1,1,228,152,0.490000," ","int(x^3*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x)","-\frac{a \,x^{2}}{2 c^{2} d}-\frac{a \ln \left(c x -1\right)}{2 c^{4} d}-\frac{a \ln \left(c x +1\right)}{2 c^{4} d}+\frac{i b \arccos \left(c x \right)^{2}}{2 c^{4} d}-\frac{b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{c^{4} d}-\frac{b \arccos \left(c x \right) \ln \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{c^{4} d}+\frac{i b \polylog \left(2, -c x -i \sqrt{-c^{2} x^{2}+1}\right)}{c^{4} d}+\frac{i b \polylog \left(2, c x +i \sqrt{-c^{2} x^{2}+1}\right)}{c^{4} d}-\frac{b \cos \left(2 \arccos \left(c x \right)\right) \arccos \left(c x \right)}{4 c^{4} d}+\frac{b \sin \left(2 \arccos \left(c x \right)\right)}{8 c^{4} d}"," ",0,"-1/2/c^2*a/d*x^2-1/2/c^4*a/d*ln(c*x-1)-1/2/c^4*a/d*ln(c*x+1)+1/2*I/c^4*b/d*arccos(c*x)^2-1/c^4*b/d*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))-1/c^4*b/d*arccos(c*x)*ln(1-c*x-I*(-c^2*x^2+1)^(1/2))+I/c^4*b/d*polylog(2,-c*x-I*(-c^2*x^2+1)^(1/2))+I/c^4*b/d*polylog(2,c*x+I*(-c^2*x^2+1)^(1/2))-1/4/c^4*b/d*cos(2*arccos(c*x))*arccos(c*x)+1/8/c^4*b/d*sin(2*arccos(c*x))","A"
2,1,207,137,0.439000," ","int(x^2*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x)","-\frac{a x}{c^{2} d}-\frac{a \ln \left(c x -1\right)}{2 c^{3} d}+\frac{a \ln \left(c x +1\right)}{2 c^{3} d}+\frac{b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{c^{3} d}-\frac{b \arccos \left(c x \right) \ln \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{c^{3} d}-\frac{b \arccos \left(c x \right) x}{c^{2} d}+\frac{i b \dilog \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{c^{3} d}-\frac{i b \dilog \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{c^{3} d}+\frac{b \sqrt{-c^{2} x^{2}+1}}{c^{3} d}"," ",0,"-1/c^2*a/d*x-1/2/c^3*a/d*ln(c*x-1)+1/2/c^3*a/d*ln(c*x+1)+1/c^3*b/d*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))-1/c^3*b/d*arccos(c*x)*ln(1-c*x-I*(-c^2*x^2+1)^(1/2))-1/c^2*b/d*arccos(c*x)*x+I/c^3*b/d*dilog(1-c*x-I*(-c^2*x^2+1)^(1/2))-I/c^3*b/d*dilog(1+c*x+I*(-c^2*x^2+1)^(1/2))+b*(-c^2*x^2+1)^(1/2)/c^3/d","A"
3,1,180,98,0.123000," ","int(x*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x)","-\frac{a \ln \left(c x -1\right)}{2 c^{2} d}-\frac{a \ln \left(c x +1\right)}{2 c^{2} d}+\frac{i b \arccos \left(c x \right)^{2}}{2 c^{2} d}-\frac{b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{c^{2} d}-\frac{b \arccos \left(c x \right) \ln \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{c^{2} d}+\frac{i b \polylog \left(2, -c x -i \sqrt{-c^{2} x^{2}+1}\right)}{c^{2} d}+\frac{i b \polylog \left(2, c x +i \sqrt{-c^{2} x^{2}+1}\right)}{c^{2} d}"," ",0,"-1/2/c^2*a/d*ln(c*x-1)-1/2/c^2*a/d*ln(c*x+1)+1/2*I/c^2*b/d*arccos(c*x)^2-1/c^2*b/d*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))-1/c^2*b/d*arccos(c*x)*ln(1-c*x-I*(-c^2*x^2+1)^(1/2))+I/c^2*b/d*polylog(2,-c*x-I*(-c^2*x^2+1)^(1/2))+I/c^2*b/d*polylog(2,c*x+I*(-c^2*x^2+1)^(1/2))","A"
4,1,170,100,0.214000," ","int((a+b*arccos(c*x))/(-c^2*d*x^2+d),x)","\frac{a \arctanh \left(c x \right)}{c d}+\frac{i b \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d}-\frac{i b \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d}+\frac{b \arctanh \left(c x \right) \arccos \left(c x \right)}{c d}+\frac{i b \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d}-\frac{i b \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d}"," ",0,"1/c*a/d*arctanh(c*x)+I/c*b/d*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-I/c*b/d*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/c*b/d*arctanh(c*x)*arccos(c*x)+I/c*b/d*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-I/c*b/d*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))","A"
