/6*I/c^3*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-1/3*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*e*Pi*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/6*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*e*Pi*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/6/c^3*b*d+1/6*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*e*Pi*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/6*I/c^3*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*e*Pi*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1/3/c*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*x^2*e-1/6/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*e*arctan(c*x)-1/3/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*Pi*e*arctan(c*x)-1/6/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*Pi*e*arctan(c*x)+1/6/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*Pi*e*arctan(c*x)-1/6/c^3*b*Pi*e*arctan(c*x)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)+1/3/c^3*b*Pi*e*arctan(c*x)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2+1/12*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*Pi*e-1/12*I/c^3*b*Pi*e*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)+1/6*I/c^3*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*Pi*e-1/6*I*b*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*x^3*e-1/6*I*b*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^3*e+1/6*I*b*arctan(c*x)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^3*e+1/12*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*x^2*e+1/12*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^2*e-1/12*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x^2*e+1/6*I/c^3*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3+1/6*I/c^3*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-1/6*I/c^3*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-1/12*I/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*e-1/6*I/c^3*b*Pi*e*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2-1/12*I/c^3*b*Pi*e*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2+5/18*b*e*x^2/c-1/3/c^3*b*ln(2)*e+1/6/c^3*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*e*arctan(c*x)+1/6/c^3*b*Pi*e*arctan(c*x)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-1/6/c^3*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*e*arctan(c*x)+1/12*I/c^3*b*Pi*e*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3+1/12*I/c^3*b*Pi*e*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-1/12*I/c^3*b*Pi*e*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3+2/3*I/c^3*b*ln(2)*e*arctan(c*x)-1/3/c^3*b*e*(-2*arctan(c*x)*x^3*c^3+c^2*x^2-2*I*arctan(c*x)+2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+1)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))","C"
1289,1,3074,125,2.679000," ","int(x*(a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),x)","\text{output too large to display}"," ",0,"3/2*b*e*x/c-1/2*a*x^2*e+1/4*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)*Pi*x^2*e+1/2*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*arctan(c*x)*Pi*x^2*e-1/4*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*arctan(c*x)*Pi*x^2*e+1/4*I*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)*Pi*x^2*e-1/2*I*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)*Pi*x^2*e-1/4*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x*e+1/2*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*Pi*x*e+1/4*I/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*e*arctan(c*x)+1/4*I/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*Pi*e*arctan(c*x)+1/2*I/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*Pi*e*arctan(c*x)-1/2*b*d*x/c+1/2*b*d*arctan(c*x)/c^2-I/c^2*b*e*ln(2)+b*ln(2)*arctan(c*x)*x^2*e-b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*arctan(c*x)*x^2*e-1/2*b*arctan(c*x)*x^2*e+1/2*a*e/c^2*ln(c^2*x^2+1)-1/4/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*e-1/4/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*e+1/4*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*Pi*x*e-1/4*I/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*e*arctan(c*x)-1/4*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)*Pi*x^2*e-1/2*I/c^2*b*d+3/2*I/c^2*b*e-1/4*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)*Pi*x^2*e-1/4*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*arctan(c*x)*Pi*x^2*e+1/4*I*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)*Pi*x^2*e+1/4*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x*e+1/4*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*x*e-1/4*I/c*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*x*e-1/4*I/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*e*arctan(c*x)-1/4*I/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*Pi*e*arctan(c*x)+1/4*I/c^2*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*e*arctan(c*x)-1/4*I/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*Pi*e*arctan(c*x)+1/4*I/c^2*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