5,1,168,98,0.154000," ","int((a+b*arccos(c*x))/x/(-c^2*d*x^2+d),x)","-\frac{a \ln \left(c x +1\right)}{2 d}+\frac{a \ln \left(c x \right)}{d}-\frac{a \ln \left(c x -1\right)}{2 d}-\frac{b \arccos \left(c x \right) \ln \left(1-\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{b \arccos \left(c x \right) \ln \left(1+\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{i b \dilog \left(1+\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d}+\frac{i b \dilog \left(1-\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d}"," ",0,"-1/2*a/d*ln(c*x+1)+a/d*ln(c*x)-1/2*a/d*ln(c*x-1)-b/d*arccos(c*x)*ln(1-(c*x+I*(-c^2*x^2+1)^(1/2))^2)+b/d*arccos(c*x)*ln(1+(c*x+I*(-c^2*x^2+1)^(1/2))^2)-1/2*I*b/d*dilog(1+(c*x+I*(-c^2*x^2+1)^(1/2))^2)+1/2*I*b/d*dilog(1-(c*x+I*(-c^2*x^2+1)^(1/2))^2)","A"
6,1,166,131,0.385000," ","int((a+b*arccos(c*x))/x^2/(-c^2*d*x^2+d),x)","\frac{c a \ln \left(c x +1\right)}{2 d}-\frac{a}{d x}-\frac{c a \ln \left(c x -1\right)}{2 d}-\frac{b \arccos \left(c x \right)}{d x}-\frac{2 i c b \arctan \left(c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{i c b \dilog \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{c b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{i c b \dilog \left(c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d}"," ",0,"1/2*c*a/d*ln(c*x+1)-a/d/x-1/2*c*a/d*ln(c*x-1)-b/d*arccos(c*x)/x-2*I*c*b/d*arctan(c*x+I*(-c^2*x^2+1)^(1/2))-I*c*b/d*dilog(1+c*x+I*(-c^2*x^2+1)^(1/2))+c*b/d*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))-I*c*b/d*dilog(c*x+I*(-c^2*x^2+1)^(1/2))","A"
7,1,301,148,0.711000," ","int((a+b*arccos(c*x))/x^3/(-c^2*d*x^2+d),x)","-\frac{c^{2} a \ln \left(c x +1\right)}{2 d}-\frac{a}{2 d \,x^{2}}+\frac{c^{2} a \ln \left(c x \right)}{d}-\frac{c^{2} a \ln \left(c x -1\right)}{2 d}+\frac{i c^{2} b}{2 d}+\frac{b c \sqrt{-c^{2} x^{2}+1}}{2 d x}-\frac{b \arccos \left(c x \right)}{2 d \,x^{2}}-\frac{c^{2} b \arccos \left(c x \right) \ln \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{i c^{2} b \polylog \left(2, c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{c^{2} b \arccos \left(c x \right) \ln \left(1+\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{i b \,c^{2} \polylog \left(2, -\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d}-\frac{c^{2} b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{i c^{2} b \polylog \left(2, -c x -i \sqrt{-c^{2} x^{2}+1}\right)}{d}"," ",0,"-1/2*c^2*a/d*ln(c*x+1)-1/2*a/d/x^2+c^2*a/d*ln(c*x)-1/2*c^2*a/d*ln(c*x-1)+1/2*I*c^2*b/d+1/2*b*c*(-c^2*x^2+1)^(1/2)/d/x-1/2*b/d*arccos(c*x)/x^2-c^2*b/d*arccos(c*x)*ln(1-c*x-I*(-c^2*x^2+1)^(1/2))+I*c^2*b/d*polylog(2,c*x+I*(-c^2*x^2+1)^(1/2))+c^2*b/d*arccos(c*x)*ln(1+(c*x+I*(-c^2*x^2+1)^(1/2))^2)-1/2*I*b*c^2*polylog(2,-(c*x+I*(-c^2*x^2+1)^(1/2))^2)/d-c^2*b/d*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))+I*c^2*b/d*polylog(2,-c*x-I*(-c^2*x^2+1)^(1/2))","B"
8,1,296,190,0.890000," ","int(x^4*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x)","\frac{a x}{c^{4} d^{2}}-\frac{a}{4 c^{5} d^{2} \left(c x +1\right)}-\frac{3 a \ln \left(c x +1\right)}{4 c^{5} d^{2}}-\frac{a}{4 c^{5} d^{2} \left(c x -1\right)}+\frac{3 a \ln \left(c x -1\right)}{4 c^{5} d^{2}}-\frac{b \sqrt{-c^{2} x^{2}+1}}{c^{5} d^{2}}+\frac{b \arccos \left(c x \right) x}{c^{4} d^{2}}-\frac{b \arccos \left(c x \right) x}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-c^{2} x^{2}+1}}{2 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{2 c^{5} d^{2}}+\frac{3 i b \polylog \left(2, -c x -i \sqrt{-c^{2} x^{2}+1}\right)}{2 c^{5} d^{2}}+\frac{3 b \arccos \left(c x \right) \ln \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{2 c^{5} d^{2}}-\frac{3 i b \polylog \left(2, c x +i \sqrt{-c^{2} x^{2}+1}\right)}{2 c^{5} d^{2}}"," ",0,"1/c^4*a/d^2*x-1/4/c^5*a/d^2/(c*x+1)-3/4/c^5*a/d^2*ln(c*x+1)-1/4/c^5*a/d^2/(c*x-1)+3/4/c^5*a/d^2*ln(c*x-1)-b*(-c^2*x^2+1)^(1/2)/c^5/d^2+1/c^4*b/d^2*arccos(c*x)*x-1/2/c^4*b/d^2/(c^2*x^2-1)*arccos(c*x)*x-1/2/c^5*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-3/2/c^5*b/d^2*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))+3/2*I*b*polylog(2,-c*x-I*(-c^2*x^2+1)^(1/2))/c^5/d^2+3/2/c^5*b/d^2*arccos(c*x)*ln(1-c*x-I*(-c^2*x^2+1)^(1/2))-3/2*I*b*polylog(2,c*x+I*(-c^2*x^2+1)^(1/2))/c^5/d^2","A"
9,1,312,163,0.828000," ","int(x^3*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x)","\frac{a}{4 c^{4} d^{2} \left(c x +1\right)}+\frac{a \ln \left(c x +1\right)}{2 c^{4} d^{2}}-\frac{a}{4 c^{4} d^{2} \left(c x -1\right)}+\frac{a \ln \left(c x -1\right)}{2 c^{4} d^{2}}-\frac{i b \arccos \left(c x \right)^{2}}{2 c^{4} d^{2}}-\frac{i b \,x^{2}}{2 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b x \sqrt{-c^{2} x^{2}+1}}{2 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \arccos \left(c x \right)}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \arccos \left(c x \right) \ln \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{c^{4} d^{2}}+\frac{b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{c^{4} d^{2}}-\frac{i b \polylog \left(2, c x +i \sqrt{-c^{2} x^{2}+1}\right)}{c^{4} d^{2}}-\frac{i b \polylog \left(2, -c x -i \sqrt{-c^{2} x^{2}+1}\right)}{c^{4} d^{2}}"," ",0,"1/4/c^4*a/d^2/(c*x+1)+1/2/c^4*a/d^2*ln(c*x+1)-1/4/c^4*a/d^2/(c*x-1)+1/2/c^4*a/d^2*ln(c*x-1)-1/2*I/c^4*b/d^2*arccos(c*x)^2-1/2*I/c^2*b/d^2/(c^2*x^2-1)*x^2-1/2/c^3*b/d^2/(c^2*x^2-1)*x*(-c^2*x^2+1)^(1/2)-1/2/c^4*b/d^2/(c^2*x^2-1)*arccos(c*x)+1/2*I/c^4*b/d^2/(c^2*x^2-1)+1/c^4*b/d^2*arccos(c*x)*ln(1-c*x-I*(-c^2*x^2+1)^(1/2))+1/c^4*b/d^2*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))-I/c^4*b/d^2*polylog(2,c*x+I*(-c^2*x^2+1)^(1/2))-I/c^4*b/d^2*polylog(2,-c*x-I*(-c^2*x^2+1)^(1/2))","A"
10,1,253,150,0.394000," ","int(x^2*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x)","-\frac{a}{4 c^{3} d^{2} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{4 c^{3} d^{2}}-\frac{a}{4 c^{3} d^{2} \left(c x -1\right)}+\frac{a \ln \left(c x -1\right)}{4 c^{3} d^{2}}-\frac{b \arccos \left(c x \right) x}{2 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-c^{2} x^{2}+1}}{2 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{2 c^{3} d^{2}}+\frac{i b \polylog \left(2, -c x -i \sqrt{-c^{2} x^{2}+1}\right)}{2 c^{3} d^{2}}+\frac{b \arccos \left(c x \right) \ln \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{2 c^{3} d^{2}}-\frac{i b \polylog \left(2, c x +i \sqrt{-c^{2} x^{2}+1}\right)}{2 c^{3} d^{2}}"," ",0,"-1/4/c^3*a/d^2/(c*x+1)-1/4/c^3*a/d^2*ln(c*x+1)-1/4/c^3*a/d^2/(c*x-1)+1/4/c^3*a/d^2*ln(c*x-1)-1/2/c^2*b/d^2/(c^2*x^2-1)*arccos(c*x)*x-1/2/c^3*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-1/2/c^3*b/d^2*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))+1/2*I*b*polylog(2,-c*x-I*(-c^2*x^2+1)^(1/2))/c^3/d^2+1/2/c^3*b/d^2*arccos(c*x)*ln(1-c*x-I*(-c^2*x^2+1)^(1/2))-1/2*I*b*polylog(2,c*x+I*(-c^2*x^2+1)^(1/2))/c^3/d^2","A"
11,1,98,51,0.007000," ","int(x*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x)","\frac{-\frac{a}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \left(-\frac{\arccos \left(c x \right)}{2 \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{4 \left(c x +1\right)}-\frac{\sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{4 \left(c x -1\right)}\right)}{d^{2}}}{c^{2}}"," ",0,"1/c^2*(-1/2*a/d^2/(c^2*x^2-1)+b/d^2*(-1/2/(c^2*x^2-1)*arccos(c*x)-1/4/(c*x+1)*(-(c*x+1)^2+2*c*x+2)^(1/2)-1/4/(c*x-1)*(-(c*x-1)^2-2*c*x+2)^(1/2)))","A"
12,1,250,146,0.133000," ","int((a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x)","-\frac{a}{4 c \,d^{2} \left(c x +1\right)}+\frac{a \ln \left(c x +1\right)}{4 c \,d^{2}}-\frac{a}{4 c \,d^{2} \left(c x -1\right)}-\frac{a \ln \left(c x -1\right)}{4 c \,d^{2}}-\frac{b \arccos \left(c x \right) x}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-c^{2} x^{2}+1}}{2 c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{2 c \,d^{2}}-\frac{i b \polylog \left(2, -c x -i \sqrt{-c^{2} x^{2}+1}\right)}{2 c \,d^{2}}-\frac{b \arccos \left(c x \right) \ln \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{2 c \,d^{2}}+\frac{i b \polylog \left(2, c x +i \sqrt{-c^{2} x^{2}+1}\right)}{2 c \,d^{2}}"," ",0,"-1/4/c*a/d^2/(c*x+1)+1/4/c*a/d^2*ln(c*x+1)-1/4/c*a/d^2/(c*x-1)-1/4/c*a/d^2*ln(c*x-1)-1/2*b/d^2/(c^2*x^2-1)*arccos(c*x)*x-1/2/c*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+1/2/c*b/d^2*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))-1/2*I*b*polylog(2,-c*x-I*(-c^2*x^2+1)^(1/2))/c/d^2-1/2/c*b/d^2*arccos(c*x)*ln(1-c*x-I*(-c^2*x^2+1)^(1/2))+1/2*I*b*polylog(2,c*x+I*(-c^2*x^2+1)^(1/2))/c/d^2","A"