*e*arctan(c*x)-1/2*I/c^2*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*Pi*e*arctan(c*x)-1/4*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*x*e-1/4*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*Pi*x*e-1/2*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*Pi*x*e+1/4*I/c*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*Pi*x*e+1/4*I*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)*Pi*x^2*e+1/4/c^2*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*Pi*e-1/c*b*ln(2)*x*e+1/c*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*x*e+1/c^2*b*ln(2)*e*arctan(c*x)-1/c^2*b*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*e*arctan(c*x)+1/c^2*b*e*(arctan(c*x)*x*c-1-I*arctan(c*x))*(I+c*x)*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+1/4/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*Pi*e+1/4/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*Pi*e+1/2/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*e*Pi-1/4/c^2*b*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*Pi*e+1/4/c^2*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*Pi*e-1/2/c^2*b*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*e*Pi-1/4/c^2*b*e*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)-5/2*b*e*arctan(c*x)/c^2+1/2*a*x^2*d+1/2*x^2*a*e*ln(c^2*x^2+1)-1/2*a*e/c^2+1/2*b*arctan(c*x)*d*x^2","C"
1290,1,192,98,0.686000," ","int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1)),x)","a x d +b d \arctan \left(c x \right) x -\frac{b d \ln \left(c^{2} x^{2}+1\right)}{2 c}+\frac{b e \ln \left(\frac{2}{1+\frac{-c^{2} x^{2}+1}{c^{2} x^{2}+1}}\right)}{c}+\frac{b \arctan \left(c x \right)^{2} e}{c}-\frac{b e \ln \left(\frac{2}{1+\frac{-c^{2} x^{2}+1}{c^{2} x^{2}+1}}\right)^{2}}{4 c}-2 b e x \arctan \left(c x \right)+b e \arctan \left(c x \right) x \ln \left(\frac{2}{1+\frac{-c^{2} x^{2}+1}{c^{2} x^{2}+1}}\right)+a x e \ln \left(c^{2} x^{2}+1\right)-2 a e x +\frac{2 a e \arctan \left(c x \right)}{c}"," ",0,"a*x*d+b*d*arctan(c*x)*x-1/2*b*d*ln(c^2*x^2+1)/c+1/c*b*e*ln(2/(1+(-c^2*x^2+1)/(c^2*x^2+1)))+1/c*b*arctan(c*x)^2*e-1/4/c*b*e*ln(2/(1+(-c^2*x^2+1)/(c^2*x^2+1)))^2-2*b*e*x*arctan(c*x)+b*e*arctan(c*x)*x*ln(2/(1+(-c^2*x^2+1)/(c^2*x^2+1)))+a*x*e*ln(c^2*x^2+1)-2*a*e*x+2*a*e/c*arctan(c*x)","A"
1291,1,6931,240,6.089000," ","int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x,x)","\text{output too large to display}"," ",0,"result too large to display","C"
1292,0,0,96,11.285000," ","int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^2,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right) \left(d +e \ln \left(c^{2} x^{2}+1\right)\right)}{x^{2}}\, dx"," ",0,"int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^2,x)","F"
1293,0,0,138,38.687000," ","int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^3,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right) \left(d +e \ln \left(c^{2} x^{2}+1\right)\right)}{x^{3}}\, dx"," ",0,"int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^3,x)","F"
1294,0,0,175,15.917000," ","int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^4,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right) \left(d +e \ln \left(c^{2} x^{2}+1\right)\right)}{x^{4}}\, dx"," ",0,"int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^4,x)","F"
1295,0,0,197,21.416000," ","int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^5,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right) \left(d +e \ln \left(c^{2} x^{2}+1\right)\right)}{x^{5}}\, dx"," ",0,"int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^5,x)","F"
1296,0,0,226,25.793000," ","int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^6,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right) \left(d +e \ln \left(c^{2} x^{2}+1\right)\right)}{x^{6}}\, dx"," ",0,"int((a+b*arctan(c*x))*(d+e*ln(c^2*x^2+1))/x^6,x)","F"
1297,1,21442,485,5.645000," ","int(x*(a+b*arctan(c*x))*(d+e*ln(g*x^2+f)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
1298,0,0,516,7.987000," ","int((a+b*arctan(c*x))*(d+e*ln(g*x^2+f)),x)","\int \left(a +b \arctan \left(c x \right)\right) \left(d +e \ln \left(g \,x^{2}+f \right)\right)\, dx"," ",0,"int((a+b*arctan(c*x))*(d+e*ln(g*x^2+f)),x)","F"
1299,0,0,89,3.470000," ","int((a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right) \left(d +e \ln \left(g \,x^{2}+f \right)\right)}{x}\, dx"," ",0,"int((a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x,x)","F"
1300,0,0,528,5.371000," ","int((a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x^2,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right) \left(d +e \ln \left(g \,x^{2}+f \right)\right)}{x^{2}}\, dx"," ",0,"int((a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x^2,x)","F"
1301,0,0,449,10.358000," ","int((a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x^3,x)","\int \frac{\left(a +b \arctan \left(c x \right)\right) \left(d +e \ln \left(g \,x^{2}+f \right)\right)}{x^{3}}\, dx"," ",0,"int((a+b*arctan(c*x))*(d+e*ln(g*x^2+f))/x^3,x)","F"