13,1,340,143,0.750000," ","int((a+b*arccos(c*x))/x/(-c^2*d*x^2+d)^2,x)","\frac{a}{4 d^{2} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{2 d^{2}}+\frac{a \ln \left(c x \right)}{d^{2}}-\frac{a}{4 d^{2} \left(c x -1\right)}-\frac{a \ln \left(c x -1\right)}{2 d^{2}}-\frac{i b \,c^{2} x^{2}}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b c x \sqrt{-c^{2} x^{2}+1}}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \arccos \left(c x \right)}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \arccos \left(c x \right) \ln \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{i b \polylog \left(2, c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b \arccos \left(c x \right) \ln \left(1+\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{i b \polylog \left(2, -\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{2}}-\frac{b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{i b \polylog \left(2, -c x -i \sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}"," ",0,"1/4*a/d^2/(c*x+1)-1/2*a/d^2*ln(c*x+1)+a/d^2*ln(c*x)-1/4*a/d^2/(c*x-1)-1/2*a/d^2*ln(c*x-1)-1/2*I*b/d^2/(c^2*x^2-1)*c^2*x^2-1/2*b/d^2/(c^2*x^2-1)*c*x*(-c^2*x^2+1)^(1/2)-1/2*b/d^2/(c^2*x^2-1)*arccos(c*x)+1/2*I*b/d^2/(c^2*x^2-1)-b/d^2*arccos(c*x)*ln(1-c*x-I*(-c^2*x^2+1)^(1/2))+I*b/d^2*polylog(2,c*x+I*(-c^2*x^2+1)^(1/2))+b/d^2*arccos(c*x)*ln(1+(c*x+I*(-c^2*x^2+1)^(1/2))^2)-1/2*I*b*polylog(2,-(c*x+I*(-c^2*x^2+1)^(1/2))^2)/d^2-b/d^2*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))+I*b/d^2*polylog(2,-c*x-I*(-c^2*x^2+1)^(1/2))","B"
14,1,260,191,0.521000," ","int((a+b*arccos(c*x))/x^2/(-c^2*d*x^2+d)^2,x)","-\frac{c a}{4 d^{2} \left(c x +1\right)}+\frac{3 c a \ln \left(c x +1\right)}{4 d^{2}}-\frac{a}{d^{2} x}-\frac{c a}{4 d^{2} \left(c x -1\right)}-\frac{3 c a \ln \left(c x -1\right)}{4 d^{2}}-\frac{3 b \arccos \left(c x \right) c^{2} x}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{c b \sqrt{-c^{2} x^{2}+1}}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \arccos \left(c x \right)}{d^{2} x \left(c^{2} x^{2}-1\right)}-\frac{2 i c b \arctan \left(c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{3 i c b \dilog \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{2 d^{2}}+\frac{3 c b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{2 d^{2}}-\frac{3 i c b \dilog \left(c x +i \sqrt{-c^{2} x^{2}+1}\right)}{2 d^{2}}"," ",0,"-1/4*c*a/d^2/(c*x+1)+3/4*c*a/d^2*ln(c*x+1)-a/d^2/x-1/4*c*a/d^2/(c*x-1)-3/4*c*a/d^2*ln(c*x-1)-3/2*b/d^2/(c^2*x^2-1)*arccos(c*x)*c^2*x-1/2*c*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+b/d^2/x/(c^2*x^2-1)*arccos(c*x)-2*I*c*b/d^2*arctan(c*x+I*(-c^2*x^2+1)^(1/2))-3/2*I*c*b/d^2*dilog(1+c*x+I*(-c^2*x^2+1)^(1/2))+3/2*c*b/d^2*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))-3/2*I*c*b/d^2*dilog(c*x+I*(-c^2*x^2+1)^(1/2))","A"
15,1,371,187,0.518000," ","int((a+b*arccos(c*x))/x^3/(-c^2*d*x^2+d)^2,x)","\frac{c^{2} a}{4 d^{2} \left(c x +1\right)}-\frac{c^{2} a \ln \left(c x +1\right)}{d^{2}}-\frac{a}{2 d^{2} x^{2}}+\frac{2 c^{2} a \ln \left(c x \right)}{d^{2}}-\frac{c^{2} a}{4 d^{2} \left(c x -1\right)}-\frac{c^{2} a \ln \left(c x -1\right)}{d^{2}}-\frac{c^{2} b \arccos \left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{c b \sqrt{-c^{2} x^{2}+1}}{2 d^{2} x \left(c^{2} x^{2}-1\right)}+\frac{b \arccos \left(c x \right)}{2 d^{2} x^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 c^{2} b \arccos \left(c x \right) \ln \left(1+c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 c^{2} b \arccos \left(c x \right) \ln \left(1+\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{2 c^{2} b \arccos \left(c x \right) \ln \left(1-c x -i \sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 i c^{2} b \polylog \left(2, -c x -i \sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 i c^{2} b \polylog \left(2, c x +i \sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{i b \,c^{2} \polylog \left(2, -\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}"," ",0,"1/4*c^2*a/d^2/(c*x+1)-c^2*a/d^2*ln(c*x+1)-1/2*a/d^2/x^2+2*c^2*a/d^2*ln(c*x)-1/4*c^2*a/d^2/(c*x-1)-c^2*a/d^2*ln(c*x-1)-c^2*b/d^2/(c^2*x^2-1)*arccos(c*x)-1/2*c*b/d^2/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+1/2*b/d^2/x^2/(c^2*x^2-1)*arccos(c*x)-2*c^2*b/d^2*arccos(c*x)*ln(1+c*x+I*(-c^2*x^2+1)^(1/2))+2*c^2*b/d^2*arccos(c*x)*ln(1+(c*x+I*(-c^2*x^2+1)^(1/2))^2)-2*c^2*b/d^2*arccos(c*x)*ln(1-c*x-I*(-c^2*x^2+1)^(1/2))+2*I*c^2*b/d^2*polylog(2,-c*x-I*(-c^2*x^2+1)^(1/2))+2*I*c^2*b/d^2*polylog(2,c*x+I*(-c^2*x^2+1)^(1/2))-I*b*c^2*polylog(2,-(c*x+I*(-c^2*x^2+1)^(1/2))^2)/d^2","A"
16,1,177,131,0.021000," ","int(x^3*(e*x^2+d)*(a+b*arccos(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} e \,c^{6} x^{6}+\frac{1}{4} x^{4} c^{6} d \right)}{c^{2}}+\frac{b \left(\frac{\arccos \left(c x \right) e \,c^{6} x^{6}}{6}+\frac{\arccos \left(c x \right) c^{6} x^{4} d}{4}+\frac{e \left(-\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{6}-\frac{5 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{24}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{16}+\frac{5 \arcsin \left(c x \right)}{16}\right)}{6}+\frac{c^{2} d \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{4}\right)}{c^{2}}}{c^{4}}"," ",0,"1/c^4*(a/c^2*(1/6*e*c^6*x^6+1/4*x^4*c^6*d)+b/c^2*(1/6*arccos(c*x)*e*c^6*x^6+1/4*arccos(c*x)*c^6*x^4*d+1/6*e*(-1/6*c^5*x^5*(-c^2*x^2+1)^(1/2)-5/24*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/16*c*x*(-c^2*x^2+1)^(1/2)+5/16*arcsin(c*x))+1/4*c^2*d*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))))","A"
17,1,161,104,0.006000," ","int(x^2*(e*x^2+d)*(a+b*arccos(c*x)),x)","\frac{\frac{a \left(\frac{1}{5} e \,c^{5} x^{5}+\frac{1}{3} c^{5} d \,x^{3}\right)}{c^{2}}+\frac{b \left(\frac{\arccos \left(c x \right) e \,c^{5} x^{5}}{5}+\frac{\arccos \left(c x \right) c^{5} d \,x^{3}}{3}+\frac{e \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}+\frac{c^{2} d \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}\right)}{c^{2}}}{c^{3}}"," ",0,"1/c^3*(a/c^2*(1/5*e*c^5*x^5+1/3*c^5*d*x^3)+b/c^2*(1/5*arccos(c*x)*e*c^5*x^5+1/3*arccos(c*x)*c^5*d*x^3+1/5*e*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))+1/3*c^2*d*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))))","A"
18,1,137,110,0.005000," ","int(x*(e*x^2+d)*(a+b*arccos(c*x)),x)","\frac{\frac{a \left(\frac{1}{4} e \,c^{4} x^{4}+\frac{1}{2} x^{2} c^{4} d \right)}{c^{2}}+\frac{b \left(\frac{\arccos \left(c x \right) e \,c^{4} x^{4}}{4}+\frac{\arccos \left(c x \right) c^{4} d \,x^{2}}{2}+\frac{e \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{4}+\frac{c^{2} d \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{2}\right)}{c^{2}}}{c^{2}}"," ",0,"1/c^2*(a/c^2*(1/4*e*c^4*x^4+1/2*x^2*c^4*d)+b/c^2*(1/4*arccos(c*x)*e*c^4*x^4+1/2*arccos(c*x)*c^4*d*x^2+1/4*e*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))+1/2*c^2*d*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))))","A"
19,1,112,71,0.011000," ","int((e*x^2+d)*(a+b*arccos(c*x)),x)","\frac{\frac{a \left(\frac{1}{3} c^{3} x^{3} e +c^{3} d x \right)}{c^{2}}+\frac{b \left(\frac{\arccos \left(c x \right) c^{3} x^{3} e}{3}+\arccos \left(c x \right) c^{3} d x +\frac{e \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}-c^{2} d \sqrt{-c^{2} x^{2}+1}\right)}{c^{2}}}{c}"," ",0,"1/c*(a/c^2*(1/3*c^3*x^3*e+c^3*d*x)+b/c^2*(1/3*arccos(c*x)*c^3*x^3*e+arccos(c*x)*c^3*d*x+1/3*e*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-c^2*d*(-c^2*x^2+1)^(1/2)))","A"
20,1,130,138,0.392000," ","int((e*x^2+d)*(a+b*arccos(c*x))/x,x)","\frac{a \,x^{2} e}{2}+d a \ln \left(c x \right)-\frac{i b d \arccos \left(c x \right)^{2}}{2}-\frac{b e x \sqrt{-c^{2} x^{2}+1}}{4 c}+\frac{b \arccos \left(c x \right) x^{2} e}{2}-\frac{b \arccos \left(c x \right) e}{4 c^{2}}+b d \arccos \left(c x \right) \ln \left(1+\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)-\frac{i b d \polylog \left(2, -\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2}"," ",0,"1/2*a*x^2*e+d*a*ln(c*x)-1/2*I*b*d*arccos(c*x)^2-1/4*b*e*x*(-c^2*x^2+1)^(1/2)/c+1/2*b*arccos(c*x)*x^2*e-1/4*b/c^2*arccos(c*x)*e+b*d*arccos(c*x)*ln(1+(c*x+I*(-c^2*x^2+1)^(1/2))^2)-1/2*I*b*d*polylog(2,-(c*x+I*(-c^2*x^2+1)^(1/2))^2)","A"
21,1,79,62,0.008000," ","int((e*x^2+d)*(a+b*arccos(c*x))/x^2,x)","c \left(\frac{a \left(c e x -\frac{c d}{x}\right)}{c^{2}}+\frac{b \left(\arccos \left(c x \right) e c x -\frac{\arccos \left(c x \right) c d}{x}-e \sqrt{-c^{2} x^{2}+1}+c^{2} d \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)\right)}{c^{2}}\right)"," ",0,"c*(a/c^2*(c*e*x-c*d/x)+b/c^2*(arccos(c*x)*e*c*x-arccos(c*x)*c*d/x-e*(-c^2*x^2+1)^(1/2)+c^2*d*arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
22,1,127,127,1.105000," ","int((e*x^2+d)*(a+b*arccos(c*x))/x^3,x)","a e \ln \left(c x \right)-\frac{d a}{2 x^{2}}-\frac{i b \arccos \left(c x \right)^{2} e}{2}+\frac{i c^{2} d b}{2}+\frac{b c d \sqrt{-c^{2} x^{2}+1}}{2 x}-\frac{b \arccos \left(c x \right) d}{2 x^{2}}+b e \arccos \left(c x \right) \ln \left(1+\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)-\frac{i b e \polylog \left(2, -\left(c x +i \sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2}"," ",0,"a*e*ln(c*x)-1/2*d*a/x^2-1/2*I*b*arccos(c*x)^2*e+1/2*I*c^2*d*b+1/2*b*c*d*(-c^2*x^2+1)^(1/2)/x-1/2*b*arccos(c*x)*d/x^2+b*e*arccos(c*x)*ln(1+(c*x+I*(-c^2*x^2+1)^(1/2))^2)-1/2*I*b*e*polylog(2,-(c*x+I*(-c^2*x^2+1)^(1/2))^2)","A"
23,1,119,75,0.010000," ","int((e*x^2+d)*(a+b*arccos(c*x))/x^4,x)","c^{3} \left(\frac{a \left(-\frac{d}{3 c \,x^{3}}-\frac{e}{c x}\right)}{c^{2}}+\frac{b \left(-\frac{\arccos \left(c x \right) d}{3 c \,x^{3}}-\frac{\arccos \left(c x \right) e}{c x}+e \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{c^{2} d \left(-\frac{\sqrt{-c^{2} x^{2}+1}}{2 c^{2} x^{2}}-\frac{\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2}\right)}{3}\right)}{c^{2}}\right)"," ",0,"c^3*(a/c^2*(-1/3/c*d/x^3-e/c/x)+b/c^2*(-1/3*arccos(c*x)/c*d/x^3-arccos(c*x)*e/c/x+e*arctanh(1/(-c^2*x^2+1)^(1/2))-1/3*c^2*d*(-1/2/c^2/x^2*(-c^2*x^2+1)^(1/2)-1/2*arctanh(1/(-c^2*x^2+1)^(1/2)))))","A"
24,1,169,119,0.023000," ","int((d*x^2+c)^2*arccos(a*x),x)","\frac{\frac{a \arccos \left(a x \right) d^{2} x^{5}}{5}+\frac{2 a \arccos \left(a x \right) c d \,x^{3}}{3}+\arccos \left(a x \right) c^{2} a x +\frac{3 d^{2} \left(-\frac{a^{4} x^{4} \sqrt{-a^{2} x^{2}+1}}{5}-\frac{4 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-a^{2} x^{2}+1}}{15}\right)+10 a^{2} c d \left(-\frac{a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-a^{2} x^{2}+1}}{3}\right)-15 a^{4} c^{2} \sqrt{-a^{2} x^{2}+1}}{15 a^{4}}}{a}"," ",0,"1/a*(1/5*a*arccos(a*x)*d^2*x^5+2/3*a*arccos(a*x)*c*d*x^3+arccos(a*x)*c^2*a*x+1/15/a^4*(3*d^2*(-1/5*a^4*x^4*(-a^2*x^2+1)^(1/2)-4/15*a^2*x^2*(-a^2*x^2+1)^(1/2)-8/15*(-a^2*x^2+1)^(1/2))+10*a^2*c*d*(-1/3*a^2*x^2*(-a^2*x^2+1)^(1/2)-2/3*(-a^2*x^2+1)^(1/2))-15*a^4*c^2*(-a^2*x^2+1)^(1/2)))","A"
25,1,270,185,0.007000," ","int((d*x^2+c)^3*arccos(a*x),x)","\frac{\frac{a \arccos \left(a x \right) d^{3} x^{7}}{7}+\frac{3 a \arccos \left(a x \right) c \,d^{2} x^{5}}{5}+a \arccos \left(a x \right) c^{2} d \,x^{3}+\arccos \left(a x \right) c^{3} a x +\frac{5 d^{3} \left(-\frac{a^{6} x^{6} \sqrt{-a^{2} x^{2}+1}}{7}-\frac{6 a^{4} x^{4} \sqrt{-a^{2} x^{2}+1}}{35}-\frac{8 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-a^{2} x^{2}+1}}{35}\right)+21 a^{2} c \,d^{2} \left(-\frac{a^{4} x^{4} \sqrt{-a^{2} x^{2}+1}}{5}-\frac{4 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-a^{2} x^{2}+1}}{15}\right)+35 a^{4} c^{2} d \left(-\frac{a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-a^{2} x^{2}+1}}{3}\right)-35 a^{6} c^{3} \sqrt{-a^{2} x^{2}+1}}{35 a^{6}}}{a}"," ",0,"1/a*(1/7*a*arccos(a*x)*d^3*x^7+3/5*a*arccos(a*x)*c*d^2*x^5+a*arccos(a*x)*c^2*d*x^3+arccos(a*x)*c^3*a*x+1/35/a^6*(5*d^3*(-1/7*a^6*x^6*(-a^2*x^2+1)^(1/2)-6/35*a^4*x^4*(-a^2*x^2+1)^(1/2)-8/35*a^2*x^2*(-a^2*x^2+1)^(1/2)-16/35*(-a^2*x^2+1)^(1/2))+21*a^2*c*d^2*(-1/5*a^4*x^4*(-a^2*x^2+1)^(1/2)-4/15*a^2*x^2*(-a^2*x^2+1)^(1/2)-8/15*(-a^2*x^2+1)^(1/2))+35*a^4*c^2*d*(-1/3*a^2*x^2*(-a^2*x^2+1)^(1/2)-2/3*(-a^2*x^2+1)^(1/2))-35*a^6*c^3*(-a^2*x^2+1)^(1/2)))","A"
26,1,393,264,0.006000," ","int((d*x^2+c)^4*arccos(a*x),x)","\frac{\frac{a \arccos \left(a x \right) d^{4} x^{9}}{9}+\frac{4 a \arccos \left(a x \right) c \,d^{3} x^{7}}{7}+\frac{6 a \arccos \left(a x \right) c^{2} d^{2} x^{5}}{5}+\frac{4 a \arccos \left(a x \right) c^{3} d \,x^{3}}{3}+\arccos \left(a x \right) c^{4} a x +\frac{35 d^{4} \left(-\frac{a^{8} x^{8} \sqrt{-a^{2} x^{2}+1}}{9}-\frac{8 a^{6} x^{6} \sqrt{-a^{2} x^{2}+1}}{63}-\frac{16 a^{4} x^{4} \sqrt{-a^{2} x^{2}+1}}{105}-\frac{64 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{315}-\frac{128 \sqrt{-a^{2} x^{2}+1}}{315}\right)+180 a^{2} c \,d^{3} \left(-\frac{a^{6} x^{6} \sqrt{-a^{2} x^{2}+1}}{7}-\frac{6 a^{4} x^{4} \sqrt{-a^{2} x^{2}+1}}{35}-\frac{8 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-a^{2} x^{2}+1}}{35}\right)+378 a^{4} c^{2} d^{2} \left(-\frac{a^{4} x^{4} \sqrt{-a^{2} x^{2}+1}}{5}-\frac{4 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-a^{2} x^{2}+1}}{15}\right)+420 a^{6} c^{3} d \left(-\frac{a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-a^{2} x^{2}+1}}{3}\right)-315 a^{8} c^{4} \sqrt{-a^{2} x^{2}+1}}{315 a^{8}}}{a}"," ",0,"1/a*(1/9*a*arccos(a*x)*d^4*x^9+4/7*a*arccos(a*x)*c*d^3*x^7+6/5*a*arccos(a*x)*c^2*d^2*x^5+4/3*a*arccos(a*x)*c^3*d*x^3+arccos(a*x)*c^4*a*x+1/315/a^8*(35*d^4*(-1/9*a^8*x^8*(-a^2*x^2+1)^(1/2)-8/63*a^6*x^6*(-a^2*x^2+1)^(1/2)-16/105*a^4*x^4*(-a^2*x^2+1)^(1/2)-64/315*a^2*x^2*(-a^2*x^2+1)^(1/2)-128/315*(-a^2*x^2+1)^(1/2))+180*a^2*c*d^3*(-1/7*a^6*x^6*(-a^2*x^2+1)^(1/2)-6/35*a^4*x^4*(-a^2*x^2+1)^(1/2)-8/35*a^2*x^2*(-a^2*x^2+1)^(1/2)-16/35*(-a^2*x^2+1)^(1/2))+378*a^4*c^2*d^2*(-1/5*a^4*x^4*(-a^2*x^2+1)^(1/2)-4/15*a^2*x^2*(-a^2*x^2+1)^(1/2)-8/15*(-a^2*x^2+1)^(1/2))+420*a^6*c^3*d*(-1/3*a^2*x^2*(-a^2*x^2+1)^(1/2)-2/3*(-a^2*x^2+1)^(1/2))-315*a^8*c^4*(-a^2*x^2+1)^(1/2)))","A"
27,1,216,485,1.041000," ","int(arccos(a*x)/(d*x^2+c),x)","-\frac{i a \left(\munderset{\textit{\_R1} =\RootOf \left(d \,\textit{\_Z}^{4}+\left(4 a^{2} c +2 d \right) \textit{\_Z}^{2}+d \right)}{\sum}\frac{\textit{\_R1} \left(i \arccos \left(a x \right) \ln \left(\frac{\textit{\_R1} -a x -i \sqrt{-a^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -a x -i \sqrt{-a^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} d +2 a^{2} c +d}\right)}{2}+\frac{i a \left(\munderset{\textit{\_R1} =\RootOf \left(d \,\textit{\_Z}^{4}+\left(4 a^{2} c +2 d \right) \textit{\_Z}^{2}+d \right)}{\sum}\frac{i \arccos \left(a x \right) \ln \left(\frac{\textit{\_R1} -a x -i \sqrt{-a^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -a x -i \sqrt{-a^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} d +2 a^{2} c +d \right)}\right)}{2}"," ",0,"-1/2*I*a*sum(_R1/(_R1^2*d+2*a^2*c+d)*(I*arccos(a*x)*ln((_R1-a*x-I*(-a^2*x^2+1)^(1/2))/_R1)+dilog((_R1-a*x-I*(-a^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(d*_Z^4+(4*a^2*c+2*d)*_Z^2+d))+1/2*I*a*sum(1/_R1/(_R1^2*d+2*a^2*c+d)*(I*arccos(a*x)*ln((_R1-a*x-I*(-a^2*x^2+1)^(1/2))/_R1)+dilog((_R1-a*x-I*(-a^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(d*_Z^4+(4*a^2*c+2*d)*_Z^2+d))","C"
28,1,1654,647,1.832000," ","int(arccos(a*x)/(d*x^2+c)^2,x)","\frac{a^{2} \arccos \left(a x \right) x}{2 c \left(a^{2} d \,x^{2}+a^{2} c \right)}-\frac{i a^{3} \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{\left(a^{2} c +d \right) d^{3}}-\frac{i a^{3} \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right)}{\left(a^{2} c +d \right) d^{2}}-\frac{i a \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{2 c \left(a^{2} c +d \right) d^{2}}-\frac{i a \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{c \,d^{3}}+\frac{i a \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right)}{2 c \,d^{2}}+\frac{i a^{3} \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right)}{d^{3}}+\frac{i a^{3} \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right)}{d^{3}}-\frac{i a^{5} \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right) c}{\left(a^{2} c +d \right) d^{3}}+\frac{i a^{3} \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{\left(a^{2} c +d \right) d^{3}}-\frac{i a \left(\munderset{\textit{\_R1} =\RootOf \left(d \,\textit{\_Z}^{4}+\left(4 a^{2} c +2 d \right) \textit{\_Z}^{2}+d \right)}{\sum}\frac{\textit{\_R1} \left(i \arccos \left(a x \right) \ln \left(\frac{\textit{\_R1} -a x -i \sqrt{-a^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -a x -i \sqrt{-a^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} d +2 a^{2} c +d}\right)}{4 c}+\frac{i a \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{c \,d^{3}}-\frac{i a^{5} \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right) c}{\left(a^{2} c +d \right) d^{3}}+\frac{i a \left(\munderset{\textit{\_R1} =\RootOf \left(d \,\textit{\_Z}^{4}+\left(4 a^{2} c +2 d \right) \textit{\_Z}^{2}+d \right)}{\sum}\frac{i \arccos \left(a x \right) \ln \left(\frac{\textit{\_R1} -a x -i \sqrt{-a^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -a x -i \sqrt{-a^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} d +2 a^{2} c +d \right)}\right)}{4 c}-\frac{i a^{3} \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right)}{\left(a^{2} c +d \right) d^{2}}+\frac{i a \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{2 c \left(a^{2} c +d \right) d^{2}}+\frac{i a \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(i \sqrt{-a^{2} x^{2}+1}+a x \right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right)}{2 c \,d^{2}}"," ",0,"1/2*a^2*arccos(a*x)*x/c/(a^2*d*x^2+a^2*c)-I*a^3*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/(a^2*c+d)/d^2-I*a*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/c/d^3*(a^2*c*(a^2*c+d))^(1/2)-I*a^5*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))*c/(a^2*c+d)/d^3+1/2*I*a*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/c/d^2+I*a^3*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/d^3-I*a^3*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/(a^2*c+d)/d^2-I*a^5*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))*c/(a^2*c+d)/d^3-1/4*I*a/c*sum(_R1/(_R1^2*d+2*a^2*c+d)*(I*arccos(a*x)*ln((_R1-a*x-I*(-a^2*x^2+1)^(1/2))/_R1)+dilog((_R1-a*x-I*(-a^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(d*_Z^4+(4*a^2*c+2*d)*_Z^2+d))+I*a^3*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/(a^2*c+d)/d^3*(a^2*c*(a^2*c+d))^(1/2)-1/2*I*a*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/c/(a^2*c+d)/d^2*(a^2*c*(a^2*c+d))^(1/2)+1/2*I*a*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/c/d^2+I*a*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/c/d^3*(a^2*c*(a^2*c+d))^(1/2)+1/4*I*a/c*sum(1/_R1/(_R1^2*d+2*a^2*c+d)*(I*arccos(a*x)*ln((_R1-a*x-I*(-a^2*x^2+1)^(1/2))/_R1)+dilog((_R1-a*x-I*(-a^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(d*_Z^4+(4*a^2*c+2*d)*_Z^2+d))+1/2*I*a*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/c/(a^2*c+d)/d^2*(a^2*c*(a^2*c+d))^(1/2)-I*a^3*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/(a^2*c+d)/d^3*(a^2*c*(a^2*c+d))^(1/2)+I*a^3*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(I*(-a^2*x^2+1)^(1/2)+a*x)/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/d^3","C"
29,0,0,16,0.428000," ","int((d*x^2+c)^(1/2)*arccos(a*x),x)","\int \sqrt{d \,x^{2}+c}\, \arccos \left(a x \right)\, dx"," ",0,"int((d*x^2+c)^(1/2)*arccos(a*x),x)","F"
30,0,0,16,0.488000," ","int(arccos(a*x)/(d*x^2+c)^(1/2),x)","\int \frac{\arccos \left(a x \right)}{\sqrt{d \,x^{2}+c}}\, dx"," ",0,"int(arccos(a*x)/(d*x^2+c)^(1/2),x)","F"
31,0,0,56,0.434000," ","int(arccos(a*x)/(d*x^2+c)^(3/2),x)","\int \frac{\arccos \left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arccos(a*x)/(d*x^2+c)^(3/2),x)","F"
32,0,0,112,0.431000," ","int(arccos(a*x)/(d*x^2+c)^(5/2),x)","\int \frac{\arccos \left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arccos(a*x)/(d*x^2+c)^(5/2),x)","F"
33,0,0,177,0.435000," ","int(arccos(a*x)/(d*x^2+c)^(7/2),x)","\int \frac{\arccos \left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{7}{2}}}\, dx"," ",0,"int(arccos(a*x)/(d*x^2+c)^(7/2),x)","F"